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% Title: A New Astronomy                                                  %
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% Author: David Peck Todd                                                 %
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% Release Date: February 13, 2011 [EBook #35261]                          %
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% Language: English                                                       %
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The Project Gutenberg EBook of A New Astronomy, by David Peck Todd

This eBook is for the use of anyone anywhere at no cost and with
almost no restrictions whatsoever.  You may copy it, give it away or
re-use it under the terms of the Project Gutenberg License included
with this eBook or online at www.gutenberg.net


Title: A New Astronomy

Author: David Peck Todd

Release Date: February 13, 2011 [EBook #35261]

Language: English

Character set encoding: ISO-8859-1

*** START OF THIS PROJECT GUTENBERG EBOOK A NEW ASTRONOMY ***
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%%%% Credits and transcriber's note %%%%
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Produced by Susan Skinner, Jonathan Webley, Marilynda
Fraser-Cunliffe and the Online Distributed Proofreading
Team at http://www.pgdp.net
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\end{minipage}
\end{center}
\vfill

\begin{minipage}{0.85\textwidth}
\small
\subsection*{\normalsize Transcriber's Note}

\raggedright
  Figures may have been moved with respect to the surrounding text.
  Presentational changes have been made without comment.
\end{minipage}


%%%%%%%%%%%%%%%%%%%%%%%%%%% FRONT MATTER %%%%%%%%%%%%%%%%%%%%%%%%%%

\frontmatter

\pagenumbering{roman}
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\frontmatter
%[Blank Page]
\DPPageSep{002.png}
% Color plate
\begin{Plate}
  \Input[1.1\textwidth]{plate_i}
%[** TN: Plate captions are taken from the original book's list of plates]
  \caption{\textsc{Plate I.---Total Eclipse of the Sun} (\textit{from a painting by Kranz}, from \emph{Himmel und Erde}, edited by Dr.\ Schwahn) Page~\protect\pageref{p298}.}
  \index{Kranz, W. (kr\u onts), Ger.\ painter}%
  \index{Schwahn, Dr.\ P.}%
  \index{sun!eclipses of|see{eclipses, solar}}%
  \index{eclipses, solar!total}%
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% Title page
\mainmatter
\pagestyle{empty}
\vfill
\begin{center}
{\huge A}\\[2ex]
{\Huge NEW ASTRONOMY}
\vfill

BY \\[2ex]
{\Large DAVID TODD}\\[2ex]
M.A., PH.D. \\[2ex]
\textit{Professor of Astronomy and Navigation and Director of the Observatory \\
Amherst College}

%[Illustration: ``hypotheses non fingo'' \\ Is.~Newton]
\Input[0.5\textwidth]{title_page}
\vfill

\textit{Copyright, 1897 and 1906, by American Book Company} \\[2ex]
{\large NEW YORK $·:·$ CINCINNATI $·:·$ CHICAGO} \\[2ex]
{\Large AMERICAN BOOK COMPANY}
\end{center}
\newpage
\DPPageSep{004.png}
\begin{quote}
---`\textit{Contemplated as one grand whole, astronomy is the most
beautiful monument of the human mind, the noblest record of
its intelligence.}'---\textsc{La Place}\index{La Place, P. S. de (lä-plass´) (1749--1827), Fr.\ ast.\ and math.}
\end{quote}

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\Strut\makebox[0.8\TmpLen][s]{\textgoth{in grateful memory}} \\
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\index{James, A. C., D. W., Am.\ patrons}
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\vfill

\begin{quote}
---`\textit{The attempt to convey scientific conceptions, without the
appeal to observation, which can alone give such conceptions
firmness and reality, appears to me to be in direct antagonism
to the fundamental principles of scientific education.}'---\textsc{Huxley}\index{Huxley, T. H. (1825--95), Eng.\ biologist}
\end{quote}
\DPPageSep{005.png}
\cleardoublepage
\pagestyle{headings}
\thispagestyle{plain}
\chapter*{Preface}

Neglect hitherto of the availability of astronomy for a laboratory
course has mainly led to the preparation of this \textit{New Astronomy}.
Written purely with a pedagogic purpose, insistence upon rightness of
principles, no matter how simple, has everywhere been preferred to
display of precision in result. To instance a single example: although
the pupil's equipment be but a yardstick, a pinhole,\DPnote{** Hyphenated elsewhere} and the `rule of
three,' will he not reap greater benefit from measuring the sun for
himself (page~\pageref{p259}) than from learning mere detail of methods employed
by astronomers in accurately measuring that luminary?

Astronomy is preëminently a science of observation, and there is no
sufficient reason why it should not be so studied. Thereby will be
fostered a habit of intellectual alertness which lets nothing slip. Sixteen
years' experience in teaching the subject has taught me many
lessons that I have endeavored to embody here. Earth, air, and
water (merely material things) are always with us. We touch them,
handle them, ascertain their properties, and experiment upon their
relations. Plainly, in their study, laboratory courses are possible. So,
too, is a laboratory course in astronomy, without actually journeying
to the heavenly bodies; for light comes from them in decipherable
messages, and geometric truth provides the interpretation. But the
student should learn to connect fundamental principles of astronomy
with tangible objects of the common sort, somewhat as in physics and
chemistry; and I have aimed to indicate practically how teachers and
pupils of moderate mechanical deftness can themselves make the apparatus
requisite for illustrating many of these principles. All of it has
been repeatedly constructed; and its use should pave the way to better
equipment for more advanced study.

Especial attention has been accorded the recommendations of `The
Committee of Ten' on secondary school studies (1892); the specifications
concerning astronomical instruction published by the Board of
Regents of the state of New York (1895); and the Action of the
\DPPageSep{006.png}
Editorial Board of \textit{The Astrophysical Journal} with regard to Standards
in Astrophysics and Spectroscopy (1896).

In order to secure the fullest educational value, I have aimed to
present astronomy, not as mere sequence of isolated and imperfectly
connected facts, but as an inter-related series of philosophic principles.
The geometrical concept of the celestial sphere is strongly emphasized;
also its relation to astronomical instruments. But even more important
than geometry is the philosophical correlation of geometric systems.
Ocean voyages being no longer uncommon, I have given rudimental
principles of navigation in which astronomy is concerned. Few young
students may ever see the inside of an observatory; but that is reason
for their knowing about the instruments there, and prizing opportunities
to visit such institutions.

Everywhere has been kept in mind the importance of the student's
thinking rather than memorizing. Mere memorizing should be rendered
facile; in treating of the planets, I have therefore presented our
knowledge of those bodies, not subdivided according to the planets
themselves as usually, but according to especial elements and features.
The law of universal gravitation has received fuller exposition than
commonly in elementary books, its significance demanding this. Biographic
notes, intrusions in the text, have been relegated to the Index.

In conclusion, I desire to thank Professor Newcomb\index{Newcomb, S. (1835--1909), Am.\ ast.} of Washington,
Professor Pickering\index{Pickering, E. C., Dir.\ Harv.\ Coll.\ Obs.}, Director of Harvard College Observatory, and my
colleague, Professor Kimball\index{Kimball, A. L., Prof.\ Amherst College}, for helpful suggestions on the proof
sheets. A few illustrations have been reëngraved from the \textit{Lehrbuch
der Kosmischen Physik} of Müller and Peters. For many of the excellent
photographs, reader, publisher, and author are indebted to the
courtesy of astronomers, in particular to M.~Tisserand\index{Tisserand, F. F. (1845--96), Fr.\ ast.}, late Director
of the Paris Observatory, to the Astronomer Royal\index{Christie, Sir W.~H.~M., Ast.\ Royal}, to Professor Pickering,
to Professor Hale\index{Hale, G. E., Dir.\ Carnegie Solar Obs.}; also to Dr.~Isaac Roberts\index{Roberts, I. (1829--1904), Eng.\ ast.} and Professor
Barnard\index{Barnard, E. E., Prof.\ Univ.\ Chicago}, both of whose series of astronomical photographs have received
the highly honorable award of the gold medal of the Royal
Astronomical Society.

\begin{flushright}
DAVID TODD.
\end{flushright}

\textsc{Amherst College Observatory.}
\cleardoublepage
\DPPageSep{007.png}
\phantomsection
\pdfbookmark[0]{Table of Contents}{Contents}
\tableofcontents*
\iffalse
CONTENTS

CHAPTER                                         PAGE

I.    INTRODUCTORY  .....  7
II.   THE LANGUAGE OF ASTRONOMY .....  22
III.  THE PHILOSOPHY OF THE CELESTIAL SPHERE .  .  43
IV.   THE STARS IN THEIR COURSES .....  59
V.    THE EARTH AS A GLOBE ......  76
VI.   THE EARTH TURNS ON ITS Axis .....  97
VII.  THE EARTH REVOLVES ROUND THE SUN  .  .  .131
VIII. THE ASTRONOMY OF NAVIGATION.....169
IX.   THE OBSERVATORY AND ITS INSTRUMENTS .  .  . 190
X.    THE MOON .  .  .  .  .  .  .  .  .221
XI.   THE SUN  .  .  .  .  .  .  .  .  .255
XII.  ECLIPSES OF SUN AND MOON  ..... 289
XIII. THE PLANETS........311
XIV.  THE ARGUMENT FOR UNIVERSAL GRAVITATION .  .371
XV.   COMETS AND METEORS.......392
XVI.  THE STARS AND THE COSMOGONY  .  .  .  .421
\fi
\DPPageSep{008.png}
\iffalse

LIST OF COLORED PLATES

PLATE                                           PAGE
I. TOTAL ECLIPSE OF THE SUN. (From Himmel und Erde,
edited by Dr. Schwahn).....  &lt;i&gt;Frontispiece&lt;/i&gt;
II. THE SUN AS REVEALED BY TELESCOPE AND SPECTROSCOPE.
(From Annals of Harvard College Observatory) ..........II
II. THE NORTH POLAR HEAVENS ......  60
IV. THE EQUATORIAL GIRDLE OF THE STARS  ...  62
V. SOLAR PROMINENCES. (From Annals of Harvard College
Observatory).........283
VI. THREE VIEWS OF MARS, SHOWING CHANGING SEASONS
OF HESPERIA. (Lowell) ...... 360
\fi
\DPPageSep{009.png}


\Chapter{I}{Introductory}

Astronomy\index{astronomy!defined}\index{astronomy!history} is the science pertaining to all the
bodies of the heavens. Parent of the sciences, it is
the most perfect and beautiful of all. Sir William
Rowan Hamilton\index{Hamilton, Sir W. R. (1805--65), Brit.\ math.}, the eminent mathematician, has called
astronomy man's golden chain between the earth and the
% Fig 1.1
\begin{figure}[hbt!]
  \centering
  \Input{page_007}
  \caption{The Yerkes Observatory, Professor Edwin B. Frost, Director}
  \label{p7}%
  \index{Frost, E. B., Prof.\ Univ.\ Chicago}%
  \index{Yerkes, C. T. (yer´kez) (1837--1905), Am.\ patron!observatory}
\end{figure}
visible heaven, by which we `learn the language and interpret
the oracles of the universe.' This noble science is
to man a possession both old and ancestral, passing with
resistless progress from simple shepherds of the Orient
watching their flocks by night, to the rulers of ancient
\DPPageSep{010.png}
empires and the giants of modern thought; until to-day
the civilized world is dotted with observatories equipped
with a great variety of instruments for weighing and
measuring and studying the celestial bodies, each of these
observatories vying with the others in pure enthusiasm for
new knowledge of the infinite spaces around us.

\textbf{Astronomy a Useful Science}.\index{astronomy!utility of}---Many devoted lives have
been grandly spent in pursuit of this branch of learning;
and it would hardly be possible for any one who has given
even a general glance at their unselfish history to make
the vulgar inquiry, `What's the use?' Only a very small
and unaspiring mind ever asks this question about any
science which adds to the sum total of our actual knowledge,
least of all with reference to this,---one of the most
practical of all sciences. Astronomy binds earth and
heaven in so close a bond that it even maps the one by
means of the other, and guides fleet and caravan over
wastes of sea and sand otherwise trackless and impassable.
By faithful study, even for a short time, it is possible
to discover many of these uses. They may not at once
appear to put money into men's pockets or clothes upon
their backs; but we have passed the primitive stage of a
rudely toiling community, where material progress alone is
the thought and aim.

\textbf{Especial Uses}.---To specify in part the relations in
which astronomy is useful: (1) In \textit{chronology}\index{chronology},---fixing
many disputed dates of ancient battles,
% Fig 1.2
\begin{wrapfigure}{o}{0.45\textwidth}
  \centering
  \Input[0.4\textwidth]{page_008}
  \caption{The Time-ball at New York}
  \label{p9}\index{time-ball}
\end{wrapfigure}
the reigns of kings,
and other important historic events, and establishing the
exact length of the units of time requisite for the calendar.
For example, the surest basis of the chronology of ancient
Assyria\index{Assyria!chronology of} rests upon an eclipse of the sun observed in Nineveh
in the middle of the reign of Jeroboam\index{Jeroboam II (\BC~770), Assyrian monarch} the Second,
which modern astronomical calculations prove to have
taken place on the 15th of June, \BC~763. (2) In \textit{navigation}\index{navigation}---conducting ships from port to port, almost without
\DPPageSep{011.png}
risk, thereby saving human life and lessening the
cost of many of the necessaries of existence. The great
national observatory at
Greenwich (page~\pageref{p433}) is
one of those founded for
the especial and practical
purpose of improving the
astronomical means of
navigation. (3) In \textit{geodesy}\index{geodesy}
and in \textit{surveying},---enabling
us to ascertain the
size of the earth, make
accurate maps of its continents
and oceans, and
run boundaries of countries
and estates. (4) In
determining exact \textit{time}\index{time},---a
vast convenience in
all the affairs of life, particularly
in the operation
of railways. In many
large cities, the dropping
of a ball on a high tower
indicates exact noon.
Every good watch has been carefully rated by an accurate
clock (perhaps in some observatory), which again
has been corrected by observations of the fixed stars---a
knowledge of the precise positions of which depends
upon the faithful patience of a multitude of astronomers
who have given their lives to this work in the past.
Indeed, it is hardly an exaggeration to say that there
is no civilized person in existence whose comfort is not
enhanced, whose life is not rendered more worth the
\DPPageSep{012.png}
living, or who is not affected, at least indirectly, by the
work of astronomers, and by those who, though not
astronomers, are yet practically applying the principles
of this science to the affairs of everyday life.

\textbf{The Sun by Day.}---Singularly few persons regard the
daytime sky. Yet this beautiful and ever-varying spectacle
may be seen
and enjoyed by all;
% Fig 1.3
\begin{wrapfigure}{o}{0.55\textwidth}
  \centering
  \Input[0.5\textwidth]{page_010}
  \caption{Clouds of the Daytime Sky (photographed by Henry)}
  \index{Henry, A. J., U. S. Weather Bureau}
\end{wrapfigure}
perhaps that is one
reason why it is so
little thought of.
Even the sordid city
court, the worst
tenement district,
may have its strip
of blue above, far
away from noise
and uncleanliness.
No buildings are
high enough to shut
out this heavenly
gift entirely. The
study of the sky in
daylight, especially
its clouds, is properly
part of a separate
science,---meteorology
as distinguished
from astronomy. The marvelous sun, too,
by which, as will be seen, we live and move and have
our being, is held hardly less a matter of course.
Here it is that meteorology joins on the boundary of the
science we take up to-day; for the sun is one of the chief
objects of study in modern astronomy,---its distance, its
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% Fig 1.4
\begin{Plate}
  \Input[0.6\textwidth]{plate_ii}
  \caption{\textsc{Plate II.---The Sun as Revealed by Telescope and Spectroscope.} (\textit{Trouvelot}, from Annals of Harvard College Observatory)}
  \label{plateII}%
  \index{Harvard College!obs.}%
  \index{prominences}%
  \index{sun|see{prominences}}%
  \index{Trouvelot, L. (1827--92), Fr.\ ast.}%
\end{Plate}
\DPPageSep{015.png}
vast size, its apparent motion, the sources of its intense
light and heat, its constantly changing spots\index{sun!spots}, its constitution,
the hydrogen prominences\index{prominences},
which seem to
spring from its edge as
tongue-like flames, and
its energies, tirelessly
radiated into space and
regnant in all the forms
of life upon the earth,
no less than in all those
phenomena of the atmosphere
which we call
weather. Many of the
spots on the sun are
larger than our globe,
like the one here pictured.
Without fine instruments
carefully adjusted, the prominences cannot be
seen except during total eclipses of the sun.

\textbf{The Stars by Night.}\index{stars!by night}---But this sense of everyday
usualness in great part gives way, once the sun has set,
and the stars have come forth, as if
% Fig 1.5
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.55\textwidth]{page_011}
  \caption{An Average Sunspot (Moreux)}
  \label{p11}\index{Moreux, T. (mo-r\=o´), Fr.\ ast.}\index{sun!spots}
\end{wrapfigure}
from their daytime
hiding. Of course they fill the sky just as truly when
the world is flooded with sunlight, shining all in their
appointed places, where the brighter ones may be seen
with the telescope during the day; but their feebler light
is conspicuous only when this greater brilliance is withdrawn
from our horizon, or when the moon comes in
between us and the sun, causing a total eclipse\index{stars!visible in daytime}. Immanuel
Kant\index{Kant, I. (känt) (1724--1804), Ger.\ phil.}, a great German philosopher, has said that two things
filled him with ceaseless awe,---the starry heavens above
and the moral law within. Even the most prosaic cannot
but notice and revere the night-time sky, and few are so
\DPPageSep{016.png}
hopelessly unimaginative as not to be impressed by the
dark blue dome spangled with its myriad stars. The positions
of the stars with reference to one another seem to
remain constant, although they are continually changing
their places relatively to objects on the earth. Hence the
term \textit{fixed stars}. But this is only seemingly the proper
expression. In reality, all are speeding through space at
% Fig 1.6
\begin{figure}[hbt!]
  \centering
  \Input{page_012}
  \caption{The Night-time Sky in a Great City}
\end{figure}
very high velocities, but so infinitely removed are the stars
from us that they appear to be at rest. Although quite
the reverse, as we now know, from `fixed,' the term is
still used, because in the astronomically brief period from
generation to generation, the changes are so slight that
the naked eye is powerless to detect them.

\textbf{Number of the Brighter Stars.}\index{stars!number of}---In ancient times the
brilliant host of the nightly sky was thought to be
countless; but surprising as it may seem, the stars actually
visible to the unaided eye at a single place in the United
States do not exceed 2000 or 3000, and only upon exceptionally
\DPPageSep{017.png}
% Fig 1.7
\begin{figure}[p]
  \Input[\textwidth]{page_013}
  \caption{The Milky Way near the Star 15 Monocerotis, \AR\ = 6~h.\ 35~m., Decl.\ N.~10° (photographed by Barnard, 1894. Exposure $3\frac{1}{2}$ hours)}
  \label{p13}%
  \index{Barnard, E. E., Prof.\ Univ.\ Chicago}\index{Monc´eros, galaxy in}\index{Milky Way}\index{photography!of stars}
\end{figure}
\DPPageSep{018.png}
favorable nights may so many be counted
without a telescope. As an average, on what may be
termed clear nights, the number thus ordinarily seen at
any given time is rather less than 2000; but this number
varies greatly with changing conditions of our atmosphere.
If one were to keep count, through the year, of
all the stars visible to the naked eye in all that part of
the heavens ever seen from a single place in the United
States, the total number would be about 4000.

\textbf{Number of the Telescopic Stars.}\index{stars!number of}---By the use of a small
telescope, or even an opera glass, the number of visible
stars is increased enormously. Even in Galileo's\index{Galile´i, G. (1564--1642), It.\ ast.} time, his
`optick tube' revealed an unsuspected and unnumbered
host, beyond the dreams of any primitive astronomer.
With our modern telescopes (in which the object glass of
almost every famous new one has been an advance in size
upon all its predecessors) the `blue field of heaven' is
estimated to contain at least 100,000,000 stars. Beyond
what is shown even by these telescopes are the remarkable
revelations of celestial photography, which reproduces
unerringly upon the sensitive plate uncounted millions of
other stars too faint for the eye to detect, even when aided
by the most powerful optical means at our command.
In a single field embracing but a slight fraction of the
whole sky, recently charted with the Bruce telescope\index{Bruce telescope} of
Harvard Observatory\index{Harvard College!obs.} (the largest photographic instrument
in existence), there were counted no less than 400,000 stars.
And who can say where this stupendous array ceases?

\textbf{The Constellations.}\index{constellations}\index{stars|see{constellations}}---The names and positions of the
brighter stars are very easy to remember. By even a casual
glance at the sky on any
% Fig 1.9
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.45\textwidth]{page_016}
  \caption{The Moon (photographed by the Brothers Henry)}
  \index{Henry, Paul (ong-ree´) (1848--1905), Fr.\ ast.}
  \index{Henry, Prosper (ong-ree´) (1849--1903), Fr.\ ast.}
  \index{photography!of moon}\index{moon!photographs}
  \label{p16}
\end{wrapfigure}
clear night, it will be seen
that the stars make all sorts of figures with one another,---squares,
triangles, half circles,---and fanciful combinations
may be traced in all directions. The ancients called these
\DPPageSep{019.png}
% Fig 1.8
\begin{figure}[hbtp!]
  \centering
  \Input{page_015}
  \caption{The Yerkes Telescope of the University of Chicago}
  \legend{%
  This great telescope was mounted in 1896--97 at Williams Bay, Wisconsin.
  It is the principal instrument of the Yerkes Observatory, and cost about
  \$125,000. The glasses for its 40-inch lenses, the largest in America, were
  made by M.~Mantois\index{Mantois, M. (man-twä´), Fr.\ glass-maker} of Paris, ground and figured by Alvan Clark\index{Clark, A. (1804--87), A. G. (1832--97), G. B. (1827--91)} \&amp; Sons
  of Cambridgeport; and the tube and all the intricate machinery for handling
  the telescope with ease and precision were built by Warner \&amp; Swasey
  of Cleveland.}
  \label{p15}
  \index{Yerkes, C. T. (yer´kez) (1837--1905), Am.\ patron!telescope}\index{Warner \&amp; Swasey}
\end{figure}
\DPPageSep{020.png}
various figures after their gods and heroes, dividing them
into 48 groups, largely named after the characters associated
with the voyage
of the fabled ship \textit{Argo}.
Although these constellations
bear little real
resemblance to the men,
animals, and other objects
named, they too
are easily learned. Properly
that is not astronomy,
but merely geography
of the heavens;
yet it is an interesting
and popular branch of
knowledge, often leading
to farther studies
into the most absorbing
and uplifting of sciences.

\textbf{The Moon.}\index{moon}---Of all
celestial bodies, meteors
alone excepted, the moon
is the nearest to us, and
apparently of about the
same size as the sun;
but this is the result of
a somewhat curious coincidence,
by which the
sun, although 400 times
broader than the moon,
is also very nearly 400
times farther away.
Even with a small telescope we may generally see the deep
craters and the rugged mountain peaks of the moon, partly
\DPPageSep{021.png}
illuminated by sunlight, while the rest of our satellite is
turned away from the sun, lying in shadow and seen very
faintly by the sunlight falling upon it after reflection from
the earth. Our companion world is dead and cold, its air
and water almost certainly gone, so that no amount of
brightest sunshine can of itself bring back any warmth
of life. Earth and other planets are dark, too, on the
surface, save for what the sun bestows of brightness and
warmth; but our own planet and some of the others are
blessed with an encircling atmosphere, best gift after
sunlight itself, to save and store for our use the sun's heat
shed lavishly upon us.

% Fig 1.10
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.37\textwidth]{page_017}
  \caption{Jupiter in a Small Telescope}
  \index{Jupiter!drawings}
\end{wrapfigure}
\textbf{The Planets.}\index{planets}\index{planets|see{Jupiter, Mars, Mercury, Neptune, Saturn, Uranus, Venus}}---When frequent looking at the nightly
sky has somewhat familiarized the evening constellations,---different
at the same hour at the various seasons of
the year,---one may notice three or four very bright
stars which do not twinkle. A few evenings' watching
will show that they are slowly changing their positions
relatively to other and fainter stars about them. These are
the planets (`wanderers'), and will at first be thought and
called stars; but although speaking
in the most general terms, it
is proper to refer to them as stars,
they are worlds, among which
the earth is one, traveling round
the sun in nearly circular paths.
Like our own planet, they receive
their light from the central orb,
and reflect it afar. The planets
and all their moons (called satellites),
as well as our moon, give
light only as reflected sunshine,---second-hand. Some of
the planets are brighter than most stars, only because
they are very much nearer to us and to the sun.
\DPPageSep{022.png}

\textbf{Differences between Stars and Planets.}\index{planets!different from stars}---Besides the
noticeable change of position of the planets, and their
shining by reflected light, another difference between
planets and fixed stars is that, when seen through a telescope,
planets appear larger in size than with the naked
eye. This the stars never do. Most planets have an
appreciable breadth, called the \textit{disk}\index{planets!disk of}; and this seems to grow larger as the power of telescopes is increased. Stars,
% Fig 1.11
\begin{figure}[hbt!]
  \centering
  \Input[0.7\textwidth]{page_018}
  \caption{The Planet Saturn in 1894 (drawn by Barnard with the Lick Telescope)}
  \index{Barnard, E. E., Prof.\ Univ.\ Chicago}\index{Saturn!drawings}
\end{figure}
on the contrary, seem to be mere points of light, intensely
luminous, and infinitely far away. They increase only in
brilliancy with the size of our largest glasses; and even
the strongest lenses cannot produce the slightest effect
upon the apparent size of these stupendously distant blazing
suns. Also some of the planets as seen in the telescope
show phases; in particular, Venus\index{Venus}, the brightest
planet, a familiar glory of the western sky, passing through
all the changing phases of our moon,---full, quarter, and
crescent. A planet called Saturn is surrounded by a
thin ring, as shown in above engraving. It suggested a
process of evolution called the nebular hypothesis, by
which stars, planets, and satellites seem to have developed
into present forms through the operation of natural
laws.
\DPPageSep{023.png}

\textbf{The Fixed Stars are Suns.}\index{stars!are suns}---All these fixed stars are
suns like our own---singularly similar, the modern revelations
of the spectroscope tell us, as to material elements
composing them. Probably, at their inconceivable distances
from us, these suns afford light and heat to
uncounted worlds not unlike those in the system of
planets\index{stars!planets belonging to} to which our earth belongs. But if such planets
exist, they are too near their own central luminaries, and
too faint for their reflected light ever to reach our far-off
eyes. One must think of the vaster brilliance of the sun
as due almost wholly to our relative nearness to him.
Were the earth to be removed as far from the sun as
it is distant from the stars, our lord of day would shrink
to the feeble insignificance of an average star.

\textbf{The Distances of the Stars.}\index{stars!distances illustrated}---The nearest star is so far
from us that its distance in figures, however expressed,
remains unapprehended by the human mind. Who can
conceive of 25 millions of millions of miles? Yet so remote
is our closest stellar neighbor. As the stars vary
enormously in their distances from us, so they are equally
diverse in their relations to each other. We see them all
by the light they emit---light which does not come to us instantaneously,
yet with speed almost inconceivably great.
While one is taking two ordinary steps, at an average
walking pace, light will travel a distance equal to eight
times round the world (nearly 200,000 miles). Now, to
realize in some sense the enormous distance of the nearest
fixed star from our earth, open a Webster's International
Dictionary, which contains over 2000 pages of three columns
each, or the equivalent. Begin to read as rapidly as
you can, and imagine a ray of light to have just left the
nearest fixed star at the instant you began. By the time
you have finished a single page, the star's light will have
sped onward toward the earth no less than 100,000,000 miles.
\DPPageSep{024.png}
Imagine that you could keep right on reading, tirelessly
and without ceasing, day and night, just as light itself
travels---how many pages would you have read when the
ray of light from Alpha Centauri\index{Centauri, Alpha}, the nearest fixed star,
had reached the earth? You would have read it completely
through,---not once, or twice, but nearly a hundred
times. So enormously distant is this nearest of the stars
that, if it were blotted out of existence this present moment,
it would continue to shine in its accustomed place
for more than three years to come. And other stars whose
distances have been measured are a hundredfold more
remote.

\textbf{The Shooting Stars and Comets.}\index{comets}---Very frequent celestial
sights, especially in April, August, and November, are
the swarms of swiftly-falling
% Fig 1.12
\begin{wrapfigure}{o}{0.45\textwidth}
  \centering
  \Input[0.4\textwidth]{page_020}
  \caption{The Great Comet of 1858}
  \label{p20}\index{Donati's comet (of 1858)}\index{comets|see{Donati's comet}}
\end{wrapfigure}
meteors\index{meteors}. They flash across
the sky and seem to vanish
into the blackness whence
they came, burning sparks in
the starry firmament. On
rare occasions a fragment of
a meteor falls down upon the
surface of the earth, and many
thousands of such specimens
are preserved as collections
of meteorites\index{meteorites} in various scientific
centers,---Vienna, London,
Paris, and Washington.
Sometimes they are of iron,
and sometimes of stone.
Much less common than the
spectacle of shooting stars
is that of a majestic comet, whose long and graceful tail
sweeps many degrees along the sky, sometimes for weeks
\DPPageSep{025.png}
or even months together. All these wandering visitors,
too, must be studied in their place.

\textbf{General Outline.}---We know that the stars are suns;
that our sun is one of them, seemingly larger only because
very much nearer; that he conducts with him through
space our earth and her companion planets with their
moons, or satellites; that the stars are all moving through
the celestial spaces with great velocity, though at such
enormous distances from us that they appear to be almost
at rest; that meteors and comets flash into our firmament,
the former to perish after one bright, sparkling clash with
our atmosphere, while the latter have their known and
regular orbits, or paths, some of them coming back within
our sight at predicted intervals.

\textbf{Gravitation.}\index{gravitation}---The mighty power called gravitation holds
all these whirling, flying, incandescent or white-hot, or
cold and dead bodies from swerving outside their paths
in space; and, little by little, the patience and ingenuity
and genius of man have interpreted many of the laws
governing them, and have brought to our knowledge
manifold facts about them,---their weights and distances,
sizes and motions, and even the elemental substances of
which they are composed. Their physical appearances,
as revealed by telescope and camera, will be abundantly
emphasized. But perhaps the most striking fact in all
astronomy is that unerring precision with which the
heavenly bodies move through the celestial spaces in accordance
with this great law of gravitation, whose action
enables us to foretell with great accuracy, hundreds of
years in advance, the places of planets in the starry
heavens, and the exact hour, minute, and second, when
eclipses\index{eclipses, solar!prediction of} will happen. And progress through the chapters
of this book will unfold in part the knowledge gained by
astronomers through centuries of careful investigation.
\DPPageSep{026.png}


\Chapter{II}{The Language of Astronomy}

\index{astronomy!language of}No one can understand even the simplest truths of
astronomy without first learning the language of precision
which astronomers use. Only a few terms in
this language will be necessary at the outset, and they will
be illustrated and ideas of them conveyed by means of common
% Fig 2.1
\begin{figure}[hbt!]
  \centering
  \Input{page_022}
  \caption{How to find True North (Approximately)}
\end{figure}
objects and simple processes. First, the four cardinal
points, east, north, west, and south,---terms in constant
use from the remotest antiquity.
\DPPageSep{027.png}

\Smaller
\label{p23} \textbf{How to find the Cardinal Points.}\index{cardinal!points}---Any sharply-pointed object,
firmly set, may be used as a gnomon\index{gnomon} for finding the cardinal points.
But the following method has greater advantages. Place a carefully
leveled board or table so that the sun may fall freely upon it, from
about nine o'clock in the morning until three in the afternoon. Fasten
securely. Near the sunward end of the table, and about eight inches
above it, fix firmly a card with a smooth pin hole through it. This will
give a small, oval image of the sun on the table, and its position must
be marked at nine o'clock, at a quarter past, and at half after nine;
again at half after two in the afternoon, a quarter to three, and three
o'clock. The principle involved is that of the gnomon of Anaximander\index{Anaximan´der (\BC~580), Gk.\ phil.}
in very compact form. Take especial care that the marked surface,
whether board or paper, shall not have moved meanwhile. Draw three
straight lines joining the sun marks, as indicated in the picture opposite;
connect the nine o'clock mark with the three o'clock one; draw
a second line connecting the 9:15 mark with that made at 2:45; and
a third, joining the 9:30 and 2:30 marks. These three lines will be
nearly parallel,
% Fig 2.2
\begin{wrapfigure}{o}{0.3\textwidth}
  \centering
  \Input[0.25\textwidth]{page_023}
  \caption{A Plumb-line}
\end{wrapfigure}
and they mark the direction east and west approximately,
the east end being indicated by the three afternoon marks.
Three pairs of points are better than one, because clouds may interfere
with the afternoon observations; also, we can take the average direction
of three lines, which will give true east and
west more accurately than a single line. By the
simple construction in geometry indicated in the
illustration, draw a perpendicular to this average
line; this perpendicular, then, will lie in the direction
north and south, north lying on the right
hand as one faces west. Extend these two straight
lines indefinitely, and they will mark the four cardinal
points called east, north, west, and south.

\textbf{Plumb-line, Zenith, and Nadir.}\index{plumb-line}\index{zenith}\index{nadir}---Suspend any
heavy object by a delicate
cord attached to a firm
support, and allow it to come to rest. Draw it to
one side or the other from its support, and let it
swing freely. Such an object capable of swinging is
called a pendulum. The force causing it to swing
back and forth is called the attraction of gravity.
We shall see subsequently that this is the same
force that makes all bodies fall to the earth; also
that it holds the moon, our satellite, in its monthly
path, or orbit, about us. After swinging back and forth many times,
the pendulum will come to rest; and it will do so more quickly if the
weight or bob of the pendulum is freely suspended in a basin of water.
A pendulum that has stopped swinging becomes a plumb-line.
\DPPageSep{028.png}
Imagine the cord of the plumb-line extended both upward to the sky
and downward through the earth indefinitely. The point overhead
where the plumb-line intersects the sky is called the \textit{zenith}\index{zenith!defined}; the opposite
point is called the \textit{nadir}\index{nadir!defined}.
\Restore

\textbf{The Apparent or Visible Horizon.}\index{horizon!apparent}\index{horizon!visible}---Looking up to the
sky, it seems to be arched over us like the inside of a great
hollow sphere. The dome of the sky is nearly hemispherical,
and seems to most eyes less distant overhead. In
ordinary inland regions the sky seems to meet the earth
in an irregular and broken line. This is called the apparent
% Fig 2.3
\begin{figure}[hbt!]
  \centering
  \Input{page_024}
  \caption{Plane of the Sensible Horizon cuts through the Mountains}
\end{figure}
or visible horizon; and nearly every point of it, even
in locations not especially mountainous, will usually be
considerably above the level of the eye. In cities the
surrounding buildings, the trees in the park, and the spires
of churches will lift themselves into our vision, too near by
to allow any observation of the sky at the exact level of
the eye. In the country, in Massachusetts, for example,
it is not always easy, without ascending some great
height, to reduce the obstacles forming the apparent horizon
to a minimum; and usually the sensible horizon lies
far below them all. Objects relatively near, then, whether
\DPPageSep{029.png}
houses, grain elevators, churches, forests, or mountains,
make irregular curves and broken lines which limit the
outward view in every direction. Their outline marks the
observer's apparent, or local, or visible horizon.

\Smaller
\textbf{The Sensible Horizon.}\index{horizon!sensible}---From the surface of the ocean, or from a
widely extended plain or prairie, the dome of the sky appears to join
the earth in a nearly perfect circle about 25 miles in diameter. In Boston,
for instance, we may take the steamer for Nahant, and for a portion
of even that short trip our perfect ocean horizon on one side will hardly
% Fig 2.4
\begin{figure}[hbt!]
  \centering
  \Input{page_025}
  \caption{The Visible Horizon on the Ocean}
  \label{p25}\index{horizon!ocean}
\end{figure}
be interfered with. In New York a boat trip to Far Rockaway or Long
Branch will give us a similar opportunity. In Chicago we have a choice
of ways to get a complete view of the sensible horizon. A car ride
in almost any direction---to Evanston, perhaps---will show widely
extended prairies, seeming to stretch to the sky on all sides; far out
upon Lake Michigan, the effect upon the observer is like that of the
ocean; or perchance the Auditorium tower may be ascended, and if the
distant view is clear, a far-away horizon of the sensible order is within
sight. Practically in this circle, the four cardinal points are located.
Imagine a plane passed through these four points. It will pass through
the eye of the observer, and will essentially be the plane of his sensible
horizon, neglecting only a small angle called the dip of the horizon, a
\DPPageSep{030.png}
term used in navigation, and explained in a later chapter. On a small
piece of cardboard draw two lines at right angles, one of them being
near the middle of the card. Pierce the card at each end of this line,
and draw a piece of twine through the holes. Fasten one end of the
twine to some firm object, and suspend a weight of a few pounds by the
other end. When the pendulum has come to rest, fasten the bottom
of the plumb-line carefully in that position, and stretch it taut. Then
twirl the card round, and the second line on it will point everywhere
in the direction of the sensible horizon.
\Restore

The sensible horizon, then, is a plane passing through
the point of observation and perpendicular to the plumb-line.
When the term \textit{horizon} alone is used, the sensible
horizon is meant. It is a fundamental plane of reference
in astronomical measurement.

\textbf{The Terrestrial Sphere.}\index{sphere!terrestrial}---A sphere is a solid figure all
points on whose surface are at the same distance from a
point within called the
center. The general
figure of the earth
being spherical, it
will be seen that the
directions indicated
by the terms north,
south, east, and west,
if extended in straight
lines into space, are
true only for a given
locality, or position of
the observer. This is
because he is situated
upon the surface of
a globe or sphere,
and the moment he
changes his position upon it, his zenith and horizon and
system of cardinal points all change with him. \textit{Down}
\DPPageSep{031.png}
always means toward the center of this globe; so that
if a plumb-line were imagined as extended downward
through the earth, at the antipodes it would coincide with
the direction \textit{up}. If we go to the opposite side of the
globe, changing our longitude by 180°, evidently the directions
called east by us in these two remote localities will
be exactly opposite to each other in space. So that a continuous
line, in order to represent a constant direction,
must have a constant curvature, corresponding to that of
the surface of the earth. The plane passing through the
earth's center parallel to the sensible horizon is called the
\textit{rational horizon}\index{horizon!rational}.

% Fig 2.5
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.45\textwidth]{page_026}
  \caption{West the same as East at Antipodes}
\end{wrapfigure}

\textbf{The Celestial Sphere.}\index{sphere!celestial}---We have spoken about the hemisphere
or dome of the sky. It is obvious from geometry
that the hemisphere above the sensible horizon must be
matched by an equal hemisphere inverted, and lying below
it. This complete and regular form, made by the two
hemispheres joined, is called the \textit{celestial sphere}. Sun,
moon, and all the stars of the firmament are scattered
apparently at random upon its inner surface. We need
not now concern ourselves about the remoteness of the
bodies in the sky. All appear to be at the same distance
from us; and the eye unaided is powerless to find out what
that distance is. But evidently there may be a very great
range in their distances, just as there is in the lights of
different sizes on ships in a harbor, or in the night signals
along a straight stretch of railway in or near a great city.
In either case, on a dark night, an inexperienced person
has little to guide him safely in judging what the distances
and relative location of the lights may be.

\textbf{Properties of the Celestial Sphere.}---The celestial sphere,
notwithstanding its inconceivable magnitude, possesses all
the properties of a geometric sphere: not only is every
point of its surface equally distant from a point within
\DPPageSep{032.png}
called its center (the point where the observer is), but all
planes cutting the sphere through its center trace out circles
of equal magnitude upon its surface. These are called
\textit{great circles}\index{circle!great, defined}. All planes cutting the sphere otherwise
than through its center trace out small circles upon its
surface. Evidently it is possible to imagine upon any
sphere as many great circles and as many small circles as
may be desired. Three systems of circles of the celestial
sphere, with their related points, lines, and arcs, are in
common use. They are:
\begin{center}
  \begin{tabular}{c l}
    (\textit{A}) &amp; the Horizon System,\index{horizon system!circles of} \\
    (\textit{B}) &amp; the Equator System,\index{equator system!circles of} \\
    (\textit{C}) &amp; the Ecliptic System.\index{ecliptic system!circles of}
  \end{tabular}
\end{center}

(\textit{A}) \textbf{The Horizon System.}\index{horizon system!circles of}---The great circle that passes
through the four cardinal points is called, as we have
seen, the \textit{horizon}. Upon it is
% Fig 2.6
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.45\textwidth]{page_029}
  \caption{Chief Circles of Horizon System (\textit{A})}
\end{wrapfigure}
based a system of circles
of the celestial sphere much used in astronomical descriptions
and measurements. Any great circle traced on
the celestial sphere by a vertical plane passing through
the point of observation is called a \textit{vertical} circle\index{circle!vertical, defined}\index{vertical circle, defined}. Clearly
an indefinitely great number of vertical circles may be imagined
as drawn. The planes of all vertical circles intersect
each other in a vertical line---the plumb-line extended,---joining
zenith and nadir. Two vertical circles are very
frequently used, and have especial names: first, the vertical
circle passing through the north and south points of the
horizon is the \textit{meridian}\index{meridian}; second, the vertical circle at
right angles to the plane of the meridian, and passing
through the east and west points of the horizon, is called
the \textit{prime vertical}\index{prime vertical, defined}. Any small circle of the celestial sphere
cutting it parallel to the horizon is called an \textit{almucantar}\index{almucantar defined}.
Evidently there is no limit to the number of almucantars;
one may be imagined as drawn through every star in the
\DPPageSep{033.png}
sky. The nearer a star is to the zenith, the smaller
its almucantar, just as parallels of geographic latitude
upon the earth become
smaller and
smaller as the poles
are approached.
Three hoops of a barrel
tied or tacked together,
with all the
angles right angles,
as in the illustration,
form an excellent representation
of horizon,
meridian, and prime
vertical; a much
smaller hoop (near
the top) may illustrate
an almucantar. Such
a concrete model is a
necessary aid to many minds in attaining an adequate conception
of the abstract circles of the celestial sphere.
Essentially they are a pattern of the armillary sphere\index{sphere!armillary} of
the ancient astronomy.


\textbf{Change of Horizon System with Change of Place.}---The
terms \textit{horizon}, \textit{meridian}, \textit{prime vertical}, and \textit{almucantar}
are generally applied to the circles upon the
celestial sphere traced by their planes. The terms are,
however, often, and properly, employed to designate
the planes themselves. It will be understood that these
four terms apply to an observer wherever he may be
located upon the surface of the earth. If he remains in
a single position, or has an observatory with a single
instrument, his horizon plane, meridian, and other circles,
planes, and points connected with it, have always a constant
\DPPageSep{034.png}
and definite position, relative to the observer himself.
They are imaginary planes and circles which the
observer carries about with him wherever he goes. The
moment he changes his locality, by so much even as a
few feet, he has thereby changed the position of all this
network, or system of celestial circles, by an amount
small, to be sure, but readily measurable by the instruments
and methods of the modern astronomer.

\textbf{Diurnal Motion and the Diurnal Arc.}\index{diurnal, motion and arc}---The sun, moon,
and stars, in their everyday motion, appear to cross these
% Fig 2.7
\begin{figure}[hbt!]
  \centering
  \Input{page_030}
  \caption{The Midsummer Sun is Highest and its Diurnal Arc is Longest}
\label{p30}\index{sun!midsummer}\index{midsummer}
\end{figure}
circles in various directions, and at various angles, and
with various velocities. A few evenings' observation will
show this. These movements are known as the phenomena
of the diurnal motion. Observe the points where
the sun rises and sets; if in the latter half of September
or March, these will be found to be almost due east and
\DPPageSep{035.png}
west. As noon approaches, near which time the sun
will cross the meridian, his course, in the latitude of the
United States, will be found to have been, not upward
along the prime vertical, but obliquely toward the south,
as illustrated: his paths at various seasons are all in
parallel planes. He will reach the highest point when
crossing the meridian, and is then said to \textit{culminate}.
Onward to sunset he describes an arc almost precisely
symmetrical with the forenoon path. This apparent track
of the sun through the daytime sky, from sunrise to sunset,
is called the \textit{diurnal arc}; and either half of it, between
meridian and horizon, is called the \textit{semidiurnal arc}. Similarly
observe the moon.

\Smaller
Perhaps it will rise considerably north of east. Watch it as it
mounts to the meridian. It will cross this plane only a few degrees
south of the zenith, and descend the western half of its diurnal arc,
setting about as far north of true west as it rose north of true east.
Select very bright stars in other parts of the sky both north and south
of sun and moon, and observe where they rise and set and culminate.
It is apparent, then, that the term \textit{diurnal arc} refers only to the interval
during which a celestial object is above the horizon; and this interval
of time (for any heavenly body except the sun) may elapse partly
during actual day and partly during night, or even entirely during the
night-time. For example, note the rising of some bright star near the
southeast. How slowly it appears to leave the horizon. Notice its low
elevation when it reaches the meridian, and its declining arc in the
southwest. Evidently its diurnal arc is very short; it has not been
above the horizon more than seven or eight hours in all.
\Restore

\textbf{The Diurnal Motion of a Star Overhead.}---Next select
a bright star almost overhead. Early in September evenings
in the United States, Vega\index{Vega} (Alpha Lyræ) will be in
this position. As it descends toward the west, its course
will seem to curve rapidly toward the north; and as it
approaches the northwestern horizon, it will seem to go
down less and less rapidly, meanwhile moving more and
more toward the north. Finally, it will disappear only a
\DPPageSep{036.png}
few degrees west of true north. In making this circuit
from the meridian to the northern horizon, it will have
consumed perhaps 10 or 11 hours; and as there will be
a similar arc of 10 or 11 hours between meridian and
eastern horizon, evidently such a star's diurnal arc may
be as much as 20 or 22 hours in length.

\textbf{The Diurnal Motion of a Circumpolar Star.}\index{stars!circumpolar}---Then
choose a star still farther north, but near the meridian,
and observe its motion critically. Very noticeable will be
the fact of its moving away from the meridian less rapidly
than the star just observed. It will not go nearly so far
west, and after about six hours it will begin to return
toward the north. Then, if we could follow it into the
daylight, six hours later still, or about 12 hours after it
was first observed, it would be seen nearly due north, and
at a considerable distance above the horizon. This plane,
in fact, it will never have reached. It will then continue
to move backward from west toward east, ascending from
the horizon at first very slowly, and making an excursion
as far east of the meridian as it was observed to the west.
After an interval of 24 hours from the first observation,
this star will be seen nearly in the first position, just like
any other star, having described an entire small circle of
the celestial sphere; and it would have been visible all the
time except for the overpowering brilliance of the sun.

\textbf{The Pole Star.}\index{Polaris}\index{Pole Star|see{Polaris}}\index{stars!pole|see{Polaris}}---If we select a star yet farther north,
we shall find that it describes an even smaller circle of the
celestial sphere. This tentative method alone would enable
us, by a few nights' observations, to select that star which
describes the smallest circle of all; the bright star known
as [Stella] Polaris, or the \textit{pole star}. Next to sun and moon
the most important object in the heavens, it is always visible
in all places in the United States when the sky is clear,
not only by night, but by day with the assistance of a
\DPPageSep{037.png}
small telescope. The center of the very small circle which
Polaris appears to describe every 24 hours is the north
pole of the heavens. Also the diurnal paths of all other
stars are central about it.

% Fig 2.8%
\begin{figure}[hbt!]
  \centering
  \Input{page_033}
  \caption{Five-hour Trails of Northern Circumpolar Stars (photographed by Barnard)}
  \label{p33}
  \index{Barnard, E. E., Prof.\ Univ.\ Chicago}\index{star trails}
\end{figure}
\Smaller
\textbf{How to find the Pole of the Heavens.}\index{pole!finding the}---First focus the camera carefully
on some very distant object, and mount it in the meridian. Secure
it firmly, with the lens directed northward and upward at an angle of
about 45°. As soon as the stars are out, and it has become quite dark,
take off the cap and leave the plate exposed as long as is convenient,
or until the beginning of dawn. Development will then show something
like the above, a series of concentric arcs, the shortest and
brightest of which will be that of Polaris. Star trails\index{star trails} will be broken
lines, if clouds temporarily intervene. At the center of all these curving
arcs is the celestial pole itself, always situated in the observer's meridian;
or strictly speaking, the meridian is the vertical circle passing
through the pole of the heavens. If the camera is pointed near the celestial
equator, star trails will be straight lines, as \vpageref{p34}.
\Restore
\DPPageSep{038.png}

% Fig 2.9
\begin{figure}[hbt!]
  \centering
  \Input{page_034}
  \caption{One-hour Trails of Stars in Orion's Belt (photographed by Barnard)}
  \label{p34}
  \index{Barnard, E. E., Prof.\ Univ.\ Chicago}\index{star trails}
\end{figure}

(\textit{B}) \textbf{The Equator System.}\index{equator system!circles of}---The north pole of the
heavens is a fundamental point of a second system of
planes and circles of the celestial sphere, just as the zenith
is the primary point of the horizon system. Imagine
this horizon system of planes and circles---horizon, prime
vertical, meridian, and almucantar---to be outlined in a
connected skeleton upon the vault of the sky. Also think
of this skeleton system as pivoted at the east and west
points, and free to turn about them. Then move the
zenith point northward along the meridian, until it coincides
with the north pole. The south point of the horizon
will then have traveled upward along the meridian by an
angle equal to the distance of the zenith from the north
pole. Also the north point of the horizon will have been
depressed below it by an equal arc. In this novel position
the circles and planes of the celestial sphere need defining
\DPPageSep{039.png}
anew. What was the zenith is now the north pole of the
heavens. The horizon has become the celestial equator\index{equator!celestial defined},
every point of which is distant 90° from the celestial pole\index{pole!celestial north, defined},
just as the horizon is everywhere 90° from the zenith. What
were vertical circles now converge toward the poles, the
southern one of which is depressed below the south horizon
as much as the northern one is elevated above it. Instead
of vertical circles they are called, in this position, meridians
of the celestial sphere, or \textit{hour circles}\index{hour circle}. They correspond
to, and are planes extended from, the terrestrial meridians
of geography. Almucantars
in system
(\textit{A}) become parallels
of declination\index{declination!parallels of} in system
(\textit{B}).

% Fig 2.10
\begin{wrapfigure}[19]{o}{0.5\textwidth}
  \centering
  \Input[0.45\textwidth]{page_035}
  \caption{Chief Circles of Equator System (\textit{B})}
\end{wrapfigure}
\textbf{The Colures.}\index{colure!defined}---Evidently
an hour circle
may, if desired, be
drawn through any
star of the sky. Two
of these hour circles
at right angles to
each other, have especial
names; they
are counterparts of
prime vertical and
meridian in the first
or horizon system,
and are called the
\textit{equinoctial colure} and
the \textit{solstitial colure}.
The equator, both the colures, and all the other hour
circles have nearly constant directions and fixed positions
among the stars, just as the prime vertical and the meridian
\DPPageSep{040.png}
 have with reference to the landscape at a particular
place. The absolute position of the north pole, the
celestial equator, and its colures among the stars can be
determined at any time; and the astronomical processes
by which this is done will be indicated farther on. Equator
and colures should be concretely illustrated by three
hoops secured at right angles, as in the horizon system.

\textbf{Equator System glides over Horizon System.}\index{equator system!glides over horizon system}---It has
already been seen that the stars themselves, by the diurnal
motion, cross the planes and circles of the horizon system
at a great variety of angles and velocities; evidently then,
as the circles of the new system are practically fixed
among the stars, the circles of this equator system must
be imagined as all the time gliding over and across those
of the horizon system. Spherical astronomy is a branch
of the science dealing very largely with the relations of
equator and horizon systems; and is mostly concerned
with the angles that the circles of the horizon system
make with those of the equator system. The problems
arising are mostly solved by means of that branch of
mathematics called spherical trigonometry, which is the
science of ascertaining all the different parts of triangles
described on the sphere, from certain parts that have been
measured by instruments.

% Fig 2.11
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.45\textwidth]{page_037}
  \caption{Chief Circles of Ecliptic System (\textit{C})}
\end{wrapfigure}
(\textit{C}) \textbf{The Ecliptic System.}\index{ecliptic system!circles of}---A third system of planes
and circles of the celestial sphere, much used in astronomy,
may best be denned and illustrated here, because it follows
naturally and readily from the horizon system and the
equator system. An idea of its relation to these other
systems is easily obtained on recalling the way in which
the equator system was derived from the horizon system---by
pivoting the latter at the east and west points, and
turning the skeleton horizon system about these pivots,
until the zenith became the north pole of the heavens.
\DPPageSep{041.png}
Now in a precisely similar way, imagine the equator
system pivoted at the two opposite points where equator
and meridian cross.
Then carry the north
pole toward the west
$23\frac{1}{2}$°. The equator
will then have assumed
a position inclined
by an angle of
$23\frac{1}{2}$° to its former
position. It will, in
short, have become
the ecliptic; and in
this novel relation
nearly all the elements
of the celestial
sphere must again
be defined. A third
system of hoops
should be arranged
as in the illustration.
The ecliptic, as we
shall see farther on,
is the path in which
the sun seems to travel completely round the sky once
every year---a motion entirely distinct from that now
under consideration.

\textbf{Parallels of Latitude, Equinoxes and Solstices.}\index{latitude (celestial)!parallels of}\index{equinoxes}\index{solstices}---What
was the north pole of the heavens becomes, in the ecliptic
system, the north ecliptic pole. The equator itself, as
has been said, is now the ecliptic. What were vertical
circles in the horizon system, and hour circles in the
equator system, are now \textit{ecliptic meridians}. As almucantars
became parallels of declination, so now parallels of
\DPPageSep{042.png}
declination become \textit{parallels of celestial latitude}. Upper
of the two pivotal points upon which equator turned
about meridian is called the \textit{Vernal Equinox}\label{p38}, or First of
Aries\index{Aries!first of}; its opposite point, 180° away, the \textit{Autumnal Equinox}.
Or the equinoxes are, simply, two opposite points of
the celestial sphere where equator and ecliptic cross each
other. \index{equinoxes!defined}The word \textit{equinox} signifies equality of day and
night; and these points have this name because when the
sun is exactly at either of them (in spring and autumn),
it rises due east and sets due west. As the relations in
the figure \vpageref{p39} show, it is 12 hours above the horizon,
making the day, and an equal interval of 12 hours below
the horizon. Day and night are therefore equal in
duration. Passing along the ecliptic eastward 90° from
the vernal equinox, a point is reached that bears the
name \textit{Summer Solstice} (the sun's place in the latter part of
June). Exactly opposite to it in the sky, or 90° beyond
the autumnal equinox, is situated the \textit{Winter Solstice} (the
position of the sun just before Christmas).

\textbf{Ecliptic System glides over Horizon System.}\index{ecliptic system!glides over horizon system}---The ecliptic
system of planes and circles maintains an almost invariable
relation to the equator system and to the fixed
stars. Therefore it also must glide over the seemingly
stationary circles of the horizon system, in much the same
manner that the planes and circles of the equator system do.
In consequence, however, of the angle of $23\frac{1}{2}$° between
equator and ecliptic the constantly varying relations of
the ecliptic system to the horizon system will be more
intricate than those of the equator system to the horizon
system. But all these relations are readily understood,
and may be completely solved by the processes of spherical
astronomy.

\Smaller
The relation of equator to ecliptic, and their apparent daily motion
through the sky, may be well illustrated by a plain model like the one
\DPPageSep{043.png}
here shown---two pasteboard disks cut together and secured to an
ordinary thread-spool slipped on a lead pencil pointing upward to the
pole, and twirled round in the direction of the arrows. In the first
place, the north pole of the ecliptic, being $23\frac{1}{2}$° from the north pole
of the heavens, is always distant $66\frac{1}{2}$° from the equator, and so seems
to move round the pole once every day, exactly as if it were a star in
that position. Everywhere in the United States the north ecliptic pole
% Fig 2.12
\begin{figure}[hbt!]
  \centering
  \Input{page_039}
  \caption{Model showing Apparent Motion of Equator and Ecliptic}
  \index{ecliptic!apparent motion}
\label{p39}
\end{figure}
is perpetually above the horizon. The solstices being points $23\frac{1}{2}$° from
the equator, the summer solstice north of it, and the winter solstice
south, they also seem to move round the sky obliquely to the vertical
circles of the horizon system. As the axis of revolution of the celestial
sphere passes through the north and south poles of the equator system,
the equator revolves round in its own plane, like a pulley on a shaft, and
is always parallel to itself. Evidently, then, the ecliptic must partake
of a wobbling motion because of its constant inclination of $23\frac{1}{2}$° to that
seemingly stationary circle among the stars, the celestial equator. These
three systems of circles---(\textit{A}) \textit{the horizon system}, (\textit{B}) \textit{the equator system},
(\textit{C}) \textit{the ecliptic system}---comprise all that are in general use by the
astronomers of the present day.
\Restore
\DPPageSep{044.png}

\textbf{Usual Astronomical Symbols.}\index{symbols, usual astronomical}---There is a variety of
symbols in common use for expressing in abbreviated form
the names of sun, moon, and planets, their location in the
sky, the signs of the zodiac, and so on. Some of them are
frequently employed in other sciences with differing significations,
but their astronomical meanings are as follows:---
\begin{center}
\TableSize
%[** TN: \ascnode, \earth, and \neptune do not match the original]
\begin{tabular}{r@{\,}c@{\,}l@{\,}cr@{\,}c@{\,}l}
\astrosun &amp;=&amp; the sun.   &amp;&amp; \mercury &amp;=&amp; Mercury.\\
\leftmoon &amp;=&amp; the moon.  &amp;&amp; \venus &amp;=&amp; Venus.\\
\newmoon &amp;=&amp; the new moon. &amp;&amp; \earth &amp;=&amp; the earth.\\
\fullmoon &amp;=&amp; the full moon. &amp;&amp; \mars &amp;=&amp; Mars.\\
\conjunction &amp;=&amp; conjunction, or the same in &amp;&amp; \jupiter &amp;=&amp; Jupiter.\\
$\square$ &amp;=&amp; quadrature, or differing 90° in
  &amp;
  \settowidth{\TmpLen}{either longitude or}%
  \smash{$\Bigg\}$\parbox[c]{\TmpLen}{\centering
      either longitude or \\ right ascension.}}
  &amp; \saturn &amp;=&amp; Saturn.\\
\opposition &amp;=&amp; opposition, or differing 180° in &amp;&amp; \uranus &amp;=&amp; Uranus.\\
\ascnode &amp;=&amp; the ascending node. &amp;&amp; \neptune &amp;=&amp; Neptune.
\end{tabular}
\end{center}

\Smaller
And for the signs of the zodiac (not the constellations of the same
name), the following:---
\label{p40}\index{zodiac!signs of}
\begin{center}
\TableSize
\begin{tabular}{lc@{\,}l@{\,}l}
(I)    &amp; \aries       &amp; Aries       &amp; \\
(II)   &amp; \taurus      &amp; Taurus      &amp;
  \settowidth{\TmpLen}{Spring}%
  \smash{$\Bigg\}$\parbox[c]{\TmpLen}{\centering Spring \\ signs.}} \\
(III)  &amp; \gemini      &amp; Gemini      &amp; \\
%
(IV)   &amp; \cancer      &amp; Cancer      &amp; \\
(V)    &amp; \leo         &amp; Leo         &amp;
  \settowidth{\TmpLen}{Summer}%
  \smash{$\Bigg\}$\parbox[c]{\TmpLen}{\centering Summer \\ signs.}} \\
(VI)   &amp; \virgo       &amp; Virgo       &amp; \\
\end{tabular}\hfill\begin{tabular}{lc@{\,}l@{\,}l}
(VII)  &amp; \libra       &amp; Libra       &amp; \\
(VIII) &amp; \scorpio     &amp; Scorpio     &amp;
  \settowidth{\TmpLen}{Autumn}%
  \smash{$\Bigg\}$\parbox[c]{\TmpLen}{\centering Autumn \\ signs.}} \\
(IX)   &amp; \sagittarius &amp; Sagittarius &amp; \\
%
(X)    &amp; \capricornus &amp; Capricornus &amp; \\
(XI)   &amp; \aquarius    &amp; Aquarius    &amp;
  \settowidth{\TmpLen}{Winter}%
  \smash{$\Bigg\}$\parbox[c]{\TmpLen}{\centering Winter \\ signs.}} \\
(XII)  &amp; \pisces      &amp; Pisces      &amp;
\end{tabular}
\end{center}

The explanation of technical terms used above will be given subsequently
in appropriate paragraphs.

\textbf{Expressing Large Numbers.}---In astronomy there is frequent occasion
to express very large numbers, because our earth is so small a
part of the universe that terrestrial units often have to be multiplied
over and over again, in order to represent celestial magnitudes. In
this book, and in accordance with American usage generally, the
French system\index{notation system!Fr.} of enumeration is used. From one million upward, it
is as follows:---
\[
\left.
\begin{tabular}{r@{ }c@{ }l}
1,000,000 &amp;=&amp;one million \\
1,000,000,000 &amp;=&amp;one billion \\
1,000,000,000,000 &amp;=&amp;one trillion \\
1,000,000,000,000,000 &amp;=&amp;one quadrillion \\
\multicolumn{1}{c}{etc.} &amp;&amp; \multicolumn{1}{c}{etc.}
\end{tabular}
\right\}
\settowidth{\TmpLen}{French system.}%
\parbox[c]{\TmpLen}{\centering The usual \\ or \\ French system}
\]
through quintillions, sextillions, and so on; the Latin terms being
employed, and each order being 1000 times that next preceding it. It
\DPPageSep{045.png}
is necessary, however, to note that in works on astronomy published in
England, and now widely circulated in America, the English system\index{notation system!Eng.} of
enumeration is always employed. The terms billion, trillion, quadrillion,
and so on are used, but with entirely different signification: each is one
million, instead of 1000, times the one next preceding it. So that
\[
\begin{tabular}{r@{ }c@{ }l}
1,000,000&amp;=&amp; one million (English)\\
&amp;=&amp; one million (French)\\
1,000,000,000,000&amp;=&amp; one billion (English)\\
&amp;=&amp; one trillion (French)\\
1,000,000,000,000,000,000&amp;=&amp; one trillion (English)\\
&amp;=&amp; one quintillion (French)
\end{tabular}
\]

Also, very large numbers are often expressed by an abridged or
algebraic notation, in which there is no ambiguity.

\begin{tabular}{l l@{ } l@{ } r@{ } l@{ }}
Thus,\qquad &amp;$3× 10^{9}$&amp;=&amp; 3,000,000,000&amp;= three billions (French)\\
&amp;$6× 10^{12}$&amp;=&amp; 6,000,000,000,000&amp;= six billions (English)\\
&amp;&amp;&amp;&amp;= six trillions (French)
\end{tabular}

The small figure above the 10 is called an exponent, and indicates
the number of times that 10 is taken as a multiplier.
\Restore

\textbf{East and West, North and South, in the Heavens.}\index{cardinal!directions in sky}---Ordinary
and restricted use of these terms, as adopted
from geography, has already been defined: north and south
state the direction of the true meridian; an east and west
line is horizontal and at right angles to a north and south
one. This use of these terms is wholly confined to the
planes and circles of system (\textit{A}), whose fundamental plane
is the horizon. When, however, we pass to systems (\textit{B})
and (\textit{C}), the meaning of the terms \textit{east} and \textit{west}, \textit{north} and
\textit{south}, changes also, to correspond with their fundamental
planes. As related to these systems, then, we must define
north, south, east, and west anew. \textit{North} is the direction
from any celestial body toward the north pole of the
heavens; it is a constantly curving direction along the
hour circle passing through that body. Similarly, \textit{south}
is the opposite direction, along the same hour circle,
toward the south pole. Immediately underneath the
pole, south, in system (\textit{B}), means toward the north point
\DPPageSep{046.png}
of the horizon. \textit{East} and \textit{west} lie along equator and
parallels of declination, in curving directions on the celestial
sphere. When facing toward the south, east is the
direction toward the left, or counter-clockwise around
equator and parallels. The farther north or south a
star is, the smaller its parallel, and the more rapid the
curvature of the direction east and west from it. Also
the terms \textit{east} and \textit{west}, \textit{north} and \textit{south}, are often used
with reference to the planes and circles of system (\textit{C});
north and south then lie along ecliptic meridians, and
east and west are at right angles to these meridians, in
the curving direction of ecliptic and parallels of celestial
latitude. East is counter-clockwise, as in system (\textit{B}), and
north is toward the north pole of the ecliptic.

We are now prepared to consider the relations of these
three systems to the work of the practical astronomer, to
study the terminology of each, and to trace their points of
geometric likeness philosophically.
\DPPageSep{047.png}


\Chapter{III}{The Philosophy of the Celestial Sphere}
\index{sphere!celestial}

% Fig 3.1
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.55\textwidth]{page_043}
  \caption{All Circles are divided into 360 Degrees}
  \label{p43}\index{circle!division of}
\end{wrapfigure}
As\index{astronomy!history} the conception of the celestial sphere is now understood,
we next give the reasons underlying the different
systems already explained. These reasons are
fundamental, having their origin in the principles of geometry
itself. They have been known, and accepted since the
days of Euclid (\BC~280)\index{Euclid (\BC~280), Gk.\ geom.}, who first gave a rational explanation
of all those ordinary phenomena of the celestial sphere
that the ancients
were able to observe.
Practical
astronomy\index{astronomy!practical defined} is the
science of accurate
observation and
calculation of the
positions of the
heavenly bodies.
In order that it
should advance
from a rudimentary
beginning, the
observations, as
well as the mathematical
processes by which they were calculated, had
to be accurate. Precise observation was possible only
when the heavenly bodies could be referred to some
established point, or circle, or plane. Naturally the
\DPPageSep{048.png}
horizon was the first plane of reference, because the
rising and setting of sun and moon and the brighter stars
could be watched quite definitely. This fact explains the
origin of the fundamental plane of the horizon system.
Its related points, circles, and planes came naturally and
necessarily from the principles of geometry.

\textbf{The Measure of Angles.}\index{angles!measure of}---In astronomical measurements,
circles of all possible sizes are dealt with; and
every circle regardless of its size is divided into 360°.
The degree is a unit of angular measure\index{unit!angular}, not of length;
and its value as described on a circular arc varies uniformly
with the size of the circle. In concentric circles, for example,
the number of degrees included between any two
radii, as illustrated \vpageref{p47}, %on the preceding page,
is the same
in all circles. Every degree is divided into $60'$, and every
minute into $60''$. Do not confuse with the same symbols,
often used to designate feet and inches.

\textbf{Light moves in Straight Lines.}\index{light!moves in straight lines}---All astronomy is based
on the truth of the proposition that, in a homogeneous
medium like the ether\index{ether, luminiferous, defined}, a weightless substance filling space,
light moves in straight lines. The physicist demonstrates
this from the wave theory of the motion of light.

\Smaller
\index{scintillation}\index{stars!scintillation}The nature of a homogeneous medium may be illustrated by contrast
with one that is not so. Look out of the window at objects seen just
above the top of a heated radiator. They appear to be quivering and
indistinct. We know that such objects---buildings, signs, trees---are
really not distorted, as they seem to be; and we refer this temporary
appearance to its true cause---the irregular expansion of the air surrounding
the radiator. A portion of the medium, then, through which
the light has passed, from the objects outside to the eye, is not homogeneous;
and we know that if the radiator and the air round it were
of the same temperature, there would be no such blending and scattering
of the rays. The light passing over a heated chimney, the air above an
asphalt walk on which the sun is shining, a flagstaff seemingly cut in
two on a sunny day (when the eye is placed close to it and directed
upward),---these and many other simple phenomena have a like origin.
That violent twinkling of the stars which adds so much to the beauty
\DPPageSep{049.png}
of a winter night is due in large part to a vigorous commingling of
warm air with cold, causing departure of the light-bearing medium from
a perfectly homogeneous structure. On such nights the telescope
cannot greatly assist the eye in astronomical observations.
\Restore

% Fig 3.2
\begin{figure}[hbt!]
  \centering
  \Input{page_045}
  \caption{The Nearer the Track, the Broader it seems (Instantaneous Photograph by Trowbridge)}
  \label{p45}\index{Trowbridge, M. L., photographer}
\end{figure}

\textbf{Angles and Distances.}\index{angles!relation to distance}---As light moves in straight lines,
the angle which a body seems to fill, or subtend, is wholly
dependent upon its distance from the eye. The more remote
a given object is, the smaller the angle it subtends, and the
nearer it is, the greater this angle. We do not always think
of this when crossing a straight stretch of railway track,
although we know that the rails are everywhere the same
distance apart. But the camera, by projecting all objects
on a plane surface regardless of their distance, brings out
prominently the great difference in the angular breadth
of the track near by and far away, so well shown in the
picture. By trial we readily verify the following law:---
\DPPageSep{050.png}
\textit{Angles subtended by a given object are inversely proportional
to the distances at which it is placed.} Consequently a
number of bodies of various sizes---the silver dollar, the
saucer, and the bicycle wheel, as shown in the illustration---may
all subtend exactly the same angle, provided
they are placed at suitable distances. Obviously, then, it
is very indefinite to say that the moon looks as big as a
dinner plate or a cart wheel, or anything else, unless at the
same time it is stated how far from the eye the dinner
plate or cart wheel or other object is supposed to be.

% Fig 3.3
\begin{figure}[hbt!]
  \centering
  \Input{page_046}
  \caption{If Bodies fill the Same Angle, their Size is Proportional to their Distance}
\end{figure}

\textbf{Moon and the Radian are Standards.}\index{moon!angular unit}\index{radian, angular unit}---Observation
shows that the moon actually subtends an angle of about
one half a degree; and it has been demonstrated by geometry
that a sphere whose distance is
\[
\left. \begin{aligned}
  \text{206,000}&amp; \\ \text{3,400}&amp; \\ 57&amp;
\end{aligned} \right\}
\text{ times its diameter just fills an angle of }
\left\{ \begin{aligned}
  &amp;1''  \\ &amp;1'  \\  &amp;1°
\end{aligned} \right.
\]

\Smaller
These numbers are obtained accurately as follows: Recalling the
rule of mensuration concerning the circle, whose radius is $r$, its circumference,
or $360° =2\pi r$, $\pi$ being the familiar 3.14159, or $3\frac{1}{7}$. But as
\[
\begin{array}{r@{\,}c@{\,}r@{\,}c@{\,}r@{\,}c@{\,}r}
  2\pi r &amp;=&amp; 360° &amp;=&amp; \text{21,600}' &amp;=&amp; \text{1,296,000}'', \\
       r &amp;=&amp; 57\frac{1}{3}°  &amp;=&amp; \text{3,438}' &amp;=&amp; \text{206,265}''.
\end{array}
\]

The angle $r$ is a convenient unit of angular measure. As it is the
arc measured on the circumference of any circle by bending the radius
round it, this angle is often called the \textit{radian}.
\Restore
\DPPageSep{051.png}

So that if the distance of an object from the eye is
equal to 115 times its diameter, it will subtend the same
angle that the moon does, and so will appear to be of
the same size as the moon. The eye is often deceived in
the distance and size of objects, generally placing them
much nearer than they should be. This experiment is
very easily tried: an ordinary copper cent, in order to
fill the same angle as the moon should be placed at a
distance of about seven feet; while a silver dollar should
be nearly $14\frac{1}{2}$ feet away. The moon, then, always filling
nearly the same angle of $\frac{1}{2}$°, is an excellent standard of
angular value; a small unit of arc measure. To express
the apparent distance of a planet, for example, from a star
alongside it, estimate how many times the moon's disk
could be contained between the two objects; then half
this number will express the distance roughly in degrees.
Though the result may be somewhat erroneous, the principle
is correct.

% Fig 3.4a, b
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input{page_047a}
    \caption{Stars of Equal Altitude}
  \end{minipage}\hfil
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input{page_047b}
    \caption{Stars of Equal Azimuth}
  \end{minipage}
  \label{p47}
\end{figure}

\textbf{Altitude and Azimuth.}\index{altitude!defined}\index{azimuth, defined}---Altitude is the angular distance
of a body above the horizon; and it is measured
along the arc of the vertical circle passing through the
body. Evidently the altitude of the zenith is 90°, and
this is the maximum altitude possible. Oftentimes the
\DPPageSep{052.png}
term \textit{zenith distance}\index{zenith!distance, defined} is used; it is always equal to the
difference between 90° and the altitude. But in order to
fix the position of a body in the sky, it is not sufficient
to give its altitude alone. That simply tells us that it
is to be found somewhere in a particular small circle, or
almucantar; but as it may be anywhere in that circle, a
second element, called \textit{azimuth}, becomes necessary. This
tells us in what part of the almucantar the star is to be
found. Azimuth is the angular distance of a body from
the meridian; and it is measured along the horizon from
the south point \textit{clockwise} (that is, in the direction of motion
of the hands of a clock), or through the points west,
north, east, to the foot of the star's vertical circle. Azimuth,
then, may evidently be as great as 360°. The position
of a star in the northwest, and 40° from the zenith, would
be recorded as follows: altitude 50°, azimuth 135°. One
at 10° from the zenith, but in the southeast, would be:
altitude 80°, azimuth 315°. The figures (\vpageref*{p47}) make
it clear that many stars may have equal altitudes, although
their azimuths all differ; while yet others, if located on
the same vertical circle, may have equal azimuths, although
their altitudes range between 0° and 90°.

\Smaller
% Fig 3.5
\begin{wrapfigure}[6]{o}{0.2\textwidth}
  \centering
  \Input[0.07\textwidth]{page_049a}
  \caption{Model Sight}\index{sight!model}
\end{wrapfigure}
\textbf{A Simple Altazimuth Instrument.}\index{altazimuth}---This simple and readily built
instrument is all that is needed to find altitudes and azimuths. Of
course the measures will be made roughly, but the principles are perfectly
correct. The illustration shows plainly the essentials of construction.
From the corners of a firm board base about two feet square, let
four braces converge, to hold an upright bearing, just below the azimuth
circle. Through this bearing run an upright pole or straight piece of
gas pipe, letting it rest in a socket on the base, in which it is free to
turn round. A broom handle run through two holes bored in the middle
of two opposite sides of a packing box will do very well, in default
of anything better. Just above the azimuth circle attach to the upright
axis a collar with a pointer equal in length to the radius of the azimuth
circle. It is more convenient if this collar is fastened by a set screw.
The circle is made of board, to which is glued a circle of paper or
\DPPageSep{053.png}
thin card, divided in degrees, beginning with 0° at S, and running
through 90° at W, 180° at N, 270° at E, and so on. After dividing
and numbering, the circle may be covered with two or three coats of
thin shellac, in order to preserve
it. Attach to the top of the
vertical axis a second circle, the
altitude circle, divided through
its upper half, from 0° on each
side up to 90°, or the zenith.
Through the center of the altitude
circle run a horizontal bearing;
it is better if large, say $\frac{1}{2}$ inch or
more, because the index arm
attached to it will then turn more
evenly, and stop at any required
position more sharply. In line
with the index point and the center
of the bearing, attach two
sights near the ends of the arm.
Essentially the altazimuth instrument
is then complete. Sights
for use upon stars with the naked
eye should be of about this size
and construction:
The aperture of
about $\frac{1}{5}$ inch does
not diminish the star's light, and
the small cross threads or wires
give the means of fairly accurate
observation.

% Fig 3.6
\begin{wrapfigure}[27]{o}{0.4\textwidth}
  \centering
  \Input[0.35\textwidth]{page_049}
  \caption{Model of the Altazimuth}
\end{wrapfigure}
\textbf{Use of the Altazimuth.}---To
use it, level the azimuth circle,
and bring the line through N
and S to coincide with the meridian,
already found. See that the
line of zeros of the altitude circle
is, as nearly as may be, at right
angles to the vertical axis.
Point the sights in the line of
the meridian, and while looking northward, clamp the azimuth pointer
exactly at 180°, by means of its collar. The instrument is then ready
for use; and on pointing it at any celestial body, its altitude and
azimuth at the time of observation may be read directly at the ends of
the pointers of the two circles. If the instrument has been made and
\DPPageSep{054.png}
adjusted with even moderate care, its readings will pretty surely be
within one degree of the truth; and for practicing the eye in roughly
estimating altitudes and azimuths at a glance, nothing could be better.
Also take the altitude of the sun and stars when on the meridian and
the prime vertical. To observe the sun most conveniently, let its rays
pass through a pin hole at the upper end of the index, or pointer, and
fall upon a card at the lower end with a cross marked upon it; care
being taken that the line of the pin hole and the cross is parallel to the
line of sights.
\Restore

\textbf{Origin of the Equator System.}\index{equator system!origin of}---The motion of the
celestial sphere is continually changing the altitude and
azimuth of a star. Consequently the horizon and its connected
circles are a very inconvenient system of noting the
positions of stars with reference to each other; even the
ancients had observed that these bodies did not seem to
move at all among themselves from age to age. It was
natural and necessary therefore to devise a system of coördinates,
as it is called, in which the stars should have
their positions fixed, or nearly so. From the time of
Euclid\index{Euclid (\BC~280), Gk.\ geom.}, at least, a philosopher here and there was satisfied
that the earth is round, that it turns on its axis, and that
the axis points in a nearly constant direction among the
stars. Readily enough, then, arose the second, or equator
system of elements of the celestial sphere; the north end
of the earth's axis prolonged to the stars gave the primal
point of the system---the north pole of the heavens.
Everywhere 90° from it is the great circle girdling the sky,
in the plane of the earth's equator extended, and called
therefrom the celestial equator.

\textbf{Declination.}\index{declination!defined}---This plane or circle (often termed the \textit{equinoctial}\index{equinoctial, defined},
but generally called the \textit{equator} simply), becomes
the fundamental reference plane of the equator system
(\textit{B}). It sustains exactly the relation to the equator system
that the horizon has to the horizon system (\textit{A}). And,
similarly, two terms are necessary to fix the position of a
\DPPageSep{055.png}
star relatively to the equator. First, the declination, which
is the counterpart of altitude in system (\textit{A}). The \textit{declination}
of a body is its angular distance from the equator; and
it is measured north or south from that plane, along the
hour circle passing through the body. If the star is north
of the equator, it is said to be in \textit{north} or plus declination;
if south, then in minus or \textit{south} declination. Evidently,
stars north of the equator may have any possible declination
up to plus 90°, the position of the north pole; and stars
south of the equator cannot exceed a declination of minus
90°. The symbol for declination is \textit{decl}, or simply $\delta$ (the
small Greek letter \textit{delta}). Sometimes the term \textit{north polar
distance}\index{north polar
distance, defined} is substituted for declination; and it is counted
along the star's hour circle southward, from the north pole,
right through the equator if necessary. North polar distance
cannot exceed 180°, the position of the south pole of
the heavens. For example, the north polar distance of a
star in declination $+20$° is 70°; and if the declination is
$-22$°, the north polar distance is 112°.

\textbf{Right Ascension.}\index{right ascension, defined}---Recalling again the terms and circles
of the horizon system, it is apparent that declination
alone cannot fix a star's position on the celestial sphere
any more than mere altitude can. It would be like trying
to tell exactly where a place on the earth is by giving its
latitude only; the longitude, or angular distance on the
earth's equator from a prime meridian must be given also.
So the companion term for declination is \textit{right ascension};
and it is the counterpart of azimuth in the horizon system
(\textit{A}). But note two points of difference. The right
ascension of a body is its angular distance from the vernal
equinox (a point in the equator whose definition has already
been given on page~\pageref{p38}). Right ascension is measured
\textit{eastward}, or counter-clockwise, along the equator, to the
hour circle passing through the body. It may be measured
\DPPageSep{056.png}
all the way round the heavens, and therefore may
be as great as 360°. But as a matter of convenience
purely, right ascension is generally denoted in \textit{hours}, not
degrees (figure on page~\pageref{p39}). As 24 hours comprise the
entire round of the sky, and 360° do the same, one may be
substituted for the other. Each hour, then, will comprise
as many degrees as 24 is contained times in 360; that
is, 15. Also hours are divided into minutes and minutes
sub-divided\DPnote{** Not hyphenated elsewhere} into seconds of time, just as degrees are, into
minutes and seconds of arc. So that we have:---
\[
\left.
\begin{array}{l@{\ }l}
1 \text{ h.} &amp;= 15°  \\
1 \text{ m.} &amp;= 15' \\
1 \text{ s.} &amp;= 15''
\end{array}
\right\}
\quad\text{and}\quad
\left\{
\begin{array}{l@{\ }l}
1°  &amp;= 4 \text{ m.} \\
1'  &amp;= 4 \text{ s.} \\
1'' &amp;= 0.0667 \text{ s.}
\end{array}
\right.
\]
These are relations constantly required in astronomy.
Usual symbols for right ascension are \textsc{r.~a.}, or \AR, or
simply $\alpha$ (the small Greek letter \textit{alpha}), standing for
\textit{ascensio recta}. The figures make it clear that stars may
have equal right ascension, although their declinations
differ widely, and \textit{vice versa.}

% Fig 3.7a, b
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input{page_052a}
    \caption{Stars of Equal Declination}
  \end{minipage}\hfil
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input{page_052b}
    \caption{Stars of Equal Right Ascension}
  \end{minipage}
  \label{p52}
\end{figure}

\textbf{The Equatorial Telescope.}\index{equatorial telescope}\index{telescope|see{equatorial telescope}}---Just as the altazimuth is
an instrument whose motions correspond to the horizon
system, so the motions of the equatorial telescope correspond
to the equator system. This instrument, generally
\DPPageSep{057.png}
called merely the \textit{equatorial}, is a form of mounting which
enables a star to be followed in its diurnal motion by turning
the telescope on only one axis.

\Smaller
\label{p53a}This axis is always parallel to the axis of the earth, and is called the
\textit{polar axis}\index{polar axis}. As it must point toward the north pole of the heavens, the
polar axis will
stand at about
the angle shown
in the picture,
for all places in
the United
States. The
simplest way to
understand an
equatorial is to
regard it as an
altazimuth with
its principal or
vertical axis
tilted northward
until it points
to the pole.
The azimuth
% Fig 3.8
\begin{wrapfigure}[28]{o}{0.65\textwidth}
  \centering
  \Input[0.6\textwidth]{page_053}
  \caption{Model of the Equatorial Telescope}
  \label{p53}
\end{wrapfigure}
circle
then becomes
the \textit{hour circle}\index{hour circle!of telescope} of
the equatorial;
the horizontal
axis becomes the
\textit{declination axis}\index{declination!axis}
of the equatorial;
and the
circle attached
to it is called the
\textit{declination circle}\index{declination!circle}
(the counterpart
of the altitude
circle in the
altazimuth). At one end of the declination axis and at right angles to
it the telescope tube is attached, as shown. The model in the illustration
may be constructed by any clever boy. The axes are pine rods
running through wooden bearings, and it is well to soak them with hot
paraffin. The telescope tube is a large pasteboard roll.
\DPPageSep{058.png}

\textbf{How to adjust and use this Equatorial.}---Having already found
direction of the meridian, the polar axis must be brought into its plane,
and the north end of this axis elevated to an angle equal to the latitude.
This can be taken accurately enough from any map of the United States.
Draw a line on the outside
of the bearing of
the polar axis parallel
to the axis itself; and
across this line, at an
angle equal to the latitude
(laid off with a
protractor), draw another
line which will be
nearly horizontal. The
adjustment\index{equatorial telescope!adjusting} is completed
by means of an ordinary
artisan's level,
placed alongside this
second line. Take out
the object glass and eyepiece,
and point the telescope
at the zenith, as
nearly as the eye can
judge. Then hang a
plumb-line through the
tube, suspending it from
the center of the upper
end, and continuing to
adjust the tube till the
line hangs centrally
through it. While the
tube remains fixed in
this position, set the
hour circle to read zero,
and the declination circle
to a number of degrees
equal to the latitude.
The model equatorial is
then ready to use. Declinations
can be read from the declination circle directly, bringing
any heavenly body into the center of the field of view. And right
ascensions can be found when the hour angle of the vernal equinox
is known. A method of finding this will be given in the next chapter
(p.~\pageref{p66}). Distinguish between the double and differing significations
\DPPageSep{059.png}
of the term \textit{hour circle}: when the equatorial is adjusted, \textit{its} hour circle,
being parallel to the terrestrial equator, is therefore at right angles to
\textit{the} hour circles of the celestial sphere.

\textbf{Telescopes as mounted in Observatories.}---Nearly all the telescopes
in observatories are mounted equatorially. The cardinal principles
of these mountings are similar to those of the model already given.
An equatorial telescope is
% Fig 3.9
\begin{wrapfigure}[32]{o}{0.65\textwidth}
  \centering
  \Input[0.55\textwidth]{page_054}
  \caption{10-Inch Equatorial (Warner \&amp; Swasey)}
  \label{p54}\index{Warner \&amp; Swasey}
\end{wrapfigure}
shown in the illustration opposite. The
small tube at the lower end of the large one and parallel to it is a
short telescope called the `finder,' because it has a large field of view,
and is used as a convenience in finding objects and bringing the large
telescope to bear upon them. Iron piers, nearly cylindrical in the best
mountings, but often rectangular, are now generally employed in supporting
the axes of telescopes. An hour circle is sometimes attached
to the upper end of the polar axis, as shown; and geared to the outside
of this circle is a screw or worm, turned by clockwork (underneath
in the middle of the pier). The clock is so regulated as to turn the
polar axis once completely round from east toward west in the same
period that the earth turns once completely round on its axis from
west toward east. When a star has been placed in the field of view,
and the axis clamped, the clock maintains it there without readjusting,
as long as the observer may care to watch. Each axis of a large
equatorial is provided with a mechanical convenience called a `slow
motion,' one for right ascension and one for declination. These
devices are operated by handles (at the right of the tube), which can
be turned by the observer while looking through the eyepiece; and
they enable him to move an object slowly from one part of the field
of view to another, as required.
\Restore

\textbf{Celestial Latitude.}\index{latitude (celestial)}---The third system of coördinates of
the celestial sphere---(\textit{C}) the ecliptic system\index{ecliptic system!origin of}---is founded
on the path which the sun seems to travel among the stars,
going once around the entire heavens every year. In fact,
the ecliptic\index{ecliptic} is usually defined as the apparent annual path
Of the sun's center. This path is a great circle of the
celestial sphere. And as it always remains constant in
position, relatively to the fixed stars, its convenience as a
fundamental plane of reference is easy to see. The name
\textit{ecliptic} is applied, because eclipses of sun and moon are
possible only when our satellite is in or near this path.
Upon the ecliptic as a fundamental plane is based a system
\DPPageSep{060.png}
 of coördinates, precisely as in the equator system (\textit{B}).
Celestial \textit{latitude}, or a star's latitude merely, is its angular
distance from the ecliptic; and it is measured north or
south from that plane, along
% Fig 3.10
\begin{wrapfigure}[20]{o}{0.55\textwidth}
  \centering
  \Input[0.45\textwidth]{page_057}
  \caption{The Ecliptic Astrolabe}
  \index{astrolabe, ecliptic}
\end{wrapfigure}
the ecliptic meridian passing
through the star. Latitude is the counterpart of altitude
in the horizon system, and of declination in the equator
system. If the star is north of the ecliptic, it is said to
be in \textit{north} or \textit{plus} latitude; if south, then in \textit{minus} or \textit{south}
latitude. No star can exceed $\pm90$° in latitude. As the
center of the sun travels almost exactly along the ecliptic,
year in and year out, its latitude is always practically zero.
The symbol for latitude is $\beta$ (the small Greek letter \textit{beta}).
Sometimes the term \textit{ecliptic north polar distance}\index{ecliptic!north polar distance} is convenient;
it is measured southward along the ecliptic meridian
passing through the star. It is independent of the ecliptic
itself, and may have any value from 0° to 180°, according
to the star's place in the heavens. A star whose latitude
is $-38$° is located in ecliptic north polar distance 128°.

\textbf{Celestial Longitude.}\index{longitude (celestial)}---Celestial longitude is the term
used to designate the angular distance of a star from the
vernal equinox, measured eastward along the ecliptic to
that ecliptic meridian which passes through the star. It
is counted in degrees from 0° all the way round the
heavens to 360° if necessary. By drawing a figure similar
to that on page~\pageref{p52}, and replacing the celestial pole
by the pole of the ecliptic, it becomes clear that all stars
on any parallel of latitude have the same latitude, no
matter what their longitudes may be; and that all stars
on any half meridian of longitude included between the
ecliptic poles must have the same longitude, although their
latitudes may differ widely. As the equinoxes mark the
intersection of equator and ecliptic, they must both be in
equator and ecliptic alike. On the ecliptic, and midway
between the two equinoxes, are two points, called the
\DPPageSep{061.png}
\textit{solstices}\index{solstices}. Hence the name of the hour circle, or colure\index{colure}
which passes through them---the solstitial colure. At the
times of the solstices, the sun's declination remains for a
few days very nearly its maximum, or $23\frac{1}{2}$°. It was this
apparent \textit{standing still} of the sun with reference to the
equator (north of the equator in summer, and south of it
in winter) which gave rise to the name \textit{solstice}.

\Smaller
In observing the positions of the heavenly bodies before the invention
of clocks, the ancient astronomers\index{astronomy!history}, particularly Tycho Brahe\index{Tycho Brahe (1546--1601), Danish ast.}, used
a type of astronomical instrument
called the ecliptic \textit{astrolabe}\index{astrolabe, ecliptic},
a kind of armillary sphere,
in which the longitude and
latitude of a star could be read
at once from the circles. But
instruments of this character
are now entirely out of date,
only a few being preserved in
astronomical museums\index{museums, astronomical}, the
principal one of which is at
the Paris Observatory\index{Paris!Observatory}. The
astronomers of to-day never
determine the longitude and
latitude of a body by direct
observation, but always by
mathematical calculation from
the right ascension and declination;
because the longitude
and latitude can be obtained in
this way with the highest accuracy.
\Restore

\textbf{Summary and Correlation of Terms.}---Correlation of the
three systems just described, and of the terms used in connection
with each, is now in order. In the first column is
the nomenclature of system (\textit{A}), with the horizon for the
reference plane; in the second column, the terminology of
system (\textit{B}), in which the celestial equator is the fundamental
\DPPageSep{062.png}
 plane; and in the third column are found the
corresponding points, planes, and elements referred to
the ecliptic system (\textit{C}):---
\begin{center}
\TableSize
\begin{tabular}{l|l|l}
\multicolumn{3}{c}{\textsc{The Philosophy of the Celestial Sphere}} \\[1em]
\hline\hline
   \parbox{3.5cm}{\center \textsc{In the Horizon System (\textit{A})}} &amp;
   \parbox{4.2cm}{\center \textsc{Becomes in the Equator System (\textit{B})}}  &amp;
   \parbox{4.2cm}{\center \textsc{Becomes in the Ecliptic System (\textit{C})}} \\[2em]
\hline
Horizon &amp; Celestial equator &amp; Ecliptic  \\
Vertical circle &amp; Hour circle &amp; Ecliptic meridian  \\
Zenith &amp; North pole &amp; N.~pole of the ecliptic  \\
Meridian &amp; Equinoctial colure &amp; Ecliptic meridian  \\
Prime vertical &amp; Solstitial colure &amp; Solstitial colure  \\
Azimuth (\textit{negative}) &amp; Right ascension &amp; Celestial longitude \\
Altitude   &amp; Declination (N.) &amp; Celestial latitude (N.)  \\
\hline\hline
\end{tabular}
\index{altitude!defined}%
  \index{azimuth, defined}%
  \index{colure!defined}%
  \index{declination!defined}%
  \index{ecliptic}%
  \index{equator!celestial defined}%
  \index{equator system!circles of}%
  \index{ecliptic system!circles of}%
  \index{horizon!rational}%
  \index{hour circle}%
  \index{latitude (celestial)}%
  \index{longitude (celestial)}%
  \index{meridian}%
  \index{prime vertical, defined}%
  \index{circle!vertical, defined}%
  \index{vertical circle, defined}%
  \index{right ascension, defined}%
  \index{zenith!defined}%
\end{center}

These three systems of planes and circles of the celestial
sphere comprise all those used by astronomers, except
in the very advanced investigations of mathematical
and stellar astronomy.
\DPPageSep{063.png}


\Chapter{IV}{The Stars in their Courses}\index{stars!in their courses}

The fundamental framework for our knowledge of the
heavens may now be regarded as complete. We
next consider its relations from different points of
view on earth, at first filling in details of the stars as necessary
points of reference in the sky.

\textbf{The Constellations.}\index{constellations}---In a very early age of the world,
the surface of the celestial sphere was imagined to be covered
by figures, human and other, connecting different
stars and groups of stars together in a fashion sometimes
clear, though usually grotesque. The groups of stars
making up these imaginary figures in different parts of
the sky are called \textit{constellations}. Eudoxus (\BC~370)\index{Eudoxus (\BC~370), Gk.\ ast.} borrowed
from Egyptian astronomers the conception of the
celestial sphere, bringing it to Greece, and first outlining
upon it the ecliptic and equator with the more prominent
constellations. About 60 are well recognized, although the
whole number is nearly twice as great. This ancient, and
in most respects inconvenient, method of naming and
designating the stars is retained to the present day. In
general, small letters of the Greek alphabet are used to
indicate the more prominent stars of a constellation, $\alpha$
representing its brightest star, $\beta$ the next, $\gamma$ the third,
and so on. The Greek letter is followed by the Latin
genitive of name of constellation; thus $\alpha$ Orionis is the
most conspicuous star in the constellation of Orion, $\gamma$ Virginis
is the third star in order of brightness in Virgo, and
\DPPageSep{064.png}
so on. Following are these letters, written either as symbols,
or as the English names of these symbols:---
\begin{center}
\TableSize
\begin{tabular}{l l&lt;{\quad} l l&lt;{\quad} l l&lt;{\quad} l l}
$\alpha$   &amp; Alpha    &amp; $\eta$    &amp; Eta    &amp; $\nu$      &amp; Nu         &amp; $\tau$ &amp; Tau  \\
$\beta$    &amp; Beta     &amp; $\theta$  &amp; Theta  &amp; $\xi$      &amp; Xi         &amp; $\upsilon$ &amp; Upsi´lon  \\
$\gamma$   &amp; Gamma    &amp; $\iota$   &amp; Iota   &amp; \textit{o} &amp; Omi´cron &amp; $\phi$ &amp; Phi  \\
$\delta$   &amp; Delta    &amp; $\kappa$  &amp; Kappa  &amp; $\pi$      &amp; Pi         &amp; $\chi$ &amp; Chi  \\
$\epsilon$ &amp; Epsi´lon &amp; $\lambda$ &amp; Lambda &amp; $\rho$     &amp; Rho        &amp; $\psi$ &amp; Psi  \\
$\zeta$    &amp; Zeta     &amp; $\mu$     &amp; Mu     &amp; $\sigma$   &amp; Sigma      &amp; $\omega$ &amp; Omeg´a \\
\end{tabular}
\index{Greek alphabet}
\end{center}

A few constellations embrace more than 24 stars requiring
especial designation, and for these the letters of the
Latin alphabet are employed; and if these are exhausted,
then ordinary Arabic numerals follow. Thus stars may
be designated as F Tauri, 31 Aquarii, and so on. About
100 conspicuous stars have other and proper names, mostly
Arabic in origin: thus Vega is but another name for $\alpha$
Lyræ, \DPtypo{Aldeb´aran}{Aldebaran}\index{Aldeb´aran} for $\alpha$ Tauri, Merak for $\beta$ Ursæ Majoris.
The lucid stars, or stars visible to the naked eye, are
divided into six classes, called \textit{magnitudes}\index{stars!magnitudes of}. Of the first
magnitude are the 20 brightest stars of the firmament,
and the number increases roughly in geometric proportion.
Of the sixth magnitude are those just visible to the naked
eye on clear, moonless nights. On page~\pageref{p423} are given
the names of the brightest stars; and from Figures~\ref{plateIII} and \ref{plateIV} can be found their location in the sky.

\Smaller
\textbf{Convenient Maps of the Stars.}\index{stars!catalogues and charts}---On the star maps given as Figures \ref{plateIII}~and~\ref{plateIV} are shown all the brighter stars ever visible in the United
States. In each figure the lower or dark chart is a faithful transcript
of the `unlanterned sky,' and the upper map is merely a key to
the lower. Notwithstanding their small scale, the asterisms are readily
traceable from the dark charts, and the names of especial stars and
constellations are then quickly identified by means of the keys. To
connect the charts with the sky, conceive the celestial sphere reduced
to the size of a baseball. At its north pole place the center
of the circular map (Figure~\ref{plateIII}); and imagine the rectangular map
(Figure~\ref{plateIV}) as wrapped round the middle of the ball, the central horizontal
\DPPageSep{065.png}
% Fig 4.1
\begin{figure}[p]
  \centering
  \Input[0.75\textwidth]{plate_iiia}
  \caption{\textsc{Key to Chart of North Polar Heavens} (Shows how the stars appear, in relation to North Horizon, at 8~\PM\ during the month held at the top.)}
  \index{Algol}%
  \index{Andromeda}%
  \index{Auriga}%
  \index{Bootes@Boötes}%
  \index{Camelopardalis}%
  \index{Canes Venatici}%
  \index{Capella}%
  \index{Cassiopeia}%
  \index{Cepheus (s\=e´fuce)}%
  \index{Cygnus}%
  \index{Deneb@Deneb, ($\alpha$ Cygni)}%
  \index{Cygni|see{Deneb}}%
  \index{Dipper}%
  \index{Great Bear}%
  \index{Hercules}%
  \index{north polar heavens}%
  \index{Perseus (per´suce)}%
  \index{Polaris}%
  \index{Ursa Minor}%
  \index{Vega}%
  \index{stars!catalogues and charts}%
% Fig 4.2
  \vfill
  \Input[0.75\textwidth]{plate_iiib}
  \caption{The North Polar Heavens}
  \label{plateIII}
\end{figure}%
\DPPageSep{066.png}
%[Blank Page]
\DPPageSep{067.png}
line of the chart coinciding with the equator of the ball. Just
as the maps, if actually applied to a baseball, would not make a perfect
cover for it without cutting and fitting, so there will be found some
distortion in comparing the maps with the actual sky, especially near
the top and bottom of the oblong chart. Whatever the season of the
year, the charts are easy to compare with the sky, by remembering that
(for 8\PM) Figure~\ref{plateIII} must be held due north, and the book turned so
that the month of observation appears at the top of the round chart, or
vertically above Polaris\index{Polaris}, which is near the center of the map. The
asterisms immediately adjacent to the name of the month will then be
found at or near the observer's zenith. Similarly with Figure~\ref{plateIV}: face
due south, and at 8~\PM\ stars directly under the month will be found
near the zenith, and the oblong chart will overlap the circumpolar one
about half an inch, or 30°. At the middle of the rectangular chart,
under the appropriate month, are found the stars upon the celestial
equator; and at the bottom of the map, the constellations faintly visible
near the south horizon. Every vertical line on this chart coincides
with the observer's meridian at eight o'clock in the evening of the
month named at the top. If the hour of observation is other than this,
allow two hours for each month; for example, at 10~\PM\ in November
the stars underneath `\textsc{december}' will be found on the meridian.
Likewise Figure~\ref{plateIV} must be turned counter-clockwise with the lapse of
time, at the rate of one month for two hours. If, for example, we
desire to inspect the north polar heavens at 6~\PM\ in December, we
should hold the book upright, with November at the top.
\Restore

\textbf{Constellations of Circumpolar Chart.}\index{stars!circumpolar}---Most notable is
Ursa Major\index{Ursa Major}, the Great Bear\index{Great Bear}, near the bottom (Figure~\ref{plateIII}).
Its seven bright stars are familiarly known in America
as the `Dipper,' and in England as `Charles's Wain,' or
wagon. Of these, the pair farthest from the handle are
called `the Pointers,' because a line drawn through them
points toward the pole star, as the arrow shows. The
Pointers are five degrees apart, and, being nearly always
above the horizon, are a convenient measure of large
angular distances. At the bend of the dipper handle is
Mizar, and very near it a faint star, Alcor. When Mizar
is exactly above or below Polaris\index{Polaris}, both stars are on the true
meridian, and therefore indicate true north (page~\pageref{p116}).
The Pointers readily show Polaris, a second magnitude star
\DPPageSep{068.png}
(near the center of Figure~\ref{plateIII}). No star of equal brightness
is nearer to it than the Pointers. From Polaris a line of
small stars curves toward the handle of the Dipper, meeting
the upper one of a pair of the third magnitude. This
pair, with another farther on and parallel to it, form the
`Little Dipper,' Polaris being the end of its handle. The
group is Ursa Minor. Opposite the handle of the great
Dipper, and at about the same distance from Polaris, are
five rather bright stars forming a flattened letter W. They
are the principal stars of Cassiopeia.

\textbf{Learning the Constellations.}---With these slender foundations,
once well and surely laid, familiarity with the
northern constellations is soon acquired. It is excellent
practice to draw the constellations from memory, and then
compare the drawings with the actual sky. An hour's
watching, early in a September evening, will show that
the Dipper is descending toward the northwest horizon,
and Cassiopeia rising from the northeast. Nearly overhead
is Vega. Capella, the large star near the right of
Figure~\ref{plateIII}, will soon begin to twinkle low down in the northeast.
Familiarity with the northern constellations is the
prime essential, and they should be committed, independently
of their relations to the horizon at a particular time,
for at some time of the year all these constellations will
appear inverted. Make acquaintance with them so thorough
that each is recognized at a glance, no matter what
its relation to the horizon may be.

\textbf{Constellations of the Equatorial Girdle.}---All the more
important ones are named on the key to Figure~\ref{plateIV}. None
is more striking than Orion, whose brilliance is the glory
of our winter nights. Hard by is Sirius, brightest of all
the stars of the firmament, which, with Procyon and the
two principal stars of Orion, forms a huge diamond, intersected
by the solstitial colure, or VIth hour circle. Eastward
\DPPageSep{069.png}
%[Blank Page]
\DPPageSep{070.png}
% Fig 4.3
\begin{Plate}
  \Input[\textwidth]{plate_iva}
  \caption{\textsc{Key to Chart of Equatorial Girdle of the Stars} (The stars under the name of the month are on the meridian (looking south) at 8~\PM)}
  \index{Aldeb´aran}%
  \index{Altair}%
  \index{Andromeda}%
  \index{Anta´res ($\alpha$ Scorpii)}%
  \index{Aquarius}%
  \index{Aquila}%
  \index{Arcturus}%
  \index{Argo}%
  \index{Aries}%
  \index{Auriga}%
  \index{Betelgeux (bet-el-gerz´)}%
  \index{Bootes@Boötes}%
  \index{Cancer}%
  \index{Canes Venatici}%
  \index{Canis major}%
  \index{Canis minor}%
  \index{Capricornus}%
  \index{Castor ($\alpha$ Geminorum)}%
  \index{Centaurus}%
  \index{Cetus}%
  \index{Columba}%
  \index{Coma Bereni´ces}%
  \index{Corona Australis}%
  \index{Corona Borealis}%
  \index{Corvus}%
  \index{Crater}%
  \index{Delphinus}%
  \index{ecliptic}%
  \index{equator}%
  \index{equatorial girdle of stars}%
  \index{Fomalhaut (f\=o´mal-\=o)}%
  \index{Fornax}%
  \index{Gemini}%
  \index{Hercules}%
  \index{Lacerta}%
  \index{Leo}%
  \index{Leo Minor}%
  \index{Lepus}%
  \index{Libra}%
  \index{Lynx}%
  \index{Lyra}%
  \index{Monc´eros, galaxy in}%
  \index{Norma}%
  \index{Orion@Ori´on}%
  \index{Pegasus, square of}%
  \index{Perseus (per´suce)}%
  \index{Pisces}%
  \index{Piscis Australis}%
  \index{Pollux ($\beta$ Geminorum)}%
  \index{Procyon}%
  \index{Regulus ($\alpha$ Leonis)}%
  \index{Rigel ($\beta$ Orionis)}%
  \index{Sagittarius}%
  \index{Scorpio}%
  \index{Serpens}%
  \index{Sextans}%
  \index{Sirius}%
  \index{Spica ($\alpha$ Virginis)}%
  \index{Taurus}%
  \index{Triangulum}%
  \index{Ursa Major}%
  \index{Virgo}%
  \index{Vulpecula}%
  \index{stars!catalogues and charts}%
\vfill
% Fig 4.4
  \Input[\textwidth]{plate_ivb}
  \caption{\textsc{Plate IV.---The Equatorial Girdle of the Stars}}
  \label{plateIV}
  \index{equatorial girdle of stars}
\end{Plate}%
\DPPageSep{071.png}
%[Blank Page]
\DPPageSep{072.png}
from Procyon to Regulus may be formed a vast
triangle; and still farther east, with Spica and Arcturus,
one vaster still. By means of similar arbitrarily chosen
figures, as in the key, all the constellations may readily
be memorized, one after another, until the cycle of the
seasons is complete. Also the ecliptic's sinuous course
is easy to trace, from Aries round to Aries again.

% Fig 4.5
\begin{figure}[hbt!]
  \centering
  \Input{page_063}
  \caption{Astral Lantern for tracing Constellations}
\end{figure}

\Smaller
\textbf{Helps to Constellation Study.}---Perhaps the easiest to use and in
every way the most convenient is the planisphere. By its aid all the
visible constellations may be expeditiously traced, the times of rising
and setting of the sun, planets, and stars found, and a variety of simple
problems neatly solved. Another excellent help in learning the constellations
is the astral lantern devised by the late James Freeman
Clarke\index{Clarke, J. F. (1810--88), Am.\ theol.}. The front side of the box is provided with a ground glass slide.
In front of and into the grooves of this may be slipped cards, figured
with the different asterisms, as indicated in the illustration. But the
peculiar effectiveness of the lantern consists in the minute punctures
through the cards, the size of each puncture being graduated according
to the magnitude of the star. Bailey's astral lantern is a similar device
\DPPageSep{073.png}
for a like purpose. Also a celestial globe is sometimes used in learning
the constellations, but the process is attended with much difficulty
because the constellations are all reversed on the surface of the globe,
and the observer must imagine himself at the center of it and looking
outward. Plainly marked upon the globe are many of the circles of
System (\textit{B}),---equator, colures, and parallels of declination. Also usually
the ecliptic. See illustration on page~\pageref{p71}. The globe turns round in
bearings at the poles, fastened to a heavy meridian ring \textsc{m~m} which can
be slipped round in its own plane through slots in the horizon circle \textsc{h}.
The process of setting the globe to correspond to the aspect of the
heavens at any time is called rectifying the globe. Bring the meridian
ring into the plane of the meridian, and elevate the north pole to an
angle equal to the latitude. On pages~\pageref{p70}, \pageref{p71}, and \pageref{p72} are globes rectified to the latitudes indicated.

\textbf{Farther Helps.}---If complete knowledge of the firmament is desired,
a good star atlas is the first essential, such as have been prepared with
great care by Proctor\index{Proctor, R.~A.\ (1837--88), Am.\ ast.}, and Klein\index{Klein, H. J., Ger.\ ast.}, and Sir Robert Ball\index{Ball, Sir R. S., Dir.\ Obs.\ Cambridge, Eng.}, and Upton\index{Upton, W., Dir.\ Brown Univ.\ Obs.}.
These handy volumes quickly give a familiarity with the nightly sky
which hurries the learner on to the possession of a telescope. By a
list or catalogue of celestial objects may be found any celestial body,
though not mapped in its true position on the charts, if an equatorial
mounting like the model illustrated on page~\pageref{p53} is constructed. A
mere pointer in place of the tube will make it into that convenient
instrument called Rogers's\index{Rogers, W. A. (1832--98), Am.\ ast.} `star finder.' The simplest of telescopes
must not be despised for a beginning. \textit{Astronomy with an Opera
Glass}, by Serviss\index{Serviss, G. P., Am.\ ast.}, shows admirably what may be done with the slightest
optical aid. When a 3-inch telescope becomes available, there is a
multitude of appropriate handbooks, none better than Proctor's \textit{Half
Hours with the Stars}. Follow it with Webb's\index{Webb, T. W. (1807--85), Eng.\ ast.} \textit{Celestial Objects for
Common Telescopes}, a veritable storehouse of celestial good things.
\Restore

\textbf{The Zodiac.}\index{zodiac}---Imagine parallels of celestial latitude as
drawn on either side of the ecliptic, at a distance of 8°
from it; this belt or zone of the sky, 16° in width, is called
the \textit{zodiac}. Neither the moon nor any one of the bright
planets can ever travel outside this belt. About 2000
years ago both ecliptic and zodiac were divided by Hipparchus\index{Hipparchus (\BC~140), Gk.\ ast.},
an early Greek astronomer, into twelve equal
parts, each 30° in length, called the signs of the zodiac.
The names of the constellations which then corresponded
to them have already been given in their true order on
\DPPageSep{074.png}
page~\pageref{p40}; but the lapse of time has gradually destroyed
this coincidence, as will be explained at the end of Chapter~\textsc{vi}.
In the figure the horizontal ellipse represents the
ecliptic, and at the beginning of each sign is marked its
appropriate symbol. \textit{E} is the pole of the ecliptic, \textit{P}
the north celestial pole, and the inclined ellipse shows
where the equator girdles the celestial sphere. The signs
% Fig 4.6
\begin{figure}[hbt!]
  \centering
  \Input{page_065}
  \caption{Celestial Sphere and Signs of the Zodiac}
  \label{p65}\index{zodiac}
\end{figure}
of the ecliptic girdle have from time immemorial been
employed to symbolize the months and the round of seasons;
and a type of ancient Arabian zodiac is embossed
on the cover of this book, reproduced from Flammarion\index{Flammarion, C. (flam-ma-re-ong´), Dir.\ Juvisy Obs.\ (Paris)}.
The signs of the zodiac are discarded in the accurate
astronomy of to-day; and the positions of the heavenly
bodies are now designated with reference to the ecliptic,
not by the sign in which they fall, but by their celestial
\DPPageSep{075.png}
longitude. Conventionalized symbols of the signs of the
zodiac, and the position of the zero point of each sign,
are shown on the sphere \vpageref{p65}, %on the preceding page,
beginning
with 0° of Aries at \textit{D}, and proceeding counter-clockwise
as the sun moves, or contrary to the direction the arrow.

\textbf{How to locate the Equinoxes among the Stars.}\index{equinoxes!how to find}---On
the earth the longitude of places is reckoned from \textit{prime
meridians} passing through well-known places of national
% Fig 4.7
\begin{figure}[hbt!]
  \centering
  \Input{page_066}
  \caption{How to locate the Vernal Equinox}
  \label{p66}
  \index{Alpheratz ($\alpha$ Andromedæ)}%
  \index{Pegasus, square of}%
  \index{Polaris}%
\end{figure}
importance. But the equinoctial colure\index{colure!equinoctial}, the prime meridian
of the heavens, is a purely imaginary circle, and is not
marked in any such significant manner, as we should naturally
expect, by means of brilliant stars. It is, however,
important to be able to point out the equinoxes roughly
among the stars. The vernal equinox is above the horizon,
at convenient evening hours in autumn and winter.
Its position may be found by prolonging a line (hour circle)
from Polaris southward through Beta Cassiopeiæ, as in
the above illustration.
\DPPageSep{076.png}

\Smaller
This will be about 30° in length. Thirty degrees farther in the
same direction will be found the star Alpheratz (Alpha Andromedæ),
equal in brightness with Beta Cassiopeiæ. Then as the equinox is a
point in the equator, and the equator is 90° from the pole, we must go
still farther south 30° beyond Alpheratz; and in this almost starless
region the \textit{vernal equinox} is at present found. It will hardly move
from this point appreciably to naked-eye observation during a hundred
years. This quadrant of an hour circle (from Polaris to the vernal
equinox) will be very nearly a quadrant of the equinoctial colure also.
Because Alpheratz and Beta Cassiopeiæ are very near it, their right
ascension is about 0 hours. Through spring and summer the autumnal
equinox will be above the horizon at convenient evening hours. This
equinox, like the other, has no bright star near it; roughly it is about
$\frac{2}{5}$ of the way from Spica (Alpha Virginis) westward toward Regulus
(Alpha Leonis), as shown in the following diagram.
\Restore
% Fig 4.8
\begin{figure}[hbt!]
  \centering
  \Input{page_067}
  \textsf{SOUTH HORIZON}
  \caption{How to locate the Autumnal Equinox}
\end{figure}

\label{p67}\textbf{How to locate the Ecliptic (approximately) at Any Time.}---It
will add much to the student's interest in these purely
imaginary circles of the sky if he is able to locate them
(even approximately) at any time of the day or night.
Only two points in the sky are necessary. By day the
sun is a help, because his center is one point in the ecliptic.
If the moon is above the horizon, that will be another
\DPPageSep{077.png}
point, approximately. Then imagine a plane passed
through sun and moon and the point of observation, and
that will indicate where the ecliptic lies. Also, if the
moon is within three or four days of the phase known
as the `quarter,' her shape will show very nearly the direction
of the ecliptic in this manner: Join the cusps by
an imaginary line, and the perpendicular to this line,
extended both ways, will mark out the ecliptic very nearly.
In early evening, the problem is easier. On about half
the nights of the year the moon will afford one point.
Usually one or more of the brighter planets (Venus, Mars,
Jupiter, Saturn) will be visible, and it has already been
shown how to distinguish them from the brightest of the
fixed stars. Like the moon, these planets never wander
far from the ecliptic; and if we pass our imaginary plane
through any two of them, the direction of the ecliptic may
be traced upon the sky.

\Smaller
If moon and planets are invisible, the positions of known stars are
all that we can rely upon, and there are few very bright stars near the
ecliptic. The Pleiades and Aldebaran (Alpha Tauri) are easy to find
all through autumn and winter, and the ecliptic runs midway between
them. Through winter and spring, the `sickle' in Leo is prominent, and
Regulus (Alpha Leonis) is only a moon's breadth from the true ecliptic.
Through the summer Spica (Alpha Virginis) is almost as favorably
placed; and Antares (Alpha Scorpii) rather less so, but not
exceeding 10 moon breadths south of the ecliptic. And in late summer
and autumn, Delta Capricorni, much fainter than all those previously
mentioned, shows where the ecliptic lies through a region
almost wholly devoid of very bright stars. As the stars before named
are so set in the firmament that at least two of them must always be
above the horizon, they show approximately where the ecliptic lies.
\Restore

\textbf{Finding the Latitude.}\index{latitude (terrestrial)!finding}---Having shown how the stars
and constellations may be learned in our latitudes, it is
next necessary to find how their
% Fig 4.9
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.45\textwidth]{page_069}
  \caption{Latitude equals Altitude of Pole}\index{latitude (terrestrial)!equals altitude of pole}
\end{wrapfigure}
courses seem to change,
as seen from other parts of the earth. It is plain that
going merely east or west will not alter their courses.
\DPPageSep{078.png}
The effect of changing one's latitude must therefore be
ascertained. Observe Polaris\index{Polaris}: attention has already been
directed to the fact that in middle northern latitudes, as
the United States, it is about halfway up from the northern
horizon to the zenith. The true north pole of the
heavens is $1° \, 15'$, or two and a half moon breadths from
it. If you had a fine instrument
of the right kind,
and the training of a skillful
astronomer, you could
measure accurately the
altitude of the pole star
when exactly below the
pole. Measure it again
12 hours later, and it would
be directly above that point.
The average of the two
altitudes, with a few slight
but necessary corrections,
would be the true altitude of the center of the little circle in
which the pole star seems to move round once each day.
This center is the true north celestial pole; and whatever
its altitude may be found to be, a facile proof by geometry
shows that it must be equal to the north latitude of the
place where the observations were made.

\textbf{Latitude equals Altitude of Pole.}\index{latitude (terrestrial)!equals altitude of pole}---Whether the earth
is considered a sphere or an oblate spheroid, the angle
which the plumb-line at any place makes with the terrestrial
equator is equal to the latitude (figure above). As
the plane of celestial equator is simply terrestrial equator-plane
extended, the declination of the zenith is the same
angle as the latitude. Now consider the two right angles
at the point of observation; (\textit{a}) the one between celestial
equator and pole, and (\textit{b}) the other between horizon and
\DPPageSep{079.png}
zenith: the angle between pole and zenith is a common
part of both. So the decimation of the zenith is equal
to the altitude of the pole. Therefore \textit{the altitude of the
pole at any given place is equal to the latitude of that place}.

\textbf{Going North the Pole Star rises.}---If, then, one were
to go north on the surface of the earth 1°, the pole of the
northern heavens must seem to rise 1°. For example, if
the latitude is 42°, one would have to travel due north 48°
(3300~miles) in order to reach the north pole of the earth.
And as the altitude of the
celestial pole would have increased
48° also, evidently
this point and the zenith
would exactly coincide. To
all adventurous explorers who
may ever reach the north
pole, we may be sure that the
pole star will be all the time
very nearly overhead, and
travel round the zenith once
every day in a small circle
whose diameter would require
about five moons to reach
across. All other stars would
seem to travel round it in
circles parallel to it and to the horizon also. This peculiar
motion of the stars as seen from the north pole was the
origin of the term \textit{parallel sphere}\index{sphere!parallel}.

\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.45\textwidth}
    % Fig 4.10
    \centering
    \Input{page_070}
    \caption{Parallel Sphere (at the Poles)}
    \label{p70}\index{sphere!parallel}
  \end{minipage}
% Fig 4.11
  \hfill
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input{page_071}
    \caption{Oblique Sphere (Northern U.~S.)}
    \label{p71}
  \end{minipage}
\end{figure}
\textbf{Daily Motion of the Stars at the North Pole.}---At the
north pole the directions east and west, as well as north,
vanish, and one can go only south, no matter what way
one may move. As seen from the north pole, the stars all
move round from left to right perpetually, in small circles
parallel to the horizon. Consequently they never rise or
\DPPageSep{080.png}
set. All visible stars describe their own almucantars once
every day. Their altitudes are constant, and their azimuths
are changing uniformly with the time. The azimuths of all
stars change with equal rapidity, no matter what their
declination may be. These are the phenomena of the
parallel sphere. All the stars north of the equator are
always above the horizon, day and night. None of those
south of the equator can ever be seen. If the observer
were at the south pole of our globe, the daily motion of
the stars relatively to the
horizon would be exactly the
same as at the north pole;
but they would all seem to
travel round from right to
left. The stars of the hemisphere
which could be seen
all the time would be those
which from the north pole
could never be seen at all.

\textbf{Daily Motion of the Stars
in the United States.}---We
have now returned from the
north polar regions to middle
latitudes, or N.~45°, about that
of places from Maine to
Wisconsin. The pole has gone down, too, and
% Fig 4.12
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.45\textwidth]{page_072a}
  \caption{Circles of Perpetual Apparition and Perpetual Occultation}
  \label{p72a}
\end{wrapfigure}
is elevated
just 45° above the horizon; consequently the circle of perpetual
apparition\index{perpetual apparition}, or parallel of north declination which is
tangent above the north horizon, has shrunk to a diameter
of 90° on the sphere. Any star ever seen between the
zenith and the north horizon can never set. Similarly
the circle of perpetual occultation\index{perpetual occultation} must be 90° in breadth:
it is the parallel of south declination which is tangent
below the south horizon. Therefore the breadth of the
\DPPageSep{081.png}
middle zone of stars,
partly above and
partly below the horizon,
is 90°. The quadrant
from the zenith
to the south horizon
is the measure of its
breadth when above
the horizon, and the
distance from the
north horizon to the
nadir is its width when
below the horizon. As
in the polar regions,
so here---the celestial
equator marks the middle of the zone. All the
stars in the northern half of it are visible longer than
they are invisible, and the farther north they are, the
longer they are above the
horizon. In the same way
all the stars of this zone
whose declination is south
are invisible longer than
they are visible, and the
greater their south declination,
the longer they are
below the horizon. It has
now been shown how the
apparent motions of the stars
are accounted for by the
geometry of the sphere.

\textbf{Daily Motion of the Stars
at the Equator.}\index{equator!terrestrial, daily motion of stars at}---Here our
latitude is zero; and as the
\DPPageSep{082.png}
altitude of the north celestial pole is always equal to the
north latitude, the north pole must now be in the horizon
itself. As the poles are 180° apart, evidently the south
pole of the heavens must now be in the south horizon.
The equator, then, must pass through the zenith, and the
stars can rise, pass over,
and set, in vertical planes
only, whence the name
\textit{right sphere}\index{sphere!right}. A star's
diurnal circle, therefore,
is coincident with its
parallel of declination.
But what is now the
size of the circles of perpetual
apparition and
occultation? It is evident
that they must
have shrunk in dimensions
more and more as
we journeyed south.
The circle of perpetual
% Fig 4.13
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.45\textwidth]{page_072b}
  \caption{Right sphere (at Equator)}
  \label{p72}\index{sphere!right}
\end{wrapfigure}
apparition is now a mere
point,---the north pole
itself; and the circle of
perpetual occultation is a point also,---the south pole.
No star, then, can be visible all the time, nor can any
be invisible all the time. The equatorial zone of stars,
visible part of the time and invisible the remainder of
each day of 24 hours, has expanded to embrace the entire
firmament. Every star, no matter what its declination, is
above the horizon 12 sidereal hours and below it 12 hours,
and so on alternately forever.

\textbf{The Equatorial at Different Latitudes.}---Remembering
that the principal axis of the equatorial telescope must
\DPPageSep{083.png}
always be directed toward the pole of the heavens, it is
easy to see what the construction of the instrument must
be, to adapt it for use in different latitudes. At the pole
itself, were an equatorial telescope required for that latitude,
the polar axis
would be vertical (\vpageref*{p73});
and the
equatorial would not
differ at all from the
altazimuth. As we
travel from the pole
into lower latitudes,
the polar axis is tilted
from the vertical accordingly;
until at the
equator it becomes actually
horizontal, as
illustrated adjacent.
An equatorial mounted
at middle latitudes
has already been
shown on page~\pageref{p53}.
It must not be thought that this change of latitude and corresponding
inclination of the polar axis modifies in any
way the relations of other parts of the equatorial. The
polar axis is always in the meridian; and its altitude,
or the elevation of its poleward end, is always equal to
the latitude. The polar axes of equatorial telescopes
in all the observatories of the world are parallel to one
another.

% Fig 4.14a, b
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input{page_073}
    \caption{Equatorial at the Poles}
    \label{p73}\index{equatorial telescope!mounted!at poles}
  \end{minipage}
  \hfill
  \begin{minipage}{0.5\textwidth}
    \centering
    \Input[0.95\textwidth]{page_074}
    \caption{Equatorial at the Equator}
    \index{equatorial telescope!mounted!at equator}
  \end{minipage}
\end{figure}
\Smaller
Large equatorial mountings, or those rigid enough to carry a telescope
above six inches aperture, always have the frame or pier head
cast by the maker in such form that the bearing for the polar axis shall
stand at the angle required by the latitude of the place where the telescope
\DPPageSep{084.png}
is to be used; smaller instruments, called portable equatorials,
generally have the bearing of the polar axis attached to the pier, stand,
or tripod, by means of a rigid clamp; the polar axis can then be tilted
to correspond to any required latitude, as shown by a graduated quadrant
or otherwise. Such portable, or universal, equatorials are an essential
part of the equipment of eclipse and other astronomical expeditions.
As the polar axis is reversed, end for end, in passing from one hemisphere
to the other, the clockwork motion must be reversible also,
because the stars move from east to west in both hemispheres.
\Restore

Our next inquiries are directed toward the astronomical
relations of the earth on which we dwell, its form and size,
and the elementary principles by which these facts are
ascertained.
\DPPageSep{085.png}


\Chapter{V}{The Earth as a Globe}

The original idea of the earth, as given in the Homeric
poems, was that of an immense, flat, circular plane,
around which Oceanus\index{Oceanus, river of mythology}, a mythical river, not the
Atlantic, flowed like a vast stream. It was thought to
be bounded above by a hollow hemisphere turned downward
over it, through and across which the heavenly
bodies coursed for human convenience and pleasure.

\textbf{Ancient Idea of the Earth.}\index{earth!ancient idea of}\index{astronomy!history}---Anaximander\index{Anaximan´der (\BC~580), Gk.\ phil.} (\BC~580) regarded
the earth as a flat, circular section of a vertical
cylinder, with Greece and the
% Fig 5.1
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.6\textwidth]{page_076}
  \caption{Curvature of the Ocean exaggerated}
  \label{p76}
\end{wrapfigure}
Mediterranean surrounding
the upper end. Herodotus (\BC~460)\index{Herodotus (\BC~460), Gk.\ hist.}, whose
geographic
knowledge was extensive,
ridiculed
the idea
of a flat and circular
earth. To Plato (\BC~390)\index{Plato (\BC~390), Gk.\ phil.},
the earth was a
cube. Even as late as \AD~550, Cosmas\index{Cosmas (\AD~550), Egypt.\ geographer} drew the earth as
a rectangle, twice as long (east and west) as it was broad
(north and south), from which conception have originated
the terms \textit{longitude}\index{longitude (celestial)!origin of term} (length) and \textit{latitude}\index{latitude (terrestrial)!origin of term} (breadth); and
from the four corners of this rectangular earth rose pillars
to support the vault of the sky. The venerable Bede\index{Bede (bead) `The Venerable' (\AD~700), Eng.\ author} (\AD~700)
promulgated the theory of an egg-shaped earth, floating
in water everywhere surrounded by fire. Long before
this, however, Thales (\BC~600)\index{Thales (\BC~600), Gk.\ phil.} and Pythagoras (\BC~530)\index{Pythagoras (\BC~530), Gk.\ phil.}
had taught that the earth was spherical in form; but the
\DPPageSep{086.png}
erroneous beliefs persisted through century after century
before the doctrine
of a globular earth
was fully established.
Final doubt was
swept away by the
famous voyage of
Magellan, one of
whose ships first
circumnavigated the
globe in the 16th
century, and in three
years returned to its
starting point.

% Fig 5.2 a, b
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input{page_077a}
    \caption{Ship's Rigging Distinct, Water Hazy}
  \end{minipage}
  \hfill
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input{page_077b}
    \caption{Water Distinct, Rigging ill-defined}
  \end{minipage}
  \label{p77}
\end{figure}

\textbf{How to see the Curvature
of the Earth.}\index{earth!curvature}---By ascending to greater and greater heights above the
earth's surface, the horizon retreats farther
and farther.
If we ascend a peak
in mid-ocean, the extension
of the radius
of vision may be seen
to be the same in
every direction, thus
indicating a spherical
earth. But a better
experimental proof
may be had. Near
the shore of a large
body of water, on a
fine day when ships
can be seen far out,
mount a telescope (as \vpageref*{p76}) upon a high building or cliff. The
\DPPageSep{087.png}
intervening water will be imperfectly seen (\vpageref*{p77}), but
the ship's masts and rigging well defined, if all conditions
are favorable. Now draw out the eyepiece of the telescope
until the waves on the horizon line appear sharply
defined. The details of the ship will then be hazy and
indistinct, because the ship is farther away than the water
which hides her hull. Repeat the observation by focusing
the telescope alternately on the ship and the water in the
same field of view,---affording ocular proof that the
earth's surface curves away from the line of vision.
Wherever this simple experiment is tried, the result will
be the same; so we reach the conclusion that the earth is
round like a ball.

% Fig 5.3
\begin{figure}[hbt!]
  \centering
  \Input{page_078}
  \caption{Earth a Plane, Local Time everywhere the Same}
\end{figure}
\textbf{Telegraphic Proof that the Earth is Round.}---Farther %[**sic]
proof that the earth is not a plane may be derived with
the assistance of the electric telegraph. If the earth were
a plane, local time would everywhere be the same. This
condition is shown in the above figure, for Denver, Chicago,
and New York: the lines of direction in which the
sun appears from all three places are parallel, because
the distance separating them is not an appreciable part
of the sun's true distance. Therefore, as the sun's angle
east of the meridian corresponds to 10~\AM\ at one place,
\DPPageSep{088.png}
it should be 10~\AM\ at all. But at 10~\AM\ at Chicago, if
the operator asks New York and Denver what time it is
at those places, he will receive the answer that
 it is 9
o'clock at Denver and 11 at New York. The sun, therefore,
must be 15° east of the meridian at New York, as
shown in the figure below, 30° at Chicago, and 45° at Denver.
So the meridian planes of these three places cannot
be parallel, as in the first illustration, but must converge
below the earth's surface, as shown in the second one.

\Smaller
By means of land lines and cables, the local time has been compared
nearly all the way round the globe, eastward from San Francisco to
New York, across the Atlantic Ocean, over the eastern hemisphere,
through Europe and Asia to Japan. Everywhere it is found that
% Fig 5.4
\begin{figure}[htb!]
  \centering
  \Input{page_079}
  \caption{Earth a Globe, Local Time depends on the Longitude}
\end{figure}
meridians converge downward in such a way that all would meet in
a single line. This geometric condition can be fulfilled only by a
solid body, all of whose sections perpendicular to this common line
are circles. Therefore the earth is round, east and west; and, by
going north and south in different parts of the earth, and continually
observing the change in meridian altitudes of given stars, it is found
that the earth is round in a north and south direction also. But all
these curvatures as observed in different places nearly agree with each
other; therefore, the earth is nearly a sphere.
\Restore

\textbf{History of the Measurement of the Earth.}\index{earth!measurement}---While the
Chaldeans are credited with having made the first estimate
\DPPageSep{089.png}
 of the earth's circumference (24,000 miles), the
Greeks, beginning with Aristotle\index{Aristotle (\BC~350), Gk.\ phil.} (\BC~350), made noteworthy
efforts to solve this important problem, which is
preliminary to the measurement of all astronomical distances.
Eratosthenes (\BC~240)\index{Eratos´thenes (\BC~240), Alex.\ geom.} and Cleomedes\index{Cleome´des (\AD~150), Gk.\ ast.} (\AD~150)
applied the gnomon\index{gnomon} to the measurement of degrees on
the earth's surface, and devised the application of geometry
to this problem essentially as it is employed to-day.
They made Syene $7° \, 12'$ south of Alexandria; and as the
measurement of distance between these places made them
5000 stadia\index{stadium (pl. stadia)} apart, the proportion
\[
7°.2:360°::5000:\text{---}
\]
gave for the circumference of the earth 250,000 stadia, or
24,000 miles.

\Smaller
Posidonius\index{Posidonius (\BC~260), Gk.\ phil.}\index{astronomy!history} (\BC~260) made a similar determination between Rhodes
and Alexandria. Early in the ninth century of our era, the Arabian
caliph Al-Mamun\index{Al-Mamun (\AD~810), Arab.\ caliph} directed his astronomers to make the first actual
measurement of an arc of a terrestrial meridian, on the plain of Singar,
near the Arabian Sea. Wooden poles were used for measuring rods,
but the result is uncertain, because the details of the corresponding
astronomical observations are not known. Fernel\index{Fernel, J. (fair-nel´) (1497--1558), Fr.\ geod.}, in France, measured
a terrestrial arc early in the 16th century, adopting a method like that
of Eratosthenes, and beginning that brilliant series of geodetic measures
which, through succeeding centuries, did much to establish the
scientific prestige of France. Also Picard\index{Picard, J. (pe-car´) (1620--82), Fr.\ geom.} measured an accurate arc of
meridian in 1671, used by Newton\index{Newton, Sir I. (1642--1727), Eng.\ ast.} in establishing his law of gravitation.
\Restore

\textbf{Geodesy.}\index{geodesy!defined}---Geodesy is the science of the precise measurement
of the earth. Accurate geodetic surveys have
been conducted during the present century in England,
Russia, Norway, Sweden, Germany, India, and Peru; and
eventually the transcontinental measurements, completed
in the year 1897 by the United States Coast and Geodetic
Survey\index{survey!U. S.\ Coast \&amp; Geod.}, will make a farther and highly important contribution
to our knowledge of the size and figure of the earth.
Evidently an arc of a latitude parallel may make additions
\DPPageSep{090.png}
to this knowledge, as well as an arc of meridian. In the
former case the astronomical problem is to find the difference
of longitude between the extremities of the measured
arc; in the latter, the corresponding difference of latitude.
The processes of geodesy proper---that is, the finding out
how many miles, feet, and inches one station is from
another---are conducted by a system of indirect measurements
called triangulation.

\Smaller
\textbf{Triangulation.}---Although Ptolemy (\AD~140)\index{astronomy!history}\index{triangulation}\index{Ptolemy@Ptolemy, C. (tol´-em-mi) (\AD~140), Alex.\ ast.} had shown that an
arc of meridian might be measured without going over every part of it,
rod by rod,
% Fig 5.5
\begin{wrapfigure}{o}{0.66\textwidth}
  \centering
  \Input[0.66\textwidth]{page_082}
  \caption{The Latitude-box in Position}
  \label{p82}\index{latitude-box}
\end{wrapfigure}
the first application of his important suggestion was made
by Willebrord Snell\index{Snell, W. (1591--1626), Dutch math.}, a Netherland geometer of the 17th century.
Trigonometry is the science of determining the unknown parts of
triangles from the known. When one side is known and the two
angles at its ends, the other sides can always be found, no matter what
the relative proportions of these sides. It is evident, then, that if a
short side has been measured, the long ones may be found by the much
simpler, less tedious, and more accurate process of mathematical calculation.
Triangulation is the process of finding the exact distance
between two remote points by connecting them by a series or network
of triangles. The short side of the primary triangle, which is actually
measured, foot by foot, is called the \textit{base}. For the sake of accuracy
the base is often measured many times over. Thenceforward, only
angles have to be measured---mostly horizontal angles; and this part of
the work is done with an altazimuth\index{altazimuth} instrument. We must pass over
the explanation of the somewhat complex process of getting the single
desired result from a rather large mass of observations and calculations.
The base must not be too short; and the stations must be so
selected as to give \textit{well-conditioned triangles}. Of course an equilateral
triangle is well-conditioned in the extreme, and good judgment is required
in deciding how great a departure from this ideal figure is allowable.
The triangle on page~\pageref{p235},
with the earth's diameter as a base,
is exceedingly ill-conditioned. Snell's base was measured near Leyden;
but it was shorter than it should have been; the telescope was not then
available for accurate measurement of angles; and some of his triangles
were ill-conditioned, consequently his result for the size of the earth
was erroneous. The geometers of to-day employ the principles of his
method unchanged, but with great improvement in every detail.
\Restore

\textbf{Earth's Size and Volume.}\index{earth!size}\index{earth!volume}---As a result of such labors, it
is found that the length of the shortest diameter of the
\DPPageSep{091.png}
earth, or the distance between the two poles, is 7900 miles.
In the plane of the equator, the diameter of our globe is
7927 miles, or about $\tfrac{1}{300}$ part greater than the diameter
through the poles.
This fraction is a
little less than the
oblateness of the
earth\index{earth!oblateness} or its polar
compression. Recent
measurements
indicate that the
equator itself is
slightly elliptical,
but this result is not
yet absolutely established.
The form of
the earth may therefore
be regarded as
an ellipsoid with
three unequal diameters,
or axes. Knowing
the lengths of
these diameters, the
volume of the earth
has been calculated
and found to be 260 billion cubic miles. As the size of
the earth was first determined by measuring the length
of a meridian arc\index{meridian!arc}, and comparing it with the difference of
latitude at the two ends of the arc, we next describe an
easy method of finding the latitude.

\textbf{How to observe the Latitude.}\index{latitude (terrestrial)!finding}---It is probable that you
can take the latitude of the place where you live, more
accurately from the map in any geography, than you can
find it by the method about to be described. But the
\DPPageSep{092.png}
principle involved is often used by the astronomer and
navigator, and it is important to understand it fully, and
to test it practically, although there may be at hand no
instrument better than a plumb-line and a pasteboard
box.

\Smaller
\index{latitude-box}A box about six or seven inches square should be selected. The
depth of the box is not important---four or five inches will be convenient.
% Fig 5.6
\begin{figure}[hbt!]
  \centering
  \Input{page_083}
  \caption{\textsf{GRADUATED QUADRANT}
  (To be copied in the latitude-box, for measuring the  Sun's zenith distance at apparent noon)}
\end{figure}
Cut a hole $\tfrac{1}{4}$ inch square (\textit{A}) through the middle of one
side, at the bottom. On the inside paste a piece of letter paper over
this hole, as indicated by the dotted line \textit{CB} (\vpageref*{p82}). Transfer
a duplicate of the above graduated arc to a stiff sheet of highly
calendered paper or very smooth bristol board about four inches
square. Trim the little quadrant accurately, taking especial care that
the edges of it at the right angle shall exactly correspond with the
lines. The quadrant is now to be pasted on the inside of the bottom
of the box, in such a way that the center of the arc, or the right-angled
point, will be in contact with the bit of paper pasted over the aperture.
\DPPageSep{093.png}
One thing more, and the latitude-box is complete: exactly opposite the
right-angled apex of the quadrant, and perhaps a sixteenth of an inch
away from its plane, pierce a pin hole through the letter paper. Now
select a window facing due south, and tack the box on the west face
of its casing, so that the quadrant will be nearly in the meridian.
The illustration on page~\pageref{p82}
shows how it should be fastened. Put in
a tack at \textit{F}. Then hang a plumb-line by a fine thread in front of the
box, and sight along it, turning the box round the tack until the line
\textit{ED} is parallel to the
plumb-line. Then tack
in final position at \textit{G}, and
verify the direction of \textit{ED}
by the plumb-line afterwards.
The latitude-box
is now ready for use.

\textbf{To make the Observation.}---On
any cloudless
day, about half an hour
before noon, the sunlight
falling through the pin
hole will make a bright
elongated image at \textit{H}.
As the sun approaches
nearer and nearer the
meridian, this image will
travel slowly toward \textit{K},
becoming all the time less
bright, but more elongate. Just before apparent noon it will appear as
a light streak, \textit{KL}, about one degree broad, and stretching across the
graduation of the quadrant. The observation is completed by taking
the reading of the middle of this light streak on the arc, to degrees
and fractional parts as nearly as can be estimated. It is better to set
down this reading in degrees and tenths decimally.

\textbf{To calculate or reduce the Observation.}---Only a single principle
is necessary here, because in our latitudes refraction by the air
(page~\pageref{p91})
will never be
% Fig 5.7
\begin{wrapfigure}[20]{o}{0.6\textwidth}
  \centering
  \Input[0.55\textwidth]{page_084}
  \caption{Latitude equals Zenith Distance plus Declination}
  \label{p84}
\end{wrapfigure}
an appreciable quantity. Take the sun's declination
from table \vpageref{p85}. The above diagram shows
how it should be applied to the reading on the arc. If declination
is south, subtract it from the reading on arc of the quadrant, and
remainder is the latitude. But if sun's declination is north, add it to
the quadrant reading, and the sum will be equal to the latitude. The
quadrant reading is sun's zenith distance; and the single principle
employed is the fundamental one: that the altitude of the pole (or
declination of zenith) is equal to the latitude.
\Restore
\DPPageSep{094.png}

\textbf{The Sun's Declination.}\index{sun!declination of}---The sun's declination is its
angular distance either north or south of the celestial
equator. It varies from day to day, and may be taken
from Table~\ref{p85}, with sufficient accuracy for the
foregoing purpose.

\begin{table}[hbt]
\TableSize
\caption{\textsc{The Sun's Declination at Apparent Noon}}
\label{p85}\index{sun!declination of}
\centering
\begin{tabular}{*{5}{r@{\ }r|} r@{\ }r}
  \hline\hline
  \multicolumn{2}{c|}{\footnotesize\textsc{Day}\rule{0pt}{4ex}}
&amp; \multicolumn{2}{c|}{\footnotesize\textsc{Decl.}}
&amp; \multicolumn{2}{c|}{\footnotesize\textsc{Day}}
&amp; \multicolumn{2}{c|}{\footnotesize\textsc{Decl.}}
&amp; \multicolumn{2}{c|}{\footnotesize\textsc{Day}}
&amp; \multicolumn{2}{c}{\footnotesize\textsc{Decl.}}
\\[2ex]  \hline
  Jan. &amp;  1 &amp; 23°.0 &amp; S.\rule{0pt}{4ex}
&amp; May  &amp;  1 &amp; 15°.2 &amp; N.
&amp; Aug. &amp; 29 &amp;  9°.2 &amp; N.
\\
       &amp; 11 &amp; 21 .7 &amp; S.
&amp;      &amp; 11 &amp; 18 .0 &amp; N.
&amp; Sept.&amp;  8 &amp;  5 .5 &amp; N.
\\
       &amp; 21 &amp; 19 .8 &amp; S.
&amp;      &amp; 21 &amp; 20 .3 &amp; N.
&amp;      &amp; 18 &amp;  1 .6 &amp; N.
\\
       &amp; 31 &amp; 17 .2 &amp; S.
&amp;      &amp; 31 &amp; 22 .0 &amp; N.
&amp;      &amp; 28 &amp;  2 .2 &amp; S.
\\
  Feb. &amp; 10 &amp; 14 .2 &amp; S.
&amp; June &amp; 10 &amp; 23 .0 &amp; N.
&amp; Oct. &amp;  8 &amp;  6 .1 &amp; S.
\\
       &amp; 20 &amp; 10 .7 &amp; S.
&amp;      &amp; 20 &amp; 23 .5 &amp; N.
&amp;      &amp; 18 &amp;  9 .8 &amp; S.
\\
  Mar. &amp;  2 &amp;  7 .0 &amp; S.
&amp;      &amp; 30 &amp; 23 .2 &amp; N.
&amp;      &amp; 28 &amp; 13 .3 &amp; S.
\\
       &amp; 12 &amp;  3 .1 &amp; S.
&amp; July &amp; 10 &amp; 22 .2 &amp; N.
&amp; Nov. &amp;  7 &amp; 16 .5 &amp; S.
\\
       &amp; 22 &amp;  0 .8 &amp; N.
&amp;      &amp; 20 &amp; 20 .6 &amp; N.
&amp;      &amp; 17 &amp; 19 .1 &amp; S.
\\
  Apr. &amp;  1 &amp;  4 .7 &amp; N.
&amp;      &amp; 30 &amp; 18 .4 &amp; N.
&amp;      &amp; 27 &amp; 21 .2 &amp; S.
\\
       &amp; 11 &amp;  8 .5 &amp; N.
&amp; Aug. &amp;  9 &amp; 15 .7 &amp; N.
&amp; Dec. &amp;  7 &amp; 22 .7 &amp; S.
\\
       &amp; 21 &amp; 12 .0 &amp; N.
&amp;      &amp; 19 &amp; 12 .6 &amp; N.
&amp;      &amp; 17 &amp; 23 .4 &amp; S.
\\
  May  &amp;  1 &amp; 15 .2 &amp; N.
&amp;      &amp; 29 &amp;  9 .2 &amp; N.
&amp;      &amp; 27 &amp; 23 .3 &amp; S.
\\[2ex]  \hline\hline
\end{tabular}
\end{table}

The values are adjusted to every tenth day through the
year. Find the value for any intermediate date proportionally.

\textbf{How the Latitude is found accurately.}\index{latitude (terrestrial)!finding}---But while a
crude method like the foregoing has a certain value as
illustrating the outline of a principle, it is of no importance
to the astronomer, because of the impossibility of
eliminating the very large errors to which it is subject.
He therefore employs a variety of other methods. The
best is the method of equal zenith distances.

\Smaller
The instrument for measuring them is called the zenith telescope\index{zenith telescope}\index{telescope|see{zenith telescope}}.
Two stars are selected whose declinations are such that one of them
\DPPageSep{095.png}
culminates as far north of zenith as the other does south of it. The
telescope is constructed with a delicate level attached to its tube, so that
it can be clamped rigidly at any angle. When the first star is observed
set the level horizontal: then turn the instrument round 180°, taking
care not to disturb the level. The second
star will cross the field of view, because
the telescope will now be pointing as far
on one side of zenith as it was on opposite
side
% Fig 5.8
\begin{wrapfigure}[19]{o}{0.5\textwidth}
  \centering
  \Input[0.375\textwidth]{page_086}
  \caption{Zenith Telescope (Warner \&amp; Swasey)}\index{Warner \&amp; Swasey}\index{zenith telescope}
\end{wrapfigure}
in the first position. Declinations
of both stars must be accurately
known; and these, with small corrections
depending upon instrument and atmosphere,
give the means of calculating latitude
with great precision. The zenith telescope
is usually a small instrument, perhaps
3 feet high. The one here shown is
employed by Doolittle\index{Doolittle, C. L., Dir.\ Obs.\ Univ.\ Penn.} at the Flower
Observatory of the University of Pennsylvania,
in making the critical observations
described at the end of this chapter. At
fixed observatories the latitude is generally
determined by means of the meridian
circle\index{meridian!circle} (described on page~\pageref{p216}).
\Restore

% Fig 5.9
\begin{wrapfigure}{o}{0.4\textwidth}
  \centering
  \Input[0.4\textwidth]{page_087}
  \caption{Degrees grow Longer toward the Poles}
  \label{p87}
\end{wrapfigure}
\textbf{Length of Degrees of Latitude and Longitude.}\index{latitude (terrestrial)!length of degrees}\index{longitude (celestial)!length of degrees}---The
length of a degree on the equator is 69$\tfrac{1}{6}$ statute miles.
At the equator a degree of longitude and a degree of
latitude are very nearly equal in length, the latter being
only about $\tfrac{1}{150}$ part shorter. Leaving the equator, degrees
of longitude grow rapidly shorter, because meridians
converge toward the pole. In latitude 30° the degree of
longitude has shrunk to 60 miles, so that a minute of longitude
is covered for every mile traveled east or west. In
the United States, average length of a minute of longitude
is $\tfrac{7}{8}$ of a mile.

\Smaller
By measuring degrees of meridian at various latitudes, they are found
invariably longer, the nearer the pole is approached. So curvature of
meridians must decrease toward the pole, because the less the curvature
of a circle, the longer are degrees upon it. The figure \vpageref{p87} shows
\DPPageSep{096.png}
this effect much exaggerated, but actual differences are not large; at
equator the length of a degree of latitude is 68$\tfrac{3}{4}$, in the United States
almost exactly 69, and at the pole 69$\tfrac{3}{8}$~miles.
The angle between equator-plane and a line
from any place to earth's center is called its
geocentric latitude; and the difference between
it and ordinary or geographic latitude
is the \textit{angle of the vertical}\index{angle of the vertical}. It is zero at poles
and equator, and amounts to about $11'$ at latitude
45°, geocentric being always less than
geographic latitude.
\Restore

\textbf{Terrestrial Gravity.}\index{gravity!terrestrial}---By gravity
is meant the natural force exerted on
all terrestrial matter, drawing or tending
to draw it downward in the direction
of the plumb-line. All objects, as air, water, buildings,
animals, earth, rock, metals, are held in position by this
attraction, and it gives them the property called weight.
As we know, if the earth were dug away from under us, we
should fall to a point of rest nearer the earth's center. If
gravity did not exist, all natural objects not anchored firmly
to earth would be free to travel in space by themselves.
The ultimate cause of this force has not yet been ascertained,
but its law of action has been fully investigated
(page~\pageref{p384}).
It diminishes as we go upward, being a thousandth
part less on a mountain 10,000 feet high. Gravity
remains constant at a given place, and is exerted upon all
objects alike. If unobstructed, all fall to the earth from a
given height in exactly the same time.

\Smaller
Try the experiment for yourself, using two objects to which the air
offers very different resistance---a silver dollar, and a piece of tissue
paper about half an inch square. Hold the coin delicately suspended
horizontally between thumb and finger. Practice releasing the coin so
that it will remain horizontal while dropping. Then place the paper
lightly on top of the coin. The paper will fall in exactly the same time
as the coin does, because the coin has partially pushed the air aside,
and permitted gravity to act upon the paper, quite unhampered by
\DPPageSep{097.png}
resistance of the atmosphere. The coin pushes the air aside and falls
as quickly as the paper falls without pushing the air aside. But the fall
of the coin is not appreciably delayed by aerial resistance, and both
coin and paper fall through the same distance in the same time.
\Restore

\label{p88} \textbf{The Earth's Form found by Pendulums.}\index{earth!form found by pendulums}\index{pendulum}---If a delicately
mounted pendulum of invariable length is carried from
one part of the globe to another, it is found from comparison
with timepieces regulated by observations of the stars,
that its period of oscillation, or swinging from one side
of its arc to the other, is subject to change. Richer\index{Richer, J. (re-shay´) (1640--96), Fr.\ ast.} first
tested this in 1672. By carrying from Paris to Cayenne
a clock correctly regulated for the former station, he found
that it lost 2m.\ 28s.\ a day at the latter; and it was necessary
to shorten the pendulum accordingly. Now, conversely,
preserve the length of the pendulum absolute, and record
the exact amount of its gain or loss at places differing
widely in latitude and longitude; then it will be possible
to find their relative distance from the center of the earth,
because the law connecting the oscillation of the pendulum
with the force of gravity at different distances from the
earth's center is known. At the sea level in the latitude
of New York, a pendulum oscillating once a second is 39.1
inches long, and the times of vibration of pendulums vary
as the square root of their lengths. This kind of a survey
of the earth is called a \textit{gravimetric survey}\index{survey!gravimetric}, and operations
in the process are termed \textit{swinging pendulums}.

\Smaller
In this manner it has been ascertained that the force of gravity at
the earth's poles must be about $\frac{1}{190}$ greater than at the equator. But
in order to find the earth's figure, this result must be corrected because
the effect of the earth's attraction is everywhere (except at the poles)
lessened on account of the centrifugal force of its rotation. It is greatest
at the equator, amounting to $\frac{1}{289}$. Subtracting this from $\frac{1}{190}$, the
remainder is about $\frac{1}{555}$. This result makes the earth's equatorial
radius about $13\frac{1}{2}$ miles longer than its polar radius, thereby verifying the
value derived from the measures of meridian arcs. Pendulum observations
\DPPageSep{098.png}
can be made at numerous localities where the contour of the
surface is so irregular that measurement of arcs is impracticable. Besides
this, the swinging of pendulums has revealed many interesting
facts regarding the earth's crust; important among them being this---that
the mountains of our globe are relatively light, and some of them
mere shells. American geometers who have contributed most to these
researches are Peirce\index{Peirce, C. S. (purse), Am.\ geom.} and Preston\index{Preston, E. D. (1851--1906), Am.\ phys.}.
\Restore

% Fig 5.10
\begin{wrapfigure}{o}{0.45\textwidth}
  \centering
  \Input[0.4\textwidth]{page_089}
  \caption{Weighing the Earth}
\end{wrapfigure}
\textbf{Weighing the Earth.}\index{earth!mass}---The mass of the earth is six
thousand millions of millions of millions of tons. Perhaps
this statement does not assist
very much in realizing how heavy
the earth actually is; but it may
arouse interest in regard to methods
of reaching such a result. Several
have been employed, but the bare
outline of the first one ever tried is
indicated by the figure of a section
of the earth surmounted by a rather
abrupt mountain. The straight lines
drawn downward (one from the
north and the other from the south
side of the mountain) converge
toward the center of the earth.
Outward toward the stars each line
would point in the direction of the
zenith of the station $a$ or $b$, if the
mountain were not there. But the
attraction of the mountain mass
draws toward itself the plumb-lines
suspended on both sides of it; so
that the difference of latitude of the two stations is made
greater by the amount that the angle of the dotted lines
exceeds the angle at the center of the earth. But the
true difference of latitude between $a$ and $b$ can be found
by surveying round the mountain. This survey, too, must
\DPPageSep{099.png}
be so extended that the volume of the mountain may be
ascertained; geologists examine its rock structure, and its
actual weight in tons is calculated. Then by a mathematical
process the earth is weighed against the mountain,
and the result in tons given above is obtained from the
ratio of the mass of our globe to the mass of the mountain.
Schiehallion\index{Schiehallion, Mt., in Scotland} in Scotland was the mountain first utilized
in this important research, about a century ago. As
a result of all the measures of different methods, the
earth's mean density is found to be 5.6. This means that
if there were a globe entirely composed of water and of
exactly the same volume as our globe, the real earth would
weigh 5.6 times as much as the sphere of water.

\textbf{Atmospheric Refraction.}\index{atmosphere!of earth}\index{earth!atmosphere}\index{refraction, atmospheric}---The earth is completely surrounded
by a gaseous medium called the atmosphere.
Even when perfectly tranquil,
the
% Fig 5.11
\begin{wrapfigure}{o}{0.55\textwidth}
  \centering
  \Input[0.55\textwidth]{page_090}
  \caption{Refraction increases the Apparent Altitude}
\end{wrapfigure}
atmosphere has
a remarkable effect upon
the motion of a ray of
light in bending it out of
its course. Two properties
true of all gases are
concerned in atmospheric
refraction---weight and
compressibility. The atmosphere is probably at least 100
miles in depth; and gravity attracts every portion of it
vertically downward. Its total weight is about $5 × 10^{15}$
(five quadrillions = 5,000,000,000,000,000) tons, or $\frac{1}{1200000}$
that of the entire earth. Conceive the atmosphere divided
into layers concentric round the earth and one another,
as above. The lowest shell must support not only the
weight of the shell next outside it, but of all the other
shells still beyond. Evidently, then, as the atmosphere
is compressible, the force of gravity renders successive
\DPPageSep{100.png}
strata more and more dense as the surface of the earth
is approached. The greater the density, the more the refraction;
so that lower strata bend, or refract, rays of light
out of their course more than upper layers do.

\textbf{Law of Refraction.}\label{p91}---According to the law of refraction,
rays of light from any celestial body striking the air in the
direction of the plumb-line,
will pass downward along
that line undeviated; but any
rays impinging on the atmosphere
otherwise than vertically---that
is, rays from
celestial bodies whose zenith
distance is not zero---will be
refracted more and more
from their original course,
the nearer they are to the
horizon. The less the altitude,
the greater the refraction;
and, as an object always seems to be in that direction
from which its rays enter the eye, refraction elevates
the heavenly bodies, or makes their apparent altitude
greater than their true altitude. The figure shows how
refraction varies from zenith to horizon.

\Smaller
If the altitude is 45°, the refraction is $58''$, or nearly one minute of
arc; but so rapidly does the density of the atmosphere increase near
the earth's surface that the refraction at zenith distance 85° is $9'\, 46''$,
more than 10 times greater than at 45°; and increase in the next five
degrees is even more rapid, so that the refraction at the horizon is
$34'\, 54''$. A correction on account of refraction must be calculated
and applied to nearly all astronomical observations. Generally thermometer
and barometer must both be read, because cold air is denser
than warm, and a high barometer indicates increase of pressure of the
superincumbent air. In both these instances the amount of refraction
is increased. To determine how much the refraction was at the time
when an astronomical observation was made at a given altitude, and to
\DPPageSep{101.png}
apply the corresponding correction suitably, is part of the work of the
practical astronomer. It is greatly facilitated by means of elaborate
\textit{Refraction Tables}.
\Restore

\textbf{Effects of Atmospheric Refraction.}\index{atmosphere!of earth}---The angular breadth
of the sun is, as we shall see, about one half a degree; and
as this is nearly the
% Fig 5.12
\begin{wrapfigure}{o}{0.45\textwidth}
  \centering
  \Input[0.45\textwidth]{page_091}
  \caption{Refraction at Different Altitudes}
\end{wrapfigure}
amount of atmospheric refraction at
the horizon, evidently the sun is really just below the sensible
horizon when at its setting we still see it just above
that plane. And as the diurnal motion of the celestial
sphere carries the sun over its own breadth in about two
minutes of time, refraction lengthens the day about four
minutes, in the latitude of the United States; this effect
being much increased as higher latitudes are reached. It
is easy to see, also, that the sun must be continually
shining on more than an exact half of the earth, refraction
adding a zone about 40 miles wide extending all the
way round our globe, and joining on the line of sunrise
and sunset. Farther effects of atmospheric refraction are
apparent in those familiar distortions of the sun's disk
often seen just before sunset. Refraction elevates the
lower edge, or limb, more than the upper one, so that
the sun appears decidedly flattened in figure, its vertical
diameter being much reduced---an effect far more pronounced
in winter than in summer.

\textbf{Scintillation of the Stars.}\index{stars!scintillation}\index{scintillation|see{stars, scintillation}}\index{twinkling|see{stars, scintillation}}---Scintillation or twinkling
of the stars is a rapid shaking or vibration of their light,
caused mainly by the state of the atmosphere, though
partly as a result of the color of their intrinsic light.
That the atmosphere is a cause of twinkling is evident
from the fact that stars twinkle more violently near the
horizon, where their rays come to us through a greater
thickness of air.

\Smaller
Also the stars twinkle more in winter than in summer; and very violent
scintillations often afford a good forecast of rain or snow. Marked
\DPPageSep{102.png}
twinkling of the stars is an indication that the atmosphere is in a state
of turmoil---currents and strata of different temperatures intermingling
and flowing past one another. The astronomer describes this state of
things by saying that the `seeing is bad.' Consequently, high magnifying
powers cannot be advantageously used with the telescope. A
star's light seems to come from a mere point, so that when its rays are
scattered by irregular refraction, at one instant very few rays reach the
eye, and at another many. This accounts for the seeming changes of
brightness in a twinkling star. Ordinarily the bright planets are not
seen to twinkle, because of their large apparent disks, made up of a
multitude of points, which therefore maintain a general average of
brightness. At a given altitude white or blue stars (Procyon, Sirius,
Vega) twinkle most, yellow stars (Capella, Pollux, Rigel) a medium
amount, and red stars (Aldebaran, Antares, Betelgeux) least.
\Restore

\textbf{Twilight.}\index{twilight}---At a particular and definite instant of contact
with the sensible horizon, the sun's upper edge comes
into view at sunrise and disappears at sunset. But long
before sunrise, and
a corresponding
time after
% Fig 5.13
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.55\textwidth]{page_093}
  \caption{The Zone of Twilight in Midwinter}
  \label{p93}
\end{wrapfigure}
sunset,
there is an indirect
and incomplete illumination
diffused
throughout the atmosphere.
This is
called \textit{twilight}.
Morning twilight is
generally called \textit{dawn}. In part twilight is due to sunlight
reflected from the upper regions of the earth's atmosphere.
As twilight lasts until the sun has sunk 18° below the
horizon, evidently its duration in ordinary latitudes must
vary considerably with the season of the year. But the
variation dependent upon latitude itself is greater still.
A vast twilight zone nearly 1500 miles wide completely
encircles the earth.

\Smaller
This zone, \textit{ABEF} in the figure, is continually slipping round as our
globe turns on its axis. One edge of it, along the line of sunrise and
\DPPageSep{103.png}
sunset, is constantly facing the sun. At the equator, where the sun's
daily path is perpendicular to the horizon, the earth turns through this
zone of twilight in about $1\tfrac{1}{4}$~hours. In the latitude of the United States,
the average length of twilight exceeds $1\tfrac{1}{2}$~hours, its duration being
greatest in midsummer, when it is more than two hours. At the
actual poles of the earth, twilight is about $2\tfrac{1}{2}$~months in duration. If
the earth had no atmosphere, there would be no twilight; the blackness
of night would then immediately follow the setting of the sun.
\Restore

\textbf{The Aurora.}\index{aurora}---The aurora borealis (often called the
northern lights) is a beautiful luminosity, striated and
variable, seen at irregular intervals, and only at night.
From the general latitude of the United States, it appears
as a soft vibrating radiance, streaming up most often into
the northern sky, occasionally as far as the zenith, but
usually in a semicircle or arch extending upward not over
30°. Its probable average height is about 75~miles. The
aurora, generally greenish yellow in color, has occasionally
been seen of a deep rose hue, as well as of a pale blue, and
other tints. The continual vibration, sometimes the rapid
pulsation, of its streamers, gives it a character of mystery
only too well enhanced by our lack of knowledge of its
causes. That these are connected with the magnetism
of the earth is certain; also that a strong influence upon
the magnetic needle is somehow exerted. Telegraph instruments
and all other magnetic apparatus are greatly
disturbed when auroras are brightest. This wonderful
spectacle grows more frequent and pronounced, as the
north pole is approached; and is closely connected, though
in a manner incompletely understood, with the period of
sun spots, and the protuberances. When there are many
sun spots, auroras are most frequent and intense. Probably
they are merely an electric luminosity of very rare
gases.

\Smaller
The spectrum of the aurora\index{aurora!spectrum} is discontinuous (page~\pageref{p272}),
and far
from uniform. Always there is one characteristic green line, all others
\DPPageSep{104.png}
being faint, and varying from one auroral display to another. At times
there appear to be two superposed spectra. A similar phenomenon in
the southern hemisphere is sometimes called \textit{aurora australis}; also the
general term \textit{aurora polaris} is often applied to the auroras of both
hemispheres.
\Restore

\textbf{The Wandering Terrestrial Poles.}\index{pole!wandering terrestrial}---Referring back to
the remarkable photograph of stars around the northern
celestial pole (page~\pageref{p33}),
we recall the fact that the center
of all these arcs is that pole itself. And we may farther
define the terrestrial north pole as that point in the earth
directly underneath this celestial pole, or that point on our
globe where the center of this system of concentric arcs
would appear to be exactly in the zenith. But without
actually going there, how can astronomers determine the
precise position of this point on the earth's surface, and so
find out whether it shifts or not? Evidently by finding as
closely as possible, at frequent intervals of time, the latitude
of numerous places widely scattered over the world.
If the latitude of a place, Berlin, for example, is found to
increase slightly, while that of another place on the opposite
side of the globe, as Honolulu, decreases at the same
time and by the same amount, the inference is that the
position of the earth's axis changes slightly in the earth
itself. So definite are the processes of practical astronomy
that the position of the north pole can be located with no
greater uncertainty than the area of a large Eskimo hut.
Nearly all the great observatories of the world are fully
3000 miles from this pole; still if this important point
should oscillate in some
% Fig 5.14
\begin{wrapfigure}{o}{0.65\textwidth}
  \centering
  \Input[0.6\textwidth]{page_096}
  \caption{Observed Wandering of the North Pole}
\end{wrapfigure}
irregular fashion by even so slight
an amount as three or four paces, the change would be
detected at these observatories by a corresponding change
in their latitude. Such a fluctuation of the pole has actually
been ascertained, and it affects a large mass of the
observations of precision which astronomers and geodesists
\DPPageSep{105.png}
 have made in the past. Technically it is called the
variation of latitude\index{latitude (terrestrial)!variation of}.

\Smaller
Only recently recognized, the physical cause of it is not yet fully established.
But the nature and amount of it are already pretty well made
out. Around a central point adjacent to the earth's north pole, draw a
circle 60 feet in diameter, as shown in the illustration. Within this circle
the pole has always been since the beginning of 1890. Its wanderings
from that time onward to the beginning of 1897 are clearly indicated
by the irregularly curved
line which has been carefully
laid down from a
discussion of a large
number of accurate observations
of latitude at
many observatories located
in different parts of the
world. Let the eye trace
the curve through all its
windings, and the meaning
of the oscillation, or
wandering of the north
pole, will be appreciated.
From the beginning of
1890 to January, 1894,
the curve seems to have
been roughly an in-winding
spiral, the pole going
round once in about 14 months. The latitudes of all places on the
globe change by corresponding amounts. Chandler\index{Chandler, S. C.@Chandler, S. C., ed.\ \emph{Astron. Jour.}} of Cambridge
first brought clearly to light the variation of latitude\index{latitude (terrestrial)!variation of}, and American
investigation of it has been farther advanced by Preston\index{Preston, E. D. (1851--1906), Am.\ phys.}, Doolittle\index{Doolittle, C. L., Dir.\ Obs.\ Univ.\ Penn.}, and
Rees\index{Rees, J. K. (1851--1907), Am.\ ast.}. This movement of the pole is already sufficiently understood
to enable astronomers to predict its future movements; and it seems
probable that they will be confined within the narrow limits here indicated.
\Restore

Were the earth at perfect rest in space, its poles would
not partake of this remarkable motion, in part dependent
upon a slow turning round on its axis. The next chapter
is concerned with this fundamental relation, of the utmost
significance in astronomy, both theoretic and practical.
\DPPageSep{106.png}


\Chapter{VI}{The Earth Turns on its Axis}\index{earth!turns on its axis}

So\index{astronomy!history} far we have dealt only with the seeming motions of
the heavenly bodies about us; in ancient times these
were regarded as their actual motions. The glory
of the sun by day, and all the magnificence of the nightly
firmament were considered accessory to the earth on which
men dwell. Till the time of Copernicus\index{Copernicus, N. (1473--1534), Ger.\ ast.} our abode was
generally believed to be enthroned at the center of the
universe. Now we know, what is far less gratifying to our
self-importance, that this earth is only one---a very small
one, too---of the vast throng of celestial bodies scattered
through space, somewhat as moving motes in a sunbeam.
All the stately phenomena of the diurnal motion, the
appearances we have been studying, are easily and naturally
explained by the simple turning completely round
of our little earth on its axis once in a given period of
time. This the ancient world naturally divided unevenly
into day and night; but the astronomers of a later day,
more philosophically, divide it into 24 hours, all of equal
length, and this division is the only one recognized at the
present day.

\Smaller
\textbf{In the Dome of the Capitol.}\index{Washington!Capitol}---Imagine yourself in the rotunda, or
directly under the center of the dome of the Capitol at Washington.
Turn once completely round from right to left, meanwhile observing
the apparent changes in the objects and paintings on the inner walls of
the dome. Just above the level of the eye, you face, one after another,
all the twelve historical paintings exhibited in the rotunda. Turning
\DPPageSep{107.png}
round again at the same speed as before, the pillars half way up, apparently
much reduced in size from their greater distance, seem to move
more slowly. Turning round the third time, with the eyes directed
still higher, the outer figures in the colossal painting at top, the ceiling
of the dome, appear to turn more slowly still; while if you watch
attentively the very apex of the dome, the central point of Constantio
Brumidi's famous fresco will seem to have no motion whatever. This
very simple experiment can be tried quite as effectively in the middle
of any ordinary square room, first imagining its corners drawn inward,
roughly to represent a dome. Seat yourself on a revolving piano stool
or a swivel chair, and, as you turn slowly round from right to left, watch
the apparent motion of pictures on the wall, figures in the frieze, and
spots on the ceiling. To confine the direction of vision look through
a pasteboard roll, or other handy tube, elevating it to different altitudes
as desired. Now it would be ridiculous to insist that the dome
(or even the room) is turning around you, thereby causing these
changes, while you are at rest in the center. Yet this was precisely
the explanation of the apparent movement of the heavens accepted
by the ancient world, false as it was, and very improbable as it would
in our age seem to be. While the true doctrine of the rotation of the
earth was held and taught by a few philosophers from very early times,
it was not universally accepted till the downfall of the Ptolemaic system.
\Restore

\textbf{The Direction in which the Earth turns.}\index{earth!turns on its axis}---When riding
swiftly through the street in a carriage or a car, it is quite
easy, by imagining yourself at rest, to see, or seem to see,
all the fixed objects---houses, shops, lamp-posts, and so
on---rushing by just as swiftly in the opposite direction.
Although you may be going east, you seem to be stationary,
and they appear to travel west. While looking at the
paintings in the Capitol (or the engravings on the wall) in
succession as you turned round from right toward left, they
appeared to be going just opposite---from left toward right.
Now simply conceive all these objects to be moved outward
in straight lines from the point of observation, each in the
direction in which it lies, to a distance indefinitely great
as if along the spokes of a vast wheel, whose hub is at the
eye, but whose tire reaches round the heavens. When removed
to a distance sufficiently great, we may imagine them
\DPPageSep{108.png}
to occupy places in the sky which some of the celestial
bodies do. But we have seen that sun, moon, and stars all
move in general from east to west, so we reach the easy
and natural conclusion that our earth is turning over from
west toward east. Once this cardinal fact of the earth's
turning eastward on its axis is established and accepted,
there is a full explanation of that apparent westward drift
of which all the heavenly bodies, sun, moon, and stars in
common, partake. Also the natural succession of day and
night is robbed of its ancient mystery.

\Smaller
\textbf{Proof that the Earth turns Eastward.}---Quite independently of
its point of suspension, a pendulum tends to swing always in that plane
of oscillation in which it is originally set going. Suspend any convenient
object, weighing one or two pounds, by a fine thread attached
to the center of a stick or ruler. Hold it in both hands, and set the
pendulum swinging in the plane of the stick. Then, without raising
or lowering it, quickly swing the ruler quarter way round its center in a
horizontal plane. The pendulum keeps on swinging in the same plane
as before, although it is now at right angles to the ruler. Repeat the
experiment several times, until you succeed in moving the stick without
changing the position
% Fig 6.1
\begin{wrapfigure}[40]{o}{0.4\textwidth}
  \centering
  \Input[0.37\textwidth]{page_100}
  \caption{Foucault's Experimental Proof of Earth's Rotation}
  \label{p100}
\end{wrapfigure}
of its center, and it will be seen that the ruler
may be swung, either slowly or rapidly, into any position whatever,
without affecting the plane of the pendulum's motion appreciably.
Now imagine the short thread replaced by a very fine wire 200~feet
long, suspending a ball weighing 70 or 80 pounds; and in place of the
ruler turned round by hand substitute the Panthéon\index{Panthéon (pon-t\=a-awng), Paris} at Paris, turned
slowly round in space by the earth itself. These are the conditions of
this celebrated experiment as tried in 1851 by Foucault\index{Foucault, J. B. L. (foo-k\=o´) (1819--68), Fr.\ physicist}, a French
physicist, who thereby provided ocular proof that the earth turns
round from west toward east. He set the pendulum swinging in the
plane of the meridian, but it did not long remain so. The south end
of the floor being nearer the equator than the north end, it traveled
eastward a little faster than the north end did, so that the floor turned
counter-clockwise underneath the swinging pendulum. Therefore, the
plane of oscillation appeared to swing round clockwise. This experiment
has been repeated in different parts of the earth, and always with
the same result. The four figures \vpageref{p100} show the varying
conditions. In the southern hemisphere the pendulum appears to turn
round counter-clockwise. As for the rate of turning, at either pole it
makes a complete revolution in the same time that the earth does, and
\DPPageSep{109.png}
the time of revolution grows greater and
greater as the latitude grows less. Exactly
on the equator, the plane of oscillation does
not change at all with reference to the
meridian.
\Restore

\textbf{Day and Night.}\index{day}\index{night}\index{day|see{night}}\index{night|see{day}}---Granted the
rotation of the earth on its axis, and
the alternation of day and night is
fully and clearly explained. The
sun may even remain fixed among
the stars of the celestial vault. By
the earth's turning round, all places
upon its surface, as New York,
Chicago, and San Francisco, are
carried into the sunshine and out
of it alternately. From the darkness
of night there comes, first, the
dawn, with twilight growing brighter
and brighter, then sunrise, followed
by the sun rising higher and higher,
till it reaches the meridian. Then
it is midday, or noon. Afterward
the order of occurrence is reversed,---noon,
afternoon, sunset, twilight,
night again. All these phenomena
are, in a general way, connected
by everybody with lapse of time, and
progress of the hours from night to
noon, and from noon back to night
again. Uniform turning of the globe
in the figure \vpageref{p101} makes this relation
obvious. Count of the hours
is begun at 0 or 12, when the sun is
highest, and continued to 12, when
\DPPageSep{110.png}
the sun is lowest; and if earth were transparent as crystal,
the sun could be seen through it from sunset to sunrise---crossing
the lower meridian directly underneath the
northern horizon at midnight.

\textbf{Day and Night at the Equinoxes.}\index{night!at equinoxes}---The ecliptic has
been defined as the yearly path of the sun round the
heavens. As it lies at an angle of $23\frac{1}{2}$° to the celestial
equator, at some time each year the sun's declination
must be $23\frac{1}{2}$°~south, and six months from that time
its declination must be $23\frac{1}{2}$°~north. Midway between
% Fig 6.2
\begin{figure}[hbt!]
  \centering
  \Input{page_101}
  \caption{Alternation of Day and Night}
  \label{p101}
\end{figure}
these points, the sun will be crossing the equator;
that is, its declination will be zero, and the sun's center
will be at those points of intersection of equator and
ecliptic, called the equinoxes. Why they are so called
will be apparent from the figure above given; for the
sun is on the celestial equator, because the earth's equator-plane
extended would pass through it. The great circle
of the globe which separates the day hemisphere from
the night hemisphere, exactly coincides with a terrestrial
meridian. Everywhere on that meridian it is 6~o'clock---6~o'clock
on the half which the globe by its turning
is carrying round toward the sun, and 6~o'clock \PM\
on the other half which is being carried out of sunlight.
\DPPageSep{111.png}
It is sunrise everywhere on the former half of this meridian,
and sunset everywhere on the latter half. As daytime is
the interval from sunrise
% Fig 6.3
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_102}
  \caption{Diurnal Circles in Middle South Latitudes}
  \label{p102}
\end{wrapfigure}
to sunset, and night-time is the
interval from sunset to sunrise, the day and the night are
each 12~hours in length, and therefore equal. Whence
the term \textit{equinox}, from the two Latin words that mean
\textit{equal} and \textit{night}. This equality of day and night all over
the world occurs only twice
during the course of each
year. When the sun is
crossing the equator and
going northward, this happens
about the 21st of
March; and going southward,
about the 21st of
September.

\textbf{Day and Night at the
Solstices.}\index{night!at solstices}---From March to
September, the sun is north
of the celestial equator. Therefore, at our middle latitudes
he is among the stars that are above the horizon longer
than they are below it, as the upper figure on page~\pageref{p72a}
clearly shows. During this period of the year, daytime
in north latitudes is always longer than the night-time
immediately preceding or following it. At the summer
solstice the sun's declination has reached its maximum,
or $23\frac{1}{2}$°. The days then will be as long as possible, and the
nights as short as possible. From September to March, on
the other hand, the sun is south of the celestial equator, and
therefore among the stars that are below the horizon longer
than they are above it. During these months, then, night-time
in our hemisphere is always longer than daytime. At
the winter solstice the sun's declination is again a maximum,
but it is $23\frac{1}{2}$°~south or about midway between \textit{E} and \textit{S}. So
\DPPageSep{112.png}
that the days are then shortest, and the nights longest. But
these relations of day and night to the different months are
true for the northern hemisphere only.

\Smaller
\textbf{Day and Night South of the Equator.}\index{night!south of equator}---The figure \vpageref{p102} has been
suitably modified from the one on page~\pageref{p72a}, in order to show the relation
of day and night at different times of the year for places of middle south
latitude. By holding the page in a vertical plane, and looking west as
you read, the diagrams will better correspond to actual conditions.
For every degree of latitude that you pass over, in traveling southward,
the north pole of the heavens goes down one degree, and the south
pole rises one degree. The diagram opposite is adapted to south latitude
45°, much farther south than either Capetown, Valparaiso, or Melbourne.
The south pole of the heavens is now as far above the south
horizon as it was below the south
horizon, in a place of equal north
latitude; and the relations of
daytime to night-time are correspondingly
reversed. From September
to March, therefore, when
the sun's declination is south, the
sun is among the stars that are
above the horizon longer than
they are below it; so that the
daytime always exceeds the
night. From March to September,
the sun being in north
declination, the daytime clearly
is shorter than the night. If at
any time of the year we compare
the length of the day at a
given north latitude with the
length of the night at an equal
south latitude, we shall find them
equal. Also the converse of this
proposition is true.

\textbf{Day and Night at the Earth's Equator.}\index{night!at equator}---We have considered the
relation of day to night at middle north latitudes; and the explanation
given holds
% Fig 6.3
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_103}
  \caption{Diurnal Circles at the Equator}
  \label{p103}
\end{wrapfigure}
good for all places in the United States. Also the opposite
relations, which obtain in south latitudes. It remains to consider
the effect at the equator. Recalling the fact that the latitude of a
place is always equal to the altitude of the visible pole of the heavens,
it is clear that if the place selected is anywhere on the earth's equator,
\DPPageSep{113.png}
both celestial poles must be visible and coincide with the north
and south points of the horizon (figure \vpageref{p103}). The
horizon, then, must coincide with the celestial meridians, or hour circles,
one after another as they seem to pass by it, in consequence of the
apparent motion of the celestial sphere; and every star's diurnal circle
is the same as its parallel of declination. But every hour circle divides
parallels of declination in half; therefore, every star of the celestial
sphere, as seen from a station on the earth's equator, is above the
horizon 12~hours and below it 12~hours. Clearly this is true no
matter what the star's declination may be; therefore it must always be
true of the sun, although its declination is all the time changing. Had
the early peoples who invented our astronomical terms lived upon the
equator where day and night are always equal, the term \textit{equinox} would
not have signified anything unusual, and a different word would have
been necessary to define the time when, and the point where, the sun
crosses the celestial equator.
\Restore

\textbf{Sunrise and Sunset.}\index{sunrise and sunset}---Refer to any ordinary almanac.
The times of sunrise and sunset are given usually for two
or three definite cities, north and south, or for zones of states
varying widely in latitude. These are local mean times
when the upper edge or limb of the true sun, as corrected
for refraction, is in contact with the sensible horizon of
the place, or of any place of equal latitude. The local
time will not often coincide with the standard time, now
almost universally used. But the correction required is
simply dependent upon the difference between the longitudes
of the place and of the standard meridian. If you
are west of the standard meridian, for each degree add
four minutes to the almanac times; if east, subtract. In
verifying the almanac times by observation, remember the
difference between sensible and apparent horizons.

\Smaller
\textbf{Almanac Sunrise and Sunset at the Equinoxes.}---We have seen
that when the sun---that is, the sun's center---is on the equator, it rises
at the same time everywhere, and that time is 6~o'clock. So, too, it sets
everywhere at 6~o'clock. Why, then, do the times predicted in the
almanacs differ from this? The reason is threefold, (\textit{a})~The times of
sunrise and sunset are all corrected for refraction, which at the horizon
amounts to nearly 0°.6, or more than the sun's own breadth. As refraction
\DPPageSep{114.png}
always increases the apparent altitude of celestial bodies,
the sun can be seen wholly above the horizon when really below it.
Therefore this effect alone lengthens the daytime about five minutes,
causing the refracted sun to rise about two and one half minutes earlier
than the true sun, and set about the same amount later, (\textit{b})~The
almanac times of sunrise and sunset refer to the upper edge or limb of
the sun, not the center. Here, again, is a cause operating in like manner
with the refraction, but with an effect about half as great. (\textit{c})~The
almanac times are mean solar times of the rising and setting of the real
sun. This difference between true sun and fictitious sun also displaces
the times of sunrise and sunset, by the amount of the equation of time
(page~\pageref{p112}): at the vernal equinox the sun is six minutes slow; at the
autumnal equinox, eight minutes fast. All three effects when combined
at the vernal equinox, delay the sunset until long after six, and cause
the sun to rise at the autumnal equinox long before six.
\Restore

\textbf{Sunrise and Sunset in Different Latitudes.}\index{sunrise and sunset}---Compare
the almanac times of sunrise and sunset in different latitudes
on the same day. At the end of the third week
of March, the times of sunrise are practically the same,
no matter what the latitude. So are the sunset times.
Through April, May, and June, the farther north, the
earlier is sunrise and the later is sunset; the daytime is
longer, and the night-time shorter. This difference on
account of latitude increases until the third week in June;
then it slowly diminishes until sunrise and sunset again
occur at the same time regardless of latitude, at the end of
the third week in September.

\Smaller
Through the remaining half of the year, a change of latitude affects
the time of sunrise oppositely; also the time of sunset: the farther
north one goes, the later is sunrise, and the earlier is sunset. The
daytime is shorter, and the night-time longer. As the year wears on,
the latitude-difference of the times of both sunrise and sunset grows
greater, until about Christmas time; afterward it as gradually decreases
until the vernal equinox. Then, go north or south as far as one may
choose, the sun will rise at the same local time; and sunset will be
unaffected also.
\Restore

\textbf{The Midnight Sun.}\index{midnight sun}\index{sun!midnight}---The farther north one travels, the
higher the pole rises toward the zenith; consequently a
\DPPageSep{115.png}
latitude must after a while be reached where the midsummer
sun, at and near the solstice, just grazes the
% Fig 6.5
\begin{wrapfigure}{o}{0.4\textwidth}
  \centering
  \Input[0.3\textwidth]{page_106}
  \caption{Midsummer Sun at Midnight}
\end{wrapfigure}
north
horizon at midnight, and so does not set
at all. The daytime period, therefore, is
24 hours long, and night-time vanishes.
For the northern hemisphere, the northern
parallel of $66\frac{1}{2}$° is this latitude. The
change in the sun's daily path will be
apparent in referring to the illustration;
it shows how much shorter the sun's arc of
invisibility below the horizon grows, as one
travels north, from Washington to Paris,
Saint Petersburg, and Lapland. Midnight
sun is the popular name for the sun when
visible in midsummer at its lower culmination
underneath the pole of the heavens.
The entire period of 24~hours is all daytime, and there is
no night. It occurs in high northern latitudes in June;
and similarly in high southern latitudes in December, the
midsummer period of the southern hemisphere. The
northern extremity of the Scandinavian peninsula is known
as the `Land of the Midnight Sun,' because this weird and
unusual phenomenon has been most often observed from
that region.

\textbf{Length of Day at Different Latitudes.}\index{day!length of}---For all places
on the earth's equator there is never any inequality of day
and night. The farther we go from the equator, either
north or south, the greater this inequality, the longer
will be the days of summer, and the nights of winter.
Regarding the day geometrically as the interval of time
during which the center of the sun is above the sensible
horizon, it is easy to calculate the greatest length of the day
at any given latitude. The results are as follows and they
are true for latitudes either north or south of the equator:
\DPPageSep{116.png}
\begin{table}
\TableSize
\centering
\caption{\textsc{Maximum Length of Day at Different Latitudes}}
\begin{tabular}{r@{.}l|r@{~}l|c|c}
\hline\hline
  \multicolumn{2}{c|}{\multirow{2}{*}{\footnotesize\textsc{At Latitude}---}}
&amp; \multicolumn{2}{c|}{\footnotesize\textsc{Greatest Length}\rule{0pt}{4ex}}
&amp; \multicolumn{1}{c|}{\multirow{2}{*}{\footnotesize\textsc{\ At Latitude}---}}
&amp; \multicolumn{1}{c}{\footnotesize\textsc{Greatest Length}}\\
  \multicolumn{2}{c|}{}
&amp; \multicolumn{2}{c|}{\footnotesize\textsc{of Day is---}\rule[-2ex]{0pt}{3ex}}
&amp; \multicolumn{1}{c|}{}
&amp; \multicolumn{1}{c}{\footnotesize\textsc{of Day is---}}\\
\hline
\quad \quad 0°     &amp;0 &amp;\qquad \quad 12 &amp;h.&amp;             &amp; Months\rule{0pt}{4ex} \\
  30$\phantom{{}° }$&amp;8 &amp; 14 &amp;   &amp; 67°.4                   &amp; 1  \\
  49$\phantom{{}° }$&amp;0 &amp; 16 &amp;   &amp; 73$\phantom{{}° }$.7&amp; 3  \\
  58$\phantom{{}° }$&amp;5 &amp; 18 &amp;   &amp; 84$\phantom{{}° }$.1&amp; 5  \\
  63$\phantom{{}° }$&amp;4 &amp; 20 &amp;   &amp; 90$\phantom{{}° }$.0&amp; 6  \\
  65$\phantom{{}° }$&amp;8 &amp; 22 &amp;   &amp;                         &amp;    \\
  66$\phantom{{}° }$&amp;5 &amp; 24\rule[-2ex]{0pt}{3ex} &amp;   &amp;    &amp;    \\
\hline\hline
\end{tabular}
\end{table}

But these results are much modified by refraction of the
atmosphere. At the time of greatest length of day in the
northern hemisphere is occurring the greatest length of
night in the southern hemisphere.

\Smaller
\textbf{The Long Polar Night.}\index{night!long polar}---Ordinary notions of the six months of the
polar night need some correction. If the actual north pole were reached,
it is true that the sun would really be below the horizon very nearly
six months, that is from the 20th of September to the 20th of March,
while it is south of the equator; and imagining the earth to turn round
on its axis inside of this atmosphere shell, as in the figure on page~\pageref{p93}, it
is clear how twilight at the pole under B continues throughout the entire
24 hours, so long as the pole is inclined away from the sun. But
the duration of twilight, longer and longer as the pole is approached, is
a very important factor not to be neglected. Supposing twilight to last
till the sun is depressed 18° below the horizon, so long is the autumn
twilight that its continuance for $2\frac{1}{2}$~months would postpone the beginning
of deep night till about the 1st of December; while the spring
dawn, equally protracted, would begin early in January. Even at the
pole, then, true night with an absolutely dark sky would be only six or
seven weeks long. So much for the sun; and fortunately for the arctic
explorer, the moon helps wonderfully to alleviate this dreary period.
As the sun is so far south, the crescent moon at old and new, being
near it, will, like the sun itself, be below the polar horizon; but during
the fortnight from first quarter to last quarter, including the period of
its full phase, it will shine continually above the horizon. As the moon
must `full' at least twice during the $1\frac{1}{2}$~months when sunlight is wholly
withdrawn, the period of absolute night is reduced to about three weeks
\DPPageSep{117.png}
at the most. And even this will now and then be broken by brilliant
auroras, especially during years of prevalent sun spots. If one retreats
from the pole only 5°, or to latitude 85° north, it is quite possible that
the period of utter night may vanish entirely; and, of course, still farther
south, the number of hours of night illumined by neither sun nor
moon must usually be exceedingly few.
\Restore

\textbf{The Sidereal Day.}\index{day!sidereal}---As referred to a fixed star, the
period of rotation of the earth on its axis does not vary.
One such rotation is called a \textit{sidereal day}, or day as referred
to the stars. It is subdivided into 24 sidereal hours,
each hour into 60 sidereal minutes, and each minute into
60 sidereal seconds. Every observatory possesses a clock
regulated to keep this kind of time, and called a sidereal
clock. The hours of sidereal time are always counted
consecutively through the sidereal day from 0 to 24.

\label{p108}
\Smaller
Approximately in the meridian, as found from the sun by the method
on page~\pageref{p23}, suspend two plumb-lines from some rigid support which
does not obstruct the view south. Secure the lower ends of the plumb-lines
in the exact position where they come to rest, taking care to stretch
the lines taut. As soon as the stars are out, observe and record the
hour, minute, and second when some bright star is in line with both of
them. Its altitude should not exceed 60° above the south horizon.
Use the best clock or watch at hand. The next clear night, repeat the
observation on the same star; also on two succeeding evenings, setting
down the day, hour, minute, and second in each case, and taking care
that the running of the timepiece shall not be interfered with meanwhile,
nor the plumb-lines disturbed. On comparing these observations
it will be found that the star has been crossing the plumb-lines
about four minutes earlier each day. If the observations were to be
continued on subsequent days, we should find only the same result,
and so on indefinitely: the star would soon come to the lines in bright
twilight, and it could not be observed without a telescope. A few days
later it would cross at sunset, and it is easy to calculate that in about
three months it would cross at noon, star and sun culminating together.
By this simple method is established that cardinal element in
astronomy, the period of the earth's turning round on its axis. Astronomers
have, to be sure, much more accurate methods than this; and the
instruments employed by them are described and pictured in a later
chapter, but only the details vary, the principle remaining the same.
\Restore
\DPPageSep{118.png}

\textbf{Telling Time by the Stars.}\index{stars!telling time by}\index{time!telling by the stars}---Our next inquiry concerns
the point that corresponds to 0~hours, 0~minutes, 0~seconds;
that is, the beginning of the sidereal day. Having found
this, our timepiece
may be set to correspond;
and if regulated,
it will continue
to keep sidereal time.
As sidereal time sustains
a relation to the
sun which is all the
while varying, it is
clear that the sidereal
day may begin when
any star is crossing
the meridian; but it
is also clear that all
astronomers should
agree to begin the
sidereal day by one
and the same star, or
reference point. This is practically what they have
% Fig 6.6
\begin{wrapfigure}[20]{o}{0.6\textwidth}
  \centering
  \Input[0.55\textwidth]{page_109}
  \caption{Telling the Sidereal Time by Cassiopeia}
\end{wrapfigure}
done;
and the point selected is the vernal equinox, often called
`the First of Aries\index{Aries!first of},' or `the First point of Aries'; also
sometimes, `The Greenwich of the Sky.'

\Smaller
The equinoctial colure passes through it; and for all stars exactly
between the vernal equinox and either celestial pole, the right ascension
is zero, no matter what their declination may be. Fortunately there is
a bright star almost on this line, and only 32° from the north pole; so
it is always above the horizon in our country, except for an hour or
two each day, in some of the most southern states. This important
star is Beta Cassiopeiæ (page~\pageref{p66}). When it is crossing the upper meridian,
being as near as possible to the zenith, sidereal time is 0\,h.\:0\,m.\:0\,s.\
and a new sidereal day begins. The relation of this conspicuous star to
Polaris is shown in the above diagram. Surrounding both stars is
drawn a clock-hand which may be imagined as turning round with the
\DPPageSep{119.png}
stars once each day. Very little practice is necessary to enable one to
tell the sidereal time by the direction of this colossal clock-hand in the
northern sky; but one must never fail to notice that it moves oppositely
to the hour hand of an ordinary watch, and only half as fast. At 6\,h.\
it points toward the west horizon, and at 18\,h.\ toward the east point of
the horizon; not horizontally, as represented in the figure, but downward
in each case by a considerable angle varying with the latitude.
Subtracting the `sidereal time of mean noon' (page~\pageref{p122}), gives ordinary
or solar time. This operation is called `telling time by the stars'---a
method of course only approximate; but an error greater than 15
or 20 minutes will not often occur.
\Restore

\textbf{The Apparent Solar Day.}\index{day!apparent solar}\index{time!apparent}---It was shown (page~\pageref{p108}) how
to ascertain by observation that the sun seems to be continually
moving eastward among the stars. It was shown,
too, that sidereal noon (noon by the stars) comes at all
hours of the day and night during the progress of the
year. Plainly, then, sidereal time is not a fit standard for
regulating the affairs of ordinary life; for, while it would
answer very well for a fortnight or so, the displacement of
four minutes daily would in six months have all the world
breakfasting after sunset, staying awake all through the
night, and going to bed in the middle of the forenoon.
As the sun is the natural time-regulator of the engagements
and occupations of humanity, he is adopted as the
standard, although you will find by observing attentively
that his apparent motion is beset with serious irregularities.
Begin on any day of the year, and observe the sun's
transit of the meridian, as you did that of a star. The
instant when the sun's center is on the meridian is
known as apparent noon. If you repeat the observation
every day for a year, and then compare the intervals
between successive transits, you will find them varying
in length by many seconds, because they are all apparent
solar days; they will not all be equal, as in the case of
the star.

\textbf{The Mean Solar Day.}\index{day!mean solar}\index{time!mean}---By taking the average of all
\DPPageSep{120.png}
the intervals between the sun's transits, that is, the mean
of all apparent solar days in course of the year, an invariable
standard is obtained, like that from the stars themselves.
In effect, this is precisely what astronomers have
done, with great care and system; and for convenience,
they imagine an average, or mean, sun, called the \textit{fictitious
sun}\index{sun!fictitious}, which they accept as their standard, and then
calculate the difference between its position and that of
the real sun which they observe. The fictitious sun may
be defined as an imaginary point or star which travels
eastward round the celestial equator, not the ecliptic, at
a perfectly uniform rate, making the entire circuit of the
heavens in course of the year. It is easy to see that the
intervals between transits of the fictitious sun must all
be equal; and obviously, too, this interval is longer than
the sidereal day, for this reason: if a star and the fictitious
sun should cross the meridian together on one day,
then on the next day the star would come to the meridian
first, thereby making the sidereal day shorter than
the solar day. The instant when the center of the fictitious
sun is on the meridian is called mean noon\index{noon (mean)}. The
mean solar day, therefore, may be defined as the interval
between two adjacent transits of the fictitious sun over the
same meridian; or the mean of all the apparent solar
days of the year. It is divided into 24 mean solar hours,
each hour into 60 mean solar minutes, and each minute
into 60 mean solar seconds. This is the kind of hours,
minutes, and seconds kept by clocks and watches in common
use.

\textbf{Astronomical and Civil Day.}\index{day!astronomical}\index{day!civil}---The mean solar day is
often called the astronomical day, because it begins at
one mean noon and ends at the one next following. Its
hours are counted continuously from 0 to 24, without a
break at midnight. It is the day recognized by astronomers
\DPPageSep{121.png}
in observatory work and records, and by navigators in using
the Nautical Almanac\index{Almanac, Nautical}. The ordinary or civil day is exactly
the same in length as the astronomical day, but it
begins at the midnight preceding noon of a given astronomical
day, and ends at the next following midnight. As
every one knows, its hours are not usually counted continuously
from 0 to 24, but in two periods of 12 each. The
hours of its first period are \textit{ante meridiem}, that is, before
midday, or \AM, and the hours of its second period are
\textit{post meridiem}, that is, after midday, or \PM\ Therefore,
civil time, \PM, of a given date is just the same as the
astronomical time; if a date recorded in astronomical time
between midnight and noon is to be converted into civil
time, it is necessary to subtract 12 from the hours and add
1 to the days. For example:---
\begin{center}
\TableSize
\begin{tabular}{c@{\ }c@{\ }c}
  {\textsc{Civil Date}} &amp;
&amp; {\textsc{Astronomical}}
\\
  6 o'clock \PM, 10th November, 1899 &amp; =
&amp; 1899 November 10 d.\ \phantom{1}6 h.
\\
  3 o'clock \AM, 15th December, 1899 &amp; =
&amp; 1899 December 14 d.\ 15 h.
\end{tabular}
\end{center}
The astronomical date is always recorded in the order
here given---year, month, day, hour, minute, second.

\label{p112} \textbf{The Equation of Time.}\index{equation of time}---Ordinary clocks and watches
are regulated to run according to the average, or fictitious,
sun, which makes all the days of equal length; the sun
itself is sometimes ahead of this `fictitious sun,' and sometimes
behind it. This deviation is called the \textit{equation of
time}, and the explanation of it is given in the next chapter.
The equation of time on any day varies a few seconds
from year to year. It is given exactly in the Nautical
Almanac; but for many purposes the following table (for
1902) may be used for any year with sufficient accuracy.
In this table S means `sun slow' (that is, the center of
the real sun does not cross the meridian until after mean
noon), and F means `sun fast.'
\DPPageSep{122.png}
\begin{table}
\TableSize
\label{p113}
\centering
\caption{\textsc{The Equation of Time}}
\begin{tabular}{c| *{3}{rrr|} rrr}
\hline\hline
% ------------------------------------------------------
{\centering\footnotesize\textsc{Day of}}
&amp; \multicolumn{3}{c|}{\multirow{2}{*}{\footnotesize\textsc{January}}}
&amp; \multicolumn{3}{c|}{\multirow{2}{*}{\footnotesize\textsc{February}}}
&amp; \multicolumn{3}{c|}{\multirow{2}{*}{\footnotesize\textsc{March}}}
&amp; \multicolumn{3}{c} {\multirow{2}{*}{\footnotesize\textsc{April}}}\\[-4pt]
 {\centering\footnotesize\textsc{Month}} &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;
\\  \hline
&amp;&amp; {\footnotesize m.} &amp; {\footnotesize s.}\rule{0pt}{3ex}
&amp;&amp; {\footnotesize m.} &amp; {\footnotesize s.}
&amp;&amp; {\footnotesize m.} &amp; {\footnotesize s.}
&amp;&amp; {\footnotesize m.} &amp; {\footnotesize s.} \\
\phantom{0}1 &amp; S &amp;  3 &amp; 31 &amp; S &amp; 13 &amp; 44 &amp; S &amp; 12 &amp; 37
             &amp; S &amp;  4 &amp;  6 \\
\phantom{0}6 &amp; S &amp;  5 &amp; 49 &amp; S &amp; 14 &amp; 15 &amp; S &amp; 11 &amp; 33
             &amp; S &amp;  2 &amp; 37 \\
          11 &amp; S &amp;  7 &amp; 57 &amp; S &amp; 14 &amp; 27 &amp; S &amp; 10 &amp; 19
             &amp; S &amp;  1 &amp; 14 \\
          16 &amp; S &amp;  9 &amp; 49 &amp; S &amp; 14 &amp; 19 &amp; S &amp;  8 &amp; 57
             &amp; F &amp;  0 &amp;  4 \\
          21 &amp; S &amp; 11 &amp; 24 &amp; S &amp; 13 &amp; 52 &amp; S &amp;  7 &amp; 28
             &amp; F &amp;  1 &amp; 12 \\
          26 &amp; S &amp; 12 &amp; 39 &amp; S &amp; 13 &amp; 10 &amp; S &amp;  5 &amp; 56
             &amp; F &amp;  2 &amp; 10 \\
          31 &amp; S &amp; 13 &amp; 35 &amp; S &amp; 12 &amp; 13 &amp; S &amp;  4 &amp; 24
             &amp; F &amp;  2 &amp; 56 \\[2ex]
  \hline
% ------------------------------------------------------
 {\centering\footnotesize\textsc{Day of}}
&amp; \multicolumn{3}{c|}{\multirow{2}{*}{\footnotesize\textsc{May}}}
&amp; \multicolumn{3}{c}{\multirow{2}{*}{\footnotesize\textsc{June}}}
&amp; \multicolumn{3}{c|}{\multirow{2}{*}{\footnotesize\textsc{July}}}
&amp; \multicolumn{3}{c} {\multirow{2}{*}{\footnotesize\textsc{August}}} \\[-4pt]
 {\centering\footnotesize\textsc{Month}} &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;
\\  \hline
&amp;&amp; {\footnotesize m.} &amp; {\footnotesize s.}\rule{0pt}{3ex}
&amp;&amp; {\footnotesize m.} &amp; {\footnotesize s.}
&amp;&amp; {\footnotesize m.} &amp; {\footnotesize s.}
&amp;&amp; {\footnotesize m.} &amp; {\footnotesize s.} \\
\phantom{0}1 &amp; F &amp;  2 &amp; 56 &amp; F &amp;  2 &amp; 30 &amp; S &amp;  3 &amp; 28 &amp; S &amp;  6 &amp; 10 \\
\phantom{0}6 &amp; F &amp;  3 &amp; 27 &amp; F &amp;  1 &amp; 41 &amp; S &amp;  4 &amp; 24 &amp; S &amp;  5 &amp; 46 \\
          11 &amp; F &amp;  3 &amp; 45 &amp; F &amp;  0 &amp; 44 &amp; S &amp;  5 &amp; 11 &amp; S &amp;  5 &amp;  8 \\
          16 &amp; F &amp;  3 &amp; 48 &amp; S &amp;  0 &amp; 18 &amp; S &amp;  5 &amp; 46 &amp; S &amp;  4 &amp; 15 \\
          21 &amp; F &amp;  3 &amp; 38 &amp; S &amp;  1 &amp; 23 &amp; S &amp;  6 &amp;  9 &amp; S &amp;  3 &amp;  9 \\
          26 &amp; F &amp;  3 &amp; 15 &amp; S &amp;  2 &amp; 27 &amp; S &amp;  6 &amp; 18 &amp; S &amp;  1 &amp; 51 \\
          31 &amp; F &amp;  2 &amp; 39 &amp; S &amp;  3 &amp; 28 &amp; S &amp;  6 &amp; 12 &amp; S &amp;  0 &amp; 24 \\[2ex]
\hline
% ------------------------------------------------------
 {\centering\footnotesize\textsc{Day of}}
&amp; \multicolumn{3}{c|}{\multirow{2}{*}{\footnotesize\textsc{September}}}
&amp; \multicolumn{3}{c|}{\multirow{2}{*}{\footnotesize\textsc{October}}}
&amp; \multicolumn{3}{c|}{\multirow{2}{*}{\footnotesize\textsc{November}}}
&amp; \multicolumn{3}{c}{\multirow{2}{*}{\footnotesize\textsc{December}}} \\[-4pt]
 {\centering\footnotesize\textsc{Month}} &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;
\\  \hline
&amp;&amp; {\footnotesize m.} &amp; {\footnotesize s.}\rule{0pt}{3ex}
&amp;&amp; {\footnotesize m.} &amp; {\footnotesize s.}
&amp;&amp; {\footnotesize m.} &amp; {\footnotesize s.}
&amp;&amp; {\footnotesize m.} &amp; {\footnotesize s.}
\\
\phantom{0}1 &amp; S &amp;  0 &amp;  6
             &amp; F &amp; 10 &amp;  8 &amp; F &amp; 16 &amp; 18 &amp; F &amp; 11 &amp;  3
\\
\phantom{0}6 &amp; F &amp;  1 &amp; 31
             &amp; F &amp; 11 &amp; 41 &amp; F &amp; 16 &amp; 17 &amp; F &amp;  9 &amp;  3
\\
          11 &amp; F &amp;  3 &amp; 13
             &amp; F &amp; 13 &amp;  4 &amp; F &amp; 15 &amp; 56 &amp; F &amp;  6 &amp; 51
\\
          16 &amp; F &amp;  4 &amp; 58
             &amp; F &amp; 14 &amp; 16 &amp; F &amp; 15 &amp; 13 &amp; F &amp;  4 &amp; 30
\\
          21 &amp; F &amp;  6 &amp; 45
             &amp; F &amp; 15 &amp; 13 &amp; F &amp; 14 &amp; 10 &amp; F &amp;  2 &amp;  2
\\
          26 &amp; F &amp;  8 &amp; 29
             &amp; F &amp; 15 &amp; 54 &amp; F &amp; 12 &amp; 45 &amp; S &amp;  0 &amp; 28
\\
          31 &amp; F &amp; 10 &amp;  8
             &amp; F &amp; 16 &amp; 16 &amp; F &amp; 11 &amp;  3 &amp; S &amp;  2 &amp; 55
\\[2ex]  \hline\hline
\end{tabular}
\end{table}

\textbf{Retardation of Sunset near the Winter Solstice.}\index{sunrise and sunset}---About
Christmas time in our latitudes we may begin to look for
the lengthening of the day, which betokens the return of
spring. At first the increase is very slight, perhaps only
two or three minutes in the course of a week. And it
is commonly observed that the increase takes place in the
afternoon half of the day; that is, the sun sets later and
later each day, although its time of rising does not show
much change until the middle or latter part of January.
The reason of this is that sunrise and sunset are calculated
for the real sun; but the times themselves are mean times,
that is, time according to the fictitious sun. The real sun
\DPPageSep{123.png}
is fast about five minutes in the middle of December, so
that the afternoon is ten minutes shorter than the forenoon.
But the equation of time is diminishing rapidly;
that is, the real sun is moving eastward more rapidly than
the fictitious sun, and will soon coincide with it, making
the equation of time zero. On account of this eastward
motion of
% Fig 6.7
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.55\textwidth]{page_114}
  \caption{Antique Form of Clepsydra}
  \index{clep´sydra, ancient}
\end{wrapfigure}
the real sun, more rapidly than usual, its mean
time of setting is retarded
so much that the
effect begins to be apparent
as a lengthening
of the day, even before
the sun reaches the solstice.
After the solstice
is passed, the sun's declination
is less, and its
longer diurnal arc conspires
with the rapid
eastward movement of
the real sun; so that by
the end of December
both causes make the
sun set a minute later
each day. For a similar
reason, operating at the
summer solstice, the
forenoon half of the day
begins to shorten as
early as the middle of
June.

\textbf{Time Keepers of the Ancients.}\index{astronomy!history}\index{time!measurement of}---It is not known that the
ancients had any clocks similar to ours; but they measured
the lapse of time by clepsydras and sundials. Frequently
also the gnomon\index{gnomon}, or pointed pillar, was used.
\DPPageSep{124.png}

\Smaller
A clepsydra\index{clep´sydra, ancient}\index{time!measurement of} is a mechanical contrivance for measuring and indicating
time by means of the flow of water. The illustration shows a common
form. Water is supplied freely to the conical vessel, an overflow maintaining
always a given level, so that the pressure at bottom is constant.
Through a small aperture and pipe, the water drops into a
larger cylindrical vessel which fills very slowly. On the surface of the
water in it rests a float, attached to which is an upright ratchet rod.
Working into the teeth of this are the teeth of a cog wheel, and on the
same arbor with it is a single hand, which revolves round the dial and
marks the progress of the hours. With a contrivance of this sort, time
could be told within five or six minutes. The day of the ancients, that
is, the variable interval between sunrise and sunset, was always divided
into 12 hours; therefore the hours continually differed in length. By
changing the aperture at bottom of the conical vessel, the clepsydra
was regulated and made to keep pace with the variable hours.
\Restore

\textbf{Sundial Time.}\index{sundial}\index{time!sundial}\index{time!measurement of}---The time indicated by a sundial is
apparent solar time, and no ordinary clock can follow it,
except by accident. Previously to the nineteenth century,
however, the attempt was made to construct clocks with
such compensating devices that they would gain or lose,
as referred to the stars, just as the sun does. But variations
in the sun's apparent motion are so complex that
fine machinery necessary to follow the sun with precision
could scarcely be made, even at the present day. Certainly
its construction was impossible a century ago.

\Smaller
Early in the 19th century apparent-time clocks were generally abandoned,
although in Paris they were in use as late as 1815. Elaborate
sundials are still occasionally met with, but their purpose is ornamental
rather than useful. In a form of sundial easily constructed, a wire is
adjusted parallel to the earth's axis, and its shadow falling upon a
divided circular arc parallel to the equator tells the apparent time.
\Restore

% Fig 6.8
\begin{figure}[hbt!]
  \centering
  \Input{page_116}
  \caption{Finding True North without Clock or Telescope (from a Photograph by Lovell)}
  \label{p116}\index{Cassiopeia}%
  \index{Dipper}%
  \index{Ursa Major}%
  \index{Lovell, J. L., photographer}%
\end{figure}

\Smaller
\textbf{To find True North quite Accurately.}\index{north, finding true}---As a preliminary to the
arrangements for setting up any instrument in the meridian, or mounting
it, as the technical expression is, true north must first be found with
some accuracy. Select a window with a northern exposure, and a view
down nearly to the north (sensible) horizon. From the top casing of
the window, hang a long plumb-line, allowing the bob to swing freely
in a basin of water. Secure it where it comes to rest, stretching the
line taut. From a small table in the room hang another plumb-line in
a similar manner, using fine, light-colored cord or cotton for the lines.
\DPPageSep{125.png}
These arrangements should be made beforehand, as in the illustration.
The problem is to adjust the short line relatively to the long
one, so that the vertical plane passing through the two plumb-lines
shall pass also through the pole star when crossing the meridian. This
vertical plane will then itself be the meridian, and must therefore
intersect the horizon in the true north and south points. But we have
seen that the pole star, not being exactly at the north pole, describes
a very small circle of the celestial sphere once every 24 sidereal hours;
therefore it must cross the meridian twice during that period. The
intervals between these crossings will be nearly 12 ordinary hours. It
is not at all necessary to know the exact local or ordinary time when
\DPPageSep{126.png}
the pole star is at the meridian; but Polaris always comes into this
position whenever Mizar (Zeta Ursæ Majoris, the middle star in the
handle of the Dipper) is also on the meridian. So it is only requisite
to watch closely for the time when the long plumb-line passes through
both these stars; then, placing the eye near the floor, to move the
table carefully until the short plumb-line hangs in the same plane with
the long line and both stars. Be sure that the short plumb-line hangs
perfectly free and still. A candle placed behind the observer's head
will show both lines, and at the same time not obscure the stars. Then
by two permanent marks\index{meridian!mark} in the plane of the plumb-lines, establish the
meridian for convenient use. In line with Mizar and Polaris, and
about as far on the opposite side of the pole, there chances to be
another star, Delta Cassiopeiæ, which, therefore, can be used in the
same way as Mizar itself. Through nearly the entire year, either one
or the other of these stars is available for finding true north, without
any reference whatever to the clock.

\textbf{Times when Mizar and Delta Cassiopeiæ are on the lower Meridian.}\index{Mizar, star in Ursa Major}---Begin
watching before the lower star comes to the meridian.
It will then appear to the left of the long plumb-line hanging through
Polaris. Table~\ref{table6.3} shows when to begin to watch.
% Table 6.3
\begin{table}[hbt]
\centering
\caption{}
\label{table6.3}
\begin{tabular}{c l@{ }lr@{ }l c l@{ }lr@{ }l}
\multicolumn{5}{c}{\textsc{For $\delta$ Cassiopeiæ}} &amp;&amp; \multicolumn{4}{c}{\textsc{For Mizar}} \\
&amp; Dec. &amp; 20 &amp;  7 &amp; \AM &amp;\rule{2em}{0pt}&amp; July &amp; 20 &amp;  5 &amp; \AM \\
&amp; Jan. &amp; 20 &amp;  5 &amp; \AM &amp;&amp; Aug. &amp; 20 &amp;  3 &amp; \AM \\
&amp; Feb. &amp; 20 &amp;  3 &amp; \AM &amp;&amp; Sept.&amp; 20 &amp;  1 &amp; \AM \\
&amp; Mar. &amp; 20 &amp;  1 &amp; \AM &amp;&amp; Oct. &amp; 20 &amp; 11 &amp; \PM \\
&amp; Apr. &amp; 20 &amp; 11 &amp; \PM &amp;&amp; Nov. &amp; 20 &amp;  9 &amp; \PM \\
&amp; May  &amp; 20 &amp;  9 &amp; \PM &amp;&amp; Dec. &amp; 20 &amp;  7 &amp; \PM \\
&amp; June &amp; 20 &amp;  7 &amp; \PM &amp;&amp; Jan. &amp; 20 &amp;  5 &amp; \PM
\end{tabular}
\end{table}

Both stars come about four minutes earlier every day, just as the
south star did. During a part of June and July this method cannot be
used, because it is strong twilight or daylight when Mizar and Delta
Cassiopeiæ are crossing the meridian. If repeated on a subsequent
night, this method of establishing the local meridian will be found
sufficiently accurate for mounting any astronomical instrument. Its
adjusting screws will then bring it into closer range, when the telescope
can be brought into service to show the amount of deviation. If no
telescope is available, a transit instrument may be made of a few common
materials, and the local time found by it approximately.

\textbf{A Rudimentary Transit Instrument.}\index{transit instrument!rudimentary}---The methods astronomers
use in finding accurate time will be sketched in outline in Chapter \textsc{ix}.
We here describe a method of getting the time within a few seconds by
\DPPageSep{127.png}
an observation of the sun. In the open air, or in a south window
with a clear meridian from the south nearly up to the zenith, hang
two fine plumb-lines accurately in the meridian by the method just
given. In line with them, firmly attach a strong box (about 18~inches
square) to the window casing, as shown in the illustration; or better,
to the east or west side of a building. By sighting along the plumb-lines,
run a pencil mark round the outside of the box, to indicate the
meridian roughly. Bore two $\tfrac{3}{4}$-inch holes in this mark, at points $A$ and
$B$. Also bore a third in the same plane near the middle of the upper
face of the box. Over this lay a strip of sheet lead or tin, with a smooth
pin hole through it, tacking it carefully so that the pin hole shall be in the
plane of both plumb-lines. By sighting past these lines and through
the holes $A$ and $B$, draw a fine straight pencil mark on the inside of the
lower face of the box, as shown, exactly in the plane of the plumb-lines.
If the box is exposed to the weather, this transit line may be scratched
on a strip of tin, which may then be tacked in position by sighting
through the holes. $A$ and $B$.

% Fig 6.9
\begin{figure}[hbt!]
  \centering
  \Input{page_118}
  \caption{Observing the Time of Apparent Noon with the Box-transit}
  \index{box-transit}
\end{figure}

If star transits are to be observed in the open, a different arrangement
of the meridian plane is necessary. Connect together the two
ends of a fine brass or copper wire about 20~feet long; pass it over two
points in the meridian about 6~feet apart (north one perhaps two feet
\DPPageSep{128.png}
above the south one); hook a heavy weight on the wire underneath,
and when it stops swinging, fasten the double wire firmly. Bright
stars at all meridian altitudes can be observed to cross this `triangle
transit,'\index{transit, triangle} with an error of only a few seconds. Comparison with a list
of their right ascensions will then give the sidereal time.

\textbf{Observing the Sun's Transit.}---Just before noon, a small round spot
of light will be seen to the west of the inside mark. It is an image of
the sun itself, about $\frac{3}{16}$ inch in diameter; and it will be pretty sharply
defined if the pin hole is smooth and round. The extreme positions of
the image at the solstices are shown in the illustration. Watch the
image as it slowly creeps toward the transit line; observe the time
with a watch when its edge first touches the line: there will be an uncertainty
of perhaps five seconds. Rather more than a minute later the
image will be bisected by the line; observe this time also, likewise observe
the time when the following edge or limb of the sun becomes tangent
to the line. Take the average of the three; add or subtract the
equation of time, as given in the table on page~\pageref{p113}. The result will be
local mean time, within a small fraction of a minute, provided the
plumb-lines have been delicately adjusted in the meridian, and the geometric
constructions of the transit box have been carefully made. A
farther and constant correction will be required when the watch keeps
standard time: if the place of observation is east of the standard meridian,
add the amount of this difference of longitude in time; if to the
west of it, subtract this difference.

\textbf{Calculating the Sun's Transit.}---On the 17th of February, 1906, at
Amherst, Massachusetts ($2° \ 28'\ 50''$ = 9~m.\ 55~s.\ east of the standard
meridian), the following times of transit were observed with the watch:---
\begin{center}
\begin{tabular}{l@{\hspace{5em}}l@{} rrr@{\,}c@{\,}p{3.8cm}}
&amp;&amp; h. &amp; m. &amp; s. &amp;\\
\multicolumn{2}{l}{First limb of \astrosun\ tangent,}
&amp; 12 &amp;  4&amp;  8 &amp;\\
\multicolumn{2}{l}{Sun bisected,}
&amp; 12 &amp;  5 &amp; 25 &amp;\\
\multicolumn{2}{l}{Second limb of \astrosun\ tangent,}
&amp; 12 &amp;  6 &amp; 33\\
\cline{3-5}
&amp; Mean,
&amp; 12 &amp;  5 &amp; 22 &amp; \ = &amp; watch time of apparent noon.\\
\multicolumn{2}{l}{Because sun is slow, subtract}
&amp;    &amp; 14 &amp; 14 &amp; \ = &amp; equation of time.\\
\cline{3-5}
&amp; Difference, &amp; 11 &amp; 51 &amp;  8 &amp; \ = &amp; watch time of Amherst mean noon.\\
\multicolumn{2}{l}{Add for longitude,}
&amp;   &amp;  9 &amp; 55 &amp; \ = &amp; east of Eastern Standard meridian.\\
\cline{3-5}
&amp; Sum, &amp; 12 &amp;  1 &amp;  3 &amp; \ = &amp; watch time of noon at standard meridian.\\
&amp;&amp; 12 &amp;  0 &amp;  0 &amp;\\
\cline{3-5}
&amp; Difference, &amp;  &amp;  1 &amp;  3 &amp; \ = &amp; watch fast of standard time.\\
\end{tabular}
\end{center}
\Restore

\textbf{How Observatory Time is found.}\index{time!observatory}---Recall the method of
counting right ascensions of the heavenly bodies---eastward
along the celestial equator from the vernal equinox
to the hour circle of the body, counting from 0~h.\ round
\DPPageSep{129.png}
to 24~h. Sidereal time, as has just been shown, elapses in
precisely the same way---from 0\,h.\:0\,m.\:0\,s.\ when the vernal
equinox is crossing the meridian, round to 24\,h.\:0\,m.\:0\,s.,
when it is next on the meridian. Clearly, then, any star is
on the meridian when the sidereal time is equal to its right
ascension. But the right ascensions of all the brighter stars
have been determined by the labor of astronomers in the
past, and are set down in the \textit{Ephemeris}\index{Ephemeris} and in star catalogues.
Also the same is given for sun, moon, and planets.
Therefore, in practice, it is the converse of this relation
which concerns us in the problem of finding the time by
observing the transit of a heavenly body. Simply observe
the time of its transit by the sidereal clock: if this time is
the same as the body's right ascension, the clock has no
error. If, as nearly always happens, the time of transit
differs from the right ascension, this difference is the correction
of the clock; that is, the amount by which it is fast
or slow. Once the correction of the sidereal clock is
found, the error of any other timepiece is ascertained
from comparison with it. In observatories the mean solar
time is rarely found by direct observation; but it is customary
to compare the mean-time clock with the sidereal
clock, and then calculate the corresponding mean time by
using the `sidereal time of mean noon.'


\textbf{Relation between Sidereal and Solar Time.}\index{time!sidereal and solar}---This relation
has been found by astronomers with the utmost precision,
and the quantities
% Fig 6.10
\begin{wrapfigure}[41]{o}{0.35\textwidth}
  \centering
  \Input[0.35\textwidth]{page_121}
%  \caption{Relation of Sidereal to Solar Time throughout an Entire Year}
\end{wrapfigure}
concerned in it are constantly used
by them in ascertaining accurate time. The true relation
is this: First, find how far the fictitious sun travels eastward
in one day. As it goes all the way round the celestial
equator (360°) in one year, or $365\tfrac{1}{4}$~days, evidently in
one day it travels nearly a whole degree ($59'\,8''.33$, accurately).
This angle, as we shall see in the next chapter,
is nearly twice the apparent breadth of the sun. Now during
\DPPageSep{130.png}
 a sidereal day an arc of 360°,
or the entire equator of the heavens,
passes the meridian of any given
place. Therefore in a mean solar
day, an arc of the equator equal to
nearly 361° (accurately 360° $59'\, 8''.33$)
must pass the same meridian. From
this relation we can calculate by
simple proportion that \\
{\small
24 mean solar hours \\
\null\qquad = 24\,h.\:4\,m.\ sidereal time \\
\null\quad\qquad (accurately, 24\,h.\:3\,m.\:56.555\,s.), \\
and 24 sidereal hours \\
\null\qquad = 23\,h.\:56\,m.\ mean solar time \\
\null\quad\qquad (accurately, 23\,h.\:56\,m.\:4.091\,s.).} \\
But we saw that the sidereal day of
24 sidereal hours is the true period
of rotation on its axis. One must,
therefore, guard against saying that
the period of the earth's rotation on
its axis is 24~hours, unless specifying
that sidereal hours are meant. By
the term \textit{hour}, as ordinarily used
without qualification, the mean solar
hour is understood. So that the
true period in which the earth turns
once on its axis is, not 24~hours, but
23\,h.\:56\,m.\:4.09\,s.

\textbf{The Sidereal Time of Mean Noon.}\index{mean noon|see{noon (mean)}}\index{noon (mean)!sidereal time of}\index{sidereal time of mean noon}---At
every working observatory are
two clocks, the one keeping sidereal
time, the other mean solar time. Let
us imagine both regulated to run
perfectly. About the 20th March,
at mean noon, when the fictitious
\DPPageSep{131.png}
sun crosses the equinoctial colure, start both clocks at 0~h.,
0~minutes, 0~seconds, indicated by both dials. At the
next mean noon, the mean-time clock will have come
round to 0\,h.\:0\,m.\:0\,s.\ again, marking the beginning of
a new astronomical day; but the sidereal clock will
indicate at the same instant 0\,h.\:3\,m.\:56.55\,s., because it
has gained this difference during the 24~hours. At mean
noon the next following day the sidereal clock will indicate
0\,h.\:7\,m.\:53.11\,s.; and so on, perpetually gaining nearly
4\,m.\ every day. The figure just given makes this relation
plain for a complete cycle of a year. The time, then,
% Table 6.4
\begin{table}[hbt]
\TableSize
\centering
\caption{\textsc{Table for finding the Sidereal Time of Mean Noon}}
\label{p122}
\begin{tabular}{lr| D{!}{\quad}{-1}@{\quad}| lr| D{!}{\quad}{-1}@{\quad}}
\hline\hline
\multicolumn{2}{m{7em}|}{\centering\footnotesize\textsc{To the Mean Time on------}}
&amp; \multicolumn{1}{m{6em}|}{\centering\footnotesize\textsc{%
\rule{0pt}{4ex}Add the Following Quantity\rule[-3ex]{0pt}{2ex}}}
&amp; \multicolumn{2}{m{7em}|}{\centering\footnotesize\textsc{To the Mean Time on------}}
&amp; \multicolumn{1}{m{6em}}{\centering\footnotesize\textsc{Add the Following Quantity}}
\\
\hline
\rule{0pt}{3ex} &amp; &amp; \text{h.} ! \text{m.}
&amp;               &amp; &amp; \text{h.} ! \text{m.}  \\
  January  &amp;  1 &amp; 18 ! 45 &amp; July      &amp;  1 &amp;  6 ! 40  \\
           &amp; 15 &amp; 19 ! 40 &amp;           &amp; 15 &amp;  7 ! 35  \\
  February &amp;  1 &amp; 20 ! 45 &amp; August    &amp;  1 &amp;  8 ! 40  \\
           &amp; 15 &amp; 21 ! 40 &amp;           &amp; 15 &amp;  9 ! 40  \\
  March    &amp;  1 &amp; 22 ! 40 &amp; September &amp;  1 &amp; 10 ! 45  \\
           &amp; 15 &amp; 23 ! 35 &amp;           &amp; 15 &amp; 11 ! 40  \\
  April    &amp;  1 &amp;  0 ! 40 &amp; October   &amp;  1 &amp; 12 ! 45  \\
           &amp; 15 &amp;  1 ! 35 &amp;           &amp; 15 &amp; 13 ! 40  \\
  May      &amp;  1 &amp;  2 ! 40 &amp; November  &amp;  1 &amp; 14 ! 45  \\
           &amp; 15 &amp;  3 ! 35 &amp;           &amp; 15 &amp; 15 ! 40  \\
  June     &amp;  1 &amp;  4 ! 40 &amp; December  &amp;  1 &amp; 16 ! 45  \\
           &amp; 15 &amp;  5 ! 40 &amp;           &amp; 15 &amp; 17 ! 40  \\
  July\rule[-2ex]{0pt}{2ex}
           &amp;  1 &amp;  6 ! 40 &amp; January   &amp;  1 &amp; 18 ! 45  \\
\hline\hline
\end{tabular}
\end{table}
shown (at each mean noon) by a sidereal clock perfectly
adjusted, is called the `sidereal time of mean noon.'\footnote
  {An approximate value is easily found by the above table: if the given
  day is not the 1st or the 15th, find the proper additive quantity by applying 4
  minutes for each day before or after the nearest day given in the table.}
But
\DPPageSep{132.png}
as no clock can be made to carry on the time with absolute
accuracy, these times are, in practice, not taken from a
clock, but they are calculated and published in the \textit{Ephemeris}\index{Ephemeris},
a set of astronomical tables issued by the Government
two or three years in advance. As the sidereal times
of all the mean noons through the year are absolutely
accurate for all places on the prime meridian, they can be
adapted to any place by simply applying a constant correction
dependent on its longitude. Clearly it is necessary
to know the sidereal time of mean noon, if we desire to
compare mean time with sidereal time at any instant; and
this calculation of one kind of time from the other is the
most frequent problem of the practical astronomer. It can
be made in a minute or two, and is accurate to the $\frac{1}{100}$ part
of a second.

\textbf{Ascertaining Longitude.}---Longitude is angular distance\index{longitude!defined}
measured on the earth's equator from a prime meridian to
the meridian of the place. In England the prime meridian\index{Greenwich!meridian of}
prime meridian of France passes through the Paris Observatory\index{Paris!Observatory},
and the prime meridian of the United States
passes through the Observatory at Washington\index{Washington!meridian of}. Longitude
is given in either arc or time. As the earth by turning
round uniformly on its axis affords our measure of time,
the meridians of the globe must pass uniformly underneath
the stars; so that finding the longitude of a place is the
same thing as finding how much its local time is fast or
slow of the local time of the prime meridian.

\Smaller
Transit instruments are mounted and carefully adjusted at the two
places whose difference of longitude is sought. By a series of observations
(usually of transits of stars), local sidereal time at each place
is ascertained. Then time at both stations is automatically compared
by means of the electric telegraph\index{longitude!(terrestrial) ascertaining by telegraph}, and the difference of their
times is the difference of their longitudes, expressed in time. The place
at which the time is faster is the farther east. If there is no telegraph
\DPPageSep{133.png}
line or cable connecting the two stations, indirect and much less accurate
methods of comparing their local times must be resorted to. So
precise is the telegraphic method that the distance of Washington from
Greenwich is known with an error probably not exceeding 300 feet on
the surface of the globe; and where only land lines are employed, the
distance of one place from another may be found even more accurately.
Usually the time will be determined and signals exchanged on a series
of six or eight nights; and the entire operation of finding the longitude
is called a longitude campaign.
\Restore

\textbf{Standard Time.}\index{time!standard}---Formerly, in traveling even a few
miles, one was subjected to the annoyance of changing
one's watch to the local time of the place visited. The
actual difference between Boston and New York is 12
minutes---between New York and Washington 12 minutes;
and until within a few years each place kept only its
own local time. But it was decided to establish a standard
of time by which railroad trains should run and all ordinary
affairs be regulated; and in November of 1883 this plan
was adopted by the country at large, and time signals from
Washington are now distributed throughout the United
States every day at noon. The whole country is divided
into four sections, or meridian belts, approximately 15
degrees of longitude in width, so that each varies from
those adjacent to it by exactly an hour. The time in the
whole `Eastern' section is that of the 75th meridian from
Greenwich, making it five hours slower than Greenwich
time. This `Eastern' standard time coincides almost
exactly with the local time of Utica and Philadelphia, and
extends to Buffalo. Beyond that, watches are set one hour
earlier, and the `Central' section begins, just six hours
slower than Greenwich time, employing 90th meridian
time, which is almost exactly the local time at Saint Louis.
This division extends to the center of Dakota, and includes
Texas. `Mountain' or 105th meridian time is yet
another hour earlier, seven hours slower than Greenwich,
\DPPageSep{134.png}
and is nearly Denver local time. It extends to Ogden,
Utah; and the `Pacific' section, using 120th meridian
time, is eight hours behind Greenwich, and ten minutes
faster than local time at San Francisco.

\Smaller
This simplifies all horological matters greatly, especially the running
of trains on the great railroads. While theoretically equal, these
divisions are by no means so in reality, because variation is made from
the straight line, in order to run each railroad system through on the
same time, or make the change at great junctions. The cities just at
the changing points may use either, and they make their own choice,
Buffalo, for instance, choosing Eastern time, though Central would
have been equally appropriate; and Ogden choosing Mountain instead
of Pacific. Wherever standard time is kept, the minute and second
hands of all timepieces are the same. Only the hours differ. In
journeying from one meridian belt into the next, it is only necessary to
change one's watch by an entire hour, setting it ahead an hour if
traveling eastward, and turning it back an hour when journeying west.
In this country, accurate time is distributed\index{time!distribution of} by time-balls\index{time-ball}, dropped
at Boston, New York, Washington, and elsewhere, and by self-winding
clocks controlled through the circuits of the Western Union Telegraph
Company. The New York time ball is illustrated on page~\pageref{p9}.
\Restore

\textbf{Standard Time in Foreign Countries.}\index{time!standard}---Within very recent
years, the adoption of standard time has become
nearly universal among the leading governments of the
world. Almost without exception, the standard meridians
adopted are a whole number of hours from the
prime meridian of Greenwich, and local time in different
parts of the world, corresponding to Greenwich noon, is
shown in the Mercator map (page~\pageref{p127}). In a few instances,
where a country lies almost wholly between two
such meridians, its accepted standard of time is referred
to the half-hour meridian between the two. In some
European cities, particularly London and Paris, accurate
time is distributed automatically from a standard clock at
a central station, or observatory. The more important
foreign countries where standard time is used, with their
adopted standards, %are as follows:---
Table~\ref{p126}.
\DPPageSep{135.png}
\begin{table}[htb]
\TableSize
\caption{\textsc{Standard Time in Foreign Countries}}
\label{p126}
\centering
\begin{tabular}{l| r@{ }r | r@{ }r@{ }r }
\hline\hline
&amp;&amp;&amp;&amp;&amp; \\
\multicolumn{1}{m{6em}|}{\centering\footnotesize\textsc{Country}}
    &amp; \multicolumn{2}{m{9em}|}{\centering\footnotesize\textsc{Standard Meridian East of Greenwich}}
    &amp; \multicolumn{3}{m{7em} }{\centering\footnotesize\textsc{Time Fast~of Greenwich}} \\[2ex]
\hline
                       &amp;                         &amp;  &amp; \footnotesize h.&amp; \footnotesize m.&amp; \footnotesize s. \\
England       \dotfill &amp; \hspace{12ex} $  0$°  &amp; $ 0'$        &amp; \hspace{7ex} 0 &amp;  0 &amp;  0 \\
Scotland      \dotfill &amp; $  0\phantom{° }$   &amp; $ 0\phantom{'}$ &amp;  0     &amp;  0 &amp;  0 \\
Belgium       \dotfill &amp; $  0\phantom{° }$   &amp; $ 0\phantom{'}$ &amp;  0     &amp;  0 &amp;  0 \\
Holland       \dotfill &amp; $  0\phantom{° }$   &amp; $ 0\phantom{'}$ &amp;  0     &amp;  0 &amp;  0 \\
Spain         \dotfill &amp; $  0\phantom{° }$   &amp; $ 0\phantom{'}$ &amp;  0     &amp;  0 &amp;  0 \\
France        \dotfill &amp; $  2\phantom{° }$   &amp; $20\phantom{'}$ &amp;  0     &amp;  9 &amp; 21 \\
Mid.~Europe   \dotfill &amp; $ 15\phantom{° }$   &amp; $ 0\phantom{'}$ &amp;  1     &amp;  0 &amp;  0 \\
East.~Europe  \dotfill &amp; $ 30\phantom{° }$   &amp; $ 0\phantom{'}$ &amp;  2     &amp;  0 &amp;  0 \\
Egypt         \dotfill &amp; $ 30\phantom{° }$   &amp; $ 0\phantom{'}$ &amp;  2     &amp;  0 &amp;  0 \\
South Africa  \dotfill &amp; $ 30\phantom{° }$   &amp; $ 0\phantom{'}$ &amp;  2     &amp;  0 &amp;  0 \\
Russia        \dotfill &amp; $ 30\phantom{° }$   &amp; $ 0\phantom{'}$ &amp;  2     &amp;  0 &amp;  0 \\
Turkey        \dotfill &amp; $ 30\phantom{° }$   &amp; $ 0\phantom{'}$ &amp;  2     &amp;  0 &amp;  0 \\
India         \dotfill &amp; $ 82\phantom{° }$   &amp; $30\phantom{'}$ &amp;  5     &amp; 30 &amp;  0 \\
Burma         \dotfill &amp; $ 97\phantom{° }$   &amp; $30\phantom{'}$ &amp;  6     &amp; 30 &amp;  0 \\
Philippines   \dotfill &amp; $120\phantom{° }$   &amp; $ 0\phantom{'}$ &amp;  8     &amp;  0 \\
W. Australia  \dotfill &amp; $120\phantom{° }$   &amp; $ 0\phantom{'}$ &amp;  8     &amp;  0 \\
Japan         \dotfill &amp; $135\phantom{° }$   &amp; $ 0\phantom{'}$ &amp;  9     &amp;  0 \\
So.~Australia \dotfill &amp; $142\phantom{° }$   &amp; $30\phantom{'}$ &amp;  9     &amp; 30 \\
Victoria      \dotfill &amp; $150\phantom{° }$   &amp; $ 0\phantom{'}$ &amp; 10     &amp;  0 \\
New So.~Wales \dotfill &amp; $150\phantom{° }$   &amp; $ 0\phantom{'}$ &amp; 10     &amp;  0 \\
Queensland    \dotfill &amp; $150\phantom{° }$   &amp; $ 0\phantom{'}$ &amp; 10     &amp;  0 \\
Tasmania      \dotfill &amp; $150\phantom{° }$   &amp; $ 0\phantom{'}$ &amp; 10     &amp;  0 \\
New Zealand   \dotfill &amp; $172\phantom{° }$   &amp; $30\phantom{'}$ &amp; 11     &amp; 30 \\
Hawaii        \dotfill &amp; *$-157\phantom{° }$ &amp; $30\phantom{'}$ &amp; *$-10$ &amp; 30 \\
Panama        \dotfill &amp; *$-\phantom{1}75\phantom{° }$ &amp; $0\phantom{'}$ &amp; *$-\phantom{1}5$&amp;  0 \\
Peru         \dotfill  &amp; *$-\phantom{1}75\phantom{° }$ &amp; $0\phantom{'}$ &amp; *$-\phantom{1}5$&amp;  0 \\
Chile        \dotfill  &amp; *$-\phantom{1}75\phantom{° }$ &amp; $0\phantom{'}$ &amp; *$-\phantom{1}5$&amp;  0 \\
&amp; \multicolumn{2}{c|}{\footnotesize *west. }
&amp; \multicolumn{3}{c}{\footnotesize *slow. } \\
\hline\hline
\end{tabular}
\end{table}

\Smaller
Travelers in these countries, therefore, have only to set their watches
according to these differences of time. Italy and Spain have abolished
\AM\ and \PM\ and count the hours from midnight to midnight consecutively
from 0 to 24.
\Restore

\textbf{Uniformity of the Earth's Rotation.}\index{earth!uniformity of rotation}---It is now clear
that the turning of the earth on its axis is of very great
service, not only to the astronomer in making his investigations,
but to mankind in general, as affording a very
convenient means of measuring time. Everything is based
on the absolute uniformity of this rotation. Reliance is---indeed,
must be---implicit. Yet it is possible to test this
important element by comparing it with known movements
of other bodies in the sky, particularly the moon,
the earth, and the planet Mercury round the sun. The
deviations, if any, are nearly inappreciable; and the slight
slackening of its rotation at one period seems to be counterbalanced
\DPPageSep{136.png}
\begin{sidewaysfigure}[p!]
  \centering
  \Input[1.1\textwidth]{page_127}
  \caption{Time all over the World when it is Noon at Greenwich}
  \label{p127}\index{time!all over the world}
\end{sidewaysfigure}%
\DPPageSep{137.png}
by an equal acceleration at another. So that
if irregularities actually do exist, they probably cancel each
other in the long run, and leave the day invariable in
length. Uniformity of the earth's rotation has been critically
investigated
by Newcomb\index{Newcomb, S. (1835--1909), Am.\ ast.}, and
no change in
the length of the
day as great as
$\frac{1}{1000}$ of a second
in a thousand years
could escape detection.

\textbf{Precession of the
Equinoxes.}\index{equinoxes!precession}\index{precession}---The
equinoxes have a
slow motion\index{equinoxes!motion of}, partly
produced by the
earth's turning on
its axis. The ecliptic
remains
% Fig 6.12
\begin{wrapfigure}[25]{o}{0.6\textwidth}
  \centering
  \Input[0.55\textwidth]{page_128}
  \caption{A Model to illustrate Precession}
  \index{precession!model to illustrate}
\end{wrapfigure}
invariable
in position
and equator and
ecliptic are always
inclined to each
other at practically
the same angle; but this motion of the equinoxes is a gliding
of equator round ecliptic, and is called \textit{precession}. The
equinoxes travel westward about $50\frac{1}{4}''$ annually; so that
in rather less than 13,000 years, the vernal equinox will
have slipped round to the position formerly occupied by
the autumnal equinox. In 25,900 years precession completes
an entire cycle, both equinoxes returning to their
position at the beginning of it.
\DPPageSep{138.png}

\Smaller
Precession is so important in astronomy that the phenomenon
should be perfectly understood. Over a tub nearly filled with water,
suspend a barrel hoop by three cords, two of which, equal in length,
are attached to the hoop at the extremities of a diameter. The third
cord, a few inches shorter than the other two, is tied to the hoop midway
between them. Fasten three weights of about one pound each at
the same points. Gather the three cords together into one, at a few
feet above the hoop, and tie them to a right-hand-twisted cord a few
feet long. To represent the earth, with axis perpendicular to the hoop,
secure any common spherical object in the center of the hoop, by a
crosspiece nailed to hoop as indicated. Suspend the whole by the
twisted cord as shown in the picture, lowering it until the hoop is immersed
to the knots of the two long cords. These represent the
equinoxes, the hoop itself the celestial equator, and the surface of water
in the tub stands for plane of ecliptic. Adjust the shorter cord so that
the hoop shall be tilted to the water about $23\frac{1}{2}$°. Now release the hoop,
and it will twirl round clockwise; the motion of the two opposite knots
will correspond to precession of the equinoxes, and represent the long
period of precession, 25,900 years in duration. This motion of the
signs of the zodiac (in the direction Aries, Pisces, Aquarius), is represented
by the arrow in the illustration on page~\pageref{p65}. Pole of ecliptic is
\textit{E}, and round it as a center moves \textit{P}, the earth's pole, in a small circle,
\textit{PpSV}, 47° in diameter.
\Restore

\textbf{Effects of Precession.}\index{astronomy!history}\index{precession!effects of}---On account of precession, right
ascensions and
declinations of stars (being referred to the
equator as a fundamental plane)
are continually changing.
Precession of
the equinoxes
was first found
% Fig 6.13
\begin{wrapfigure}{o}{0.55\textwidth}
  \centering
  \Input[0.55\textwidth]{page_129}
  \caption{Vernal Equinox in Taurus (\BC~2200)}
  \index{Pleiades (ple´ya-deez)}\index{equinoxes!position of}
\end{wrapfigure}
out by Hipparchus\index{Hipparchus (\BC~140), Gk.\ ast.}
(\BC~150).
About \BC~2200,
the vernal equinox
was near
the Pleiades as
in the adjacent figure. Since that time it has traveled
back, or westward, about 60°, through Aries, until now it is
in the western part of Pisces, as \vpageref{p130}. So
\DPPageSep{139.png}
the signs of the zodiac do not now correspond with constellations
which bear the same names, as they did in the
time of Hipparchus; and the two systems are becoming
more and more separated as time elapses. Because the
direction of earth's axis in space is changing\index{earth!axis moving in space}, the north
celestial pole is slowly
moving among the
stars, in a small circle
whose center is the
north pole of the ecliptic;
and it will complete
its circle in the period of
precession itself. That
important star Polaris, our present north star because now
so near the intersection of earth's axis prolonged northward
to the sky, has not always been the pole star in the
past, nor will it always be in the future. If circumpolar
stars were photographed in trails, as on page~\pageref{p33}, at intervals
of a few hundred years, the curvature of arcs traversed
by a given star would change from time\break
\vspace{-\baselineskip}
%[** TN: Hack to place two wrapfigures in one paragraph

\noindent to time. About
200 years hence, the true north pole will be slightly
nearer
% Fig 6.14
\begin{wrapfigure}[11]{o}{0.55\textwidth}
  \centering
  \Input[0.55\textwidth]{page_130}
  \caption{Vernal Equinox now in Pisces}
  \index{equinoxes!position of}
  \label{p130}
\end{wrapfigure}
Polaris than it now is, and afterward the pole will
retreat from it. About \BC~3000, Alpha Draconis\index{Draconis, Alpha} was the
pole star; and 12,000 years hence, Vega\index{Vega} (Alpha Lyræ)
will enjoy that distinction. Regarding positions of stars
as referred to the ecliptic system, their latitudes\index{latitude (celestial)!precession does not effect} cannot
change, because ecliptic itself is fixed. But longitudes\index{longitude!of stars changes by precession} of
stars must change, much as right ascensions do, because
counted from the moving vernal equinox. Besides rotation
about its axis, the earth has another motion of prime
importance, which we shall now discuss.
\DPPageSep{140.png}


\Chapter{VII}{The Earth Revolves Round the Sun}\index{earth!revolves around the sun}

Hitherto\index{astronomy!history} explanation has been given only of that
apparent motion of the heavenly bodies which is
common to all---a rising in the east, crossing the
meridian, and setting in the west. Although this motion
was regarded as real in the ancient systems of astronomy,
we have seen that it is satisfactorily explained as a purely
apparent motion, due to the simple turning round of the
earth on its axis once each day. Now we shall consider
an entirely different class of celestial motions; we know
that they take place because our observations show that
none of the bodies which are tributary to the sun are
stationary in the sky. This point will be fully dwelt upon
in a subsequent chapter on the planets. On the contrary,
all seem to be in motion among the stars; at one time forward
or eastward, and at another backward or toward the
west. All through the period of the infancy of astronomy,
a fundamental mistake was made; too great importance
was attached to the earth, because men dwell upon it, and
it seemed natural to regard it as the center about which
the universe wheeled. Centuries of investigation were
required to correct this blunder; and true relations of
the celestial mechanism could be understood only when
real motions had been thought out and put in place of
apparent ones. The earth was then forced to shrink into
its proper and insignificant rôle, as a planet of only modest
\DPPageSep{141.png}
proportions, itself obedient in motion to the overpowering
attraction of the sun.

\textbf{The Sun's Apparent Annual Motion.}\index{sun!apparent annual motion}---First, let us again
observe the sun's seeming motion toward the east. Soon
after dark, the first clear night, observe what stars are due
south and well up on the meridian. A week later, but at
the same time of the evening, look for the same stars;
they will be found several degrees west of the meridian.
Why the change? These stars, and all the others with
them, seem to have moved westward toward the sun; or
what is the same thing, the sun must have moved eastward
toward these stars. But while this appears to be a motion
of the sun, we shall soon see that it is really a motion of
the earth round the sun. If our globe had no atmosphere,
the stars would be visible in the daytime, even close beside
the sun; and it would be possible, directly and without
any instruments, to see him approach and pass by
certain stars near his path from day to day. A few observations
would show that the sun seems to move eastward
about twice his own breadth, that is 1°, every day. His
path among the stars would be found to be practically the
same from year to year. This annual path of the sun
among the stars is called the \textit{ecliptic}\index{ecliptic}, and invariability
of position has led to its adoption by astronomers from
the earliest times, as a plane of reference. Its utility as
such has already been considered in Chapters \textsc{ii} and \textsc{iii}; it
is the fundamental plane of the ecliptic system.

\textbf{Sun's Apparent Motion really the Earth's Motion.}---What
causes that apparent motion of the sun just described?

\Smaller
Select a room as large as possible in which there is a tall lamp.
Place this in the center of the room, and walk around it counter-clockwise,
facing the lamp all the time; notice how it seems to move round
among and pass by the objects on the wall. It appears to travel with
the same angular speed that you do, and in the same direction. Now
imagine yourself the earth, the lamp to be the sun, and the objects on
\DPPageSep{142.png}
the wall the fixed stars. The horizontal plane through the lamp and
the eye will represent the ecliptic; one complete journey round the
lamp will correspond to a year.
\Restore

A simple experiment of this character will convey a
clear idea of the true explanation of the sun's apparent
motion: that great luminary is himself stationary at the
center of a family or system of planets, of which our earth
is merely one; and our globe by traveling round the sun
once each year causes him to appear to move. If, however,
it is not clear how the earth's motion is the true cause of
the sun's seeming to describe his annual arc round the
ecliptic, put yourself in place of the lamp and have some
one carry the lamp round you, counter-clockwise. Meanwhile
keep your eye constantly upon the lamp, and observe
that it seems to move round on the wall in just the same
direction and at the same speed as when the lamp was stationary
and you walked around it.

\textbf{Earth's Orbit the Ecliptic Plane.}\index{earth!orbit|see{orbit (earth)}}\index{orbit (earth)}---The real path which
one body describes round another in space is called its
\textit{orbit}. The path our globe travels round the sun each year
is called the earth's orbit. We cannot see the stars close
to the sun, nor observe his position among them each day;
but practically the same thing is done by means of instruments
in government observatories. While these observations
of the sun's position are going on from the earth,
imagine a similar observatory on the sun, at which the
earth's positions among the stars are recorded at the same
times. Every earth observation of the sun will differ from
its corresponding sun observation of the earth by exactly
180°. But the earth observations of the sun are all included
in that great circle of the sky called the ecliptic,
therefore all the sun-observed positions of the earth (that
is, the earth's own positions in space) must also be in the
ecliptic. They are therefore included in a plane.
\DPPageSep{143.png}
% Fig 7.1, 2
\begin{figure}[hb!]
  \begin{minipage}{0.55\textwidth}
    \Input{page_134a}
    \caption{6~\AM---Earth traveling up}
  \end{minipage}
  \hfill
  \label{p134}
\end{figure}

\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \raisebox{-2in}{\smash[t]{\Input[0.5\textwidth]{page_134b}}}
  \caption{12~Noon---Earth traveling Westward}
\end{wrapfigure}
\textbf{Which Way is the Earth traveling?}\index{earth!direction of motion in space}---In attempting to
pass from a conception of the earth at rest as it seems, to
the earth moving round the sun as it really
is, no help can be greater than the frequent
pointing toward the direction in which the
earth is actually traveling. The gradual
and regular variation of this direction with
the hours of day and night, and its relation
to fixed lines in a
room or building, will
soon impress firmly
upon the mind the great truth of
the earth's annual motion
round the sun.

\begin{wrapfigure}{i}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_135a}
  \caption{6~\PM---Earth traveling Downward}
\end{wrapfigure}
\Smaller
Extend the arms at right angles
to each other as in the illustration.
Swing round until the left arm is
pointed toward the sun, whether
above or below the horizon. This
arm will then be in the plane
of the ecliptic. Still keeping
the arms at right angles, bring
the right arm as nearly as may be
into the plane of the ecliptic at the
time. This may be done as already
indicated on page~\pageref{p67}. The right arm
will then be pointing in the direction in which
the earth is journeying in space. The right arm
holding the ball and arrow is always pointing in
the direction of earth's motion through space,
relatively to the local horizon in the latter part
of September:

(1) at 6~\AM, upward toward a point about
20° south of the zenith;

(2) at noon, toward the northwest, at an altitude
of about 10°;

\begin{wrapfigure}[21]{o}{0.5\textwidth}
  \centering
  \Input[0.45\textwidth]{page_135b}
  \caption{12~Midnight---Earth traveling Eastward}
  \label{p135}
\end{wrapfigure}
(3) at 6~\PM, downward to a point about 20°
below the north horizon;

(4) at midnight, toward the northeast at an altitude of about 10°.
\DPPageSep{144.png}

\noindent It is apparent that the direction of the earth's motion is simply the
direction of a point whose celestial longitude is 90° less than that of
the sun. This moving point
is often called the earth's
goal, or the \textit{apex of the
earth's way}.
\Restore

\textbf{Change in Absolute
Direction of Earth's Motion.}---In an
early chapter was explained how east
and west, north and south at a given
place are always changing with the
earth's turning on its axis, and that it is
necessary to think of these directions as
curving round with the surface of the
earth. We saw, too, that the same relations
exist with reference to the cardinal
points of the celestial sphere, so that
east, for example, in one part of the heavens, is the same
absolute direction as west on the opposite part of the
celestial sphere. In precisely
the same way we have now to
think of the absolute direction
of earth's movement round the
sun as continually changing in
space. If at one moment there is a star
exactly toward which the earth is traveling,
three months before that time and
three months afterward we shall be going
at right angles to a line from the sun to
that star; and six months from the given
time we shall be traveling exactly away
from it. In the chapter relating to the
stars it will be shown how this motion of
the earth in space can actually be demonstrated
\DPPageSep{145.png}
 by a delicate observation with an instrument
called the spectroscope.

\label{p136} \textbf{Earth's Orbit an Ellipse.}\index{orbit (earth)!an ellipse}---The angle which the sun
seems to fill, as seen from the earth, is called the sun's
apparent diameter. Measures of this angle, made at
intervals of a few days throughout the year, are found to
differ very materially. It is not reasonable to suppose
that the size of the sun itself varies in this manner.
What, then, is the explanation? Obviously the sun's distance
from us, or, what is the same thing, our distance
from him, is a variable quantity. The earth's orbit, then,
cannot be a circle, unless the sun is out of its center. But
the observations themselves, if carefully made, will show
the true shape of the orbit. It is not necessary to know
what the real distance of the sun is, because we are here
concerned with relative distance merely, nor need the observations
be made at equal intervals. In an early chapter
we saw that the apparent size of a body grows less as its
distance becomes greater. Apply this principle to the
measures of the sun.

% Fig 7.5
\begin{wrapfigure}[14]{o}{0.6\textwidth}
  \centering
  \Input[0.6\textwidth]{page_137}
  \caption{Ellipse, Foci, Axes, and Radii Vectores}
  \label{p137}\index{radius vector}
\end{wrapfigure}
\Smaller
Plot the observations by drawing radial lines at angles corresponding
to various directions in the ecliptic when observations of the sun's
breadth were made. Cut off the radial lines at distances from the
radial point proportional to the observed diameters, and then draw a
regular curve through the ends of the radial lines. On measuring this
curve, it is found that it deviates only slightly from a circle, but that it
is really an ellipse, one of whose foci is the radial point. Earth's orbit
round the sun, then, is an \textit{ellipse}, with the sun at one focus.
\Restore

\textbf{The Ellipse.}\index{ellipse!defined}---The ellipse is a closed plane curve, the
sum of the distances from every point of which, measured
to two points within the curve, is a constant quantity. This
constant fixes size of the ellipse, and is equal to its longer
axis, or major axis (figure \vpageref{p137}). At right angles to
the major axis, and through its center is the minor axis.
The two determining points are called foci, and both of
\DPPageSep{146.png}
them are situated in the major axis, at equal distances
from the center of the ellipse. Divide the distance from
the center to either focus by the half of the major axis,
and the quotient is called
the \textit{eccentricity}\index{ellipse!eccentricity}. This
quantity fixes the form
of the ellipse. If the
foci are quite near the
center, the eccentricity
becomes very small, and
the curve approaches the
circle in form. If the
center and both foci are
merged in a single point, evidently the ellipse becomes an
actual circle. This is called one limit of the ellipse. But
if the foci recede from the center and approach very near
the ends of the major axis, then the corresponding ellipse
is exceedingly flattened; and its limit in this direction
becomes a straight line.

\textbf{Limits of the Ellipse.}\index{ellipse!limits of}---These two limits are easy to
illustrate, practically, by looking at a circular disk (\textit{a})
perpendicularly, and (\textit{b}) edge on. In tilting it 90° from
one position to the other, the ellipse passes through all
possible degrees of eccentricity. The orbits of the heavenly
bodies embrace a wide range of eccentricity. Some of
them are almost perfectly circular, and others very eccentric.
In drawing figures of the earth's orbit, the flattening
is necessarily much exaggerated, and this fact should
always be kept in mind. The eccentricity of the earth's
orbit is about $\frac{1}{60}$; that is, the sun's distance from the
center of the orbit is only $\frac{1}{60}$ part of the semi-major axis.
If it is desired to represent the earth's orbit in true proportions
on any ordinary scale, the usual way is to draw
it perfectly circular, and then set the focus at one side of
\DPPageSep{147.png}
the center, and distant from it by $\frac{1}{60}$ the radius. If the
center is obliterated, a well-practiced eye is required to
detect the displacement of the focus from the center. And
as we shall see, many of the celestial orbits are even more
nearly circular than ours.

\Smaller
\textbf{How to draw an Ellipse.}\index{ellipse!how to draw}---The definition of an ellipse suggests at
once a practical method of drawing it. Lay down the major axis and
the minor axis. From either extremity of the latter, with a radius equal
to half the major axis, describe a circular arc cutting the major axis in
two parts. These will be the foci. Tie together the ends of a piece of
fine, non-elastic twine, so that the entire length of the loop shall be
equal to the major axis added
to the distance between the
foci. Set two pins in the foci,
place the cord around them,
and carry the marking point
round the pins, holding the
cord all the time taut. The
point will then describe an
ellipse with sufficient accuracy.
\Restore

\textbf{Lines and Points in Elliptic
Orbits.}---The earth
is one of the planets, and
in treating of them the
laws of their motion in
elliptic orbits will be
% Fig 7.6
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.55\textwidth]{page_138}
  \caption{Earth's Orbit (Ellipticity much exaggerated)}
  \index{orbit (earth)}
\end{wrapfigure}
given. In a still later
chapter the reason why
they move in orbits of
this
character will be explained.
Here are defined
such terms as are
necessary to understand in dealing with the earth. Only
one of the foci of the orbit need be considered. In that one
the primary body is always located. Any straight line
drawn from the center of that body, as \textit{S}, to any point of
\DPPageSep{148.png}
the ellipse, as \textit{E}, is called a \textit{radius vector}\index{radius vector}. The longest
radius vector is drawn to a point called \textit{aphelion}\index{aphelion}; the shortest
radius vector, to perihelion\index{perihelion, defined}. Together these two radii
vectores make up the major axis of the orbit. Perihelion is
often called an apsis; aphelion also is called an apsis. A
line of indefinite length drawn through them, or simply the
major axis itself unextended, is called the \textit{line of apsides}\index{ap´sides, line of, defined}.
Imagine the point where the line of apsides, on the perihelion
side, meets the celestial sphere to be represented by
a star. The longitude of that star, or its angular distance
measured counter-clockwise from the first of Aries, is technically
called the longitude of perihelion. This is 100°
in the case of the earth. The longitude of perihelion increases
very slowly from year to year; that is, the apsides
travel eastward, or just opposite to the equinoxes. But,
slow as the equinoxes move, the apsides travel only one
fourth as fast.

\textbf{Earth's Orbit in the Future.}\index{orbit (earth)}---Not only does the line
of apsides revolve, but the obliquity of the ecliptic (page~\pageref{p150})
changes slightly, and even the eccentricity of the
earth's orbit varies slowly from age to age. These facts
were all known a century or more ago; but with regard
to the eccentricity, it was not known whether it might
not tend to go on increasing for ages. Should it do so,
the earth would be parched at every perihelion passage,
and congealed on retreating to aphelion: it seemed among
the possibilities that all life on our planet might thus be
destined to come to an end, although remotely in the
future. But in the latter part of the eighteenth century,
a great French mathematician, La~Grange\index{La Grange, J. L. (l\=a-gr\=onzh´) (1736--1813), Fr.\ math.}, discovered
that although the earth's orbit certainly becomes more and
more eccentric for thousands of years, this process must
finally stop, and it then begins to approach more and
more nearly the circular form during the following period
\DPPageSep{149.png}
of thousands of years. The eccentricity, now near the
average value, will be decreasing for the next 24,000 years.
He showed, too, that the obliquity of the ecliptic simply
fluctuates through a narrow range on either side of an
average value. These slight changes are technically
called secular variations\index{orbit (planetary)!secular variations}\index{secular variations}\index{planets!secular variations}, because they consume very long
periods of time in completing their cycle. The mean or
average distance, and with it the time of revolution round
the sun, alone remains invariable. As we know this
period for the earth, and the eccentricity of its orbit
together with the location of its perihelion point, by calculating
forward or backward from a given place in the
sky on a given date, we can find the position of the sun
(and therefore of the earth in its orbit) with great accuracy
for any past or future time.

\textbf{Earth's Motion in Orbit not Uniform.}\index{orbit (earth)}\index{earth!motion in orbit}---Refer back to
the observations of the sun's diameter by which it was
shown that our orbit round
% Fig 7.7
\begin{wrapfigure}{o}{0.55\textwidth}
  \centering
  \Input[0.55\textwidth]{page_140}
  \caption{Radius Vector sweeps Equal Areas in Equal Times}
  \label{p140}
\end{wrapfigure}
the sun is not a circle, but an
ellipse. Had they been made at equal intervals of time,
it would at once have been seen, on plotting them, that
the angles through which
the radius vector travels
are not only unequal, but
that they are largest at
perihelion, and smallest at
aphelion. By employing
mathematical processes,
it is easy to show from the
observations of diameter,
connected with the corresponding angles, that a definite
law governs the motion of the earth in its orbit. Kepler\index{Kepler, J. (1571--1630), Ger.\ ast.}
was the first astronomer who discovered this fact, and
from him it is called Kepler's law. It will seem remarkable
until one apprehends the reason underlying it. The
\DPPageSep{150.png}
law is simply this: The radius vector passes over equal
areas in equal times. That the figure \vpageref{p140} may illustrate
this, an ellipse is drawn of much greater eccentricity
than any real planetary orbit has. What the law asserts is
this: Suppose that in a given time, say one month, the
earth in different parts of its orbit moves over arcs equal
to the arrows; then the lengths of these arrows are so proportioned
that their corresponding shaded areas are all
equal to each other. And this relation holds true in all
parts of the orbit, no matter what the interval of time.

\textbf{The Unit of Celestial Measurement.}\index{unit!of celestial distance}---By taking the
average or mean of all the radii vectores, a line is found
whose length is equal to half the major axis. This is
called the \textit{mean distance}. The mean distance of the
center of the earth from the center of the sun we shall
next find from the velocity of light. This distance is
93,000,000 miles\index{sun!distance of}, and it is the unit of measurement universally
employed in the astronomy of the solar system.
Consequently, it is often called \textit{distance unity}; and as
other distances are expressed in terms of it, they have
only to be multiplied by 93,000,000, to express them in
miles also.

\Smaller
Trying to conceive of this inconceivable distance is worth the
while. Illustrations sometimes help. Three are given: (\textit{a})~If you had
silver half dollars, one for every mile of distance from the earth to the
sun, they would fill three ordinary freight cars. If laid edge to edge in
a straight line, they would reach from Boston to Denver. (\textit{b})~It has been
found by experiment that the electric wave in ordinary wires travels as
far as from New York to Japan and back in a single second (about
16,000 miles). If you were to call up a friend in the sun by telephone,
the cosmic line would be sure to prove more exasperating than terrestrial
ones sometimes are; for even if he were to respond at once, you
would have to wait $3\frac{1}{4}$~hours. (\textit{c})~Suppose that as soon as Abraham
Lincoln was born, he could have started for the sun on a fast express
train, like the one illustrated on page~\pageref{p45}, which can make long runs
at the rate of 60~miles an hour. Suppose, too, that it had been keeping
up this speed ever since, day and night, without stopping. A
\DPPageSep{151.png}
long, long time to travel continuously, but his body would still be on
the road, for the train would not reach the sun till 1984.
\Restore

\textbf{Finding the Velocity of Light by Experiment.}\index{light!velocity of}---Light
travels from one part of the universe to another with
inconceivable rapidity. Light is not a substance, because
experiment proves that darkness can be produced by the
addition of two portions of light. Such an experiment is
not possible with substances. All luminous bodies have
the power of producing in the ether\index{ether, luminiferous, defined} a species of wave
motion. The ether is a material substance which fills all
space and the interstices of all bodies. It is perfectly
elastic and has no weight. As light travels by setting up
very rapid vibrations of the particles of the ether, it is
usually called the luminiferous ether. Different from the
vibrations of the atmospheric particles in a sound wave,
light waves travel by
vibrations of the ether
athwart the course of the
ray. The velocity of wave
transmission is called the
velocity of light. It is not
difficult to find by actual
experiment.

% Fig 7.8
\begin{wrapfigure}{o}{0.55\textwidth}
  \centering
  \Input[0.5\textwidth]{page_142}
  \caption{Finding Velocity of Light}
\end{wrapfigure}
\Smaller
One method is illustrated by
the figure. A ray of light is
thrown into the instrument at
\textit{B}, in the direction of the dotted
line. It is reflected at \textit{C}, and
goes out of the telescope \textit{A} to
a distant mirror, which reflects
it directly back to the telescope
again, and the observer catches
the return ray by placing the eye
at \textit{D}. In the field of the telescope are the teeth of a wheel \textit{E}, through
which outgoing and returning rays must pass. With the wheel at rest,
the return ray is fully seen between the teeth of the wheel. Whirl the
\DPPageSep{152.png}
wheel rapidly. While the direct ray is going out to the mirror and
coming back to the wheel, a tooth will have moved partly over its own
width, and will therefore partly shut off the ray, so that the star appears
faint instead of light. Whirl the wheel faster, and the return ray becomes
invisible. Keep on increasing the velocity of the wheel, and the
star again reappears gradually. And so on. More than twenty disappearances
and reappearances can be observed. The speed of the wheel
is known, because its revolutions are registered automatically by the
driving apparatus (omitted in the figure); and the distance of the mirror
from the wheel can be accurately measured, so that the velocity of
light can be calculated.
\Restore

This and other similar experiments have often been
repeated by Cornu\index{Cornu, M. A. (1841--1902), Fr.\ physicist}, Michelson\index{Michelson, A. A., Prof.\ Univ.\ Chicago}, Newcomb\index{Newcomb, S. (1835--1909), Am.\ ast.}, and others, in
Europe and America; and the result of combining them
all is that light waves, regardless of their color, travel
186,300 miles in a second of time.

\textbf{Size of the Earth's Orbit.}\index{earth!size of  orbit}---Where matters pertaining
to elementary explanation are simplified by so doing, it is
evident that the earth's orbit may be regarded as a circle.
From several hundred years' observation of the moons
which travel round the planet Jupiter, it has been found
that reflected sunlight by which we see them consumes
998 seconds in traveling across a diameter of the earth's
orbit (page~\pageref{p345}). So that $\frac{1}{2} × 998 × 186,300$ is the radius
of that orbit, or the mean distance of the sun\index{sun!distance of}\index{distance|see{sun, distance}}. This
distance is 93,000,000 miles, just given. Earth is at
perihelion about the 1st of January each year, and on
account of eccentricity of our orbit we are about 3,000,000
miles nearer the sun on the 1st of January than on the
1st of July. Our globe travels all the way round this
vast orbit, from perihelion back to perihelion again, in
the course of a calendar year. Clearly, its motion must
be very swift. Hold a penny between the fingers at a
height of four feet. Suddenly let it drop: in just a half
second it will reach the floor. So swiftly are we traveling
in our orbit round the sun, that in this brief half second
\DPPageSep{153.png}
we have sped onward $9\frac{1}{4}$~miles. And in all other half
seconds, whether day or night, through all the weeks and
months of the year, this almost inconceivable speed is
maintained.

\label{p144} \textbf{Earth's Deviation from a Straight Line in One Second.}\index{earth!motion in orbit}---As
our distance from the sun is approximately 93,000,000
miles, the circumference of our orbit round him (considered
as a circle) is 584,600,000 miles. But
% Fig 7.9
\begin{wrapfigure}[23]{o}{0.5\textwidth}
  \centering
  \Input[0.45\textwidth]{page_144}
  \caption{Earth's Deviation in One Second}
\end{wrapfigure}
as we shall
see in a later paragraph, the
earth goes completely round
the sun in one sidereal year,
or 365\,d.\:6\,h.\:9\,m.\:9\,s.; therefore
in one second our globe
travels through space $18\frac{1}{2}$~miles.
In that short interval,
how far does our path bend
away from a straight line, or
tangent to the orbit? Suppose
that in one second of
time, the earth would move
in a straight line from $M$
to $N$, if the sun exerted no
attraction upon us. Because
of this attraction, however, we
travel over the arc $Mn$. The length of this arc is $18\frac{1}{2}$~miles,
or about $0''.04$ as seen from the sun; and as this
angle is very small, the arc $Mn$ may be regarded as a
straight line, so that $MnU$ is a right angle. Therefore
\[
  MU : Mn :: Mn : Mm\DPtypo{}{.}
\]
But $MU$ is double our distance from the sun; therefore
$Mm$ is 0.119~inch, which is equal to $Nn$, or the distance
the earth falls from a straight line in one second. So
that we reach this very remarkable result: The curvature
\DPPageSep{154.png}
of our path round the sun is such that in going $18\frac{1}{2}$
miles we deviate from a straight line by only $\frac{1}{9}$ of an
inch.

\textbf{Reason for the Difference between Solar and Sidereal
Day.}\index{day!sidereal and solar compared}---The real reason why the sidereal day is shorter
than the solar day can now be made clear. The figure is
a help. If earth were not moving round the sun, but
standing still in space, one sidereal day would be the time
consumed by a point on the equator, \textit{A}, in going all the way
% Fig 7.10
\begin{figure}[hbt!]
  \centering
  \Input{page_145}
  \caption{Sidereal and Solar Day compared}
\end{figure}
round in direction of the lower arrows, and returning to
the point of starting. But while one sidereal day is elapsing,
the earth is speeding eastward in its orbit, from $O$ to $O'$.
Sun and star were both in the direction $AS$ at the beginning;
but after the earth has turned completely round,
the star will be seen in the direction $O'A$, which is parallel
to $OA$, because $OO'$ is an indefinitely small part of
the whole distance of the star. This marks one sidereal
\DPPageSep{155.png}
day. The sun, however, is in the direction $O'S$; and the
solar day is not complete until the earth has turned round
on its axis enough farther to bring $A$ underneath $S$. This
requires nearly four minutes; so the length of the solar
day is 24 hours of solar time, while the sidereal day, or
real period of the earth's rotation, equals 23\,h.\:56\,m.\:4.09\,s.\
of solar time. Also in the ordinary year of $365\frac{1}{4}$ solar
days, there are $366\frac{1}{4}$ sidereal days.

\textbf{Sun's Yearly Motion North and South.}\index{sun!apparent annual motion}---You have found
out the eastward motion of the sun among the stars from
the fact that they are observed to be farther and farther
% Fig 7.11
\begin{figure}[hbt!]
  \centering
  \Input[0.8\textwidth]{page_146}
  \caption{Direction of Sun's Rays at Equinoxes and Solstices}
  \index{sun!rays at equinox and solstice}
\end{figure}
west at a given hour each night. You must next ascertain
the nature of the sun's motion north and south. The
most convenient way will be to observe where the noon
shadow of the top of some pointed object falls. Begin
at any time of the year; in autumn, for example. This
shadow will grow longer and longer each day; that is, the
noonday sun is getting lower and lower down from the
zenith toward the south. How low will it actually go?
And when is this epoch of greatest length of the shadow?
Even the crudest observation shows that the noonday
\DPPageSep{156.png}
shadow will continue lengthening till the 20th of December;
but the daily increase of its length just before that
date will be difficult to observe, it is so very slight. Then
for a few days there will be no perceptible change; in so
far as motion north or south is concerned, the sun appears
to stand still. As this circumstance was the origin of the
name \textit{solstice}\index{solstices}, notice that it indicates both time and space:
the winter solstice is the time \textit{when} (or the point in the
celestial sphere \textit{where}) the sun appears to `stand still' at
its greatest declination south. The time is about the 20th
of December. Not until after Christmas will it be possible
to observe the sun moving north again; and then, at first,
by a very small amount each day.

\textbf{The Sun in Midwinter.}\index{sun!midwinter}\index{midwinter}---For the sake of comparison
with other days in the year, let us photograph (at noon
on a bright day near the winter solstice) some familiar
object with a south exposure; for example, a small and
slender tree, with its shadow (\vpageref*{p148}). Observe how
much
% Fig 7.12
\begin{wrapfigure}{o}{0.58\textwidth}
  \centering
  \Input[0.57\textwidth]{page_148}
  \caption{Midwinter Shadows Longest}\index{midwinter}
  \label{p148}
\end{wrapfigure}
shorter tree is than shadow, because the sun culminates
low. So far north does the shadow of the tree fall
that a part of it actually reached the house where the camera
stood. Verify the northeast-by-east direction of the sunset
shadow of the tree; and the corresponding direction (north-west-by-west)
of its sunrise shadow, also; for the sun will
now rise at a more available hour than in midsummer.
Notice, too, how sharply defined the shadow is, near the
trunk of the tree; and how ill-defined the shadows of the
branches are. This is because the sun's light comes from
a disk, not a point; the shadows are penumbral, that is,
not quite like dark shadows; and they grow more and
more hazy, the farther the surface upon which they fall.

\textbf{The Sun's Yearly Motion North.}---Onward from the
beginning of the year, continue to watch the sun's slow
march northward. With each day its noontime shadow
\DPPageSep{157.png}
will grow shorter and shorter. Watch the point in the
western horizon where the sun sets; with each day this,
too, is coming farther and farther north. Note the day
when the sun sets exactly
in the west; this
will be about the 20th
of March. As the
sun sets due west,
evidently it must previously
have risen due
east; therefore the
great circle of its
diurnal motion (which
at this season is the
equator) must be bisected
by the horizon.
Day and night, then,
are of equal length.
The vernal equinox is
the time when (or the
point where) the sun
going northward
crosses the celestial
equator.

\textbf{The Sun in Midsummer.}\index{sun!midsummer}\index{midsummer}---Now
begin
again the observations
of the noontime
shadow. Shorter
and shorter it grows and perceptibly so each
% Fig 7.13
\begin{wrapfigure}{o}{0.64\textwidth}
  \centering
  \Input[0.6\textwidth]{page_149}
  \caption{Midsummer Shadows Shortest}\index{midsummer}
\end{wrapfigure}
day. But it
will be noticed that the difference from day to day is less
than the daily increase of length six months before. That
is simply because the shadows fall nearer the tree, and are
measured more nearly at right angles to the sun's direction
\DPPageSep{158.png}
than they were in the autumn and winter. The azimuth
of its setting will increase. How many weeks will the
length of the shadow continue to decrease? How short
will it actually get? About the middle of June, it will be
almost impossible to
notice any further decrease
in the shadow's
length, and on
20th June we may
again photograph
the same tree. But
how changed! The
short shadow of its
trunk is all merged
in the shadow of
the foliage where it
falls upon the lawn.
Points of the compass
alone are unchanged.
Here again at midsummer,
the sun
stands still, and there
is a second solstice.\index{solstices}
Summer solstice is
the time when (or
the point on the celestial sphere where) the sun appears
to `stand still' at greatest declination north. Do not fail
to notice the points of the compass. Also verify at midsummer
the indicated direction (southeast-by-east) in which
the tree's shadow falls at sunset; and near the beginning
of the summer vacation it will be worth while to arise once
at five o'clock in the morning, in order to verify also the
southwest-by-west direction of the shadow just after sunrise.
By the latter part of June, the noontime shadow
\DPPageSep{159.png}
again begins to lengthen; more and more rapidly with
each day it lengthens until the equinox of autumn, when
the cycle of one year of observation is complete.

\Smaller
\label{p150} \textbf{To observe the Inclination of Equator to Ecliptic.}---As equator and
ecliptic are both great circles, the sun goes as far north in summer as
it goes south in winter. Half the extreme range is the angle of inclination
of ecliptic to equator, and it is technically termed the obliquity\index{obliquity}
of the ecliptic. Its value for 1900 is $23° \, 27'\, 8''.02$, and it changes very
slowly. A rough value is readily found for any year by making use of
the latitude-box already described on page~\pageref{p82}. At noon on the 20th,
21st, and 22d of December, observe the readings on the arc where
the sun's line falls. Be sure that the box remains undisturbed, or test
the vertical arm of the quadrant by the plumb-line each day. Leave the
box in position through the winter and spring, or set up the same box
again in June, and again apply the plumb-line test. At noon on the
20th, 21st, and 22d of June, observe the sun's reading as at the other
solstice. Take the difference of readings as follows:---
\begin{center}
\begin{tabular}{l@{ }l}
Reading of&amp;22d December from 20th June;\\
&amp;21st December from 21st June;\\
&amp;20th December from 22d June.\\
\end{tabular}
\end{center}
Then halve each of the three differences, and the results will be three
values for the inclination of equator to ecliptic. Take the average of
them for your final value. Thus in about six months' time you will
have all the observations needed for a new value of the obliquity of
the ecliptic. True, its accuracy may not be such that the government
astronomers will ask to use it in place of the refined determinations of
Le~Verrier\index{Le Verrier, U. J. J. (l\u uh-vay-rya´) (1811--77), Fr.\ ast.} and Hansen\index{Hansen, P. A. (1795--1874), Ger.\ ast.}, but your practical knowledge of an elementary
principle by which the obliquity is found will be worth the having.
\Restore

Following are readings made in this manner at Amherst,
Massachusetts:---
\begin{center}
\TableSize
\begin{tabular}{rr@{ }l@{}l}
  \footnotesize\textsc{Arc-Reading}
&amp; \multicolumn{1}{c}{\footnotesize\textsc{Arc-Reading}}
&amp; \multicolumn{2}{@{}l}{\footnotesize\textsc{Obliquity}}
\\
  June 20, $71° .2$
&amp; Subtract December 22, \ $24° .3 = 46° .9$ {\qquad}
&amp;$23° .45$
\\
  21,   $71\phantom{° }.0$
&amp; 21, \ $24\phantom{° }.0 = 47\phantom{° }.0$ {\qquad}
&amp;$23\phantom{° }.5$
\\
  22,   $70\phantom{° }.9$
&amp; 20, \ $24\phantom{° }.1 = 46\phantom{° }.8$ {\qquad}
&amp;$23\phantom{° }.4$
\\[.2ex] \cline{3-3}
&amp; Mean value of obliquity = &amp;$23° \, 27'$\rule{0pt}{2.5ex}
\end{tabular}
\index{obliquity!of ecliptic}
\end{center}

\textbf{Explanation of the Equation of Time.}\index{equation of time!explained}\index{time|see{equation of time}}---The reason may
now be apprehended why mean sun and real sun seldom
\DPPageSep{160.png}
cross the meridian together. It is chiefly due to two independent
causes, (1)~The orbit in which our earth travels
round the sun is an ellipse. Motion in it is variable---swiftest
about the 1st of January, and slowest about the
1st of July. On these dates, the equation of time due
to this cause vanishes. Nearly intermediate it has a mean
rate of motion; therefore at these times (about 1st April
and 1st October),
the true sun and
the fictitious sun
must both travel
at the same
% Fig 7.14
\begin{wrapfigure}{o}{0.68\textwidth}
  \centering
  \Input[0.65\textwidth]{page_151}
  \caption{Relation of True Sun to Mean Sun}
\end{wrapfigure}
rate in
the heavens. But
the real sun has
been running ahead
all the time since
the beginning of
the year, as this
figure shows; so
that on the 1st of April, the equation of time, from this
cause alone, is eight minutes. The sun is slow by this
amount because it has been traveling eastward so rapidly.
On 1st October it is fast a like amount, because it has
been moving very slowly through aphelion in the summer
months; therefore the real sun comes to the meridian
earlier than it should, and it is said to be fast.

(2) The second cause is the obliquity of the ecliptic.
Suppose that the sun's apparent motion in the ecliptic
were uniform: near the solstices its right ascension would
increase most rapidly, because the hour circles converge
toward the celestial poles just as meridians do on the earth.
The case is like that of a ship sailing due east or west at
a uniform speed: when in high latitudes she `makes longitude'
much faster than she does near the equator. As
\DPPageSep{161.png}
due to the second cause the equation of time vanishes four
times a year; twice at the equinoxes and twice at the solstices.
At intermediate points (about the 8th of February,
May, August, and November), the sun is alternately slow
and fast about 10 minutes. Combining both causes gives
the equation of time as already presented in the table on
page~\pageref{p113}. It is zero on 16th~April, 15th~June, 1st~September,
and 25th~December. The sun is slowest ($14\frac{1}{2}$
minutes) about 11th~February, and fastest ($16\frac{1}{3}$ minutes)
about 3d~November. Attention is next in order turned to
that remarkable yearly variation in conditions of heat
and cold in our latitudes, called the seasons.

\Smaller
\textbf{The Seasons in General.}\index{seasons}---Those great changes in outward nature
which we call the seasons are by no means equally pronounced everywhere
throughout our extended country. It is well, therefore, to
sketch them in outline, from a naturalist's point of view, which is quite
different from that of the astronomer. The earliest peoples noted
% Fig 7.15
\begin{figure}[hb]
  \centering
  \Input[\textwidth]{page_152}
  \caption{Earth's Axis inclined $66\frac{1}{2}$° to the Plane of its Orbit}
\end{figure}
these variations for practical purposes, chiefly seedtime and harvest.
But as men grew past the necessities of mere living, they began to observe
the natural beauty of each season as it came. Not knowing what
occasioned the unvarying succession of these fixed, yet widely different
conditions of the year, all sorts of fanciful explanations were invented.
Clearly it is not the simple nearness or distance of the sun, as we approach
or recede in our orbit, which causes our changing seasons,
for in our winter we are, as has already been said, 3,000,000 miles
nearer than in summer. But as earth passes round the sun in its yearly
path, the axis remains always from year to year practically parallel to
itself in space (neglecting the effect of precession), its inclination to the
ecliptic being $66\frac{1}{2}$° as shown in the outline figure above. Alternately,
then, the poles of earth are tilted toward and from that all-potent and
heat-giving luminary. So in the sunward hemisphere summer prevails
because of accumulated heat: more is received each day than is
\DPPageSep{162.png}
lost by radiation each night. But in the hemisphere turned away from
the sun for the time, gradually temperature is lowered by withdrawal of
life-giving warmth, more and more each day. Medium temperatures
of autumn follow, and eventually it becomes midwinter.

\textbf{Spring and Summer.}\index{spring!in general}\index{summer!in general}---But when, by the earth's journeying onward
in its orbital round, the pole again becomes tilted more and more toward
the sun, soon an awakening begins. The melting of ice and
snow, the gradual reviving of brown sods, the flowing of sap through
branches apparently lifeless, the mist of foliage beginning to enshroud
every twig until the whole country is enveloped in a soft haze of palest
green and red, gray and yellow,---all these are Nature's signs of spring.
Biologists tell us that this vegetal awakening comes when the temperature
reaches $44$°~Fahrenheit. Soon come the higher temperatures
requisite for more mature development, and midsummer follows rapidly.
The astronomer can, of course, say just when in June our longest day
comes---when the sun rises farthest north and sets farthest north,
thereby shining more nearly vertically upon us at noon, and remaining
above the horizon as long as possible; when daylight lasts with us
until long past eight o'clock, and in England and Scotland until nearly
ten. But who can divine just when the country stands at the fullest
flood tide of summer, with the rich growth of vegetation, tangled
masses of flowers and foliage, roadsides crowded with beauty, the
shimmer of heat above ripening fields, perfecting grains, and early
fruits? Or when it first begins to ebb? That is for another observer
no less subtile than the astronomer with his measuring instruments and
geometric demonstrations. Very different, too, is the time in different
places; often there is a wide range of local conditions which modify
greatly the effects produced by purely astronomical causes.

\textbf{Autumn and Winter.}\index{autumn!in general}---Thoreau, that keen observer of times and
seasons, used always to detect signs of summer's waning in early July.
But persons in general notice few of the advance signals of a dying
year. Not until falling leaves begin to flutter about their feet, and
grapes and apples ripen in orchard and vineyard, do they realize that
autumn is really here---that season of fulfillment, when everything is
mellow and finished. Our hemisphere of the earth is turning yet
farther away from that sun upon which all growth and development
depend. When trees are a glory of red and yellow and russet brown,
when corn stands in full shocks in fields, and day after day of warmth
and sunshine follow through royal October,---it seems impossible to
believe that slowly and surely, winter can be approaching. But soon
chilly winds whistle through trees from which the bright leaves are
almost gone; a thin skim of ice crystals shoots across wayside pools
at evening, and speedily shivering winter is upon us. Just before
Christmas, this part of our earth is tipped its farthest away from the
\DPPageSep{163.png}
sun. Then, for a few days, the hours of darkness are at their longest.
The sap has withdrawn far into the roots of trees until the cold shall
abate; leaden skies drop snowflakes, and earth sleeps under a mantle
of white. Cold is apt to increase for a month after the sun has actually
begun to journey northward. His rays, warm and brilliant, flood every
nook and crevice in leafless forests; but where is their mysterious
power to call life into bare branches, to wake the flowers, and stir the
grass? It is almost startling to think that a permanent withdrawal of
even a slight amount of the sun's warmth would freeze this fair earth
into perpetual winter---that a small change in the tilt of our axis
might make arctic regions where now the beauty of summer reigns in
its turn. But the laws of the universe insure its stability; and changes
of movement or direction are very slow and gradual, so that all our
familiar variation of seasons, each with its own charm, cannot fail to
continue for more years than it is possible to apprehend. In late January,
weeks after our hemisphere has begun again to turn sunward, even
the most careless observer notes the lengthening hours of daylight, and
knows that spring is coming. That thrill of mysterious life which this
earth feels at greater warmth, and the quiet acceptance of its withdrawal,
have been celebrated by poets in all ages; and the astronomer's
explanations of whys and wherefores cannot add to these marvelous
changes anything of beauty or perennial interest, although they may
conduce to completeness and precision of statement.
\Restore

\textbf{Explanation of the Change of Seasons.}\index{seasons}---So much for
mere description: the explanation has already been hinted.
Our change of season is due to obliquity of the ecliptic,
or to the fact that the axis of our planet, as it travels round
the sun, keeps parallel to itself, and constantly inclined to
its orbit-plane by an angle of $66\frac{1}{2}$°. The opposite illustration
should help to make this clear.

% Fig 7.16
\begin{figure}[hbt!]
  \centering
  \Input{page_155}
  \caption{View of Earth's Orbit from the North Pole of the Ecliptic}
  \label{p155}
\end{figure}

\Smaller
Beginning at the bottom of the figure, or at midsummer, it is apparent
how the earth's northern pole is tilted toward the sun by the full
amount of the obliquity, or $23\frac{1}{2}$°. It is midsummer in the northern
hemisphere, also it is winter in the southern, because the south pole is
obviously turned away from the sun. Passing round to autumn, in
the direction of the large arrows, reason for the equable temperatures
of that season is at once apparent: it is the time of the autumnal equinox,
or of equal day and night everywhere on the earth, and the sun's
rays just reach both poles. Going still farther round in the same direction,
to the top of the illustration, the winter solstice is reached; it is
\DPPageSep{164.png}
northern winter because the north pole is turned away from the sun
and can receive neither light nor heat therefrom; also the southern hemisphere
is then enjoying summer, because the south pole is turned $23\frac{1}{2}$°
toward the sun. Again moving quarter way round, to the left side of the
illustration, the season of spring is accounted for, and the temperature
is equable because it is now the vernal equinox. Another quarter
year, or three months, finds the earth returned to the summer solstice;
and so the round of seasons runs in never-ending cycle.
\Restore

\textbf{Earth receives most Heat at Midday.}\index{heat!sun's greatest at midday}---It is necessary to
examine into the detail of these changes of light and heat
a little more fully. Every one is aware how much warmer
it usually is at noon than at sunrise or sunset, mostly because
of change in inclination of the sun's rays from one
time of day to another. Any surface becomes the warmer,
\DPPageSep{165.png}
the more nearly perpendicularly the sun's rays strike it,
simply because more rays fall upon it.

% Fig 7.17
\begin{wrapfigure}{o}{0.4\textwidth}
  \centering
  \Input[0.35\textwidth]{page_156a}
  \caption{A Surface receives most Rays when they fall Perpendicularly upon it}
\end{wrapfigure}
\Smaller
In the figure, $ab$, $cd$, and $ef$ are equal spaces, and $R$ is the bundle
of solar rays falling upon them. Obviously more rays fall upon $cd$ than
upon $ab$, because the rays are parallel. But the
lessened warmth of sunrise and sunset is partly
due to greater absorption of solar heat by our
atmosphere at times when the sun is rising and
setting, because its rays must then penetrate
a much greater thickness of the air than at
noon. Suppose the observer to be located
within the tropics, because there the sun's rays
may be perpendicular to the earth's surface, as
shown in the diagram below, while in our latitudes
they never can be quite vertical even at
midsummer noon. There the sun's rays may
travel vertically downward at apparent noon; and it is evident from
the illustration that a beam of sunlight of a given width $KL$ traverses
only that relatively small part of the earth's atmosphere included between
$KL$, $MN$. Now at sunrise observe the different conditions under
which a beam of sunlight of the same breadth as $KL$ is obliged to traverse
the atmosphere. Observe, too, how much more atmosphere
$ABCD$ this beam must pass through. As the sun's energy is absorbed
% Fig 7.18
\begin{figure}[hb!]
  \centering
  \Input{page_156b}
  \caption{The Solar Beams are spread out and absorbed at Sunrise and Sunset}
\end{figure}
in heating this greater volume of air, evidently the amount of heat arriving
at the earth's surface, $CD$, where we are directly conscious of it,
must be less by the amount which the atmosphere has absorbed. Besides
this the amount of solar heat which falls upon a given area between
$C$ and $D$ will evidently be less than that received by an equal area between
$M$ and $N$, in proportion as $CD$ is greater than $MN$. Like conditions
prevail at sunset as shown.
\Restore
\DPPageSep{166.png}

\textbf{Our Latitudes receive most Heat at the Summer Solstice.}\index{heat!at summer solstice}---In
an earlier chapter it was explained how the
sun, by its motion north, crosses
% Fig 7.19
\begin{wrapfigure}{o}{0.65\textwidth}
  \centering
  \Input[0.6\textwidth]{page_157a}
  \caption{The United States as seen from the Sun in Midwinter}
  \index{sun!midwinter}\index{midwinter}
\end{wrapfigure}
higher and higher on
our meridian every day, from the winter solstice to the
summer solstice. Just as
each day the heat received
increases from sunrise to
noon, and then decreases to
sunset, so the heat received
at noon in a given place of
middle north latitude, increases from the winter solstice to a
maximum at the summer solstice. Also the sun's diurnal arc
has all this time been increasing, so that a given hour of
the morning, as nine o'clock,
and a given hour of the afternoon,
as three o'clock, places the sun higher and higher.
The heat received, then, increases for two independent
though connected reasons: (1)~the sun culminates higher
each day, and (2)~it is above the horizon longer each day.
The illustration (page~\pageref{p30}) makes both reasons clear. The
greater length of daytime
exerts a powerful influence
in modifying the summer
temperatures of regions in
very high latitudes where
the summer sun shines continually
through the 24
hours. For example, at the
summer solstice, the sun
pours down, during the 24
hours, one fifth more heat upon the north pole than upon
the equator, where it shines but 12 hours. So it is not
easy to calculate the relative heat received at different
latitudes, even if we neglect absorption by the atmosphere.
With
this effect included, the problem becomes
\DPPageSep{167.png}
more complicated still. If earth and atmosphere could
retain all the heat the sun pours down upon them, the
summer solstice would mark also the time of greatest
heat. But in our latitudes radiation of heat into space
retards the time of greatest accumulated heat more than
a month after the summer solstice. For evidently the
atmosphere and the earth are storing heat so long as the
daily quantity received exceeds the loss by radiation. For
a similar reason, the time of greatest cold, or withdrawal
of warmth, is not coincident with the winter solstice, but
lags till the latter part of January.

% Fig 7.20
\begin{figure}[hbt!]
  \centering
  \Input[0.6\textwidth]{page_157b}
  \caption{The United States as seen from the Sun in Midsummer}
\end{figure}

\Smaller
\textbf{Accumulation ceases when Loss equals Gain.}---Illustration by a
three weeks' petty cash account should make this apparent. You start
with 50 cents
% Fig 7.21
\begin{wrapfigure}[21]{o}{0.5\textwidth}
  \centering
  \Input[0.45\textwidth]{page_158}
  \caption{Cash increases till Expenses and Income are Equal}
\end{wrapfigure}
cash in hand. For
the first week, you receive 25
cents Monday, and spend 15; 30
cents Tuesday, and spend 18;
and so on, receiving five cents
more each day, and spending
three cents more than the day
before. At the end of the week
you will have \$1.40. The second
week, your receipts and expenditures
are equal in amount
to the first, but reversed as to
days---your allowance is 50
cents Monday, and you spend
30; 45 cents Tuesday, and you
spend 27; and so on. On the
second Saturday your expense
account will be the same as for
the first Monday---you receive
25 cents and spend 15; but your
accumulated wealth will then be
\$2.30. The third week you
receive 25 cents Monday, 20
cents Tuesday, and so on, but through the week you spend 15 cents
each day. For two weeks your income has steadily been falling off,
from 50 cents daily to nothing; but your total cash in hand kept on
accumulating, and did not begin to decrease until the middle of the
\DPPageSep{168.png}
third week, and on the third Saturday you close the account with \$2.15
in hand. Cash in hand at the beginning is the temperature about
the middle of May, and the end of the first week corresponds to the
summer solstice. Income is the amount of heat received from the
sun, and expenditure is the amount radiated into space. Just as cash
in hand went on accumulating long after receipts began to fall off, so
the average daily temperature keeps on rising for more than a month
after the solstice, when the amount received each day is greatest. The
diagram shows the entire account at a glance, and illustrates at the same
time a method of investigation much employed in astronomical and other
researches, called the graphical method. Its advantages in presenting
the range of fluctuations clearly to the eye are obvious.
\Restore

\textbf{The Seasons Geographically.}\index{seasons}---The astronomical division
of the seasons has already been given in the figure on
page~\pageref{p155}. It is as follows:---
\begin{center}
\TableSize
\begin{tabular}{l}
  Spring, from the vernal equinox, three months.   \\
  Summer, from the summer solstice, three months.  \\
  Autumn, from the autumnal equinox, three months. \\
  Winter, from the winter solstice, three months.
\end{tabular}
\end{center}

But according to the division among the months of the
year, as commonly recognized in this part of the world,
each season precedes the astronomical division by nearly
a month, and is as follows:---
\begin{center}
\TableSize
\begin{tabular}{l@{~}l}
  Spring &amp;= March, April, May.\index{spring!months of}            \\
  Summer &amp;= June, July, August.\index{summer!months of}           \\
  Autumn &amp;= September, October, November.\index{autumn!months of} \\
  Winter &amp;= December, January, February.\index{winter!months of}
\end{tabular}
\end{center}
Differences of climate and in the forward or backward
state of vegetable life, in part dependent upon local conditions,
have led to different divisions of the calendar months
among the seasons, varying quite independently of the
latitude. Great Britain's spring begins in February, its
summer in May, and so on. Toward the equator the
difference of season is less pronounced, because the annual
variation of the sun's meridian altitude is less; and
as changes in rainfall are more marked than those of
\DPPageSep{169.png}
temperature, the seasons are known as dry and rainy,
rather than hot and cold. These marked differences of
season are recognized by the division of the earth's surface
into five zones.

\textbf{Terrestrial Zones.}\index{zones, terrestrial}---From the relation of equator to ecliptic,
and from the sun's annual motion, it is plain that \DPtypo{thrice}{twice}
every year the sun must shine vertically over every place
whose latitude is less than $23\frac{1}{2}$°, whether north or south.
This geometric relation gives rise to the parallels of latitude
called the \emph{tropics}; the Tropic of Cancer\index{Cancer!tropic of} being at $23\frac{1}{2}$°
north of the equator, and the Tropic of Capricorn\index{Capricornus!tropic of} at $23\frac{1}{2}$°
south. They receive their names from the zodiacal signs in
which the sun appears at these seasons. The belt of the
earth included between these small circles of the terrestrial
sphere is called the \emph{torrid zone}. Its width is $47$°, or nearly
3300 miles. Similarly there are zones around the earth's
poles where, for many days during every year, the sun
will neither rise nor set. These polar zones or caps are
also $47$° in diameter. Between them and the torrid zone
lie the two temperate zones, one in the northern and one
in the southern hemisphere, each $43$°, or about 3000 miles
in width. The sun can never cross the zenith of any place
within the temperate zones. If equator and ecliptic were
coincident, that is, if the axis of the earth were perpendicular
to the plane of its path round the sun, day and
night would never vary in length, and our present division
into zones would vanish.

\textbf{The Seasons of the Southern Hemisphere.}\index{seasons}---Our earth
in traveling round the sun preserves its axis not only
at a constant angle to the plane of its orbit, but always
for a limited period of years pointing to nearly the same
part of the heavens, as shown in the figure on page~\pageref{p65}.
Plainly, then, the seasons of the southern hemisphere must
occur in just the order that our northern seasons do. In
\DPPageSep{170.png}
its turn the south pole inclines just as far toward the sun
as the north one does. But in so far as astronomical conditions
are concerned, the southern seasons will be displaced
just six months of the calendar year from ours.
The following figures of the earth at solstices and equinoxes
make these relations clear. Midwinter in the southern
% Fig 7.22
\begin{figure}[htb]
  \centering
  \Input{page_161a}
%  \caption{}
\end{figure}
hemisphere comes in June and July, and Christmas
falls in midsummer. The opening of their spring comes
in August and September, and autumn approaches in
February and March. But while in the northern hemisphere
the difference between the heat of midsummer and
the cold of midwinter is somewhat lessened by the changing
distance of the sun, in the southern hemisphere this
effect is intensified, because the earth comes to perihelion
in the southern midsummer. However, on account of the
swifter motion of the earth from October to March than
% Fig 7.23
\begin{figure}[hbt!]
  \centering
  \Input{page_161b}
%  \caption{}
\end{figure}
from April to September, the southern summer is enough
shorter to compensate for the sun's being nearer, so that
the southern summer is practically no hotter than the
northern. On the other hand, the southern winter not
only lasts about seven days longer than the northern, but
\DPPageSep{171.png}
it is colder also, because the sun is then farthest away.
The range of difference in the heat received at perihelion
and aphelion is about $\frac{1}{15}$ part of the total amount.

% Fig 7.24
\begin{figure}[hbt!]
  \centering
  \Input{page_162}
  \caption{Aberration of the Raindrop is Greater as the Body moves Swifter}
\end{figure}

\textbf{Annual Aberration.}\index{aberration!annual}---In looking from a window into a
quiet, rainy day, the drops are seen to fall straight down
earthward from the sky. But if, instead of watching from
shelter, you go out in the rain and run swiftly through it,
the effect is as if the drops were to slant in oblique lines
against the face. For the man under the umbrella, the
leisurely boy with rubber coat and hat on, and the courier
caught in the rain, how different the direction from which
the drops seem to come. A similar but even more exaggerated
effect may be watched in a railway train speeding
through a quiet snowstorm; it seems as if the flakes sped
past in an opposite direction, in white streaks almost horizontal,---the
\DPPageSep{172.png}
result of swift motion of the train, combined
with that of the slowly falling snow. This appearance is
called \textit{aberration}, and in reality the same effect is produced
by the progressive motion of light. Now replace the moving
train by the earth traveling in its orbit round the sun,
and let the falling raindrop or snowflake represent the
progressive motion of light; then as the angle between
the plumb-line and the direction from which rain or snow
seems to come is the aberration of the descending drop or
flake, so the angle between the true position of the sun
and the point which its light seems to radiate from is the
annual aberration of light. It is usually called aberration
simply, and was discovered by Bradley\index{Bradley, J. (1693--1762), Ast.\ Royal}\index{Astronomer Royal|see{Bradley}} in 1727.

\textbf{The Constant of Aberration.}\index{aberration!constant of}---Notice two things: (\textit{a})~that
raindrop and snowflake both appear to come from points
in advance of their true direction; (\textit{b})~that this angle of
aberration is less as the velocity of the falling drop or flake
is greater. The snowflake falls very slowly in comparison
with the speed of the train, so the angle of aberration was
observed to be perhaps 80° or more; but where the velocity
of the raindrop was nearly the same as the speed of the
train, the angle of aberration was only 45°. Now imagine
the velocity of the drop increased enormously, until it is
10,000 times greater than the speed of the train: then we
have almost exactly the relation which holds in the case of
the moving earth and the velocity of a wave of light. In
a second of time the earth travels $18\frac{1}{2}$~miles, and light
186,300 miles. But we found that any object which fills
an angle of $1''$ is at a distance equal to 206,000 times its
own breadth; so that the angle of annual aberration of the
sun must be the same as that filled by an object at a distance
of only 10,000 times its own breadth. This angle is
$20''.5$, and it is called the constant of aberration. It corresponds
to the mean motion of the earth in its orbit. At
\DPPageSep{173.png}
aphelion, where this motion is slowest, the sun's aberration
drops to $20\frac{1}{6}''$; at perihelion, where fastest, it rises to $20\frac{5}{6}''$.
The constant of aberration has been determined with great
accuracy from observations of the stars; and its exact correspondence
with the motion of the earth may be regarded
as indisputable proof of our motion\index{earth!proof of motion} round the sun.

\textbf{Aberration of the Stars.}\index{aberration!stellar}---Aberration is by no means
confined to the sun; but it affects the apparent position
of the fixed stars as well. Observation shows that every
star seems to describe every year in the sky a small ellipse.
These aberration ellipses traversed by the stars all have
equal
% Fig 7.25
\begin{wrapfigure}{o}{0.65\textwidth}
  \centering
  \Input[0.6\textwidth]{page_164}
  \caption{Aberration Ellipses of the Stars}\index{aberration!ellipses}
  \label{p164}
\end{wrapfigure}
major axes; that
is, an arc of $41''$, or
double the constant of
aberration. But their
minor axes vary with
the latitude, or distance
of the star from the
ecliptic. Try to conceive
these ellipses in
the sky; the major
axis of each one coincides
with the parallel
of latitude through the
star, and their size is
such that they are just
beyond the power of human vision. About 50 aberration
ellipses placed end to end with their major axes in line would
reach across the disk of the moon. For a star at the pole of
the ecliptic, the minor axis is equal to the major axis; that
is, the star's aberration ellipse is a circle $41''$ in diameter.
As shown in the illustration, the ellipses grow more and
more flattened, for stars nearer and nearer the ecliptic;
and when the star's latitude is zero, the aberration ellipse
\DPPageSep{174.png}
becomes seemingly a straight line, but actually a small arc
of the ecliptic itself, $41''$ in length. In calculating all
accurate observations of the stars, a correction must be
applied for the difference between the center of the ellipse
(the star's average place), and its position in the ellipse on
the day of the year when the observation was made. Every
star partakes of this motion, and thus proof of earth's motion\index{earth!proof of motion}
round the sun becomes many million fold.

\textbf{The Year.}\index{year}---Just as there are two different kinds of day,
so also there are two different kinds of year. Both are
dependent upon the motion of the earth round the sun,
but the points of departure and return are not the same.
Starting from a given star and returning to the same star
again, the earth has consumed a period of time equal to
365\.d.\:6\,h.\:9\,m.\:9\,sec. This is the length of the sidereal year\index{year!sidereal}.
But suppose the earth to start upon its easterly tour from
the vernal equinox, or first of Aries: while the year is
elapsing, this point travels westward by precession of the
equinoxes, so that the earth meets it in 20\,m.\:23\,sec.\ less
than the time required for a complete sidereal revolution.
This, then, is the tropical year\index{year!tropical}, and its length is equal to
365\,d.\:5\,h.\:48\,m.\:46\,sec. It is the ordinary year, and
forms the basis of the calendar. Another kind of year,
strictly of no use for calendar purposes, is called the
anomalistic year\index{year!anomalistic}, and is the time consumed by the earth
in traveling from perihelion round to perihelion again.
We saw that the line of apsides moves slowly forward,
at such a rate that it requires 108,000 years to complete
an entire circuit of the ecliptic. The anomalistic year,
therefore, is over $4\frac{1}{2}$~minutes longer than the sidereal
year, its true length being 365\,d.\:6\,h.\:13\,m.\:48\,s.

\textbf{The Calendar.}\index{calendar}---Two calendars are in use at the present
day by the nations of the world: the Julian calendar and
the Gregorian calendar.
\DPPageSep{175.png}

\Smaller
\label{p166}
The former\index{calendar!reform of} is named after Julius Cæsar\index{astronomy!history}\index{Caesar@Cæsar, Julius, reforms calendar}, who, in \BC~46, reformed the
calendar in accordance with calculations of the astronomer Sosigenes\index{Sosig´enes, Alex.\ st.}.
The true length of the year was known by him to be very nearly $365\frac{1}{4}$
days; so Cæsar decreed that three successive years of 365~days should
be followed by a year of 366~days perpetually. But as the Julian year
is 11.2~minutes too long, the error amounts to about three days every
400~years. In the latter part of the 16th century, the accumulation of
error amounted to 10~days. Pope Gregory XIII\index{Gregory XIII, reforms calendar} corrected this, and
established a farther reform, whereby three leap-year days are omitted
in four centuries. Years completing the century, as 1900 and 2000, are
\emph{centurial} years. Every year not centurial whose number is exactly divisible
by 4 is a leap year; but centurial years are leap years only when
exactly divisible by 400. The year 1900, then, is not a leap year, but
the year 2000 is. In 1752 England adopted the Gregorian calendar, and
earlier dates are usually marked \textsc{o.~s.}\ (old style). At the same time,
England transferred the beginning of the year from 25th March to 1st
January, the date adopted by Scotland in 1600, and by France in 1563.
Thus before 1752, dates between 1st January and 24th March fell in different
years in England and in Scotland or France, and frequently both
years are written in early English dates---as 23d January, $17\frac{26}{27}$, the lower
figure indicating the year according to Scotch and French, and the
upper to early English, reckoning. Russia and Greece still employ the
Julian calendar. Dates in these countries are usually written in fractional
form; for example, July $\frac{10}{23}$, the numerator referring to the Julian
calendar, and the denominator to the Gregorian. The year 1900 is,
therefore, a leap year in Russia and Greece, and their difference of reckoning
from ours is 13~days through the 20th century.
\Restore

\textbf{The Week.}\index{week}---It embraces seven days, and has been
recognized from the remotest antiquity. Its days are:---
\begin{center}
\TableSize
\begin{tabular}{l|c|l|l|l}
\multicolumn{5}{c}{\textsc{The Days of the Week}}  \\[1ex]
\hline \hline
&amp;&amp;&amp;&amp;\\[-1.5ex]
  \multicolumn{1}{c|}{\footnotesize \textsc{English}    }
&amp; \multicolumn{1}{c|}{\footnotesize \textsc{Symbol}     }
&amp; \multicolumn{1}{c|}{\footnotesize \textsc{Derivation} }
&amp; \multicolumn{1}{c|}{\footnotesize \textsc{French}     }
&amp; \multicolumn{1}{c }{\footnotesize \textsc{German}     }
\\
&amp;&amp;&amp;&amp;\\[-1.5ex]
\hline
&amp;&amp;&amp;&amp;\\[-1.5ex]
  Sunday    &amp; \astrosun  &amp; Sun's day    &amp; Dimanche  &amp; Sonntag     \\
  Monday    &amp; \rightmoon &amp; Moon's day   &amp; Lundi     &amp; Montag      \\
  Tuesday   &amp; \sagittarius &amp; Tuisco's day &amp; Mardi   &amp; Dienstag    \\
%[** The printed symbol doesn't quite match \mars.]
  Wednesday &amp; \mercury   &amp; Woden's day  &amp; Mercredi  &amp; Mittwoch    \\
  Thursday  &amp; \jupiter   &amp; Thor's day   &amp; Jeudi     &amp; Donnerstag  \\
  Friday    &amp; \venus     &amp; Freya's day  &amp; Vendredi  &amp; Freitag     \\
  Saturday  &amp; \saturn    &amp; Saturn's day &amp; Samedi
&amp; Sonnabend\rule[-1.5ex]{0pt}{2ex}  \\
\hline\hline
\end{tabular}
\end{center}
\DPPageSep{176.png}

\Smaller
Tuisco is Saxon for the deity corresponding to the Roman Mars,
Woden for Mercury, Thor for Jupiter, and Freya for Venus; therefore
the symbols of the corresponding planets were adopted as designating
the appropriate days of the week. These symbols are more often used
in foreign countries than in our own. The relation of the week to the
year is so close $(52× 7 = 364)$ as to suggest a possible improvement in
the calendar.
\Restore

\textbf{Memorizing the Days in the Month.}---To many persons
the varying number of days in the months of our year is
a great inconvenience. This time-worn stanza is sometimes
helpful:---
\Smaller
\begin{verse}
  Thirty days hath September,          \\
  April, June, and November;           \\
  All the rest have thirty-one,        \\
  Save February, which alone           \\
  Hath twenty-eight, and one day more  \\
  We add to it one year in four.
\end{verse}

The facts are there, even if the rhythm cannot be defended. An
easier method of memorizing the succession is apparent from the illustration
below: Close the
% Fig 7.26
\begin{wrapfigure}[13]{o}{0.5\textwidth}
  \centering
  \Input[0.45\textwidth]{page_167}
  \caption{To recall the Number of Days in Each Month}
\end{wrapfigure}
hand and count out the months on the
knuckles and the depressions between them, until July is reached, then
begin over again. The knuckles represent long months, and the depressions
short ones.

\textbf{Reforming the Calendar.}\index{calendar!reform of}---The inconveniences of our present Gregorian
calendar are many. Some authorities think it on the whole no
improvement on the Julian
calendar; and certainly much
confusion would have been
avoided, if the Julian calendar
had been continued
in use everywhere. A return
to the Julian reckoning
at the beginning of the 20th
century, 1st January, 1901,
was once suggested by Newcomb\index{Newcomb, S. (1835--1909), Am.\ ast.},
the eminent American
astronomer; but any such
change can be brought about
only by wide international agreement. An obvious change having
many advantages would be the division of the year into 13 months,
each month having invariably 28 days, or exactly four weeks. Legal
holidays and anniversaries would then recur on the same days of the
\DPPageSep{177.png}
week perpetually. The chief difficulty would arise in the proper disposition
of the extra day at the end of each ordinary year; and of two
extra days at the end of each leap year.

\textbf{Easter Sunday.}\index{Easter Sunday}---Easter Day is a movable festival, because it falls
on different dates in different years. It is kept on the Sunday next
after the fourteenth day of the Paschal moon; the Paschal moon\index{Paschal moon|see{moon, Paschal}}\index{{moon!Paschal}} being
that moon of which the fourteenth day (approximately the full moon)
occurs on or next after the 21st of March. Hence Easter cannot occur
earlier than March~22 (when the fourteenth day of the Paschal moon is
Saturday, March~21), nor later than April~25 (when the fourteenth day
of the Paschal moon is Sunday, April~18).

Easter is not, however, determined by the true sun and moon, but by
the motion of the fictitious sun and of a fictitious moon imagined to
travel round the celestial equator uniformly with the time. Consequently
the above rule must sometimes fail if applied to the phases of
the moon as given in the almanac. Many have been the bitter controversies
about the proper day to be observed as Easter, through differing
methods of calculation as well as through differing rules. Following are
the dates of Easter for about a third of a century:---
\enlargethispage{36pt}
\begin{table}[h]
\centering
\TableSize
\begin{tabular}{c|l@{~}r|c|l@{~}r|c|l@{~}r|c|l@{~}r}
\hline \hline
  \footnotesize\textsc{Year}\rule{0pt}{3ex}
&amp; \multicolumn{2}{c|}{\footnotesize\textsc{Date}}
&amp; \footnotesize\textsc{Year}\rule[-1.5ex]{0pt}{1ex}
&amp; \multicolumn{2}{c|}{\footnotesize\textsc{Date}}
&amp; \footnotesize\textsc{Year}
&amp; \multicolumn{2}{c|}{\footnotesize\textsc{Date}}
&amp; \footnotesize\textsc{Year}
&amp; \multicolumn{2}{c}{\footnotesize\textsc{Date}}
\\
\hline
  1890 &amp; April &amp;  6 &amp; 1899 &amp; April &amp;  2\rule{0pt}{3ex}
&amp; 1908 &amp; April &amp; 19 &amp; 1917 &amp; April &amp;  8
\\
  1891 &amp; March &amp; 29 &amp; 1900 &amp; April &amp; 15
&amp; 1909 &amp; April &amp; 11 &amp; 1918 &amp; March &amp; 31
\\
  1892 &amp; April &amp; 17 &amp; 1901 &amp; April &amp;  7
&amp; 1910 &amp; March &amp; 27 &amp; 1919 &amp; April &amp; 20
\\
  1893 &amp; April &amp;  2 &amp; 1902 &amp; March &amp; 30
&amp; 1911 &amp; April &amp; 16 &amp; 1920 &amp; April &amp;  4
\\
  1894 &amp; March &amp; 25 &amp; 1903 &amp; April &amp; 12
&amp; 1912 &amp; April &amp;  7 &amp; 1921 &amp; March &amp; 27
\\
  1895 &amp; April &amp; 14 &amp; 1904 &amp; April &amp;  3
&amp; 1913 &amp; March &amp; 23 &amp; 1922 &amp; April &amp; 16
\\
  1896 &amp; April &amp;  5 &amp; 1905 &amp; April &amp; 23
&amp; 1914 &amp; April &amp; 12 &amp; 1923 &amp; April &amp;  1
\\
  1897 &amp; April &amp; 18 &amp; 1906 &amp; April &amp; 15
&amp; 1915 &amp; April &amp;  4 &amp; 1924 &amp; April &amp; 20
\\
  1898 &amp; April &amp; 10 &amp; 1907 &amp; March &amp; 31\rule[-1.5ex]{0pt}{1ex}
&amp; 1916 &amp; April &amp; 23 &amp; 1925 &amp; April &amp; 12 \\
\hline \hline
\end{tabular}
\end{table}
\Restore

Having now learned the A~B~C's of the language which
astronomers use, and having studied the earth as a revolving
globe and the seeming motions of the stars relatively
to it; also having ascertained many facts connected with
our yearly journey round the sun,---we may next seek
to apply that knowledge in a long voyage, begun early
in December, from New York to Yokohama by way of
Cape Horn.
\DPPageSep{178.png}


\Chapter{VIII}{The Astronomy of Navigation}\index{navigation!astronomy of}

On an actual voyage to Japan and back, we shall investigate
new astronomical questions in the order
of their coming to our notice, and verify many
astronomical relations founded on geometric truth. So
we shall be learning a cosmopolitan astronomy of use in
foreign countries as well as at home, and acquiring some
knowledge of astronomical methods by which ships are
safely guided across the oceans.

\textbf{Navigation.}---Navigation is the art of conducting a ship
safely from one port to another. When a ship has gone
20~miles out to sea, all landmarks will usually have disappeared,
and the sea horizon will extend all the way round
the sky. Look in whatsoever direction we will, nothing
can be seen but an expanse of water (page~\pageref{p25}), apparently
boundless in extent. Outside the ship there is
nothing whatever to tell us where we are, or in what
direction to steer our craft. Every direction looks like
every other direction. Still the accurate position of the
ship must be found. The only resource, then, is to
observe the heavenly bodies, and their relation to the
horizon.

\Smaller
The navigator must previously have provided himself with the lesser
instruments necessary for such observation; and the technical books
and mathematical tables by means of which his observations are to be
calculated. These processes of navigation are astronomical in character,
and the principles involved are employed on board every ship.
\DPPageSep{179.png}
The computations required in ordinary navigation are based upon the
data of an astronomical book called the \textit{Nautical Almanac}.

\label{p170} \textbf{The Nautical Almanac.}\index{Almanac, Nautical}---The Nautical Almanac contains the accurate
positions of the heavenly bodies. They are calculated three or
four years in advance, and published by the leading nations of the
globe. Foremost are the British, American, German, and French Nautical
Almanacs. Table~\ref{tab8.1} is a part of a page of \textit{The American Ephemeris
and Nautical Almanac for 1899}, showing data relating to the sun.

The intervals here are one day apart; but for the moon, which moves
among the stars much more rapidly, the position is given for every hour.
Also the angular distance of the moon from certain stars and planets is
given at intervals of three hours. Upon the precision of the Nautical
Almanac depends the safety of all the ships on the oceans. Besides
the figures required in navigating ships, the Nautical Almanacs contain
a great variety of other data concerning the heavenly bodies, used by
surveyors in the field and by astronomers in observatories.
\Restore

\begin{sidewaystable}[p]
\caption{\textsc{October, 1899}}
\label{tab8.1}
\begin{center}
\TableSize
\begin{tabular}{l|r|l|l|r|r|r|c|r|r}
\hline\hline
\multicolumn{10}{c}{\textsc{at greenwich apparent noon}\rule{0pt}{3ex}}\\[1ex]
\hline
\multirow{3}{*}{\begin{sideways}Day of the Week\ \ \rule{0mm}{3.5ex} \end{sideways}}
&amp;\multirow{3}{*}{\begin{sideways}Day of the Month\end{sideways}}
&amp;\multicolumn{5}{c|}{\rule{0mm}{5ex} THE SUN'S }
 &amp;\multicolumn{1}{p{12ex}|}{\multirow{2}{12ex}{\centering Sidereal Time of Semi\-diam\-eter Passing Merid\-ian}}
&amp;\multicolumn{1}{p{15ex}|}{\multirow{2}{15ex}{\centering Equation of Time, to be Subtracted from Apparent Time}}
&amp;\multirow{3}{*}{\begin{sideways}Diff. for 1 Hour\ \ \ \rule[-2ex]{0pt}{2ex}\end{sideways}}
\\
&amp;&amp;\multicolumn{5}{c|}{}&amp;&amp;
\\
\cline{3-7}
&amp;&amp;\multicolumn{1}{p{9.5ex}|}{\rule{0mm}{6ex}\centering Apparent Right Ascension\rule[-5ex]{0mm}{3ex}}
&amp;\multicolumn{1}{p{5ex}|}{ \centering Diff.\ for 1 Hour}
&amp;\multicolumn{1}{p{11ex}|}{ \centering Apparent Declination}
&amp;\multicolumn{1}{p{5ex}|}{ \centering Diff.\ for 1 Hour}
&amp;\multicolumn{1}{p{8ex}|}{ \centering Semi-diame\-ter}
&amp;&amp;&amp; \\
%&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;
%\\
\hline
&amp;  &amp;h.\ \  m. \ \ s. \ &amp;\ \ \ s.
&amp;$° \ \ \ \  '\ \ \ \ ''$&amp;$''$\ \ \  &amp;$'\ \ \ \ ''$ \
&amp; s. &amp;m. \,\ \ s. \ \ \ &amp;s. \ \ \rule{0pt}{2.5ex}
\\
\textit{SUN.} &amp;1 &amp;12 29 39.39          &amp;9.058&amp;S. 3 12 15.5                &amp;$-58.27$&amp;16 1.37         &amp;64.37     &amp;10 \ 19.23 \   &amp;0.796
\\
Mon. &amp;2 &amp;12 33 16.94          &amp;9.071&amp;   3 35 33.0                &amp; 58.18&amp;16 1.64         &amp;64.41     &amp;10 \ 38.18 \   &amp;0.783
\\
Tues.&amp;3 &amp;12 36 54.82          &amp;9.085&amp;   3 58 48.0                &amp; 58.07&amp;16 1.91         &amp;64.46     &amp;10 \ 56.81 \   &amp;0.769
\\[1ex]
Wed. &amp;4 &amp;12 40 33.03          &amp;9.099&amp;   4 22 00.3                &amp;$-57.95$&amp;16 2.19         &amp;64.51     &amp;11 \ 15.10 \   &amp;0.755
\\
Thur.&amp;5 &amp;12 44 11.59          &amp;9.114&amp;   4 45 09.4                &amp; 57.81&amp;16 2.47         &amp;64.56     &amp;11 \ 33.04 \   &amp;0.740
\\
Frid.&amp;6 &amp;12 47 50.52          &amp;9.130&amp;   5  \phantom{0}8 14.9                &amp; 57.65&amp;16 2.75         &amp;64.62     &amp;11 \ 50.61 \   &amp;0.724
\\[1ex]
Sat. &amp;7 &amp;12 51 28.94          &amp;9.147&amp;   5 31 16.5                &amp;$-57.48$&amp;16 3.03         &amp;64.68     &amp;12 \ 07.80 \   &amp;0.708
\\
\textit{SUN.} &amp;8 &amp;12 55  \phantom{0}9.56          &amp;9.164&amp;   5 54 13.8                &amp; 57.29&amp;16 3.31         &amp;64.74     &amp;12 \ 24.59 \   &amp;0.691
\\
Mon. &amp;9 &amp;12 58 49.70          &amp;9.182&amp;   6 17  \phantom{0}6.4                &amp; 57.09&amp;16 3.60         &amp;64.80     &amp;12 \ 40.96 \   &amp;0.673
\\[1ex]  \hline\hline
\end{tabular}
\end{center}
\end{sidewaystable}

% Fig 8.1
\begin{wrapfigure}[21]{o}{0.5\textwidth}
  \centering
  \Input[0.475\textwidth]{page_171}
  \caption{The Chronometer}
  \label{p171}
\end{wrapfigure}
\Smaller
\textbf{The Ship's Chronometers.}\index{chronometer, marine}---Some hours before the departure of the
vessel, two boxes about a foot square are brought on board with the
greatest care, and secured in the safest part of the ship, where the temperature
will be nearly constant. Within each box is another, about
eight inches square, shown open in the picture opposite. Inside it is a
large watch, very accurately made and adjusted, forming one of the
most important instruments used in conducting ships from port to port.
\DPPageSep{180.png}
It is called the marine chronometer, or box chronometer, but generally
the chronometer simply. The face, about $4\frac{1}{2}$~inches in diameter, is
usually dialed to 12~hours, as in ordinary watches. In addition to the
second hand at the bottom of the face, there is a separate index at the
top to indicate how many hours the chronometer has been running
since last wound up; for, like all good watches, winding at the same
hour every day is essential.
Spring and gears are so related
that a chronometer
ordinarily runs 56~hours,
though it should be wound
with great care at regular
intervals of 24~hours---the
extra 32 being a concession
to possible lapses of memory.
Other chronometers,
wound regularly every week,
are constructed to run an
extra day, and so are called
`eight-day' chronometers.
All these instruments are so
jeweled that they will run
perfectly only when the face
is kept horizontal; they are
therefore hung in gimbals, a
device with an intermediate
ring, and two sets of bearings
with axes perpendicular to
each other. As the chronometer
case is hung far above its center of gravity, its face always
remains horizontal, no matter what may be the tilt of the outer box,
in consequence of the rolling or pitching of the ship. The instrument
shown in the illustration is of that particular type known as a \textit{break-circuit}
chronometer, so called because an electric circuit (through wires
attached to the two binding posts on the left side of the box) is automatically
broken at the beginning of every second, by means of a very
delicate spring attached alongside one of the arbors. Such a chronometer
is generally employed by surveying expeditions in the field, where
a chronograph (page~\pageref{p213}) is needed to record the star observations,
and where a clock would be too bulky and inconvenient.

\textbf{What the Chronometers are for.}---The real purpose of chronometers
is to carry Greenwich time\index{Greenwich!in navigation}, and the need of this is made clear farther
on. For at least a fortnight before they are brought on board ship, all
chronometers are carefully tested and compared with a standard clock,
\DPPageSep{181.png}
regulated by frequent observations of the sun and stars, usually at
some astronomical observatory. So at the outset of our voyage we
see how intimate is the relation between practical astronomy and the
useful art of navigation. The navigator of the ship is provided with a
memorandum for each chronometer, showing how much it is fast or
slow on Greenwich time, and how much it is gaining or losing daily.
The amount by which it is fast or slow is called the chronometer error
or correction; and the rate is the amount it gains or loses in 24 hours.
If the chronometer is a good one and well adjusted, the rate should be
only a small fraction of a second. As a rule, on voyages of moderate
length, the Greenwich time can always be found from the chronometers
within three or four seconds of the truth. This uncertainty amounts
to about a mile in the position of the ship. To avoid the possibility of
entire loss of the Greenwich time by any accident to a single chronometer,
ships nearly always carry two, and often many more.

% Fig 8.2
\begin{figure}[hbt!]
  \centering
  \Input{page_172}
  \caption{Works of the Chronometer (Size compared with Ordinary Watch)}
\end{figure}

\textbf{The Works of the Chronometer.}---Familiarity with the interior of any
watch will help in understanding the finer and more complicated works
of the chronometer, well shown in the illustration. The ordinary watch
alongside indicates the relative size of the parts. The chronometer
balance is about one inch in diameter, and the hairspring about $\frac{1}{3}$~inch
in diameter, and $\frac{1}{4}$~inch high. Fusee, winding post, and some other details
are well seen. On the left is the glass crystal, set in a brass cell
which screws on top of the brass case, shown on the right. On the
right-hand side of this case is seen one of the pivot bearings by which
it swings in the gimbals.

% Fig 8.3
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_173}
  \caption{The Chronometer Balance}
\end{wrapfigure}

\textbf{The Chronometer Balance.}---A balance compensated for temperature
is necessary to the satisfactory running of a chronometer, because a
chronometer with a plain, uncompensated brass balance will lose $6\frac{1}{9}$
seconds daily for each Fahrenheit degree of rise in temperature. In
\DPPageSep{182.png}
order to counteract this effect, marine chronometers (and all good
watches) are provided with a balance, the principle of which is shown
in the illustration. The arm passing centrally through the balance is
of steel, and at its ends are two large-headed screws, for making the
chronometer run correctly at a
standard temperature, say $62$°.
The semicircular halves of the
rim are cut free, being attached
to the arm at one end only.
The rim itself is composed of
strips of brass and steel firmly
brazed together. The outer
part is brass, and the inner
steel, of one half the thickness of
the brass. With a rise of temperature,
brass tends to expand
more rapidly than steel; and
by overpowering the steel, it
bends the free ends of the rim
inward, practically making the
balance a little smaller. When
the temperature falls, the balance
enlarges again slightly. Near the middle of each half rim is a weight,
which can be moved along the rim. Delicate adjustment for heat and
cold is effected by trial, the chronometer being subjected to varying
temperatures in carefully regulated ovens and refrigerating boxes. The
weights are moved along the rim until gain or loss is least, no matter
what the thermometer may indicate.

\textbf{Time on Board Ship.}\index{time!on board ship}---The time for everybody on board ship is
regulated according to an arbitrary division adopted by navigators.
The day of 24~hours is subdivided into six periods of four hours each,
called \textit{watches}. A watch is a convenient interval of duty for both
officers and sailors; and this division of the ship's day is recognized
by mariners the world over. The period from 4~\PM\ to 8~\PM\ is subdivided
into two equal parts, called dogwatches; so that the seven
watches of the ship's day, with their names, are as follows:---
\begin{center}
\begin{tabular}{l l@{ }r@{ }l@{ } c@{ }r@{ }l}
The first watch,     &amp; from &amp; 8 &amp; \PM      &amp; to &amp; 12 &amp; midnight. \\
The mid watch,       &amp; from &amp;12 &amp; midnight &amp; to &amp;  4 &amp; \AM \\
The morning watch,   &amp; from &amp; 4 &amp; \AM      &amp; to &amp;  8 &amp; \AM \\
The forenoon watch,  &amp; from &amp; 8 &amp; \AM      &amp; to &amp; 12 &amp; noon.   \\
The afternoon watch, &amp; from &amp;12 &amp; noon     &amp; to &amp;  4 &amp; \PM \\
The first dogwatch,  &amp; from &amp; 4 &amp; \PM      &amp; to &amp;  6 &amp; \PM \\
The second dogwatch, &amp; from &amp; 6 &amp; \PM      &amp; to &amp;  8 &amp; \PM
\end{tabular}
\end{center}
\DPPageSep{183.png}

The dogwatches differ in length from the regular watches, so that
during the cruise the hours of duty for officers and men may be distributed
impartially through day and night. Every watch of four hours
is again divided into eight periods, each a half hour long, called \textit{bells}.
Each watch, except the dogwatches, therefore, continues through eight
bells. The end of the first half-hour period of each watch is called \emph{one
bell}; of the second, \textit{two bells}; of the third, \textit{three bells}; and so on.
Four bells, for example, corresponds to two o'clock, six o'clock, and ten
o'clock; and seven bells to half past three, half past seven, and half
past eleven, whether \AM\ or \PM, of time on shore.
\Restore

\textbf{Low Tide delays the Ship's Departure.}---Another point of
contact between astronomy and navigation was well illustrated
as the ship was about to depart. The tide was low,
and she must wait a few hours until it rose. The times of
high tide and low tide are predicted by calculations based
in large part upon the labors of astronomers. The mere
phenomena of tides are inquired into here, leaving the
explanation of them to a subsequent chapter on universal
gravitation.

\textbf{The Tides in General.}\index{tides}---A visit of one day to the seashore
is sufficient to show the rising and falling of the ocean. It
may happen that in the morning a walk can be taken
along the broad, sandy beach, which later in the day will be
covered under the risen waves. Or rocks where one sat in
the morning are in the afternoon buried underneath green
water. A single day will always show these changes; and
another single day will exhibit similar fluctuations, only at
other hours. The photographic picture opposite indicates
a typical range of the tides, and horizontal markings on
the rocks show the level of high tide, seven or eight feet
above water level in the illustration. A week's stay at the
shore will establish the regularity of variation. High tide
at ten o'clock in the morning means low tide a little after
four in the afternoon, or approximately six hours later,
high tide occurs again soon after ten in the evening, and
low tide at about half past four in the morning. So there
\DPPageSep{184.png}
are two high tides and two low ones in every 24~hours, or
more properly, in nearly 25~hours. And if it is high tide
one morning at ten o'clock, the next day full tide will occur
at about eleven o'clock. So that gradually the times of
high and low tide change through the whole 24~hours, lagging
about 50~minutes from one day to another.

% Fig 8.4
\begin{figure}[hbt!]
  \centering
  \Input{page_175}
  \caption{At Low Tide---(Markings on Rocks are Level of High Tide)}
\end{figure}

\textbf{The Tides defined.}---A tide is any bodily movement of
the waters of the earth occasioned by the attraction of
moon and sun. The word \textit{tide}, as used by the sailor,
often refers to the nearly horizontal flow of the sea, forth
and back, in channels and harbors. To the astronomer,
the word \textit{tide} means a vertical rise and fall of the waters,
very different in different parts of the earth, due to the
westerly progress of the tidal wave round the globe. The
time of highest water is called high tide; and of lowest
water, low tide. From high tide to low is termed ebb tide;
from low to high, flood tide. Near new moon and full
moon each month (as explained on page~\pageref{p388}) occur the
highest and lowest tides, termed spring tides. As the
moon comes to new and full every month, or lunation, and
as there are about $12\frac{1}{2}$~lunations in the year, there are
nearly 25~periods of spring tides annually. Spring tides
\DPPageSep{185.png}
have nothing to do with the season of spring. Intermediate
and near the moon's first and third quarters, the ebb
and flood, being below the average, are called neap tides
(\textit{nipped}, or restricted tides). So valuable to the navigator
is a knowledge of the times of high tide and low tide
at all important ports, that these times are carefully calculated
and published by government authority a year or
two in advance. This duty in our country is fulfilled by
the United States Coast and Geodetic Survey\index{survey!U. S.\ Coast \&amp; Geod.}, a bureau of
the Department of Commerce and Labor.

\textbf{Direct and Opposite Tides.}---The tide formed on the
earth as a whole is made up of two parts: (\textit{a})~the direct
tide, which is the bulge
or protuberance, or tidal
wave on the side of the earth toward the tide-raising
body, and (\textit{b})~the opposite tide, which is
the tidal wave on the side away from it. The
figure shows a section of the earth surrounded
as it always is by such a double tide. Gravitation,
as explained in the chapter on that subject,
elongates the watery envelope of the earth very
slightly in two opposite directions. Thus the
earth and its waters are a prolate spheroid; that
is, slightly football-shaped. As the earth turns
round on its axis eastward, this watery bulge
seems to travel from east to west, in the form
of a tidal wave twice every 25~hours. To illustrate:
It is as if a large cannon ball were turning
on the shorter axis of a football and inside
of it. If the waters could at once respond to
the moon's attraction, the time of high tide would coincide
with the moon's crossing the upper or lower meridian
But on account of inertia of the water, the comparatively
% Fig 8.5
\begin{wrapfigure}{o}{0.25\textwidth}
  \centering
  \Input[0.2\textwidth]{page_176}
  \caption{Direct and Opposite Tides}
\end{wrapfigure}
feeble tide-producing force requires a long time to start
the wave. The time between moon's meridian transit and
\DPPageSep{186.png}
arrival of the crest of the tidal wave is called the \textit{establishment
of the port}. This is practically a constant quantity
for any particular port, but is different for different ports.
It is $8\frac{1}{4}$~hours for the port of New York.

\Smaller
\textbf{Only the Wave Form travels.}---Guard against thinking that the
tides are produced by the waters of the ocean traveling bodily round
the globe from one region to another. The deep waters merely rise
and fall, their advance movement being very slight, except where the
tidal wave impinges upon coasts. It is only the form of the wave that
advances westerly. Illustrate by extending a piece of rope on the floor
and shaking one end of it. A wave runs along the rope from one end
to the other; but only the wave form advances, the particles of the
rope simply rising and falling in their turn. So with the waters of
the tidal wave.
\Restore

\textbf{Movement of the Tidal Wave.}---Originating in the deep
waters of the Pacific Ocean, off the west coast of South
America, the tidal wave travels westerly at speeds varying
with the depth of the ocean. The deeper the ocean, the
faster it travels. During this progressive motion of a
given tidal wave it combines with other and similar tidal
waves, so that the resultant is always complex. In about
12~hours it reaches New Zealand, passes the Cape of
Good Hope\index{Cape of Good Hope!tide} in 30~hours, where it unites with (\textit{a})~the
direct tide in the Atlantic off Africa, and (\textit{b})~a reversed
wave, which has moved easterly round Cape Horn into
the Atlantic. The united wave then travels northwesterly
through the Atlantic Ocean about 700~miles hourly, reaching
the east coast of the United States in 40~hours. On
account of the irregular contour of ocean beds, there is
never a steadily advancing tidal wave, as there would
be if the oceans covered the entire earth to a uniform
depth. Tidal charts of the oceans have drawn upon them
irregularly curved lines connecting places where crests of
tidal waves arrive at the same hour of Greenwich time.
These are called cotidal lines\index{cotidal lines}.
\DPPageSep{187.png}

\Smaller
\textbf{Extent of Rise and Fall.}---The extent of rise and fall of the tide
varies in different places. Speaking generally, in mid-ocean the difference
between high and low water is between two and three feet, while
on the shores of great continents, especially in shallow and gradually
narrowing bays, the height is often very great. The average spring
tide at New York is about $5\frac{1}{2}$~feet, and at Boston about 11. In the
Bay of Fundy, spring tides rise often 60~feet, and sometimes more.
The tide also rises in rivers, but less as the distance from the river's
mouth increases, where it is more and more neutralized by the current.
A tide of a few inches advances up the Hudson River from New York
to Albany in about nine hours. It is possible for a river tide to rise to
a higher level than that of the ocean itself, where the momentum of the
wave is expended in raising a relatively small amount of water, on
the principle of the hydraulic ram. At Batsha in Tonquin there is no
tide whatever, because the waters enter by two mouths or channels
of unequal depth and length, the lagging in the longer channel being
about six hours more than in the shorter one.

\textbf{Tides in the Great Lakes.}---Theoretically there are tides in large
bodies of inland water also; but even the largest lakes are too small
for their share in the moon's tide-producing force to be very pronounced.
A tide of less than two inches occurs in Lake Michigan at Chicago;
and in the Mediterranean there is a slight tide of about 18 inches.
Height of the tide in landlocked seas depends in part upon the ratio
of the length of such seas (east and west), to the diameter of the earth.
Meager tides like these are often completely masked by the tides which
local winds raise.
\Restore

% Fig 8.6
\begin{figure}[hbt!]
  \centering
  \Input[\textwidth]{page_178}
  \caption{Ebb Tide always longer than Flood Tide}
  \label{fig8.6}
\end{figure}

\textbf{Duration of Flood and Ebb Tides.}---In mid-ocean the
tidal wave rises much less than on the coasts; for on
reaching shallow water, friction retards the wave, shortening
its length from crest to crest, and greatly increasing
the height of the tide, particularly if the advancing wave
is forced to ascend a somewhat shallow and gradually
narrowing channel.

\Smaller
Figure~\ref{fig8.6} illustrates this change in the section of a tidal wave
advancing toward a coast on the right. The crest of the wave is farther
\DPPageSep{188.png}
from the bottom and therefore less retarded by friction, so that it
advances more rapidly, and makes the wave steeper on its front than
on its after slope. Under all ordinary conditions, then, flood tide is
evidently shorter in duration than ebb tide. At Philadelphia, for
example, where the difference is accentuated by coast configurations
ebb tide is nearly two hours longer than flood tide. An extreme case
is that known as the tidal bore\index{tidal bore}, in which the advancing slope of the
tidal wave in certain favorably conditioned rivers becomes perpendicular.
The crest then topples over, and flood tide takes the form of a swiftly
advancing breaker; in only a few minutes the waters rise from low to
high, and ebb tide consumes rather more than 12 hours following. This
strong tidal wave surmounting the seaward current of the river, sometimes
piling up a cascade of overlapping waves, is well marked in the
Seine, the Severn, and the Ganges.
\Restore

% Fig 8.7
\begin{figure}[hbt!]
  \centering
  \Input{page_179}
  \caption{Tidal Bore at Caudebec, a town on the Seine (according to Flammarion)}\index{Flammarion, C. (flam-ma-re-ong´), Dir.\ Juvisy Obs.\ (Paris)}\index{tidal bore}
\end{figure}

\textbf{Diurnal Inequality of the Tides.}---If the earth's equator
coincided with the plane of the moon's orbit, and if there
were no obliquity of the ecliptic, evidently the tide-producing
\DPPageSep{189.png}
force of both sun and moon would always act perpendicular
to the earth's axis. The direct tide and the opposite
tide would then be symmetrical with reference to the
equator; and, generally speaking, equal latitudes would
experience equal tides. When, however, the moon is at her
greatest declination north, the direct tide is highest at those
north latitudes where the moon culminates at the zenith;
while the opposite tide is slight in the northern hemisphere,
but highest at the antipodes of the direct tide, or
in south latitudes equal to the north declination of the
moon. This difference in height of the two daily tidal
waves is called the diurnal inequality.

% Fig 8.8
\begin{figure}[hbt!]
  \centering
  \Input{page_180}
  \caption{Diurnal Inequality of the Tides at San Francisco}
\end{figure}

\Smaller
In the case of lunar tidal waves, the diurnal inequality becomes
zero twice each month, when the moon crosses the celestial equator;
and the diurnal inequality of the solar tide vanishes at the equinoxes.
But this obvious difference in height of the two daily tides is greatly
modified by coast configurations and other conditions. The illustration
above is plotted from a fortnight's record of the tide gauge at San
Francisco. The wave line represents the rise and fall of the surface
of the water; the distance from one horizontal line to another being
two feet. Vertical lines divide off periods of 24~hours, the succession
of days being
% Fig 8.9
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_181}
  \caption{Sextant for measuring Angles}
  \index{sextant}
\end{wrapfigure}
indicated at the top. The difference between direct and
opposite tide is very marked each day, except when the moon is near
the equator, when the diurnal inequality is much reduced. Small dots
are placed adjacent to the highs and lows of the direct tide, which
illustrate the diurnal inequality excellently, having a very wide range
in northern latitudes when the moon culminates nearest the zenith, a
medium range when she is crossing the equator, and a minimum range
when her south declination is near a maximum.
\Restore
\DPPageSep{190.png}

\textbf{The Sextant.}\index{sextant}---The sextant is a light, portable instrument
arranged for measuring conveniently arcs of a great
circle of the celestial sphere in any plane whatever. With
it are made the astronomical
observations which are
calculated by means of the
Nautical Almanac. Next
to the compass, the sextant
is more frequently
used than any other instrument;
for by the
angles measured with it,
the navigator finds his
position upon the ocean
from day to day.

% Fig 8.10
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_182}
  \caption{How Angles are measured}
  \label{p182}
\end{wrapfigure}
\Smaller
\index{sextant!adjustments}In navigation the sextant is generally used in a vertical plane; that
is, in measuring altitudes\index{altitude!measuring} of heavenly bodies. The sextant was invented
by Hadley\index{Hadley, J. (1682--1744), Eng.\ math.} in 1730. A finely graduated arc \textit{A}, of $60$° (whence
the origin of its name) has an arm (from \textit{I} downward toward the right)
sliding along it, as the radius of a circle would, if pivoted at the center
and moved round the circumference. Rigidly attached to the pivot
end of this moving arm, and at right angles to the plane of the arc, is
a mirror, \textit{I}, called the index glass. Also firmly attached to the frame
of the arc is another mirror, \textit{FH}, only partly silvered, called the
horizon glass. A telescope \textit{K}, parallel to the frame and pointed
toward the center of horizon glass, helps accuracy of observation.
Shade glasses of different colors and density (at \textit{D} and \textit{E}) make it
possible to observe the sun under all varying conditions of atmosphere---haze,
fog, thin cloud, or a perfectly transparent sky; for that orb
is, of all heavenly bodies, the most frequently observed in navigation.
Shade glasses tone down the light, whatever its intensity, and farther increase
the accuracy of observation. A clamp and tangent screw (below
the arc) facilitate the details of actual observation; antecedent to
which, however, the adjustments of the sextant must be carefully made.
The most important are these: when the arm is set at the zero of the arc,
the plane of the principal mirror also must pass through the zero of the
arc; and the horizon glass must be parallel to the mirror, both being
perpendicular to the plane of the graduated arc or limb. The horizon
line is \textit{CH} (Figure~\ref{p182}), and the heavenly body is in the direction \textit{CS}.
%[** The letters labeling parts of the sextant are italicized in the text, but upright in the illustration.
\DPPageSep{191.png}
The distant horizon is seen by the eye through the telescope at \textit{K}, and
its line of sight passes through the upper or unsilvered part of the horizon
glass \textit{LL'}. When the arm is
at 0°, the index glass stands in the
direction \textit{AK} but when an altitude,
\textit{HCS}, is to be measured, the arm
is pushed along the limb to \textit{O}.
The index glass then stands in the
position \textit{II'}, so that light will travel
in the direction of the arrows \textit{SABK}.
After reflection from the two mirrors,
the object will appear in contact
with the horizon. The arc is read,
and the observation is complete.
As the angle between index and
horizon glasses is half the angle
measured, the limb is graduated at
the rate of 1° for each actual $30'$.
\Restore

\textbf{Finding the Latitude at Sea.}\index{latitude!finding at sea}---Usually the first astronomical
observation at sea will be made for the purpose of
finding the latitude of the ship. There are many methods,
but all are based on the fundamental principle already
given, that the latitude is always equal to the altitude of
the celestial pole. Usually latitude is found by observing
the altitude of some celestial body when crossing the meridian
on the opposite side of the zenith from the pole.
So it is referred directly to the equator, whose distance
from the zenith always equals the latitude also.

\Smaller
For example: a few minutes before noon, the navigator will begin
to observe the sun's altitude with the sextant, repeating the observation
as long as the altitude continues to increase. When the sun no longer
rises any higher, it is on the local meridian. The time is high noon, or
apparent noon. The officer then gives the order `Make it Eight Bells,'
and proceeds to ascertain the latitude from the observation just made.
The diagram on page~\pageref{p84} elucidates the principle involved. Once the
meridian zenith distance is found by observation, latitude is ascertained
from it by the same principle, whether at sea or on land.
\Restore

\textbf{Finding the Longitude at Sea.}\index{longitude!finding at sea}---As on land, so at sea,
finding the longitude of a place is the same thing as finding
\DPPageSep{192.png}
how much the local time differs from the time of a
standard meridian. The prime meridian of Greenwich is
almost universally employed in navigation. First, then,
local time must be found.

\Smaller
A portable instrument like the sextant must be used, because of the
continual motion of the ship. With it the navigator observes the altitude
of some familiar heavenly body toward the east or west. This
operation is called `taking a sight.'\index{sight!taking a} Most often the sun is observed for
this purpose---either early in the morning, or late in the afternoon.
The nearer the time of its crossing the prime vertical, the better, because
its altitude is then changing most rapidly, and so the observation can be
made more accurately. First, the latitude must be known. Then the
local time is worked out by a branch of mathematics called spherical
trigonometry. This computation forms part of the everyday duty of the
navigator; and as simplified for his use, it is an arithmetical process,
greatly facilitated by specially prepared tables of the relation of the
quantities involved. These are three: the altitude of the body (given
by observation), its declination (obtained from the Nautical Almanac),
and the latitude of the ship. Having found the local time, take the
difference between it and the chronometer (Greenwich) time\index{Greenwich!in navigation}; the result
is the longitude sought. If local time is greater than Greenwich time,
longitude is east; west, if less. There are many methods of ascertaining
longitude, and each navigator, as a rule, has his favorite. Sumner's\index{Sumner's method}\index{Sumner, T. B. (1810--70), Am.\ navigator}
method is generally conceded to be the best. Except in overcast
weather, the navigating officer will usually feel sure of the position of his
ship within two miles of latitude, and three to five miles of longitude. It
is difficult to find her position nearer than this unless the observations
are themselves made with exceptional care, and the errors of sextant
and chronometer have been specially investigated with greater precision
than is either usual or necessary. Once the position of the ship is
known, it is plotted on the chart, and the proper course is calculated
and the ship maintained on it by constant watch of the compass, a delicate
magnetic instrument by which true north can always be found.
\Restore

% Fig 8.11
\begin{figure}[hbt!]
  \centering
  \Input{page_184}
  \caption{Dip of the Horizon}
  \index{dip of the horizon}\index{horizon!dip of}
\end{figure}

\textbf{Dip of the Horizon.}---In calculating any observation of
altitude of a heavenly body taken at sea, a correction for
dip of the horizon is always applied. Dip of the horizon
is the angle between a truly horizontal line passing
through the observer's eye, and the line of sight to his
visible horizon, or circle which bounds the view.
\DPPageSep{193.png}

\Smaller
As the surface of our globe may be regarded as spherical (always
so considered in practical navigation), it must curve down from the
ship equally in every direction. The figure shows this clearly. Also,
as altitude is angular distance above the sensible horizon, it is apparent
that every observation of altitude must be diminished by the correction
for dip. Plainly, too, dip is greater, the higher the deck of the ship
from which the observation is taken. If the deck is 10~feet above the
water, the correction for dip is about three minutes of arc; if 18~feet,
about four minutes. From the elevation of a deck of ordinary height,
the visible horizon is about seven miles distant in every direction;
and generally speaking a ship will never be visible at more than double
this distance, even with a telescope. Usually an approaching ship will
not become visible until about eight miles away; but the condition
of the atmosphere, the character of the distant ship's rigging, the way
in which sunlight falls upon it, and the rising and falling of both ships
on the waves,---all affect this distance materially.

\textbf{Where does the Southern Cross become Visible?}\index{Southern Cross}---A question of
perennial interest to the southward voyager. Its answer may come
appropriately now, but first it is necessary to know how far this famous
asterism is south of the celestial equator; that is, its south declination.
Consulting charts of the southern heavens, we find that the central
region of the Cross is in south declination $60$°. Consequently, it will
just come to the southern horizon when the latitude is equal to $90° - 60$°;
that is, $30$°. But haze and fog near the sea horizon will usually
obscure the Cross until a latitude six or seven degrees farther south
has been reached. Good views of it may be expected at the Tropic
of Cancer, and they improve with the journey farther south. It must,
however, be said that the Southern Cross is a disappointment, for it
is by no means so striking a configuration as the Great Bear.
\Restore

\textbf{Where will the Sun be overhead at Noon?}\index{sun!overhead at noon}---Not before
we reach the tropics, because the sun never can pass overhead
at any place whose latitude exceeds $23\frac{1}{2}$°.
\DPPageSep{194.png}

% Fig 8.12
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_185}
  \caption{Apparent Motion of the South Polar Heavens}
\end{wrapfigure}
\Smaller
But in Chapter \textsc{iv} it was shown that the latitude is always equal to
the declination of the zenith. If, therefore, it is desired to find the
place where the sun will pass through the zenith at noon, we must
first ascertain the sun's declination from the almanac (or approximately
from page~\pageref{p85}). Then it is apparent that the zenith sun will be met at
noon, when the latitude of the ship is exactly the same as the sun's
declination. From vernal equinox to autumnal equinox, when the sun
is all the time north of the equator, the ship must be in the northern
hemisphere, in order that the sun may pass directly over her. And,
in general, the sun will pass through the ship's zenith on the day when
her latitude is the same in sign and amount as the declination of the
sun. For example, on the 2d of March the sun will be overhead at
noon to all ships which are crossing the 7th parallel of south latitude,
because the sun's declination is $7$° south on that day.

\textbf{In Southern Latitudes.}---Looking northward, or away from the pole
now visible, the stars appear to rise on our right hand, passing up over
the meridian, and setting on
our left. They still rise in the
east and set in the west. But
looking poleward, the stars circulate
round the pole clockwise
by diurnal motion, as indicated
by arrows in the diagram adjacent.
The south pole of the
heavens rises one degree above
the south horizon for every
higher degree of south latitude.
If the south pole were
actually reached, all the stars
south of the equator would be
perpetually visible, and no star
of the northern hemisphere
could ever be seen. But the
region overhead in the sky
would not be conspicuously
marked, as at the north pole,
by Polaris and the Little Bear,
because there is no conspicuous
south polar star. In fact, there is no star as bright as the fifth magnitude
within the circle drawn five degrees from the pole. The pair of
stars in the Chamæleon, here shown underneath the pole, are of the
fifth magnitude, and Beta Hydri is a third magnitude star. All are
easy to find from the Southern Cross, which is $2\frac{1}{2}$ times farther from
the pole than the Chamæleon stars.
\DPPageSep{195.png}

\textbf{Rounding Cape Horn to San Francisco.}---On the remainder of our
ship's voyage to latitude about $57$°~south, where she rounded the Cape,
little or nothing new arose, involving any astronomical principle. The
Southern Cross passed practically through the zenith, because the latitude
was nearly equal to the declination of the asterism. The mild
temperature nearly all the way was a verification of the opposite
season in the southern hemisphere; for although it was winter (December,
January, and February) at home, it was summer at the same
time in south middle latitudes. Approaching the equator, it was
observed that the inequality of day and night was gradually obliterated,
quite independently of the season; for at the equator the diurnal arcs
of all heavenly bodies are exact semicircles, no matter what their
declination. At the equator, too, the brief twilight attracted attention---brief
because the sun sinks at right angles to the horizon, instead of
obliquely; so that it reaches as quickly as possible the angle of depression
($18$°) below the horizon, at which twilight ceases. On approaching
the California coast, after a voyage of nearly four months, in which land
had been sighted only once, it was a matter of much concern what the
deviation of the chronometers might be from the rates established at
New York. It was evidently not large, for the landfall off the Golden
Gate was made without any uncertainty. On coming to anchor in San
Francisco bay, it was easy to verify the chronometers, by observing the
time signal at local noon (nearly) each day, which is given by the
dropping of a large and conspicuous time-ball\index{time-ball} at exactly 8\,h.\:0\,m.\:0\,s.\
\PM, Greenwich time. Comparison of the chronometers with this
signal showed that the Greenwich time, as indicated by their dials,
differed only 8\,s.\ from the time-ball; so that the average daily deviation
from the rate as determined at New York was only $\frac{1}{16}$ of a second.
\Restore

\textbf{Standard Time Signals.}\index{standard time|see{time, standard}}\index{time!standard}\index{time!signals}---About a dozen time-balls\index{time-ball} are
now in operation in the United States. The principal
ones are dropped every day at noon, Eastern Standard or
75th meridian time, in Boston, New York, Philadelphia,
Baltimore, and Washington; at noon, Central time, in
New Orleans; and at noon, Pacific Standard, or 120th
meridian time, in San Francisco.

\Smaller
The error of the signal, only a fraction of a second, is published in
the local newspapers of the following day. In foreign countries, time
signals are now regularly furnished, chiefly for the convenience of shipping,
in about 125 of the principal ports of the world. In England
and the British possessions, it is customary to give the time signal at
\DPPageSep{196.png}
1~\PM, often by firing a gun. But the dropping of a time-ball\index{time-ball} (page~\pageref{p9})
is the favorite signal throughout the world generally. In many of these
ports, the time is determined with precision at a local observatory, and
the time-ball may be utilized in re-rating the ship's chronometers.
\Restore

\textbf{Where does the Day change?}\index{day!change of}---Imagine a railway girdling
the world nearly on the parallel of New York, and
equipped with locomotives capable of maintaining a speed
of 800 miles an hour. At noon on Wednesday, start westward
from New York; in about an hour, reach Chicago, in
another hour Denver, in still another hour San Francisco.
As these places are about $15$°, or one hour of longitude
from each other, evidently it will be Wednesday noon on
arrival at each of them, and at all intermediate points,
because the traveler is going westward just as fast as the
earth is turning eastward; so it will be perpetual midday.
Continue the journey westward at the same rate all the
way round the earth. Night will not come because the sun
has not set. So there can be no midnight. How, then,
can the day change from Wednesday to Thursday? Will
it still be Wednesday noon when the traveler returns to
New York? On arrival there, 24~hours after he started,
he will be told that it is Thursday noon. Where did the
day change? Manifestly it must change somewhere once
every 24~hours. Nearly the whole world has agreed to
change at the 180th~meridian from Greenwich, because
there is little land adjacent to this meridian, and very few
people are inconvenienced. Noon at Greenwich is midnight
on the 180th~meridian. If, therefore, a ship westward
bound on the Pacific Ocean comes to this meridian at midnight
of, say, Wednesday, on crossing that meridian it is
immediately after 12~\AM\ of Friday. As a rule ships will
not arrive at the 180th~meridian exactly at midnight; but
this does not affect the principle involved: a whole day,
or 24~hours, is dropped or suppressed in every case.
\DPPageSep{197.png}

\Smaller
If, for example, it is Friday afternoon at four o'clock when this line
is reached, it becomes Saturday immediately after 4~\PM\ as soon as
the 180th meridian is crossed. This experience, familiar to all trans-pacific
voyagers, is called `dropping the day.' If a person born on
the 29th of February were crossing the Pacific Ocean westward on a
leap year, and should arrive at the 180th meridian at midnight on the
28th of February, the change of day would bring the reckoning of time
forward to the first of March; so that he would have the novel experience
of living eight years with strictly but a single birthday anniversary.
Journeying eastward across the 180th meridian, the reverse of this process
is followed, and 24~hours are subtracted from the reckoning. If,
for example, the ship reaches this meridian at 10~\AM\ Wednesday, it
immediately becomes 10~\AM\ Tuesday on crossing it. When, in 1867,
the United States purchased Alaska\index{Alaska transferred to U. S.}, it was found necessary to set the
official dates of the new territory forward 11~days (page~\pageref{p166}), because
the reckoning had been brought eastward from Russia, its former owner.
Russian dates were then 12~days behind ours; but the difference in
Alaska was only 11~days, because it is east of the 180th meridian.
\Restore

\textbf{Time at Home compared with Time in Japan.}---The
arrival of a ship at Yokohama will usually be cabled to
her owners,---in New York very probably. Sending such
a message naturally gives rise to inquiry as to when it
will be received. The table of `Standard Time\index{time!standard} in Foreign
Countries' (page~\pageref{p126}) shows that the time service of the
Japanese Empire corresponds to the 135th meridian (9~hours)
east of Greenwich. As Eastern Standard time is
five hours slower than Greenwich time, evidently Japan is
10~hours west of our standard meridian; and its standard
time would be 10~hours slower than ours, except for the
change of day. On account of this, the standard time of
Japan is 24~hours in advance, minus 10~hours slower; that
is, 14~hours in advance of Eastern Standard time.

\Smaller
The same result is reached, if we go round the world eastward to
Japan, thereby avoiding the troublesome 180th meridian. The Eastern
Standard meridian is five hours west of Greenwich, and Japan is nine
hours fast of Greenwich. So that it is 14~hours east of us; that is, its
time is 14~hours faster than ours. Allow six hours of actual time for the
transmission of a cablegram from Yokohama to New York; if one
\DPPageSep{198.png}
were sent at 7~\AM\ on Tuesday, it would be delivered at 11~\PM\ on
Monday, or seemingly eight hours before it was dispatched.
\Restore

\textbf{Great Circle Courses the Shortest in Distance.}\index{great circle|see{circle, great}}\index{circle!great, courses}---In ocean
voyages, in steamships, particularly in crossing the Pacific,
the captain will usually choose the course which makes
his run the shortest distance between the two ports. Imagine
a plane through the center of the earth and both
ports; the arc in which this plane cuts the earth's surface
is part of a great circle. This arc, the shortest distance
between the two ports, is called a great circle course. If
both are on the equator, the equator itself is the great
circle connecting them; and the ship goes due east or due
west, when sailing a great circle course from one to the
other. If, however, the ports are not on the equator,
but both in middle latitudes, as San Francisco and Yokohama,
the parallel of latitude
(which nearly joins them and
is a small
% Fig 8.13
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.6\textwidth]{page_189}
  \caption{Great Circle Course the Shortest}
\end{wrapfigure}
circle of the globe)
has a greater degree of curvature
than the great circle,
which clearly must pass
through much higher latitudes.
As shown by the diagram
of the two arcs, seen from above the pole, the great
circle arc, lying farther north, deviates less from a straight
line than the corresponding arc of a parallel (upper curve).
It is therefore a shorter distance. Consequently ships
sailing great circle courses will usually pass through latitudes
higher than either the point of departure or destination.

Before passing on to a study of sun, moon, and
planets, we digress to consider the instruments by whose
aid our knowledge of these orbs has mainly been acquired.
\DPPageSep{199.png}


\Chapter{IX}{The Observatory and its Instruments}\index{observatories}

Observatories are buildings in which astronomical
and physical instruments are housed, and
which contain all the accessories for their convenient
use. Most important of all instruments of a
modern observatory are telescopes and spectroscopes.

\textbf{Astronomy before the Days of Telescopes.}\index{astronomy!before telescopes}\index{astronomy!history}\index{telescope!astronomy before}---The progress
of astronomy has always been closely associated with
the development and application of mechanical processes
and skill. Earlier than the seventeenth century, the size of
the planets could not be measured, none of their satellites
except our moon were known, the phases of Mercury and
Venus were merely conjectured, and accurate positions of
sun, moon, and planets among the stars, and of the stars
among themselves, were impossible---all because there
were no telescopes. More than a half century elapsed
after the invention\index{telescope!invention} of the telescope before Picard\index{Picard, J. (pe-car´) (1620--82), Fr.\ geom.} combined
it with a graduated circle in such a way that the
measurement of angles was greatly improved. Then arose
the necessity for accurate time; but although Galileo\index{Galile´i, G. (1564--1642), It.\ ast.} had
learned the principles governing the pendulum, astronomy
had to wait for the mechanical genius of Huygens\index{Huygens, C.\ (hy´genz) (1629--95), Dutch ast.} before
a satisfactory clock was invented, about 1657. Nearly all
the large reflecting telescopes ever built were constructed
by astronomers who possessed also great facility in practical
mechanics; and the rapid and significant advances in
nearly all departments of astronomy during the last half
\DPPageSep{200.png}
century would not have been possible, except through the
skill and patience of glass makers, opticians, and instrument
builders, whose work has reached almost the limit of
perfection. Before 1860, if we except the meager evidence
from meteoric masses of stone and iron, some of which had
actually been seen to fall, it is proper to say that our ignorance
of the physical constitution of other worlds than ours
was simply complete. The principles of spectrum analysis
as formulated by Kirchhoff\index{Kirchhoff, G.~R.\ (keerk´hof) (1824--87), Ger.\ physicist} led the way to a knowledge of
the elements composing every heavenly body, no matter
what its distance, provided only it is giving out light intense
enough to reach our eyes. But since Newton\index{Newton, Sir I. (1642--1727), Eng.\ ast.}, no
necessary step had been taken along this road until the
way to this signal discovery was paved by the deftness of
Wollaston\index{Wollaston, W.~H.\ (1766--1828), Eng.\ physicist}, who showed that light could not be analyzed
unless it is first passed through a very narrow slit; and
of Fraunhofer\index{Fraunhofer@v.\ Fraunhofer, J. (frown´h\=o-fer) (1787--1826)}, the eminent German optician, who first
mapped dark lines in the spectrum of the sun. So, too,
in our own day the power of telescope and spectroscope
has been vastly extended by the optical skill and mechanical
dexterity of the Clarks\index{Clark, A. (1804--87), A. G. (1832--97), G. B. (1827--91)} and Rowland\index{Rowland, H.~A.\ (r\=o´land) (1848--1901), Am.\ physicist}, Hastings\index{Hastings, C. S., Prof.\ Yale Univ.} and
Brashear\index{Brashear, J. A.}, all Americans.

\textbf{Best Sites for Observatories.}\index{atmosphere!steady}\index{observatories!best sites}---An observatory site
should have a fairly unobstructed horizon, as much freedom
from cloud as possible, good foundations for the
instruments, and a very steady atmosphere.

\Smaller
All of these conditions except the last are self-evident. To realize
the necessity of a steady atmosphere, look at some distant out-door
object through a window under which is a register, a stove, or a radiator.
It appears blurred and wavering. Similarly, currents of warm
air are continually rising from the earth to upper regions of the atmosphere,
and colder air is coming down and rushing in underneath.
Although these atmospheric movements are invisible to the eye, their
effect is plainly visible in the telescope as blurring, distortion, quivering,
and unsteadiness of celestial objects seen through these shifting
\DPPageSep{201.png}
air strata of different temperatures, and consequently of different
densities. The trails on photographic star plates, exposed with the
camera at rest, make this very evident. That a perfect telescope may
perform perfectly, it must be located in a perfect atmosphere. Otherwise
its full power cannot be employed. All hindrances of atmosphere
are most advantageously avoided in arid or desert regions of the globe,
at elevations of 3000 to 10,000~feet above sea level. On the American
continent have been established several observatories at mountain elevation,
the most important being the Boyden\index{Boyden, U. A. (1804--79) Am.\ engineer and patron} Observatory of Harvard
College, Peru (8000~feet); Carnegie Solar Observatory\index{Carnegie Solar Obs.}, California
(6000~feet); and the Lick Observatory\index{Lick Observatory}, California (4000~feet). Higher
mountains have as yet been only partially investigated; and it is not
known whether difficulties of occupying them permanently would more
than counterbalance the gain which greater elevation would afford.

% Fig 9.1
\begin{figure}[hbt!]
  \centering
  \Input{page_192}
  \caption{The Dearborn Observatory at Evanston, Professor Philip Fox, Director}
\end{figure}

\textbf{A Working Observatory.}---Chief among exterior features is the great
dome, usually hemispherical, and capable of revolving all the way
round on wheels or cannon balls. The opening through which the
telescope is pointed at the stars is a slit\index{slit!dome}, two or three times as broad as
the diameter of the object glass. The slit opens in a variety of ways,
often as in the above picture, by sliding to one side on pivots and
rollers. Solidly built up in the center of the tower is a massive pier,
to support the telescope, wholly disconnected from the rest of the building.
By means of the universal or equatorial mounting\index{equatorial telescope} (page~\pageref{p54}), the
\DPPageSep{202.png}
open slit, and the revolving dome, the telescope is readily directed
toward any object in the sky. Observatories are provided with a
meridian room\index{meridian!circle}, with a clear opening from north to south, in which a
transit instrument\index{transit instrument!room} or meridian circle is mounted. Part of it shows at
the right of the tower. Here also are the chronograph, and clock or
chronometer for recording transits of the heavenly bodies. Modern
observatories are provided with a library and computing room, a photographic
dark room, and other accessories of equipment, varying with
the nature of their work. The best type of observatory construction
utilizes a minimum of material, so that very little heat from the sun is
stored in its walls during the day, and local disturbance of the air in
the evening, caused by radiation of this heat, is but slight. Louvers
and ivy-grown walls contribute much to this desirable end. It is considered
best to house each instrument in a suitable structure of its own,
as remote as possible from many or massive buildings.
\Restore

\textbf{Instruments classified.}\index{instruments classified}---Instruments used in astronomical
observatories are divided into three classes:---

(\textit{a}) \textit{Telescopes}\index{telescope!classified}, or instruments for aiding or increasing
the power of the human eye. There are two kinds, the
dioptric, or refracting telescope\index{refractor}, and the catoptric, or reflecting
telescope\index{reflector}.

(\textit{b}) \textit{Instruments for measuring angles.}\index{angles!instruments for measuring} These, also, are
subdivided into two kinds; the arc-measuring instruments,
like graduated circles\index{circle!graduated}, for measuring very large arcs, the
micrometer\index{micrometer} for measuring very small ones, and the heliometer\index{heliometer}
for measuring arcs intermediate in value, as well
as very small ones. The second class of instruments
concerned in the measurement of angles are transit instruments\index{transit instrument}
for observing time (measured by the uniform angular
motion of a point on the equator), chronographs\index{chronograph} for
recording the time, clocks\index{clock} and chronometers\index{chronometer, marine} for carrying
the time along accurately and continuously from day to
day.

(\textit{c}) \textit{Physical instruments}, of which many varieties are employed
in most modern observatories, for investigating the
light and heat radiated from celestial objects. Chief among
them are spectroscopes\index{spectroscope}, or light-analyzing instruments, of
\DPPageSep{203.png}
which there are numerous forms, adapted to especial
uses. Heliostats are plane mirrors moved by clockwork,
for the purpose of throwing a reflected beam of light from
a heavenly body in a constant direction. The bolometer\index{bolometer}
is an exceedingly sensitive measurer of heat, and the
thermopile\index{thermopile} is used for the same purpose, though much
less sensitive. The photometer\index{photometer} is used for measuring the
light of the heavenly bodies. The actinometer\index{actinometer} and pyrheliometer\index{pyrheliometer}
are physical instruments used in measuring the
heat of the sun. The photographic camera is extensively
employed at the present day, to secure, by means of telescope,
photometer, spectroscope, and bolometer, permanent
record, unaffected by small personal errors to which all
human observations are subject.

\textbf{Telescopes.}---The telescope is an optical instrument for
increasing the power of the eye by making distant objects
seem larger and therefore nearer.

% Fig 9.2
\begin{figure}[hbt!]
  \centering
  \Input[0.6\textwidth]{page_194}
  \caption{Illustrating the Visual Angle}
\end{figure}


\Smaller
It does this by apparently increasing the visual angle. A distant
object fills a relatively small angle to the naked eye, but a suitable
combination of lenses\index{lenses}, by changing the direction of rays coming from
the object, makes it seem to fill a much larger angle, and therefore
to be nearer. Such a combination is called a telescope. The
parts of all telescopes are of two kinds,---optical and mechanical.
The optical parts are lenses, or mirrors, according to the kind of telescope;
and the mechanical parts are tubes\index{telescope!tube}, and various appliances for
adjusting the lenses or mirrors, including also the machinery for pointing
the tube. All the different lenses used in telescopes are illustrated
in Figure~\ref{fig9.3} (in section). One principle is the same in all telescopes:
a lens or mirror (called the objective\index{objective}) is used to form near at hand
an image of a distant object; and between image and eye is placed
\DPPageSep{204.png}
a microscope (called the eyepiece\index{eyepiece} or ocular) for looking at the image---just
as if it were a fly's wing, or the texture of a feather. The point to
which the lens converges the parallel rays from a star is called the
principal focus (Figure~\ref{fig9.4}). The central
ray, which passes through
the centers of curvature
of the two faces of the
lens, traverses a line called
the optical axis\index{axis, optical}. The
plane passing through
% Fig 9.3
\begin{wrapfigure}[20]{o}{0.6\textwidth}
  \centering
  \Input[0.5\textwidth]{page_195a}
  \caption{Lenses of Different Shapes (in Section)}
  \label{fig9.3}\index{lenses}
\end{wrapfigure}
the
principal focus perpendicular
to the optical axis is
called the focal plane.
\label{p195} Objective and eyepiece
must be so adjusted and
secured that their axes
shall lie accurately in a
single straight line. If
objective and eyepiece
could be held in this position
by hand, also at the
right distance apart, there
would be no need of a tube. The tube is sometimes made square, as
well as round, and is to be regarded simply as a mechanical necessity
for keeping the optical parts of the telescope in proper relative position.
Also the tube is of some use in screening extraneous light from the
eyepiece, although that service is slight.

% Fig 9.4
\begin{figure}[hbt!]
  \centering
  \Input{page_195b}
  \caption{A Convex Lens refracts Parallel Rays to the Principal Focus}
  \label{fig9.4}\index{lenses}
\end{figure}

\textbf{Kinds of Telescopes.}\index{telescope!kinds of}---As to the principal kinds of telescopes:
(\textit{a})~If the objective is a lens (in its simplest form an equi-convex
\DPPageSep{205.png}
lens), then the image is produced by bending inward or refracting to
the focus all rays of light which strike the lens; and the telescope
is called a refractor\index{refractor}, or refracting telescope. This sort of instrument
appears to have been first known in Holland, early in the seventeenth
century; also it was invented by Galileo\index{Galile´i, G. (1564--1642), It.\ ast.} in 1609, and first used by him
in observing the heavenly bodies. If a telescope is to perform properly,
its object glass cannot be made of plate glass, because the eyepiece
would reveal defects in it similar to those which the eye plainly
sees in ordinary window glass. But the objective must be made of
that finest quality known as optical glass\index{glass!optical}. Through a perfect specimen
of optical glass polished with parallel sides, a perpendicular ray
of light will pass without appreciable refraction, and with very little
absorption. (\textit{b})~If the objective is a concave mirror or speculum\index{speculum}, the
image is then formed by reflection, to the focus, of all rays of light
which fall upon the highly polished surface of the mirror, and the telescope
is called a reflector, or reflecting telescope\index{reflector}. The above figures
show the principle involved, the angle of reflection being in every case
equal to angle of incidence. An actual speculum may be regarded as
made up of an infinite number of plane mirrors, arranged in a
concave surface differing slightly from that of a sphere, and being
in section a parabola (page~\pageref{p398}). As shown in Figure~\ref{fig9.7}
the focal point is halfway from mirror to center of curvature.

% Fig 9.5, 6
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.4\textwidth}
    \centering
    \vspace{5ex}
    \Input {page_196a}
    \caption{Angle of Reflection equals Angle of Incidence}
  \end{minipage}
  \hfill
  \begin{minipage}{0.4\textwidth}
    \centering
    \Input {page_196b}
    \caption{Concave Mirror reflects Parallel Rays to Focus}
  \end{minipage}
  \label{p196}
\end{figure}

\textbf{Growth of the Refracting Telescope.}\index{refractor}\index{telescope|see{reflector}}\index{telescope|see{refractor}}---An ordinary convex lens\index{lenses}, in
converging rays of light to a focus, must refract them, or bend them
toward the axis of the lens. But light is commonly composed of a
variety of colored rays, ranging through the spectrum from red to
violet. Soon after the invention of the telescope\index{telescope!invention} Sir Isaac Newton\index{Newton, Sir I. (1642--1727), Eng.\ ast.}
discovered by experiment that prisms do not bend rays of different
color alike; violet light is much more strongly refracted than red, and
intermediate colors in different proportions, according to the kind of
light employed. We may regard a lens as an infinitely large collection
\DPPageSep{206.png}
of tiny prisms. Clearly, then, a perfect telescope seemed to be
an impossibility from the very nature of the case, because no single
lens had power to gather all rays at a given focus, and could only
scatter them along the axis---the focus for violet rays being nearest
the object glass, and for the red farthest from it. However, by grinding
% Fig 9.7
\begin{figure}[th!]
  \centering
  \Input{page_197a}
  \caption{Focus halfway from Mirror to Center of Curvature}
  \label{fig9.7}
\end{figure}
the convex lens almost flat, so that its focal length became very
great, this serious hindrance to development of the telescope was in
part overcome, and many telescopes of bulky proportions were built
during the 17th century, which were most awkward and almost impossible
to manipulate\index{telescope!early}. Sometimes the object glass was mounted in
a universal joint on top of a high pole, and swung into the proper
direction by means of a cord, drawn taut by the observer who held
the eye-lens in his hand as best he could. Telescopes were built over
% Fig 9.8
\begin{figure}[bh!]
  \centering
  \Input{page_197b}
  \caption{A Prism both refracts and disperses White Light}
\end{figure}
200~feet in length and some observations of value were made with
them, though at an inconceivable expenditure of time and patience.
Newton\index{Newton, Sir I. (1642--1727), Eng.\ ast.} concluded that it was hopeless to expect a serviceable telescope
of this kind; so the minds of inventors were turned in other
directions.
\DPPageSep{207.png}
\textbf{Why a Single Lens is not Achromatic.}\index{lenses}---For the sake of clear explanation,
regard the lens made up as in the last figure, so that a section
of it is the same as a section of two triangular prisms placed base to base.
Let two parallel beams of white light fall upon the prisms as shown.
Each will then be refracted toward the axis of the lens, and at the same
time decomposed into the various colors of the spectrum. Red rays
being refracted least, their focus will be found farthest from the lens.
Violet rays undergoing the greatest angular bending, their focus will
be nearest the lens. Foci for the other colors will be scattered along
the axis as indicated. If we consider the actual lens, with an infinitude
of faces or prisms, the effect is the same. So that, speaking generally,
it cannot be said that the lens brings the rays of white light to any
single focus whatever, and the image of a white object will be variously
colored, wherever the eyepiece may be placed.
\Restore

\textbf{Principle of the Achromatic Telescope.}\index{telescope!achromatic}---The two lenses\index{lenses}
of the objective\index{objective!achromatic} must be of different kinds of glass: (1)~a
double-convex lens of crown glass, not very dense, which
ordinarily the light passes through first; (2)~a plano-concave
lens of dense flint glass, usually placed close to the
crown lens in small telescopes.
% Fig 9.9
\begin{figure}[hbt]
  \centering
  \Input{page_198}
  \caption{Illustrating Principle of Achromatic Object Glass}
\end{figure}

\Smaller
Similar prisms of these two kinds of glass bend the rays about equally;
so that while the double-convex lens converges the rays toward the
axis, the single or plano-concave diverges them again, by an amount
half as great. So much for refraction merely: and it is plain from the
above figure that the double object glass must have a greater focal length
on account of the diverging effect of the flint lens. Next consider
the effect of the two lenses as to dispersion of light, and the colors
which each would produce singly. If we try equal prisms of the two
kinds of glass, it is found that the flint, on account of its greater density,
produces a spectrum about twice as long as the crown; therefore
\DPPageSep{208.png}
its dispersive power, prism for prism, is twice as great. Now a lens
may be regarded as composed of a multitude of prisms,---a mosaic of
indefinitely small prisms. Evidently, then, the plano-concave lens of
flint glass, although it has only half the refracting power of the crown
lens, will produce the same degree of color as the double-convex lens
of crown glass. Therefore, the dispersion or color effect of the convergent
crown lens is neutralized by the passing of the rays through
the divergent flint lens, and a practically colorless image is the result.
Thus is solved the important problem of refraction without dispersion,
opening the way for the great refractors of the present day.

% Fig 9.10
\begin{figure}[b]
  \centering
  \Input{page_199}
  \caption{Achromatic Telescope (in Section)}
\end{figure}

\textbf{History of the Achromatic Telescope.}\index{astronomy!history}\index{telescope!achromatic}---Half a century after Newton,
Hall\index{Hall, C. M. (1703--71), Eng.\ math.} in 1733 found that the color of images in the refractor could be
nearly eliminated by making the object glass of two lenses
instead of one, as just explained; a significant invention
usually attributed to Dollond\index{Dollond, J. (1706--61) Eng.\ opt.}, who about 1760 secured a
patent for the same idea which had occurred to him independently.
Progress of the art of building telescopes
was thus assured; and the only limitation to size appeared
to be the casting of large glass disks. About 1840, these
obstacles were first overcome by glass makers in Paris;
but in the larger telescopes, a new trouble arose, inherent
in the glass itself; for the ordinary form of double object
glass cannot be made perfectly achromatic. An intense
purple light surrounds bright objects, an effect of the secondary
spectrum, as it is called, because dispersion or
decomposition of the crown glass cannot be exactly neutralized
by recomposition of the flint. Farther progress,
then, was impossible until other kinds of glass were invented.
Recent researches by Abbe\index{Abbe, E. (1840--1905), Ger.\ ast.} under the auspices
of the German Government have led to the discovery of
many new varieties of glass\index{glass!new}, by combining which object
glasses of medium size have already been made almost
absolutely achromatic. Hastings\index{Hastings, C. S., Prof.\ Yale Univ.} in America and Taylor\index{Taylor, H.~D., Eng.\ opt.}
in England have met with marked success. Some of the
new objectives are made of two lenses\index{lenses}, and others of three;
but there is great difficulty in procuring very large disks
of this new glass.


\textbf{Efficiency of Object Glasses.}\index{objective!efficiency}---This depends upon two
separate conditions: (\textit{a})~the light-gathering power of
an objective is proportional to its area. Theoretically a
6-inch glass will gather four times as many rays as a 3-inch
objective, because areas of objectives vary as the squares of their
diameters. But practically the light of the larger glass will be somewhat
reduced, because of the thicker lenses; for all glass, no matter
\DPPageSep{209.png}
how pure, is slightly deficient in transparency. In the same way, the
light-gathering power of any lens may be compared with that of the
naked eye. In the dark, the pupil of the average eye expands to
a diameter of about $\frac{1}{5}$~inch. The ratio of its diameter to that of a
3-inch glass is 15, as in
the illustration (reduced
$\frac{1}{2}$); so a star in a 3-inch
telescope appears nearly
225 times brighter than
it does to the naked eye.
Calculating in the same
% Fig 9.11
\begin{wrapfigure}[23]{o}{0.6\textwidth}
  \centering
  \Input[0.6\textwidth]{page_200}
  \caption{Eye and Objective collect Rays to Proportion to their Areas}
\end{wrapfigure}
way the efficiency of the
great 40-inch lens of the
Yerkes Observatory\index{Yerkes, C. T. (yer´kez) (1837--1905), Am.\ patron!observatory}, it is
found to be 40,000 times
that of the eye. Test
light-gathering power by
ascertaining the faintest
stars visible in the telescope,
and comparing with
lists of suitable objects.
(\textit{b})~The defining power
of an objective is partly
its ability to show fine
details of the moon and
planets perfectly sharp
and clear; but more precisely it is the power of separating the component
members of close double stars (page~\pageref{p451}). This power varies directly
with the size or diameter of object glasses, if they are perfect; that is
a 6-inch glass will divide a double star whose components are $0''.8$
apart, whereas it will require a 12-inch glass to separate a double star
of only $0''.4$ distance. But defining power is quite as dependent upon
perfection of the original disks of glass, as upon the skill and patience
of the optician who has ground and polished them. A large defect of
either makes a worthless telescope.

% Fig 9.12
\begin{figure}[hb!]
  \Input{page_201a}
  \caption{One Method of Testing a Telescope}
\end{figure}
\textbf{Method of Testing a Telescope.}\index{telescope!testing}---Unscrew the cell of the objective
from the tube, but do not take the lenses out of the cell. If on looking
through it at the sky, the glass appears clear and colorless, or nearly so,
the light-gathering power may be regarded as satisfactory. Small
specks and air bubbles will never be numerous enough to be harmful;
each only obstructs a small pencil of light equal to its area. The defining
power may be tested in a variety of ways. Following is the method
by an artificial star: Point the telescope on the bulb of an ordinary
thermometer which lies in the sunshine, 50~feet or more distant. Or
\DPPageSep{210.png}
the convex bottom of a broken bottle of dark glass may be used, \textit{R} in
the illustration. On focusing, an artificial star will appear, due to reflection
of the sun from the bulb, sometimes surrounded by diffraction
rings\index{diffraction!rings} (\textit{A}, Figure~\ref{fig9.13}). Slide eyepiece inward and outward from focus,
until bright point of light spreads out into a round luminous disk,
\textit{B}. This is called the spectral image\index{spectral image test}. A dark center, when the eyepiece
is pulled out, and a brighter central area when pushed in, show
that curvature of the glasses is more or less imperfect. A spectral
image having a piece cut out, or a brush of scattering light, is a sign
of bad defects inherent in the glass itself. An excellent objective gives
spectral images perfectly circular, and evenly illuminated
throughout, \textit{B}. Repeat these tests on stars of the first
% Fig 9.13
\begin{wrapfigure}[8]{o}{0.6\textwidth}
  \centering
  \Input[0.5\textwidth]{page_201b}
  \caption{Spectral Images}
  \label{fig9.13}
\end{wrapfigure}
magnitude. Heat from a lighted lamp placed where shown
will simulate many deleterious effects of a very unsteady
atmosphere. \textit{A} and \textit{B} then become \textit{C} and \textit{D}, rays and
spots of the latter being continually in motion.

\textbf{A Small but Useful Telescope.}\index{telescope!making a small}---By expending a few
cents for lenses, a person of average mechanical ability
may, by a few hours' work, become possessed of a telescope
powerful enough to show many mountains on the moon,
spots on the sun, satellites of Jupiter, and a few of the
wider double stars. Buy from an optician two spectacle
lenses, round rather than oval, and of very different powers;
for instance, No.~5 and No.~30. These numbers
express the focal lengths of the lenses\index{lenses}. Fit together
two pasteboard tubes so that one will slide inside the other quite
smoothly. Their combined length must be about six inches greater
\DPPageSep{211.png}
than the sum of the numbers of the two lenses. Blacken the inside
of tubes, and attach the lenses to their outside ends. No.~30 being
the objective, and pointed toward the object, the magnifying power of
the two lenses, when separated by a distance equal to the sum of their
focal lengths, will be equal to their ratio, or six diameters. It was with
a telescope made in this way that the writer, when a boy of fourteen,
got his first glimpse of the satellites of Jupiter. A few dollars will buy
a good achromatic object glass (of perhaps two inches diameter) and a
pair of suitable eyepieces (powers about 25 and 100). A suitable
mounting for such telescopes has already been described on page~\pageref{p53a}.
The most important optical requisite is stated on page~\pageref{p195}.
\Restore

\textbf{The Great Refractors.}\index{refractor}---The largest is M.~Gautier's
50-inch horizontal telescope at Paris, 186 feet long. A
moving mirror reflects the light into it. Next comes
the 4O-inch telescope, 65~feet long, of the Yerkes Observatory\index{Yerkes, C. T. (yer´kez) (1837--1905), Am.\ patron!telescope}
(pages \pageref{p7} and \pageref{p15}). More favorably located is its rival
in size, the famous Lick telescope\index{Lick telescope} of~36 inches aperture,
situated on the summit of Mount Hamilton, California,
4300~feet above the sea.

\Smaller
The mountings or machinery for both these great instruments were
built in Cleveland, by Messrs.\ Warner \&amp; Swasey\index{Warner \&amp; Swasey}; but the object
glasses were made by the celebrated firm of Alvan Clark\index{Clark, A. (1804--87), A. G. (1832--97), G. B. (1827--91)} \&amp; Sons, of
Cambridgeport, from glass disks manufactured in Paris. No optical
glass of the highest quality has yet been made in America, the process
being, in some essentials, secret. Steinheil\index{Steinheil, R.\ (st\=yn´hile), Ger.\ opt.} of Munich completed in
1900 an objective of $31\frac{1}{2}$~inches aperture, of the new glass, for the astrophysical
observatory near Berlin. A glass of like dimension by Henry
is at the Meudon Observatory\index{Meudon Observatory}, Paris. The Clarks have made also an
objective of 30~inches aperture, mounted by Repsold\index{Repsold, J.~A., Ger.\ instrument maker}, at the Russian
Observatory of Pulkowa\index{Pulkowa (pul-ko´va) Obs.}, near Saint Petersburg. A glass of equal size,
figured by the Brothers Henry\index{Henry, Paul (ong-ree´) (1848--1905), Fr.\ ast.}\index{Henry, Prosper (ong-ree´) (1849--1903), Fr.\ ast.} of Paris, is mounted at the splendid
observatory founded by Bischoffsheim\index{Bisch´offsheim, R., Fr.\ banker and patron} at Nice\index{Nice (n\=ece), Observatory of}, in the south of France.
A 29~inch by Martin\index{Martin, M.~A.\ (mär-tang´), Fr.\ opt.} is at the Paris Observatory\index{Paris!Observatory}. The next three telescopes
were made at Dublin, by Sir Howard Grubb\index{Grubb, Sir H., Brit.\ opt.}, one of 28~inches
and one of 26 inches aperture, located at the Royal Observatory, Greenwich\index{Greenwich!Observatory},
and the other, of 27~inches, at Vienna. Following these in order
are a pair of telescopes of 26~inches aperture, made by Alvan Clark \&amp;
Sons, one of which is the principal instrument of the United States
Naval Observatory\index{U.~S. Naval Obs.}, at Washington, and the other is located at the
University of Virginia. Between the dimensions of 25~inches and 15
\DPPageSep{212.png}
inches there are about two dozen refracting telescopes in all, many
of which were made by Alvan Clark \&amp; Sons, although Brashear\index{Brashear, J. A.} of
Alleghany, an optician of the first rank, has made an 18-inch glass,
now at the University of Pennsylvania. Quite the opposite of reflectors,
it is noteworthy that most of the great refractors have been
built in America; and that they have contributed in a more marked
degree to the progress of astronomical science.

\textbf{Invention and Growth of the Reflecting Telescope.}\index{astronomy!history}\index{reflector}\index{telescope!invention}---If converging
the rays of light by refraction could never make a perfect telescope,
clearly the only method left was to gather them at a focus by reflection
from a highly polished surface. Although this way of making a telescope
seems to have been understood as early as 1639, still a quarter
century elapsed before Gregory\index{Gregory, J. (1638--75), Scot.\ math.} built the first one (1663). He used
% Fig 9.14
\begin{figure}[ht!]
  \centering
  \Input{page_203}
  \caption{Three Types of Reflecting Telescope}
  \index{telescope!Gregorian}%
  \index{telescope!Newtonian}%
  \index{telescope!Cassegrainian}%
  \index{Gregorian telescope|see{telescope, Gregorian}}%
  \index{Newtonian telescope|see{telescope, Newtonian}}%
  \index{Cassegrainian telescope|see{telescope, Cassegrainian}}%
  \index{reflector}%
\end{figure}
two concave mirrors as in the illustration; the one large to form the
image, and the other small to reflect the rays out of the tube to the
eyepiece. Ten years later Cassegrain made a farther improvement,
replacing the small concave mirror of Gregory by a convex one (shown
in the illustration also). Both these forms of reflector have the advantage
that the observer looks directly toward the object at which the
telescope is pointed; but there is a great disadvantage in that the center
or best part of the mirror has to be cut away, in order to let the rays
through it to the eyepiece. The mirror is left whole, and less of its
light is sacrificed in the form invented by Newton (1672), who interposed
a small flat mirror, at an angle of $45$° with the axis of the larger
mirror. This arrangement, most commonly used in reflecting telescopes
at the present day, has a slight disadvantage in that the observer
must look into the eyepiece at right angles to the direction of the object
under examination (see figure); but a small right-angled or totally
\DPPageSep{213.png}
reflecting prism is now universally employed in lieu of the little
diagonal mirror, thereby saving a large percentage of light. A fourth
form of reflector, first suggested by Le Maire, was used by Herschel\index{Herschel, Sir F. W. (1738--1822), Eng.\ ast.},
in the latter part of the 18th century; he tilted the speculum slightly,
to bring its focus at the side of the tube. Tilting the mirror saves all
the light, but distortion of the image is not easy to avoid. Recently,
for the purpose of reducing this distortion, an instrument called the
`oblique Cassegrain' has been brought out in England; also in Germany
% Fig 9.15
\begin{figure}[hbt!]
  \centering
  \Input{page_204a}
  \caption{Le Mairean or Herschelian Reflecting Telescope}\index{reflector}
\end{figure}
the `brachy-telescope\index{brachy-telescope},' or short telescope, has been invented to overcome
this difficulty, by second reflection from a small and oppositely
inclined convex mirror. Down to the middle of the 19th century,
specula\index{speculum} were always made of an
alloy, generally composed of 59
parts of tin and 126 of copper.
Specula are now almost universally
made of glass, with a very
thin film of silver deposited
chemically upon the front surface,
not upon the back as in
the common mirror. These
telescopes are often called silver-on-glass
reflectors. As the light
does not pass through the glass,
it may be much inferior in quality
to that required for a lens. Because
less difficult to build, the
great telescope of the future will
probably be a reflector\index{telescope!great, of future}, although
of inferior definition. Great refractors
are, however, less clumsy
and more effective for actual use.
\DPPageSep{214.png}

\textbf{The Great Reflecting Telescopes.}\index{reflector}---The largest, sometimes called the
`leviathan,' was built by the late Lord Rosse\index{Rosse, Lord (1800--67), Brit.\ ast.} in 1845 at Birr Castle,
Parsonstown, Ireland. The speculum\index{speculum} is of metal, six feet in diameter,
and about eight inches thick. Its excessive weight of four tons makes a
very heavy mounting necessary.
% Fig 9.16
\begin{wrapfigure}[23]{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_204b}
  \caption{The Great Paris Reflector (Martin)}
  \index{Martin, M.~A.\ (mär-tang´), Fr.\ opt.}\index{reflector}
\end{wrapfigure}
Lord Rosse's telescope is Newtonian\index{telescope!Newtonian}
in form. The giant tube is 56~feet long, and 7~feet in diameter. The
next in size is a five-foot silver-on-glass reflector, built by Common\index{Common, A. A. (1841--1903), Eng.\ ast.}
in 1889 at Ealing, England. This powerful telescope was remounted at
Harvard College Observatory\index{Harvard College!obs.} in 1904--1906, with many novel conveniences
for facilitating its use. The Carnegie Solar Observatory\index{Carnegie Solar Obs.}, Mount
Wilson, California, possesses a reflector of equal size. In 1867 Thomas
Grubb\index{Grubb, T., (1800--78), Brit.\ opt.} built a four-foot silver-on-glass `Gregorian' for the observatory
at Melbourne, Australia, and it is one of the most convenient in use of
all the great reflectors. In the latter part of the 18th~century Sir William
Herschel\index{Herschel, Sir F. W. (1738--1822), Eng.\ ast.} built numerous reflecting telescopes, among them one of
four feet diameter, and another of half that size; he made many important
discoveries with them, but none are now in condition to use. Lassell\index{Lassell, W.\ (1799--1880), Eng.\ ast.},
an eminent English astronomer, built two great reflectors, one of four
feet, and the other of two feet aperture, which he used on the island of
Malta, 1852--1865. Several reflectors, three
feet aperture, have been constructed, the most
important of which is owned by the present
Lord Rosse; also one by the Lick Observatory\index{Lick Observatory}.
At the Paris Observatory\index{Paris!Observatory} is a great
silver-on-glass reflector of nearly four feet
aperture, which Deslandres employed effectively
in finding motions of stars toward or
from the earth. It is interesting to note that
few of these great instruments have been
constructed in America. One of the largest
reflectors ever built in the United States is 28~inches
in diameter. It was made by Henry
Draper\index{Draper, H. (1837--82), Am.\ ast.}, New York, in 1871, and is now at the
Harvard Observatory. Among present builders
of reflecting telescopes in America are
Edgecomb\index{Edgecomb, W. C., Am.\ opt.} of Mystic, Connecticut; and
Brashear\index{Brashear, J. A.}, one of whose lesser instruments
is pictured in the adjoining illustration.

% Fig 9.17
\begin{wrapfigure}{o}{0.35\textwidth}
  \centering
  \Input[0.35\textwidth]{page_205}
  \caption{A Modern `Newtonian' by Brashear}\index{telescope!Newtonian}\index{reflector}
\end{wrapfigure}
\textbf{Reflectors and Refractors compared.}\index{refractor}\index{reflector}---In
reflectors of medium size, tarnish and deterioration
of the polished surface are the
chief disadvantage. But the film of a mirror
less than a foot in diameter is readily renewed.
When freshly silvered, a 12-inch speculum\index{speculum} will collect the same amount
\DPPageSep{215.png}
of light as a 12-inch object glass, loss by reflection from the former
being about equal to loss by absorption in passing through the latter.
Well figured and newly polished mirrors of no greater dimension than
this usually perform excellently; and there is a marked advantage from
the gathering of rays of all colors at the same focus. But from 12~inches
upward, flexure of the mirror begins to cause difficulties which
increase rapidly with the size of the speculum\index{speculum}. The mirror may be
given a perfect parabolic figure for the position in which it is polished;
but as soon as turned to another angle of elevation, gravity distorts
its figure. As a result, rays from a star are not collected at a single
point, but scattered round it. The larger the mirror, the greater this
difficulty, becoming almost impossible to alleviate entirely. Glass
mirrors, in order to be least affected by it, should have a thickness
equal to one sixth of their diameter. With object glasses, on the other
hand, bending of the lens by its own weight in different positions has
not been found to affect appreciably the character of images formed by
any of the great glasses, except the 40-inch, which suffers a slight deformation
of images in certain positions. Still, it must be remembered
that the objective, although called achromatic, is not completely so;
and in some of the very large refractors, the intense blue light surrounding
a bright object is often a serious obstacle in the work of
practical observation. On the whole, the refractor is generally preferred
to the reflector. It is easier to adjust and keep in order; and
its tube being closed, it is much less subject to harmful effect of local
air currents. It is a fact, too, that more than three fourths of all the
work of astronomical observation has been done with refracting
telescopes.

% Fig 9.18
\begin{figure}[htb!]
  \centering
  \Input{page_206}
  \caption{Path of Rays through a Negative (Huygenian) Eyepiece}
  \index{eyepiece!negative}
\end{figure}
\textbf{The Eyepiece.}\index{eyepiece}---The eyepiece of a telescope is simply a magnifying
glass, or microscope for examining the image of an object formed
at the focus by the objective. Any small, convex lens, then, may
be used as an eyepiece, but its effective field of view is very limited.
\DPPageSep{216.png}
So a combination of two plano-convex lenses\index{lenses} is usually employed, in
order that the field may be enlarged, and vision be distinct everywhere
in that field. Two forms of celestial eyepiece are common, called the
\textit{negative} and the \textit{positive} eyepiece. Both forms have a smaller, or
eye lens, and a larger, or field lens; the latter toward the objective,
the former nearer the eye. In the negative (sometimes called from
Huygens, its inventor, the Huygenian) eyepiece\index{Huygenian eyepiece}, both eye lens and
field lens have their flat faces turned toward the eye, as in the
% Fig 9.19
\begin{figure}[htb!]
  \centering
  \Input{page_207a}
  \caption{Path of Rays through a Positive (Ramsden) Eyepiece}
  \index{eyepiece!positive}
\end{figure}
preceding figure. In the positive (called, also, from its inventor the
Ramsden\index{Ramsden, J.\ (1735--1800), Eng.\ opt.}) eyepiece, the convex faces of both lenses are turned inward,
or toward each other, as in the above figure, where the eye lens is drawn
double its proper diameter. The negative eyepiece has its focus between
the two lenses. The focus of the positive eyepiece lies beyond
both lenses, a short distance toward the objective. Positive eyepieces
are always used for transit instruments\index{transit instrument} and micrometers\index{micrometer}. Both these
forms of eyepiece do not themselves invert, but when employed in conjunction
with an object glass, they show all objects inverted, the objective
% Fig 9.20
\begin{figure}[hbt!]
  \centering
  \Input{page_207b}
  \caption{Path of Rays through a Terrestrial or Erecting Eyepiece}
\end{figure}
itself causing the inversion, because the rays cross in passing through it.
A terrestrial or day eyepiece is one which, when employed with an object
glass, shows all objects right side up. The re-inversion of the image
necessary to effect this is produced, as shown in the preceding illustration,
by constructing the eyepiece of four lenses instead of two. Different
eyepieces of different magnifying powers may generally be used
with the same objective, by means of suitable draw-tubes, called
\textit{adapters}. The same eyepiece can be used in either reflectors or refractors.
\DPPageSep{217.png}

\textbf{To ascertain the Magnifying Power.}\index{magnifying power}---Following is an easy method:
Select a convenient object marked with dividing lines at pretty regular
intervals---clapboards on a house, bricks in a wall, or better the joints
where plates of tin are lapped on a roof. When the sun is shining
obliquely across them, set up the telescope as distant as possible, yet
near enough so that the joints can readily be counted with the naked
eye. Then point the telescope at the roof. Look at it through the
eyepiece with one eye, and with the other look along the outside of
the telescope at the roof also; first with one eye, then with the other,
then with both together. Amplification, or magnifying power (at that
distance of the telescope from the roof) is equal to the degree of this
enlargement; and it can be ascertained by simply counting the number
of divisions (as seen by the naked eye) which are embraced between
any two adjacent joints as seen in the telescope. The two images
of the same object will be seen superposed, and a little practice will
enable one to make the count with all necessary accuracy. Good telescopes
are usually provided with an assortment of eyepieces whose magnifying
powers range approximately between seven and 70 for each inch of
aperture of the object glass. For example, a four-inch telescope would
have perhaps four eyepieces, magnifying about 25, 90, 200, and 300 times.

% Fig 9.21
\begin{figure}[hbt!]
  \centering
  \Input{page_208}
  \caption{A Modern Micrometer with Electric Illumination (Ellery)}
  \index{micrometer}\index{Ellery, R.~L.~J.\ (1827--1907), Eng.\ ast.}
\end{figure}

\textbf{How to measure Small Angles.}\index{angles!instruments for measuring}---The micrometers\index{micrometer} is an instrument
for measuring small angles. It is attached to the telescope in place of
the eyepiece. The illustration shows all the important working parts.
Crossing the oblong field of view are seen two spider lines (\textit{aa}), with
which the measuring is done. All parts of the micrometer are so devised
and related that these two lines can be seen at night in the
dark field of view; moved with accuracy slowly toward or from each
other; and their exact position recorded. In the best modern micrometers,
either the lines or the field of view can be illuminated at will by
a small incandescent electric lamp (\textit{L}). The spider lines are attached
to separate sliding frames; each frame can be moved by a thumbscrew,
\DPPageSep{218.png}
the head of which projects outside the micrometer box. One
of these, called the micrometer screw, has enlarged heads ($h^1h^2$)
graduated to show the number of turns and fraction of a turn of this
screw. The eyepiece (not shown) is a positive one attached to the
% Fig 9.209
\begin{figure}[ht!]
  \centering
  \Input{page_209}
  \caption{A Compact Modern Transit Instrument (from a Design by Heyde)}
  \label{p209}\index{transit instrument}
\end{figure}
micrometer box in front of the sliding frames. To measure a small arc,---for
example, the diameter of a planet\index{planets!measuring diameter}---point the telescope so that the
disk of the planet appears in the center of the field of view. Then turn
the two thumbscrews until the spider lines are both seen tangent to
opposite sides of the disk at the same time. Read the micrometer-head.
\DPPageSep{219.png}
Then turn the micrometer-screw, until the two lines appear as one.
Read the head again; take the difference of readings, and multiply it
by the arc-value of one turn (which must have been previously determined).
Resulting is the diameter of the planet in arc.

\textbf{The Transit Instrument.}\index{transit instrument}---Soon after the invention of the telescope,
early in the 17th century, an instrument was devised by a Danish
astronomer, Roemer\index{Roemer, O.\ (reh´mer) (1644--1710), Danish ast.},
\begin{wrapfigure}[10]{o}{0.35\textwidth}
  \centering
  \Input[0.25\textwidth]{page_210a}
  \caption{Adjustable Reticle}\index{reticle}
\end{wrapfigure}
which has now supplanted
nearly every other for determining
time with precision. It is called the
transit instrument, because used in observing
the passage, or transit, of heavenly
bodies across the field of view. Ordinarily
it is mounted in a north and south line.
On top of the two rigid triangular piers
(\vpageref*{p209}) are bearings in which the
axis of the transit instrument turns. The
telescope \textit{F} is secured at right angles to
the axis \textit{C}. When turned round in its
bearings, the telescope describes the plane of the meridian. On that
account it is sometimes called a meridian transit. In the convenient
type of transit here pictured, the axis forms half of the telescope tube.
A glass prism in the central cube reflects the rays through \textit{C} to the eye
at the left. Such an instrument is often called a `broken transit.'
Until the instrument is reversed, the eye remains stationary, no matter
what the declination of the star observed.

\iffalse
% Fig 9.23, 24
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input {page_210a}
    \caption{Adjustable Reticle}\index{reticle}
  \end{minipage}
  \hfill
  \begin{minipage}{0.48\textwidth}
    \centering
    \vspace{2ex}
    \Input {page_211a}
    \vspace{3ex}
    \caption{Reticle of Transit}\index{reticle}
  \end{minipage}
\end{figure}
\fi

% Fig 9.25
\begin{figure}[b]
  \centering
  \Input{page_210b}
  \caption{To show the Line of Collimation}\index{collimation, line of}
\end{figure}


\textbf{Observing with the Transit Instrument.}\index{transit instrument!adjusting}---First, it must be adjusted.
A level, \textit{L}, hanging below, makes the axis horizontal. In the field of
view is a reticle\index{reticle}, often made of spider lines, but sometimes by ruling
very fine lines with a diamond point on a thin plate of optical glass.
The reticle is accurately adjusted in focal plane of object glass, and in
smaller instruments, surveyor's transits, for example, lines are arranged
as in the two illustrations above. The lines are often called threads
or wires. The \textit{line of collimation} is the line from the center of object
glass to the central intersection of lines of reticle. This line is adjusted
perpendicular to the axis of revolution of the telescope. Then by
repeated trials upon stars, the Y's, or bearings, are shifted very slightly
north or south, on pivots
\begin{wrapfigure}{o}{0.35\textwidth}
  \centering
  \Input[0.3\textwidth]{page_211a}
  \caption{Reticle of Transit}\index{reticle}
\end{wrapfigure}
(page~\pageref{p209}) under the left-hand end of the
\DPPageSep{220.png}
base, until the axis lies precisely east and west. When the foregoing
adjustments have been made, the telescope, or more accurately the line
of collimation, swings round in the true plane of the meridian. To
observe a star, count the beats of the clock
while looking in the field of view; and set
down the second and tenth of its crossing
the central vertical line of the reticle. In the
illustration a star is seen approaching the
vertical or transit lines. If a very accurate
value is desired, observe the passage over
the five central lines, and then take the
average. This will be the time required.

% Fig 9.26
\begin{wrapfigure}[16]{i}{0.5\textwidth}
  \centering
  \Input[0.4\textwidth]{page_211b}
  \caption{View into Clock-room (Lick Observatory)}\index{Lick Observatory}
\end{wrapfigure}
\textbf{The Astronomical Clock.}\index{clock}---Timepieces used in observatories are of
two kinds, clocks and chronometers. One or the other is indispensable.
The astronomical clock has a pendulum\index{pendulum} oscillating once each second:
if it oscillates once a sidereal second, it is a sidereal clock; if once a
mean solar second, it is a mean time clock. A seconds hand records
each oscillation. Also it has hour and minute hands, like ordinary
clocks, except that the dial is
usually divided into 24~hours
instead of 12, for the convenience
of the astronomer, in
recording hours of the astronomical
day, or in following the
stars according to right ascension.
If, at any instant, the
clock does not show exact
time, the difference between
true time and clock time is
called the correction, or error
of the clock\index{clock!error of}. This must be
found from day to day, or from
night to night, by observing
transits of the heavenly bodies
with the meridian circle or the
transit instrument. If a clock
does not keep exact pace with
the objects of the sky, it is
said to have a rate. As with the chronometer, daily rate is the amount
by which the error changes in 24~hours. A large rate is inconvenient,
but does not necessarily imply a bad clock. The less the rate changes
the better the clock. Dampness of the air and sudden changes of
temperature are hostile to the fine performance of timekeepers of
every sort. Equality of surrounding conditions is secured as much
\DPPageSep{221.png}
as possible by keeping clocks and chronometers, as the last illustration
shows, in a small and separate room, where the air may readily be kept
dry and its temperature nearly constant.

\textbf{Pendulum and Escapement.}\index{pendulum}\index{escapement}---Horology\index{horology} is the science which embraces
everything pertaining to measurement of time, and to mechanical
contrivances for
% Fig 9.27, 28
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \begin{minipage}{0.165\textwidth}
    \centering
    \Input{page_212a}
    \caption{Compensation Pendulum}
  \end{minipage}
  \index{pendulum}
  \hfill
  \begin{minipage}{0.31\textwidth}
    \centering
    \raisebox{2ex}{\Input{page_212b}}
    \caption{Gravity Escapement}
  \end{minipage}
  \index{escapement!gravity}
\end{wrapfigure}
effecting this end. The chronometer is described
and pictured in the preceding chapter (page~\pageref{p171}). Accurate running of
a clock is dependent mainly upon two parts of its mechanism, (\textit{a})~the
pendulum, and (\textit{b})~the escapement.
The pendulums of all
observatory and standard
clocks are compensated for
temperature, so that the
natural fluctuations of this
element may have little or no
effect upon the length of the
pendulum, and therefore upon
its period of oscillation.
There is a variety of methods
by which the compensation
is effected. The illustration
shows the simplest of them.
The steel pendulum rod
passes through a zinc tube
(shaded), to the bottom of
which is attached the heavy
pendulum-bob. With a rise
of temperature, the downward
expansion of the steel
is just equalized by the upward
expansion of the zinc;
so the center of oscillation
remains at the same distance
from the point of support.
The center of oscillation is
that point of a pendulum in which, if the whole mass of the pendulum
were concentrated, the period of oscillation would not vary. The gridiron
pendulum and the mercurial pendulum are other forms of compensation.
Next in importance to the pendulum is the escapement. The
illustration represents in outline one of the best forms. It is called
the gravity escapement, because the pendulum is driven by the pressure
alternately of two gravity arms, which are swung aside by the six black
pins in the hub of the escapement wheel. The clock train does the
work of raising the arms outward from the pendulum rod; so that the
\DPPageSep{222.png}
pendulum swings almost perfectly free, having no work to do except
to raise the gravity arms just enough to trip the escapement at the
smoothly polished jewels \textit{AA}.

\textbf{The Chronograph.}---In recording transits of the heavenly bodies,
greater convenience, rapidity, and precision are attained by using the
chronograph, a mechanical contrivance first devised by American
astronomers about 1850, and now used in observatories universally.
The illustration (\vpageref*{p214}) shows an excellent type of this instrument. The
chronograph consists of a cylinder about 8~inches in diameter and
% Fig 9.29
\begin{figure}[htb!]
  \centering
  \Input{page_213}
  \caption{A Modern Chronograph by Warner \&amp; Swasey}
  \label{p213}\index{Warner \&amp; Swasey}\index{chronograph}
\end{figure}
16~inches in length, which revolves once every minute at a uniform
speed. Wound upon it is a sheet of blank paper, and above it trails
a pen connected with an armature, so that every vibration of the pendulum,
by closing an electric circuit, joggles the pen or throws it aside a
fraction of an inch at the beginning of each second. The illustration
shows a small part of a chronograph sheet, full size. As
the barrel or cylinder revolves, the pen carriage travels slowly along, so
that the trail of the pen is a continuous spiral round the barrel, with
60 notches or breaks in every revolution. In the circuit of the pen
armature is a small push button, called an observing key. This is held
in the hand of the observer while the star is passing the field. Whenever
it crosses a spider line, a tap of the observing key records the
instant automatically on the chronograph paper, which may be removed
and read at leisure. As is apparent from the illustration, tenths of a
second are readily estimated, even without any measuring scale. The
breaks at regular intervals are made automatically by the timepiece.
The short breaks between \textit{A} and \textit{B} are made in quick succession by
\DPPageSep{223.png}
the observer, to show that a star is just coming to the
lines. Transit of the star over the first two lines took
place at \textit{C} (7\,h.\:16\,m.\:7.4\,s.), and at \textit{D} (7\,h.\:16\,m.\:11.4\,s.),
reading in all cases from the preceding (or lower) side of
the break. By transits of ten stars of five lines each, a
good observer can determine the error of his timepiece
within two or three hundredths of a second. Hough\index{Hough, G.~W.\ (huff) (1836--1909), Am.\ ast.} has
recently perfected a printing chronograph\index{chronograph!printing} which records
the time in figures on a paper fillet.

% Fig 9.30
\begin{figure}[hbt!]
  \centering
  \Input[\textwidth]{page_214}
  \caption{Part of the Chronograph Sheet}
  \label{p214}
\end{figure}

\textbf{Personal Equation.}\index{personal equation}---Few observers, no matter how
practiced, tap the key exactly when a star is crossing a
line. Most of them make the record just after the star
has crossed, and still others always press the button a
small fraction of a second before the star reaches the
wire. It does not matter how much too early or too late
the record is made, because the difference can usually be
found by methods known to the practical astronomer;
but a good observer is one who makes this difference
invariable; that is, his personal equation should be a constant
quantity. The personal equation of an observer
is the difference between his record of any phenomenon,
and the thing itself. In observing transits of heavenly
bodies, most observers have a personal equation amounting
to one or two tenths of a second of time. Personal
equation is usually found by observing with a personal
equation machine, an instrument which records on a
single chronograph sheet, not only the observer's time of
transit, but also the absolute instant when the star is
crossing the lines. Figure~\ref{fig9.31} shows such a
machine. Light from the lamp on the right provides an
artificial star which the clockwork makes to travel across
the lines in front of the observing tube on the left. Absolute
time is time corrected for personal equation. It is
nearly always required in the accurate determination of
longitudes by the electric telegraph.

\textbf{The Photo-chronograph.}\index{chronograph!photo-chronograph}\index{photo-chronograph}---As the effect of personality
is usually absent from all records made by photography,
many attempts have been made to register star-transits
by photographic means. The instrument which does this
takes the place of both eyepiece and chronograph, and
is called the photo-chronograph. Opposite is a picture
of this ingenious little instrument. If a photographic
plate is firmly fixed in the focal plane of a transit instrument,
and a star is allowed to move through the field, the
% Fig 9.31
\begin{figure}[htb!]
  \centering
  \Input{page_215a}
  \caption{Machine for determining Personal Equation (Eastman)}
  \label{fig9.31}\index{Eastman, J. R., U. S. Navy (ret.)}
  \index{personal equation!machine}
\end{figure}
\DPPageSep{224.png}
negative will show a fine, dark line or trail, crossing the plate horizontally
from west to east. By holding a lantern in front of the object
glass a few seconds, the vertical
lines in the field may
also be obtained on
% Fig 9.32
\begin{wrapfigure}[18]{o}{0.625\textwidth}
  \centering
  \Input[0.425\textwidth]{page_215b}
  \caption{The Photo-chronograph (Fargis-Saegmüller)}
  \index{Fargis, G. A., Am.\ ast.}\index{Saegmüller, G.~N.\ (seg´miller)}
\end{wrapfigure}
the same
plate. There will be, then,
an absolute record of the
star's path through the field
and across the lines; but
nothing will be known as to
the time when the star was
crossing any particular line.
Now instead of fastening the
plate, insert it in a little
frame which slides north and
south a small fraction of an
inch. So arrange the details
of the mechanism that an
armature will move the frame
automatically. Connect this
armature into a suitable clock
circuit, in place of the ordinary
chronograph pen. Instead
\DPPageSep{225.png}
 of a star transit, or ordinary, horizontal trail like this---
% Fig 9.33
\begin{figure}[h!]
  \centering
  \Input[0.4\textwidth]{page_216a}
  \caption{Ordinary Star Trail}\index{star trails}
\end{figure}

\noindent
the plate when developed will show this---
% Fig 9.34
\begin{figure}[h!]
  \centering
  \Input[0.4\textwidth]{page_216b}
  \caption{Interrupted Star Trail}\index{star trails}
\end{figure}

It is easy to find the particular second corresponding to each one
of the little broken trails on the plate, and by using a magnifying
glass the fractional parts of seconds where the reticle lines cross the
trails can be measured with accuracy and with almost no effect of personal
equation. In another form of photo-chronograph, the plate is
stationary, and the armature actuates an occulting bar, which screens
the plate except for an instant, once every three seconds. The star
trail is then reduced to a series of equidistant dots.

\label{p216}\textbf{The Meridian Circle.}---The meridian circle is an instrument for
measuring right ascensions and declinations of heavenly bodies. Its
foundations are two piers or
pillars, in an east and west line.
On top of each is a {\sffamily\textbf{Y}} or bearing,
and in these turn two
pivots, accurately fashioned,
cylindrical in form. On top of
them rests an accurate striding
level. The pivots are attached
solidly to the massive axis
proper, this latter being made
up of two cylinders, or inverted
cones, and a central
cube between them, through
which passes the telescope,
rigidly fastened perpendicular
to axis. On either side of
the telescope, a finely divided circle is secured at right angles to the
axis. Circles, axis, telescope, and pivots, then, all revolve round in the
\DPPageSep{226.png}
{\sffamily\textbf{Y}}'s together, as one solid piece. The delicate bearings are in part relieved
of this great weight by means of counterpoises. Firmly attached
to the right pier are microscopes for reading with high accuracy the
graduation on the rim of the circle. The zero point of the circle is
usually found by placing a basin of mercury underneath the telescope,
which is then pointed downward
% Fig 9.35
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.55\textwidth]{page_216c}
  \caption{Meridian Circle (from a Design by Landreth)}
  \index{Landreth, O.~H., Prof.\ Union Coll.}\index{meridian!circle}
\end{wrapfigure}
upon the mercury. When the horizontal
lines in the field of view are seen to correspond exactly with
their images reflected from the mercury, the position of the circle is read
from the microscopes; and this is the zero point, because the line of
sight through the telescope is then vertical. The operation of obtaining
this zero point is called `taking a nadir.' Combining it with the
latitude of the place gives the circle reading for pole or equator, and
so any star's declination may be found. The meridian circle is often
called also the transit circle. Right ascensions are observed with
the meridian circle exactly as with the transit instrument previously
described.

\textbf{The Equatorial Coudé.}---A very advantageous and convenient combination
of refractor and reflector is the {\sffamily\textbf{T}}-shaped or `elbow telescope,'
called the equatorial coudé. It was invented by Loewy\index{Loewy, M.\ (1833--1907), Fr.\ ast.}, the present
director of the Paris Observatory\index{Paris!Observatory}, and is a type of instrument well known
in the observatories of
% Fig 9.36
\begin{wrapfigure}{i}{0.6\textwidth}
\centering
  \Input[0.5\textwidth]{page_217}
  \caption{The Equatorial Coudé (Loewy)}\index{Coudé (coo-day´), equatorial}
\end{wrapfigure}
France,
although there are as yet none
in the United States. The
chief advantage is that the
instrument itself, as shown in
the illustration, is nearly all
in open air, while the observer
sits in a fixed position, as if
working at a microscope on
a table. The eyepiece, therefore,
is in a room which may be kept at comfortable temperatures
in winter. The instrument can be handled easily and rapidly, and is
very convenient for the attachment of spectroscopes and cameras. The
splendid lunar photographs on pages \pageref{p16} and \pageref{p248} were taken with this
telescope. Its chief disadvantage is loss of light by reflection from
two plane mirrors, set at an angle of 45° in two cubes shown at the
lower end of the polar axis. The object glass is mounted in one
side of the right-hand cube, near the attendant. This cube with its
mirror and objective turns round on an axis in line with the central
cube, and forming the declination axis. Beneath the central cube is
the lower pivot of the polar axis. The long oblique telescope tube is
itself the polar axis, and its upper bearing is near the eyepiece. A
powerful clock carries the whole instrument round to follow the stars,
and the upper cube is counterpoised by a massive round weight at the
\DPPageSep{227.png}
lower end of the declination axis. First cost of the equatorial coudé
is about double that of the usual type of equatorially mounted telescope;
but the large expense for a dome is mostly saved, as the coudé is
housed under a light structure which rolls off on rails to the position
shown in the engraving.

\textbf{Common Mistakes about Telescopes.}\index{telescope!mistakes about}---Perhaps the question most
often asked the astronomer by persons uninformed is, How far can you
see with your telescope? Evidently no satisfactory answer can be given,
for all depends upon what one wants to see. If terrestrial distance is
meant, the large telescope does not possess an advantage proportionate
to its size. All objects on the earth must be observed through lower
strata of the atmosphere, and these regions are so much disturbed in
the daytime by intermingling of air currents, warm and cold, that
the high magnifying powers of large telescopes cannot be advantageously
used. If celestial distance is meant by the question, How far?
the answer can only be inconclusive, because the telescope enables us
to see as far as starlight can travel. The brighter the star, the greater
distance it can be seen, independently of the telescope. The smallest
glass will show stars so far away that light requires hundreds of years
to reach us from them. The larger the telescope, the fainter the star it
will show; but it is not known whether these fainter stars are fainter
because of their greater distance or simply because they are smaller or
less luminous. Another common question is, How much does your
telescope magnify? as if it had but one eyepiece. Actually it will have
several, for use according to the condition of the atmosphere and the
character of the object. A more intelligent question would be, What is
the highest magnifying power? This will never exceed 100~diameters
to each inch of aperture of the objective, and 70 to the inch is an
average maximum. Even this, however, is high, if advantageous
magnifying power is meant. So unsteady is the atmosphere in the
eastern half of the United States that magnifying powers exceeding
50 to the inch cannot often be used to advantage in observing the
planets.

\textbf{Celestial Photography.}\index{photography!celestial}---As soon as Daguerre\index{Daguerre, L. J. M. (dä-gêr´) (1789--1851), Fr.\ painter}, in 1839, had invented
photography, it was at once seen that the brighter heavenly bodies
might be photographed, because telescopes are used to form images
of them in exactly the same way that the camera produces an image of
a person, a building, or a landscape. Photography is simply a process
of fixing the image. In 1840 the moon was first photographed, in 1850
a star, in 1854 a solar eclipse, in 1872 the spectrum of a star, in 1880
a nebula, in 1881 a comet, in 1897 the spectrum of a meteor, and in
1898 a stellar occultation by the moon. All these photographs were
first made in America. Continued improvement in processes of photography
makes it possible to take pictures of fainter and fainter celestial
\DPPageSep{228.png}
bodies, and the larger telescopes have photographed exceedingly faint
stars which the human eye has never seen---perhaps never can see.
This is done by exposing the sensitive plate for many hours to the
light of such bodies; for, while in about 10~seconds the human eye,
by intense looking, becomes weary, the action of faint rays of light
upon the photographic plate is cumulative, so that the result of several
hours' exposure is rendered readily visible when the plate is developed.
In this way, an extra sensitive dry plate, of the sort most generally
employed, will often record many thousand telescopic stars in a region
of sky where the naked eye can see but one (page~\pageref{p458}). Nearly every
branch of astronomical research has been advanced by the aid of photography,
so universal are its applications to astronomy.

\textbf{How to take Photographs of the Heavenly Bodies.}---Any good telescope
or camera may be satisfactorily used in taking photographs of
celestial objects. Remove the eyepiece, and substitute in its place a
small, light-tight plate-holder. Fasten it to the tube temporarily, so
that the plate will be in the focus of the object glass. This point may
be found by moving forth and back a piece of greased or paraffin paper,
until the image of the moon is seen sharply defined. Adjust plate-holder
and finder so that when an object is in the field of the finder,
it will also be on the center of the plate. Insert a plate in this position,
and make an exposure of about half a second on the moon, if within
two or three days of the `quarter.' The object glass should be covered
by a cap or diaphragm having about three fifths the full aperture of the
lens. On developing, the moon's image will be somewhat blurred. In
part this is because the best focus for photographing is either outside or
inside the visual focus, found by the greased paper. To find the best
focus, move the plate-holder farther from the lens, first $\frac{1}{4}$~inch, then $\frac{1}{2}$~inch,
then $\frac{3}{4}$~inch, then 1~inch, making at each point an exposure of
the same length as before. Compare the negatives. The true photographic
focus lies nearest the point where the best-defined picture was
taken. If desired, the process may be repeated near this point, shifting
the plate only a few hundredths of an inch each time. If the
pictures are more and more blurred the farther the plate is moved from
the lens, the focus for photography may be inside the visual focus
first found, and the plate-holder should then be moved in accordingly,
making trials at different points. When the photographic focus is
finally found, the plate-holder should be securely fastened to the eyepiece
tube, or adapter; and a mark made so that it may readily be
adjusted to the same spot whenever needed in the future. A meniscus
of suitable curvature is sometimes attached in front of the object glass,
to focus the photographic rays (about $\frac{1}{7}$ nearer the objective). Also
E.~C.\ Pickering\index{Pickering, E. C., Dir.\ Harv.\ Coll.\ Obs.} has found that an achromatic objective with crown lens
properly figured can be converted into a photographic telescope by
\DPPageSep{229.png}
reversal of the crown lens. In achromatic objectives of the new Jena\index{glass!Jena (yay´na)}\index{Jena glass|see{glass, Jena}}
glass\index{glass!new}, visual and photographic foci are practically coincident. Ritchey\index{Ritchey, G.~W., Am.\ ast.}
and others have secured excellent photographic results with visual refractors
by inserting a yellow screen close in front of the sensitive plate
(isochromatic) and lengthening the exposure accordingly.

\textbf{Astronomical Discoveries made by Photography.}\index{photography!discoveries by}---The great benefit
to astronomy from the application of photography in making discoveries
was first realized when, during the total eclipse of 1882 in Egypt, the
photographic plate discerned a comet close to the sun (page~\pageref{p301}). But
interest was intensified when a hazy mass of light was seen to surround
the star Maia of the Pleiades\index{Pleiades (ple´ya-deez)}, on a plate exposed for about an hour to
that group of stars in November, 1885. This astronomical discovery
by means of photography was soon after verified by the 30-inch telescope
at Pulkowa\index{Pulkowa (pul-ko´va) Obs.}, Russia. Many other nebulæ, both large and small,
have since been discovered by photography, some of which have been
verified by the eye. By photographing spectra of stars, peculiarities of
constitution have been immediately revealed which the eye had long
failed to discover directly (page~\pageref{p444}). Several new double stars have
been found in this way, and important discoveries as to classification
of stars have been made from critical study of stellar spectrum photographs
(page~\pageref{p444}). Long exposures of comets have brought to light
certain details of structure which the eye has failed to detect (page~\pageref{p406}).
In discovering minor planets, photography has, since 1890, been
of constant assistance because of ease and accuracy in mapping fixed
stars in the neighborhood of these minute objects. It is about 20 times
easier to find a small planet on a photographic plate than by the former
method of mapping the sky optically. But discoveries in solar physics
by means of photography are most important of all, for it has been
found that the faculæ, or white spots, extend all the way across the sun's
disk in about the same zones that spots do (page~\pageref{p269}); and complete
photographic records of the sun's chromosphere and prominences are
now made every day by means of radiations to which photographic
plates are very sensitive, but which our eyes unaided are powerless to
see. Lunar photographs, too, are thought by some astronomers to have
revealed minute details which the eye has failed to detect. Also the
new satellites of Jupiter and Saturn (pp.\ \pageref{p344}, \pageref{p346}) were first discovered,
and their orbits found, by photography.
\Restore

We now turn to a consideration of present knowledge of
our satellite, and of the other and more remote orbs of
heaven, as disclosed by the instruments of which we have
just learned.
\DPPageSep{230.png}


\Chapter{X}{The Moon}\index{moon}

The moon was the subject of the most ancient astronomical
observations, for elementary study of her
motion was found both easy and useful. The waxing
and waning phases, too, must have excited the curiosity
of early peoples, who were unacquainted with the
true explanation of even so elemental a phenomenon. Let
us now watch our satellite from night to night. A few
evenings' observations show how easy it is to find out the
general facts of her motion around us.

\Smaller
\textbf{To observe the Moon's Motion.}\index{moon!motion}---The September new moon, first
becoming visible in the southwest, will, in about five days, reach the
farthest declination south, and culminate near the lowest point on the
meridian. Thenceforward, for about a fortnight, she will be farther and
farther north each night, journeying at the same time eastward, and in
a general way following the ecliptic. During the subsequent fortnight,
the moon will be traveling southward, always within the zodiac; and
in a little less than a month, will have returned very nearly to the
point where we first began to observe. And so on, throughout all
time, with a regularity which became useful to the ancients as a measure
of time; for our month took its origin from the moon's period round
the earth. But her motion is even more useful to the modern world,
because employed by navigators on long voyages in finding the position
of ships. So important is the moon in this relation that the lives of
many great mathematical astronomers have been almost wholly devoted
to the study of her motion. Americans prominent in this line of research
are Newcomb\index{Newcomb, S. (1835--1909), Am.\ ast.} and G.~W.\ Hill\index{Hill, G.~W., Am.\ ast.}. As soon as the new moon can
first be seen in the western sky, make a long, narrow chart of the
brighter stars to the east within the zodiac as \vpageref{p222}. A line
drawn eastward from the moon, perpendicular to the line joining the
\DPPageSep{231.png}
horns of the crescent, called \textit{cusps}, will show this direction accurately
enough. Then plot the moon among the stars on the chart each clear
night. Also draw the phase as
accurately as possible. It is better
to chart the position about half
an hour later each night. This
simple series of observations may
continue nearly three weeks, if
desired. Much will be learned
from it,---position of the ecliptic;
progressive phases of the moon;
the amount of
% Fig 10.1
\begin{wrapfigure}[40]{o}{0.5\textwidth}
  \centering
  \Input[0.425\textwidth]{page_222}
  \caption{Illustrating the Moon's Eastern Progress among the Stars from Day to Day}
  \label{p222}
\end{wrapfigure}
motion each day
(about her own breadth every
hour, or $13$° in a day); and if a
telescope is used, the observer will
occasionally be rewarded by the
opportunity of watching the moon
pass over, or occult, a star. Disappearance
of a star at the moon's
dark limb is the most nearly instantaneous
of all natural phenomena.
\Restore

\textbf{The Terminator.}\index{moon!terminator}\index{terminator|see{moon, terminator}}---Observe
the slender moon in
the west, as soon as she can
be seen in a dark sky. The
inside edge of the bright
crescent, or the line where
the lucid part of the moon
joins on the dark or faintly
illuminated portion, is called
the terminator; and its general
curvature is always a
half ellipse, never a semicircle.

\Smaller
The moon's terminator is elliptical
in figure because it is a semicircle
seen obliquely. Any circle
not seen perpendicularly seems to
\DPPageSep{232.png}
be shaped like an ellipse; and the more obliquely it is seen, the more
the ellipse appears elongate or drawn out. When turning a curve on
your bicycle, observe the changing figure of the shadows of its wheels
cast by the sun. Owing to mountains on the lunar surface, the actual
terminator, if examined with a telescope, is always a broken, jagged
line. This is because sunlight falls obliquely across the rough surface,
and all its irregularities are accentuated as if magnified---like pebbles
and ruts in the road, at a considerable distance from an arc light.
\Restore

% Fig 10.2 a, b
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input{page_223a}
    \caption{Phases as seen from above Moon's Orbit}
  \end{minipage}
  \hfill
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input{page_223b}
    \caption{Corresponding Phases from the Earth}
  \end{minipage}
  \caption{Explaining Phases of the Moon}\index{moon!phases}
\end{figure}

\textbf{The Moon's Phases.}\index{moon!phases}---The moon's phases afforded travelers
and shepherds the first measure of time. When two
or three days after new moon our satellite is first seen in
the western sky, her form is a crescent, convex westward
or toward the sun, with the horns, or cusps turned toward
the east. Three or four days later the slender crescent
having grown thicker and thicker, and the terminator less
and less curved, the moon has reached quadrature\index{quadrature|see{moon, quadrature}}\index{moon!quadrature}, or first
quarter, and her shape is that of a half circle. The terminator
is then a straight line, the diameter of this circle.
Passing beyond quadrature, the terminator begins to curve
\DPPageSep{233.png}
in the opposite direction, making the moon appear shaped
somewhat like a football, with one side circular and the
other elliptical. The eastern edge is the elliptical one,
and is still called the terminator. Gradually its curvature
increases, the apparent disk of the moon growing
larger and larger, until, about a week after first quarter,
the phase called full moon is reached. This oblong
moon, between first quarter and full, is called gibbous
moon\index{moon!gibbous}. From full moon onward for a week, our satellite
is again gibbous in form, but the terminator has now
changed to the west side of the lunar disk, instead of
the eastern. Then quadrature is reached, and the moon
is again a half circle, but turned toward the east, not
the west. This phase is known as third quarter. Onward
another week to new moon, the figure is again crescent,
but curving eastward or toward the sun, and the
horns pointing toward the west. All the figures previously
shown---crescent, quarter, gibbous, and full---represent
phases of the moon.

\textbf{Cause of the Moon's Phases.}\index{moon!phases}---Our satellite is herself a
dark, opaque body. But the half turned toward the sun is
always bright, as in the last figure; the opposite half is
unillumined, and therefore usually invisible. While the
moon is going once completely round the earth, different
regions of this illuminated half of our satellite are turned
toward us; and this is the cause of phases of the moon.

% Fig 10.3
\begin{wrapfigure}[24]{o}{0.6\textwidth}
  \centering
  \Input[0.5\textwidth]{page_225}
  \caption{Illustrating the Moon's Progressive Phases}\index{moon!phases}
\end{wrapfigure}
\Smaller
To illustrate in simple fashion: accurately remove the peel from the
half of an orange. Let a lamp in one corner of a room otherwise dark
represent the sun. Standing as far as convenient from the lamp, let
the head represent the earth, and the orange held at arm's length,
the moon. Turn the white half of the orange toward the lamp. Now
turn slowly round toward the left, at the same time turning the orange
on its vertical axis, being careful always to keep the peeled side of the
orange squarely facing the lamp. While turning round, keep the eye
constantly fixed on the white half of the orange, and its changing
\DPPageSep{234.png}
shape will represent all the moon's successive phases: new moon when
orange is between eye and lamp; first quarter (half moon) when orange
is at the left of lamp and
at a right angle from it;
full moon when orange is
directly opposite lamp;
last quarter, orange opposite
its position at first
quarter. When the orange
shows a slender crescent,
at either old or new moon,
shield the eye from direct
light of lamp. Again repeat
the experiment, and
watch the gradually curving
terminator from phase
to phase. The unpeeled
half of the orange, too,
represents very well the
moon's ashy light, or
earth shine on the moon,
when a narrow crescent.
\Restore

\textbf{Earth Shine.}\index{moon!earth shine on}---The
nights on the moon
are brightened by reflected
light from the
neighborly earth, and
our shining is equal to more than a dozen full moons.
This light it is that makes the faint appearance on the
moon, as of a dark globe filling the slender crescent of the
new moon, causing a phenomenon called `the old moon
in the new moon's arms.' Similarly with the decrescent
old moon\index{moon!decrescent}\index{decrescent|see{moon, decrescent}}.

\Smaller
The copper color of the earth-illumined portion is explained by the
fact that the earth light has passed twice through our atmosphere before
reaching the moon, and by a peculiar property of the atmosphere, it
absorbs bluish rays and allows reddish ones to pass. Always the
phase of this portion of the moon is the supplement of the phase of the
bright portion. Also its figure is exactly that which the bright earth
\DPPageSep{235.png}
would appear to have, if seen from the moon. When our satellite is
crescent or decrescent to us, the earth shows gibbous to the moon.
\Restore


\textbf{North and South Motion of the Moon.}\index{moon!north and south motion}---Just as the sun
has a north and south motion in a period of a year, so the
moon has a similar motion in a period of about a month;
for she follows in a general way the direction of the ecliptic.
Every one has observed that midsummer full moons always
cross the meridian low down, and that the full moons of
midwinter always culminate high.

\Smaller
The reason is that the full moon is always about 180 degrees from
the sun. Similarly midwinter crescent moons, whether old or new, are
always low on the meridian, and crescent moons of midsummer always
high. So when in summer you see in early evening the new moon in
the northwest, you know that in winter the old moon's slender crescent
must be looked for in the early morning in the southeast. Remember
that our satellite from new to full is always east of the sun. And
whether the moon in this part of its lunation is to be found north or
south of the sun will depend upon the season. For example, the moon
at first quarter will run highest in March, because the sun is then at the
vernal equinox, and the moon at the summer solstice. For a like reason
the first-quarter moon which runs lowest on the meridian will `full' in
the month of September.
\Restore

\textbf{The Moon rises about Fifty Minutes later Each Day.}\index{moon!daily retardation}---Her
own motion eastward among the stars, about 13° every
day, causes this delay. As our ordinary time is derived
from the sun (itself not stationary among the stars, but
also moving eastward every day about twice its own
breadth, or 1°), therefore the eastward gain of the moon
on the sun is about 12°. Now suppose the moon on
the eastern horizon at 7~o'clock this evening; then, to-morrow
evening at~7, it is clear that if her orbit stood vertical,
she would be 12° below the horizon, because in that
part of the sky the direction east is downward. But by
the earth's turning round on its axis, the stars come above
the eastern horizon at the rate of 1° in four minutes of
time; therefore to-morrow evening the moon will rise at
\DPPageSep{236.png}
about 50~minutes after 7. And so on, about 50~minutes
later on the average each night.

\textbf{Variation from Night to Night.}---Consult the almanac
again. In it are printed the times of moonrise for every
day. Wait until full moon, and verify these times for a
few successive days, if the eastern horizon permits an unobstructed
view. Having found the almanac reliable, at
least within the limits of error of observation, we may use
its calculations to advantage for other days of the year;
for on many of these it will not be possible to watch
the moon come up, because she rises in the daytime. The
difference of rising (or of setting) from one day to another
may sometimes be less than half an hour, and again about
a fortnight later, a full hour and a quarter.

\Smaller
There are two reasons for this: (1) The apparent monthly path of
the moon lies at an angle to the horizon which is continually changing;
when the angle is greatest, near the autumnal equinox, a day's eastward
motion of our satellite will evidently carry her farthest below the
eastern horizon. (2)~The moon's path around us is elliptical, not circular,
and the earth is not at the center of the ellipse, but at its focus,
so that earth and moon are nearest together and farthest apart alternately
at intervals of about two weeks. By the laws of motion in such
an orbit, the moon travels her greatest distance eastward in a day
when nearest the earth (perigee)\index{moon!perigee}\index{perigee|see{moon, perigee}}; and her least distance eastward when
farthest from the earth (apogee)\index{moon!apogee}\index{apogee|see{moon, apogee}}. And this change in speed of the
moon's motion also affects the time of rising and setting.
\Restore

% Fig 10.4
\begin{figure}[b]
  \centering
  \Input{page_228}
  \caption{Circumstances of Harvest Moon}\index{moon!harvest}
\end{figure}

\textbf{Harvest and Hunter's Moon.}\index{moon!harvest}\index{moon!hunter's}---Every month the moon
goes through all the changes in the amount of delay in her
rising, from the smallest to the largest. But ordinarily
these are not taken especial account of, unless at the time
when least retardation happens to coincide nearly with
time of full moon. Now the epoch of least retardation
occurs when the moon is near the vernal equinox, because
there the moon's path makes the smallest angle with
the eastern horizon. And as sun and full moon must be
\DPPageSep{237.png}
in opposite parts of the sky, autumn is the season when
full moon and least retardations come together.

\Smaller
The daily advance of the moon along the September ecliptic is from
$1$ to $2$, and from $2$ to $3$. In March the same amount of eastward
advance, from $1$ to $2'$, and from $2'$ to $3'$, brings the moon much farther
below the horizon, and therefore retards the time of rising by the greatest
amount, as the dotted lines drawn parallel to the equator show. Similarly
the positions at $2$ and $3$ give the least delay; and this September
full moon, rising less than a half hour later each evening, is called the
harvest moon. A month later the retardation is still near its least
amount for a like reason; and the October full moon is called the
hunter's moon. Approaching the tropics, where equator and ecliptic
stand more nearly vertical to the horizon, it is clear that the phenomena
of the harvest moon become much less pronounced.
\Restore

\textbf{The Moon's Period of Revolution.}\index{moon!period}---The moon revolves
completely round the starry heavens in $27\frac{1}{3}$~days (or more
exactly 27\,d.\:7\,h.\:43\,m. 11.5\,s.). This is called the \textit{sidereal
period} of the moon, because it is the time elapsed while she
is traveling from a given star eastward round to the same
star again. This motion of the moon must be kept entirely
distinct from the apparent diurnal motion, or simple
rising in the east and setting in the west; for the latter
is a motion of which all the stars partake, and is wholly
\DPPageSep{238.png}
due to the earth's revolution eastward upon its axis. But
our satellite's own motion along her path round the earth is
in the opposite direction; that is, from west toward east.
A rough value for the sidereal period is easy to determine.

\Smaller
Select any bright star (not a planet) near the moon, and notice the
hour when the star and the center of the moon are nearly on the same
hour circle; that is, when their right ascensions are about equal. The
following month watch for the moon's return to the same star, and find
the interval. For example, the moon was seen to be on the same hour
circle with Alpha Scorpii on 11th September, 1899, at about 7~\PM\ At
the same hour on 8th October the moon had not yet reached the star,
but was about eight times her own breadth west of it; so star and
moon were not together till about 3~\AM\ of 9th October---an interval
of 27\,d.\:8\,h.

\textbf{The Moon's Synodic Period.}\index{moon!period}\index{synodic period|see{moon, period}}---Let sun and moon appear together
in the sky as seen from the earth at $E$, sun being at $S$, and moon at $M_1$.
While earth
% Fig 10.5
\begin{wrapfigure}{o}{0.7\textwidth}
  \centering
  \Input[0.7\textwidth]{page_229}
  \caption{Synodic Period exceeds Sidereal Period}\index{moon!period}
\end{wrapfigure}
is traveling
eastward round
the sun in the direction
of the large arrow,
moon is all the
time going round
earth in the direction
$M_1M_2$ indicated
by the small arrow.
When earth has
reached $E'$, moon is
at $m_1$, and her sidereal
period is then
complete, because
$m_1E'$ is parallel to
$M_1E$. But the sun
is in the direction
$E'S$. So the moon must move on still further, making the period relatively
to the sun longer than her sidereal period, just as the sidereal day
is shorter than the solar day. In round numbers, the sun's apparent
motion, while the moon has been traveling round us, amounts to about
$30$°; therefore the moon must travel eastward by this amount, or nearly
$2\frac{1}{3}$~days of her own motion, in order to overtake the sun.
\Restore

The period of the moon's motion round the earth relatively
to the sun is called the synodic period. It is $29\frac{1}{2}$
\DPPageSep{239.png}
days in duration, or accurately 29\,d.\:12\,h.\:44\,m.\:2.7\,s., as
found by astronomers from several thousand revolutions
of the moon. It is an average or mean period, depending
upon the mean motion of the sun and the mean motion of
the moon; for we shall soon find that our satellite travels
round us with a speed far from uniform, just as we found
our own motion round the sun to be variable. The synodic
period may be roughly verified by observing the times of
a given phase of the moon with about a year's interval
between them, and dividing by the whole number of lunations.
For example, on 12th September, 1899, at about
six in the evening, the terminator was judged to be straight,
and it was first quarter. Similarly, on 1st October, 1900,
at 5~o'clock \PM\ Dividing the entire interval of 384.0
days by 13, the number of intervening lunations, gives a
result of 29.54\,d., about 0.2~hour in error.

\textbf{The Lunation.}\index{moon!lunation}\index{lunation|see{moon, lunation}}---The term \textit{lunation} is often used with
the same signification as the synodic period. More properly
the lunation is the period elapsing from one new
moon to the next. Its value cannot be found directly by
observation, but only from calculation, because at new
moon the dark half of our satellite is turned toward us,
and the disk is merged in the background of atmosphere
strongly illuminated by the sun. Take from any almanac
the difference between the times of adjacent new moons
at different times of the year. Some of these will be
longer and some shorter by several hours than the synodic
period. These differences are mainly due to (\textit{a})~the sun's
varying motion along the ecliptic, and (\textit{b})~the moon's
varying motion in her path round the earth.

% Fig 10.6
\begin{figure}[hbt!]
  \centering
  \Input[0.65\textwidth]{page_231}
  \caption{Illustrating Inclination and Nodes of Lunar Orbit}
  \label{fig10.6}\index{moon!inclination of orbit}\index{moon!nodes}\index{nodes|see{moon, nodes}}
\end{figure}
\textbf{The Moon's Apparent Orbit.}\index{moon!apparent orbit}---So far the moon's motion
has been accurately enough described by saying that its
path coincides with the ecliptic. But closer observation
will soon show that, twice each month, our satellite deviates
\DPPageSep{240.png}
from the ecliptic by 10 times her own breadth. This angle,
more accurately $5$°\, $8'$\, $40''$, is the inclination\index{moon!inclination of orbit} of the moon's
orbit to the ecliptic, and it varies scarcely at all. Just as
ecliptic and equator cross each other at two points $180$°
apart, called the equinoxes, so the moon's path and the
ecliptic intersect at two opposite points, called nodes of
the moon's orbit, or more simply the moon's nodes\index{moon!nodes}.

\Smaller
In the preceding\DPnote{** TN: Word added} figure they are represented at \textit{a} and \textit{b}, as coincident with the
equinoxes, $\aries$ and $\libra$. That, however, is their position for an instant
only; for they move constantly westward just as the equinoxes do, only
very much more rapidly. During the time consumed by our satellite
in traveling once around us, the moon's nodes travel backward more
than twice the moon's breadth; so that in $18\frac{1}{2}$~years the nodes themselves
travel completely round the ecliptic, and return to their former
position. When journeying from south to north of the
% Fig 10.7
\begin{wrapfigure}[30]{o}{0.3\textwidth}
  \centering
  \Input[0.3\textwidth]{page_232}
  \caption{Orbit Concave to Sun, even at New Moon}
\end{wrapfigure}
ecliptic, as from
\textit{d} to \textit{c}, in the direction indicated by the arrow, the moon passes her
\textit{ascending node}, at \textit{a}. And when going from \textit{c} to \textit{d}, she passes her
\textit{descending node} at \textit{b}. When the inclination of the moon's orbit is
\DPPageSep{241.png}
added to the obliquity of the ecliptic, our satellite moves in the plane
$acbd$, in the direction of the arrows; when the inclination is subtracted,
she moves in the plane \textit{agbf}. In both cases the nodes coincide with the
equinoxes; but in the latter the ascending node has moved round to $b$,
and the descending node to \textit{a}. Extreme range of moon's declination
is from 28°.6 north to 28°.6 south.
\Restore

\textbf{Cardinal Points of the Moon's Orbit.}---When our satellite
comes between earth and sun, as at new moon, she is
said to be in conjunction\index{conjunction!moon's}; at the opposite
part of her orbit, with sun and moon
on opposite sides of the earth, as at full
moon, she is said to be in opposition.
Both conjunction and opposition are
often called syzygy. Halfway between
the syzygies are the two points called
quadrature. At quadrature the difference
of longitude between sun and moon
is 90°; at the syzygies, this difference is
alternately 0° and 180°. The term \emph{syzygy}\index{moon!syzygy}\index{syzygy|see{moon, syzygy}}
is derived from the Greek word meaning
a yoke, and is applied to these two relations
of sun, earth, and moon, when all
these bodies are in line in space---or
nearly so.

\Smaller
\textbf{True Shape of the Moon's Orbit in Space.}\index{moon!orbit in space}---If
the earth did not move, the moon's orbit in space
would be nearly circular. But during the month
consumed by the moon in going once around us,
we move eastward about $\frac{1}{12}$ of an entire circumference,
or 30°. The moon's orbital motion is
relatively slow, the earth's relatively rapid; and
on this account the moon winds in and out, along
our yearly path round the sun. As that illuminating
body is about 400 times more distant than the moon, the true
shape of the lunar orbit cannot be shown in a diagram of reasonable
size. But a small portion of the orbit can be satisfactorily shown, as
above; and it readily appears that the moon's real path in space is
always concave to the sun.
\Restore
\DPPageSep{242.png}

\textbf{Form of the Moon's Orbit round the Earth.}---In the
case of sun and earth, we found that the shape of our
yearly path round him is an ellipse, without knowing anything
about our distance from him. In like manner we
can find the form of the moon's monthly orbit round the
earth. That also is an ellipse.

% Fig 10.8
\begin{wrapfigure}{o}{0.3\textwidth}
  \centering
  \Input[0.3\textwidth]{page_233}
  \caption{Relative Size at Perigee, and Apogee (Dotted Circle)}
  \index{moon!perigee}\index{moon!apogee}
\end{wrapfigure}
\Smaller
By measuring the moon's diameter in all parts of her orbit, we shall
find variations which can be due only to the changing distance of our
satellite from us. The two circles adjacent
correspond to extremes of this variation: the
moon when nearest to us, is said to be at
perigee, and the outer circle represents its
apparent size. About a fortnight later, on
arrival at greatest distance, called apogee\index{moon!apogee}, the
moon's apparent size will have shrunk to the
inner dotted circle. Evidently the variation
of apparent diameter is much greater than
that of the sun; therefore the moon's path
is a more elongated ellipse than the earth's.
We saw that the eccentricity of the earth's
orbit is $\frac{1}{60}$: that of the moon's orbit is $\frac{1}{18}$. So great is this variation
in distance of our satellite that full moons occurring near perigee are
noticeably brighter than those near apogee. While at new moon, as
we shall see in Chapter~\textsc{xii}, this change of the moon's apparent diameter
happens to be very significant; for it produces different types of
eclipses of the sun.
\Restore

\textbf{Distance of the Moon.}\index{moon!distance}\index{distance|see{moon, distance}}---Of all celestial bodies, excepting
meteors and an occasional comet, the nearest to us is the
moon. Astronomically speaking, and relatively, the moon
is very near, and yet her distance is too great to be apprehended
by reference to any terrestrial standard. As her
orbit is elliptical instead of circular, and as the earth is
situated in one of the foci of the ellipse, the average or
mean distance of the moon's center from the center of our
globe is 239,000 miles.

\Smaller
If the New York--Chicago limited express could travel from the earth
to the moon, and should start on New Year's, although it might run
\DPPageSep{243.png}
day and night, it would not reach the moon till about the 1st of September.
Recalling definitions of the ellipse previously given, it will be
remembered that the mean distance is not the half sum of the greatest
and least distances, but the mean of the distances at all points of the
orbit. Also it is equal to half the major axis of the orbit. But in
traveling round the earth, our satellite is not free to pursue a path
which is a true ellipse, for the attraction of other bodies, in particular
the sun, pulls her away from that path. So the moon's center sometimes
recedes to a distance of 253,000 miles, and approaches as near as
221,000 miles.
\Restore

\textbf{What is Parallax?}\index{moon!parallax}---The moon's distance is found by
measuring the parallax. Parallax is change in apparent
direction of a body due to change of the point of observation.
It is by no means so puzzling as it may look.

% Fig 10.9
\begin{figure}[hb!]
  \centering
  \Input[0.9\textwidth]{page_234}
  \caption{Parallax decreases as Distance increases}
  \label{p234}\index{moon!parallax}
\end{figure}
\Smaller
Place a yardstick on its edge at the farther side of a table, as shown.
Set up a pin, a nail, and a screw, at convenient intervals; the nail at
twice, and the screw at three times, the distance of the pin from the
notch in the card between the eyes. It is better if notch, pin, nail, and
screw are in a straight line nearly at right angles to the yardstick at its
middle point. First, from the aperture in the card at \textit{a}, observe and
set down in a horizontal line the readings of pin, nail, and screw, as
projected against the rule; then repeat the observation from \textit{b}, in the
same order, setting down readings in line underneath. Screw, nail, and
pin all seem to change their direction as seen from the two apertures.
This apparent change of direction is parallax; it is the angle formed
at the object by lines drawn from it to each eye. Now take the differences
of the pairs of readings as they stand: the difference of the pin
readings is twice that of the nail readings, and three times that of the
\DPPageSep{244.png}
screw readings. Parallax, then, is less, the farther an object is removed
from the base, or line joining the two observation points. And considering
these points fixed, we reach the general law that---
\Restore

\textit{The parallax of an object decreases as its perpendicular
distance from the base of observation increases.}

%[Sidenote (handwritten):
%  Equatorial and diurnal parallax are the same as
%  horizontal parallax (p.236) \\
%  Annual parallax. see p.~435 ]

\textbf{The Moon's Equatorial Parallax.}\index{moon!parallax}\index{parallax|see{moon, parallax}}---In measuring celestial
distances, obviously it is for the interest and convenience
% Fig 10.10
\begin{figure}[ht!]
  \centering
  \Input{page_235a}
  \caption{Size and Distance of Earth and Moon in True Proportion}
  \label{p235}
\end{figure}
of all astronomers to agree upon some standard by which
to measure and indicate parallaxes. Such a standard line
has been universally adopted; it is the radius of the earth
at the equator. The moon's parallax, then, is the angle at
the center of that body subtended by the equatorial radius
of the earth. This
constant of lunar
parallax is nearly a
degree in amount
($57'\, 2''$). It means
that an astronomer,
if he could take his
telescope to the
moon and there
measure the earth,
would find its equator
to fill twice the
angle of the moon's
equatorial parallax;
that is, the earth
would be 1°\, $54'$ in diameter---an angle correctly represented
in the slim figure \vpageref{p235}.

\textbf{Moon's Parallax at Different Altitudes.}\index{moon!parallax}---Whatever the
\DPPageSep{245.png}
latitude of the place, the moon's parallax is the angle
filled by the radius of the
% Fig 10.11
\begin{wrapfigure}{o}{0.58\textwidth}
  \centering
  \Input[0.55\textwidth]{page_235b}
  \caption{Parallax increases with Zenith Distance}
  \label{p235a}
\end{wrapfigure}
earth at that place, as seen
from the moon. When moon is in horizon, that radius
$AC$ (preceding diagram) is perpendicular to the horizon
$AB$, and the parallax $AMC$ is consequently a maximum,
called the horizontal parallax. Higher up, as at $M'$, change
in apparent direction of the moon, as seen from $A$ and $C$,
is less; that is, the parallax is less. With the moon at
$M''$, in the zenith, the parallax becomes zero, because
the direction of $M''$ is the same, whether viewed from $A$
or $C$. Thus we derive the important generalization, true for
sun and planets as well as moon: \textit{For a heavenly body at a
given distance from the earth's center parallax increases
with the zenith distance.}

\textbf{Parallax lessens the Altitude}.---True altitude of the
moon and other bodies is measured upward from the rational
horizon to the center of the body. In the diagram
\vpageref{p235a}, these altitudes are $HCM$, $HCM'$,
and $HCM''$. But as seen from the point of observation
$A$, the moon's apparent altitudes are 0° at $B$, $BAM'$, and
$BAM''$. It is clear that these altitudes must always be less
than the true altitudes, except when moon is in zenith.
And by inspection we reach the general proposition that
parallax lessens altitude, and its effect decreases as altitude
increases, until it becomes zero when the body is exactly
in the zenith. Both parallax and refraction vanish at
the zenith; but at all other altitudes, their effects are
just opposite, refraction always seeming to elevate, and
parallax to depress, the heavenly bodies.

\textbf{How the Distance of the Moon is found.}\index{moon!distance}---By precisely
the principle of the illustration on page~\pageref{p234} is the distance
of the moon from the earth found---that is, by calculation
from its parallax. And the parallax can be found only by
observations from two widely distant stations on the earth.
\DPPageSep{246.png}

% Fig 10.12
\begin{wrapfigure}[20]{o}{0.4\textwidth}
  \centering
  \Input[0.4\textwidth]{page_237}
  \caption{Moon as seen from Berlin and Capetown}
  \index{Pleiades (ple´ya-deez)}
\end{wrapfigure}
\Smaller
\label{p237a} Imagine a being of proportions so huge that his head would be as
large as the earth. Then think of his two eyes as two observatories;
for example, Berlin and Capetown, one in the northern and one in the
southern hemisphere. Also imagine the moon to take the place of the
screw and replace the divisions on the rule by fixed stars. Evidently
then, the observer at Berlin will see the moon close alongside of different
stars from those which the Capetown observer will see adjacent
to the edge. The amount of displacement can be judged from this
illustration, which shows the well-known
group of stars called the
Pleiades\index{Pleiades (ple´ya-deez)} in the constellation Taurus.
The bright disk represents the moon
as seen from Berlin, the darker disk
where seen from Capetown. As the
angular distances of all these stars
from each other are known, the angular
displacement of the moon in
the sky (or its parallax referred to
the line joining Berlin and Capetown
as a base) can be found. Now the
length of this straight line, or chord,
through the earth's crust is known,
because the size of the earth is
known. So it is evident that the
distance of the moon can be calculated
from these data. The process,
however, requires the application of
methods of plane trigonometry. It
was primarily for the purpose of finding
the moon's distance that the Royal Observatory at Capetown was
founded by the British government early in the 19th century.
\Restore

\label{p237} \textbf{Moon's Deviation from a Straight Line in One Second.}\index{moon!deviation}---As
the moon's distance from the earth is approximately
240,000 miles, the circumference of her orbit (considered
as a circle) is 1,509,000 miles. But our satellite passes
over this distance in 27\,d.\:7\,h.\:43\,m.\:11.5\,s.; therefore in one
second she travels 0.640 mile. In that short interval how
far does her path bend away from a straight line, or tangent
to her orbit?

% Fig 10.13
\begin{wrapfigure}{o}{0.4\textwidth}
  \centering
  \Input[0.4\textwidth]{page_238}
  \caption{Fall of Moon in One Second}
\end{wrapfigure}
\Smaller
Suppose that in one second of time the moon would move from $S$
to $T$, if the earth exerted no attraction upon her. On account of this
\DPPageSep{247.png}
attraction, however, she passes over the arc $St$. This arc is 0.640 mile
in length, or about $0''.5$ as seen from the earth; and as this angle is
very small, the arc $St$ may be regarded
as a straight line, so that $StU$
is a right angle. Therefore
\[
  SU : St :: St : Ss\DPtypo{}{.}
\]
But $SU$ is double the distance of the
moon from us; therefore $Ss$ is 0.053
inch, which is equal to $Tt$, or the
distance the moon falls from a straight
line in one second.
\Restore

So that we reach this remarkable
result: The curvature
of the moon's path is so
slight that in going $\frac{6}{10}$ of a
mile, she deviates from a
straight line by only $\frac{1}{20}$ of an
inch.

\textbf{Dimensions of the Moon.}\index{moon!dimensions}---First her apparent diameter\index{moon!apparent diameter} is
measured: it is somewhat more than a half degree (accurately,
the semidiameter is $15'\, 32''.6$). But the moon's
parallax, or what is the same thing, the angle filled by the
earth's radius as seen from the moon, is $57'$. So that,
as the length of the earth's radius is 3960 miles, we can
form the proportion---
\begin{center}
\TableSize
\begin{tabular}{ @{\,} *{7}{c@{\,}} }
$\left\{\parbox{6em}{\centering\tiny
    Radius of earth as~seen from moon} \right\}$ &amp;:&amp;
$\left\{\parbox{6em}{\centering \tiny
    Radius of moon as~seen from earth} \right\}$ &amp;::&amp;
$\left\{\parbox{6em}{\centering \tiny
    Length of earth's radius in miles} \right\}$ &amp;:&amp;
$\left\{\parbox{6em}{\centering \tiny
    Length of moon's radius in miles}  \right\}$
\\[1ex]
  57 &amp; : &amp; 15.5 &amp; :: &amp; 3960 &amp; : &amp; 1077
\end{tabular}
\end{center}
The diameter of the moon, therefore, from this proportion
is 2154 miles. A more exact value, as found by astronomers
from a calculation by trigonometry is 2160 miles. The
moon's breadth, then, somewhat exceeds one fourth the
diameter of our globe. So far as known, the diameter is
the same in all directions; that is, the moon is spherical.
As surfaces of spheres vary with the squares of their
\DPPageSep{248.png}
diameters, the surface-area of our satellite is about $\frac{1}{14}$ that
of our planet, or $4\frac{1}{2}$ times that of the United States. The
bulk of the moon is only $\frac{1}{49}$ that of the earth, because
volumes of globes vary as the cubes of their diameters.

\Smaller
\textbf{To measure the Moon's Diameter.}---You need not take the diameter
of the moon on faith: measure it for yourself. When our satellite is
% Fig 10.14
\begin{figure}[hbt!]
  \centering
  \Input{page_239}
  \caption{Measuring the Moon's Diameter without Instruments}
\end{figure}
within a day or two of the full, select a time from a half hour to three
hours after moonrise. Open a window with an easterly exposure, close
one of the shutters, and turn its slats (opposite the open sash) so that
their planes shall be directed toward the moon. The observation now
consists of four parts: (1)~so placing the head that the moon can be
seen through the slats, (2)~making the distance of the eye from the
window such that the moon will just seem to fill the interval between
two adjacent slats, (3)~measuring the eye's distance from the slats, (4)~measuring
the distance of the slats from each other. A pile of books
will be a help in fixing the point where the eye was when making the
observation. Placing the head beyond the books, and about seven feet
from the sash, move slowly away from the window till the moon just
fills the space between two adjacent slats. Or if size of the room will
allow, let the moon fill the space between two slats not adjacent. Make
a mark on the frame of the shutter between these slats. Bring the pile
\DPPageSep{249.png}
of books close up to the eye so that a near corner of the top book may
mark where the eye was. Next thing necessary is a non-elastic cord
about 15~feet long. Tie one end to the slat or frame, near mark just
made, then draw it taut to corner of pile of books where the eye was.
Measure along the cord the distance (in inches) of the eye from the
slats. Also measure perpendicular distance (in inches) between the
inner faces of the two slats marked. Then approximate diameter of
moon (in miles) is found from the following proportion:---
\begin{center}
\begin{tabular}{ @{\,} *{7}{c@{\,}} }
$\left\{\parbox{5em}{\centering
    Distance of slats from the eye} \right\}$ &amp;:&amp;
$\left\{\parbox{5em}{\centering
    distance of slats from each other} \right\}$ &amp;::&amp;
239,000 &amp;:&amp;
$\left\{\parbox{5em}{\centering
    diameter of the moon (in miles)}  \right\}$
\\[1ex]
\end{tabular}
\end{center}
Repeat observation at least twice, moving pile of books each time,
adjusting it anew, and measuring distance over again.
\Restore

\textbf{Measures of the Moon and their Calculation.}---On 26th
January, 1899, at about 6~o'clock \PM, or an hour after
the moon had risen, the following measures were made:---
\begin{center}
\TableSize
\begin{tabular}{l@{\quad}l@{}l c r@{}r@{}l}
  \multicolumn{3}{m{7em}}{\centering\footnotesize
     Distances of shutter from eye.}
&amp;&amp;\multicolumn{3}{m{13em}}{\centering\footnotesize
     Perpendicular distance between inner faces of slats.}
\\
(1) &amp;            139.5&amp;\ inches &amp; \hspace{3em}
    &amp;                 &amp;                     1&amp;$\frac{1}{4}$ inches.
\\
(2) &amp;            136  &amp;          &amp;
&amp;              &amp;    \underline{239,000} &amp;
\\
(3) &amp; \underline{137\phantom{.5}} &amp;     &amp;
&amp;       &amp; \underline{\phantom{0}59,750} &amp;
\\
    &amp;            137.5&amp;\ average &amp;
&amp; \qquad 137.5 &amp;\,\underline{)\,298750}
\\
    &amp;  &amp;  &amp;  &amp;  &amp;  2170
\end{tabular}
\end{center}

So the moon's diameter from these crude measures is
2170 miles, only about $\frac{1}{200}$ part too great.

\Smaller
\textbf{Why the Moon seems Larger near the Horizon.}---Because of an
optical illusion. With two strips of blank paper, cover everything
near the bottom of this page except the line of dots. Before reading
further, decide which seems longer, $xy$ or $yz$?
\[
\begin{array}{ccccc}
  \bullet &amp; \hdotsfor[4]{1}           &amp; \bullet &amp;                           &amp; \bullet \\
  x       &amp; \rule{.35\textwidth}{0pt} &amp; y       &amp; \rule{.35\textwidth}{0pt} &amp; z
\end{array}
\]

Distance almost invariably seems longer if there are many intervening
objects. For example, $xy$ seems longer than $yz$, because $xy$ is
filled with dots, and $yz$ is not. Thus horizon appears to be more
distant than zenith, because the eye, in looking toward the horizon,
rests upon many objects by the way. This accounts for the apparent
flattening of the celestial vault. Now the moon near the horizon and
\DPPageSep{250.png}
at the zenith is seen to be the same object in both positions; but when
near the horizon she seems larger because the distance is apparently
greater, the mind unconsciously reasoning that being so much farther
away, she must of course be larger in order to look the same. Often the
sun is seen through thick haze or fog near the horizon, and a like
illusion obtains. But we know that the true dimensions of these bodies
do not vary in this manner, nor do their distances change sufficiently.
And whether illusion of sun or moon, it is easy to dispel. Roll a thin
sheet of paper round a lead pencil, making a tube about 12~inches
long. With one eye look through this tube at the much-enlarged sun
or moon near the horizon; instantly the disk will shrink to normal proportions.
Then close this eye and open the other---as instantly the
% Fig 10.15
\begin{figure}[hbt!]
  \centering
  \Input{page_241}
  \caption{Why the Moon is really largest at the Zenith}
\end{figure}
illusion deceives again. Repeat the experiment, opening and closing
the eyes alternately as often as desired; the eye behind the tube is
never deceived, because it sees only a narrow ring of sky round the
moon, and the tube cuts off all sight of the intervening landscape.

\textbf{Moon Larger at Zenith than at Horizon.}\index{moon!apparent size}---The actual fact is just the
reverse of the illusion; for if the moon's horizontal diameter is measured
accurately when near the horizon, it is actually less than on the meridian.
The above diagram makes this at once apparent. The moon
at $M$ is in the horizon of a place $A$ on the surface of the earth, and
in the zenith of $B$, which may be conceived the same as $A$, after the
earth has turned about 90° on its axis. As $M$ is nearer $B$ than $A$ by
almost the length of the earth's radius, or nearly 4000 miles, clearly the
zenith moon must be larger than the horizon moon by about $\frac{1}{60}$ part
because $CB$ is about $\frac{1}{60}$ of $CM$.
\Restore

\textbf{The Moon's Mass.}\index{moon!mass}---The mass of the moon is 81~times
less than that of the earth; partly because of her smaller
size, and partly because materials composing our satellite
are on the average only three fifths as dense as those of
the earth.
\DPPageSep{251.png}

\Smaller
Gravity\index{moon!gravity at surface} at the moon's surface is about $\frac{1}{6}$ that of the earth: it is only
$\frac{1}{81}$ as great because of the moon's smaller mass; but greater by 14
times because, as will be explained in a later chapter, gravity increases
as the square of the distance from the center of attraction becomes less;
and the square of the moon's radius is about 14 times less than the
square of the earth's. Surface gravity on the moon is therefore $\frac{14}{81}$, or
about $\frac{1}{6}$, that on the earth. So a man weighing 144~pounds would
weigh only 24~pounds on the moon, if weighed by a spring balance.
An athlete who is lauded for his running high jump of 78~inches could,
with no greater expenditure of muscular energy, jump 39~feet on the
moon. Probably this deficiency of attraction at the moon's surface
explains, too, why many of the lunar mountains are much higher than
ours. Our satellite's attraction for the oceans of the earth, producing
tides, is a basis of one method of weighing the moon. Another
method is by the moon's influence on the motion of the earth: when
in advance, or at third quarter the moon's attraction quickens our motion
round the sun as much as possible; when behind the earth in its orbit,
or at first quarter, our satellite retards our orbital motion round the
sun by the greatest possible amount.
\Restore

\textbf{Axial Rotation.}\index{moon!rotation}---Our globe revolves on its axis a little
more than $27\frac{1}{3}$ times as swiftly as the moon does. For while
our sidereal day is 23\,h.\:56\,m.\ long, the moon's sidereal day
is equal to $27\frac{1}{3}$ of our 24-hour days; that is, the moon turns
round once on her axis while going once round the earth.

\Smaller
The simplest sort of an experiment will clearly illustrate this: let a
lighted lamp represent the sun; the teacher standing in the middle of
the room represent the earth; and let a pupil, representing the moon,
walk slowly around the teacher in a circle, the pupil being careful to
keep the face always turned toward the teacher. It will readily be seen
that the pupil while walking once around has turned his face in succession
toward all objects on the wall. In other words, he will have made
one slow revolution on his own axis in exactly the same time it took
him to walk once completely round the teacher. So the two motions
being accomplished in just the same time, a given side of the moon is
always turned toward the earth, just as the face of the pupil was always
toward the teacher. So, too, the opposite side of our satellite is perpetually
invisible to us.
\Restore

\textbf{Librations.}\index{moon!librations}---By a fortunate dip of the moon's axis to
the plane of the orbit, however, we are sometimes enabled
\DPPageSep{252.png}
to see a little more of the region, now around one pole, and
now around the other. The inclination is 83°\, $21'$, and our
ability to see somewhat farther over, as it were, arises from
this \textit{libration in latitude}. Again, the rate of the moon's
motion about the earth varies, while her axial turning is
perfectly uniform, so that one can see around the edge
farther, alternately on the western and eastern sides;
this is called \textit{libration in longitude}. When the moon
is near the zenith, there is little or no effect of libration
due to position of observer on the earth. When, however,
the moon is in the horizon, observer is nearly 4000 miles
above the plane passing through earth's center and the
moon. Consequently he can see a little farther around
the western limb at moonrise and around the eastern limb
at moonset. This effect is known as \textit{diurnal libration}.
As a sum total of the three librations, about four sevenths
of the moon's entire surface can be seen in all.

\textbf{No Lunar Atmosphere.}\index{moon!atmosphere}\index{atmosphere!of moon}---One reason for our believing
that the moon has no atmosphere is this: when our satellite
passes over a star (or occults it, as the technical
expression is), disappearance at the edge of the moon is
exceedingly sudden. There is no dimming of the star's
light before it is extinguished, as there would be if partly
absorbed by lunar air and clouds. The spectroscope, too,
shows no change in the star's spectrum when it is close to
the moon's edge. Also during solar eclipses, the moon's
outline seen against the sun is always very sharply defined.
Some writers have thought it possible that there may be
traces of water and atmosphere yet lingering at the bottom
of deep valleys, but no observations have yet confirmed
this hypothesis. Perhaps the moon, in some early stage
of her history, had an atmosphere, though not a very extensive
one; and it may have been partly absorbed by
lunar rocks during the process of their cooling from an
\DPPageSep{253.png}
original condition of intense heat, common to both earth
and moon. Observations show that a possible lunar atmosphere
cannot exceed in density $\frac{1}{5000}$ that of the earth.

\Smaller
\label{p244} \textbf{Why No Air and Water on the Moon.}\index{moon!water on}---Supposing that these elements
once surrounded the moon in remote past ages, their absence
from our satellite at the present time is easy to explain according to the
kinetic theory of gases\index{gases, kinetic theory of}, accepted by modern physicists. This theory
asserts that the particles of a gas are continually darting about in all
possible directions. The molecules of each gas have their own appropriate
or normal speed, and this may be increased as much as seven
fold in consequence of their collisions with one another. From the
known law of attraction it is possible to calculate the velocity of a moving
body which the moon is capable of overcoming; if a rifle ball on
the moon were fired with a velocity of about 7000 feet per second, or
three times the speed so far attained by artificial means on the earth,
it would leave our satellite forever, and pursue an independent path in
space. Physicists have ascertained that the molecules of all gases
composing the atmosphere can have velocities of their own far exceeding
this limit; and as earth and moon are many millions of years old,
it is easy to see how the moon may have completely lost her atmosphere\index{hydrogen!in moon's atmosphere}
by this slow process of dissipation. Surface attraction of the
moon, only one sixth that of the earth, has simply been powerless to
arrest this gradual loss. The possible speed of molecules of hydrogen
is greatest, and even exceeds the velocity which the earth is able to
overcome; so that this theory explains, too, the absence of free hydrogen
in our own atmosphere\index{hydrogen!in earth's atmosphere}. Water on the moon would gradually
become vaporized into atmosphere, and complete disappearance as a
liquid may readily have taken place in this manner. Whether it may
be present in the form of ice, it is not possible to say.
\Restore

\textbf{The Moon's Light and Heat.}\index{moon!light}---The amount of moonlight
increases from new to full more rapidly than the illumined
area of the moon's disk; so our satellite at the quarter
gives much less than half her light at the full. Mainly,
this is due to gradually shortening shadows of lunar elevations,
which vanish at the full. As is very apparent to
the eye at this phase, some parts of the moon are much
darker than others; but on the average, the lunar surface
reflects about one sixth of the sunlight falling upon it.
The spectroscope shows no difference in kind between
\DPPageSep{254.png}
moonlight and sunlight. The brightness of the full moon
is deceptively small, being at average distance only $\frac{1}{600,000}$
that of the sun. Heat\index{moon!heat}\index{heat|see{moon, heat}} from the full moon is nearly four
times greater than the amount of light, and the larger
part of it is heat, not reflected, but radiated from the moon
as if first absorbed from the sun. Our satellite having no
atmosphere to help retain this heat, it radiates into space
almost as soon as absorbed, so that temperature\index{moon!temperature} at the
lunar surface, even under vertical sunlight, probably never
rises to centigrade zero. At the end of the fortnight
during which the sun's rays are withdrawn, temperature
must drop to nearly that of interplanetary space, probably
about 300° below zero. In America Langley\index{Langley, S.~P.\ (1834--1906), Am.\ ast.\ and physicist} and
Very\index{Very, F.~W., Am.\ ast.} are foremost in this research.

\Smaller
\textbf{The Moon and the Weather.}\index{moon!weather}---A wide, popular belief, hard\-ly more
than mere superstition, connects the varying position of the lunar
cusps with the character of weather. The line of cusps is continually
changing its angle with the horizon, according to the relation of
ecliptic (or moon's orbit) to the horizon, as already explained; and
it is impossible, therefore, to see how or why this should indicate a
wet moon or a dry moon. As for changes of weather occasioned by,
or occurring coincidently with, the moon's changing phases, one need
only remember that the weekly change of phase necessarily comes near
the same time with a large per cent of weather changes; and these
coincidences are remembered, while a large number of failures to coincide
are overlooked and forgotten. Weather, too, is very different at
different localities, and probably there is always a marked change going
on somewhere when our satellite is advancing from one phase to
another. Critical investigation fails to reveal a decided preponderance
either one way or the other, and any seeming influence of the moon
upon weather is a natural result of pure chance. The full moon, too, is
popularly believed to clear away clouds; but statistical research does
not disclose any systematic effect of this nature. Moon's apogee and
perigee are known to occasion a periodic disturbance of magnetic
needles\index{magnetic disturbances}, and may possibly be concerned in the phenomena of earthquakes\index{earthquakes and moon};
but the latter effect is not yet fully established.
\Restore

\textbf{Surface of the Moon.}---In days of earlier and less perfect
telescopes, darker patches very noticeable on the moon's
\DPPageSep{255.png}
disk were named seas\index{moon!seas}, and these titles still cling to them,
although it is now known that they are only desert plains,
and not seas. All the more important features\index{moon!features} can be
accurately located from the accompanying illustration.
% Fig 10.16
\begin{figure}[hbt!]
  \centering
  \Input{page_246}
  \caption{Telescopic Features of the Moon as seen in an Inverting Telescope}
  \label{fig10.16}\index{moon!features}
\end{figure}
Since great modern telescopes, using a power of 1500 bring
the moon within about 150 miles, much detail can be seen
in the inexpressibly lonely scenery diversifying our satellite.
A great city might be made out, but the greatest building
ever built on our earth could not be seen except as a mere
speck. Also the best modern photographs, like those reproduced
\DPPageSep{256.png}
on pages \pageref{p16} and \pageref{p248}, are amply sufficient for
critical study; and examination of them is much more
satisfactory than the ordinary view through a telescope.
The `seas,' so-called, may in truth be the beds of primeval
% Fig 10.17
\begin{figure}[hbt!]
  \centering
  \Input{page_247}
  \caption{Key to the Chart of the Moon Opposite}
  \index{Albategnius, M. J. (\AD\ 900), Arab.\ ast.}%
  \index{d'Alembert, J. B. le R. (dä-long-bêr´) (1717--83), Fr.\ math.}%
  \index{Archime´des (\BC~250), Gk.\ geom.}%
  \index{Aristarchus (\BC~270), Gk.\ ast.}%
  \index{Aristotle (\BC~350), Gk.\ phil.}%
  \index{Arzachel, A. (\AD~1080), Heb. ast.}%
  \index{Copernicus, N. (1473-1534), Ger.\ ast.}%
  \index{Eudoxus (\BC~370), Gk.\ ast.}%
  \index{Herodotus (\BC~460), Gk.\ hist.}%
  \index{Hipparchus (\BC~140), Gk.\ ast.}%
  \index{Kepler, J. (1571--1630), Ger.\ ast.}%
  \index{Newton, Sir I. (1642--1727), Eng.\ ast.}%
  \index{Plato (\BC~390), Gk.\ phil.}%
  \index{Ptolemy@Ptolemy, C. (tol´-em-mi) (\AD~140), Alex.\ ast.}%
  \index{Tycho Brahe (1546--1601), Danish ast.}%
  \index{Herschel, Sir F. W. (1738--1822), Eng.\ ast.}%
  \index{Clavius, C.\ (1537--1612), Ger.\ math.}%
  \index{crater, lunar}%
  \index{Flamsteed, J.\ (1646--1719), Ast.\ Royal}%
  \index{Astronomer Royal|see{Flamsteed}}%
  \index{Fracastor, J.\ (1483--1553), It.\ physician}%
  \index{Gassendi, P.\ (1592--1655), Fr.\ ast.}%
  \index{Geminus (\BC~50), Gk.\ ast.}%
  \index{Grimaldi, F.~M.\ (1618--63), It.\ physician}%
  \index{Leibnitz@v.\ Leibnitz, G.~W.\ (l\=ib´nits) (1646--1716), Ger.\ math. and phil.}%
  \index{Maskelyne, N.\ (1732--1811), Ast.\ Royal}%
  \index{Astronomer Royal|see{Maskelyne}}%
  \index{moon!maps}%
  \index{Triesnecker crater}%
  \index{Petavius, D.\ (1583--1652), Fr.\ chronologist}%
  \index{Proclus (\AD\ 450), Gk.\ phil.}%
  \index{Schickard, W.\ (1592--1635), Ger.\ math.}%
  \index{Schiller, J.~C.~F.\ (1759--1805), Ger.\ poet}%
  \index{Walther (1430--1504), Ger.\ ast.}%
  \index{Doerfel, G.~S.\ (1643--88), Ger.\ ast.}%
\end{figure}
oceans, which have dried up and disappeared hundreds of
thousands of years ago. They are not all at the same
level. Earlier stages of cosmic life are characterized by
intense heat; but as development of the moon progressed,
original heat gradually radiated into space, leaving her
surface finished. Evidently she has gone through experiences
\DPPageSep{257.png}
some of which the earth may already have known,
and through others still in our remote future. Being so
much smaller
than the earth,
as well as less in
mass, our satellite
cooled much
faster than the
parent planet. A
few surface features
are to be
explained as due
to the consequent
shrinkage.

\textbf{Maps and Photographs
of the
Moon.}\index{photography!of moon}\index{moon!maps}\index{moon!photographs}---All the
lunar mountains,
plains, and craters\index{crater, lunar}
are mapped
and named; and
astronomers are
quite as familiar
with `Copernicus'\index{Copernicus, N. (1473--1534), Ger.\ ast.}
and `Eratosthenes'
(a great,
crater, and a
mountain nearly
16,000 feet high)
as geographers
are with Vesuvius
and the
Matterhorn. Hevelius\index{Hevelius, J.\ (1611--87), Ger.\ ast.} of Danzig made the first map of
the moon in 1647. He named the mountains and craters
\DPPageSep{258.png}
and plains after terrestrial seas and towns and mountains.
But Riccioli\index{Riccioli, G.~B.\ (rit-se-o´le) (1598--1671), It.\ ast.}, who made a second lunar map some
% Fig 10.18
\begin{wrapfigure}{o}{0.7\textwidth}
  \centering
  \Input[0.65\textwidth]{page_248}
  \caption{Moon's North Cusp (photographed by the Brothers Henry of the Paris Observatory)}
  \label{p248}\index{Henry, Paul (ong-ree´) (1848--1905), Fr.\ ast.}\index{Henry, Prosper (ong-ree´) (1849--1903), Fr.\ ast.}\index{Paris!Observatory}
\end{wrapfigure}
time
after, renamed the moon's physical features, immortalizing
in this way himself and many friends. His names, with
numerous modern additions, are still current.

\Smaller
One astronomer has counted 33,000 craters\index{crater, lunar} on the moon, of course on
only the four sevenths of her surface ever turned toward us; and as there is
no reason for supposing the remainder to contain features differing in kind
from those on the hemisphere so familiarly known, probably there are
not less than 60,000 craters on the entire surface of our satellite. During
the last half century many astronomers have interested themselves
in producing photographs of the moon, with very remarkable success.
By an exposure of a second or two, a vast degree of detail is secured
with perfect accuracy, which the pencil could not depict in months; indeed,
critical study with a microscope has brought to light lesser features
of hill and valley which had escaped the eye and the telescope alone.
Photographic maps or atlases of the moon on a very large scale have
recently been published by the Paris Observatory\index{Paris!Observatory}, the Lick Observatory\index{Lick Observatory},
and the Prague Observatory; and the material already accumulated will,
in the present century, show any considerable changes, should such be
taking place.

\textbf{Changes on the Moon.}\index{moon!changes on}---Probably the observers who a century ago
recorded volcanoes in activity and progressive changes on the moon
were deceived by the highly reflective character of materials forming
the summits of certain mountains. Some craters are alleged to have
disappeared, and in other instances new craters to have formed; but
evidence has in no case amounted to absolute proof as yet. It is still
an open question whether surface activity of any kind characterizes the
lunar disk, except perhaps on a very small scale, too minute for detection
with present instrumental means. Varying conditions of illumination
by the sun are so marked, even from hour to hour, that nearly all
reputed changes are sufficiently explained thereby. Size and power
of the telescope, and in drawings the personal equation of the artist,
together with the state of atmosphere, all tend to introduce elements
making sketches far from comparable.
\Restore

\textbf{The Mountains on the Moon.}\index{moon!mountains on}---Although of all the satellites
of the solar system, the moon is nearest the size and
% Fig 10.19, 20
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input{page_250a}
    \caption{Lunar Volcanoes}
  \end{minipage}
  \index{moon!volcanoes}\index{volcanoes}
  \hfill
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input{page_250b}
    \caption{Terrestrial Volcanoes}
  \end{minipage}
  \index{Naples, Bay of}
\end{figure}
mass of its primary, still this neighbor world is no copy of
the present earth. The difference between them is accentuated
in the character of their mountains---on the earth
\DPPageSep{259.png}
ridges and mountain chains for the most part, with relatively
few craters; on the moon quite the reverse, craters
being far in excess. In large part they seem to be volcanic
in formation, but many of the largest ones with low walls
are probably ruins of molten lakes. When the mountains
of the moon are illuminated by a strong cross-light---as
along the terminator at sunrise and sunset---they are
thrown into sharp relief, as in this picture of lunar volcanoes,
set opposite a model of Vesuvius and neighboring
volcanoes photographed under like circumstances of
illumination. Similar volcanic origin is self-evident.

\Smaller
Nearly 40 lunar peaks are higher than Mont Blanc, and the greater
relative height of lunar than terrestrial peaks is doubtless due to lesser
surface gravity of our satellite. The Leibnitz Mountains\index{Leibnitz Mountains}, perhaps the
highest on the moon, are 30,000 to 36,000 feet in elevation, much
exceeding the highest peaks on earth. As there is no softening atmospheric
effect, shadows of all lunar objects are so sharply defined that
the height, depth, and extent of nearly all natural features of the moon's
surface can be accurately measured.
\DPPageSep{260.png}

\textbf{To find the Height of a Lunar Mountain.}\index{moon!mountains on}---Heights of many mountains
on the moon have been found by this method: with a suitable
instrument, called
% Fig 10.21
\begin{wrapfigure}[13]{o}{0.65\textwidth}
  \centering
  \Input[0.6\textwidth]{page_251}
  \caption{Measuring Height of a Lunar Mountain}\index{moon!mountains on}
\end{wrapfigure}
the
micrometer, attached
to the telescope for
measuring small arcs,
measure $AM$, distance
of terminator from
peak of a mountain
which sunlight from
$S$ just grazes. Length
of moon's radius $AB$
is known, and distance
$AM$ is given by the
measures. So the value
$BM$, or moon's average
radius as increased by the height of mountain, can be found by
solving the right-angled triangle $ABM$.
\Restore

\textbf{A Typical Crater highly magnified.}\index{crater, lunar}\index{moon|see{crater, lunar}}---Somewhat north
and east of the center of the lunar disk is the great crater
Copernicus\index{Copernicus, N. (1473-1534), Ger.\ ast.}. Rising from its floor is a cluster of conical
mountains about 2500 feet high. The walls of the crater
itself are about 50 miles in diameter, and 13,000 feet high.
As the drawing \vpageref{p252} shows, the surroundings of
Copernicus are rugged in the extreme, and near full moon a
complex network of bright streaks\index{moon!streaks} may be seen extending
more than a hundred miles on every side. They do not
appear in the illustration because it was drawn near the
quarter. The streaks do not radiate from the great crater
itself, but from some of the craterlets alongside, by which
Copernicus is especially thickly surrounded. Probably the
streaks are due to light-colored gravel or powder scattered
radially. Most of the adjacent craterlets are very minute,
and they are counted by hundreds.

\Smaller
\textbf{The Lunar Cliffs or Rills and Other Features.}---Almost at the center
of the moon, but slightly toward the northwest, is Triesnecker\index{Triesnecker crater}, a well-pronounced
crater, along the west side of which is the remarkable cliff
\DPPageSep{261.png}
system shown on
% Fig 10.22
\begin{wrapfigure}[33]{o}{0.7\textwidth}
  \centering
  \Input[0.7\textwidth]{page_252}
  \caption{Region Surrounding Copernicus (highly magnified)}
  \label{p252}\index{Copernicus, N. (1473-1534), Ger.\ ast.}
\end{wrapfigure}
page~\pageref{p253}.
Their radiation and intersection are strongly
marked---chasms about a mile in breadth, and nearly 300 miles in
length. Little is known about their nature and even less about their
origin. The bottom of the cliffs is seen to be nearly flat, presenting
to some extent the appearance of an ancient river bed. The few mountain
chains on the moon resemble those on the earth in one respect:
they are much
steeper on one side
than on the other,
as if the tiltings had
been similarly produced.
Craggy and
irregular pyramids
are sparsely scattered
on the plains.
There are many
valleys, some wide
and deep, others
mere clefts or
cracks. The term
\textit{rill} is often applied
to them although
waterless, and there
are many hundreds,
passing for the most
part through seas
and plains, though
occasionally intersecting
the craters.
Some are straight,
others bent and
branching. Possibly
they are fissures
in a surface still
shrinking. In a few
instances, the geological
feature
known as a fault may be observed---the crack is not an open one,
and the surface on one side is higher than on the other. Also there
are walled plains, from 40 to 150 miles in diameter, with interiors
generally level, but broken by slight elevations and circular pits or
depressions. Nearly the entire visible surface is astonishingly diversified
by clean-cut irregularities looking much as if neither water nor
atmosphere had ever been present on the moon. Even a small
\DPPageSep{262.png}
telescope helps greatly in examining them, and their position on or
near the terminator is most favorable for their study. Intervals of a
double lunation, or 59\,d.\:$1\frac{1}{2}$\,h.\ bring the terminator through very nearly
the same objects, so that the nature and extent of illumination are
comparable.

\textbf{If One were to visit the Moon.}\index{moon!visit to}---Of course no human being could
visit the moon without taking air and water along with him. But what
we know about the surface of our satellite enables us to describe some
of the natural phenomena.
% Fig 10.23
\begin{wrapfigure}[27]{o}{0.7\textwidth}
  \centering
  \Input[0.6\textwidth]{page_253}
  \label{p253}\caption{Triesnecker and Lunar Rills}\index{moon!rills}\index{Triesnecker crater}\index{crater|see{Triesnecker crater}}
\end{wrapfigure}
Absence of atmosphere
means no diffused light;
nothing could be seen
unless the direct rays of
the sun were shining upon
it. The instant one
stepped into the shadow
of a lunar crag, he would
become invisible. No
sound could be heard,
however loud; in fact,
sound would be impossible.
A landslide, or the
rolling of a rock down the
wall of a lunar crater, could
be known only by the
tremor it produced---there
would be no noise.
So slight is gravity that a
good player might bat a
baseball half a mile without
trying very hard.
Looking up, the stars
would be appreciably
brighter than here, in a
perpetually cloudless sky. Even the fainter ones would be visible in
the daytime quite as well as at night. If one were to land anywhere on
the opposite side of the moon and remain there, the earth could never be
seen; only by coming round to the side toward our planet would it become
visible. Even then the earth would never rise or set\break
\vspace{-\baselineskip}
%[** TN: Hack to coax two wrapfigures into one paragraph]

% Fig 10.24
\begin{wrapfigure}[28]{o}{0.65\textwidth}
  \centering
  \Input[0.6\textwidth]{page_254}
  \caption{Typical Lunar Landscape (full Earth)}
\end{wrapfigure}
\noindent at any given place,
but it would constantly remain at about the same altitude above the
lunar horizon. Earth would go through all phases that the moon
does here, only they would be supplementary, full earth occurring
there when it is new moon here. Our globe would seem to be about
four times as broad as the moon appears to us. Its white polar caps of
\DPPageSep{263.png}
ice and snow, its dark oceans, and the vast but hazy cloud areas
would be conspicuous,
seen through our upper
atmosphere. Faint stars,
the filmy solar corona, also
the zodiacal light, would
probably be visible close
up to the sun himself; but
although his rays might
shine for a fortnight without
intermission upon the
lunar landscape, still the
rocks would probably be
too cold to touch with
safety.
\Restore

From the chief luminary
of our nightly
skies, we turn to an
investigation of discoveries
made by
astronomers concerning
the orb of day,
describing at the
same time instruments
and processes
of the `new astronomy'
with which many of these researches have been
conducted.
\DPPageSep{264.png}


\Chapter{XI}{The Sun}\index{sun}

Man in the ancient world worshiped the sun. Primitive
peoples who inhabited Egypt, Asia Minor,
and western Asia from four to eight thousand
years ago have left on monuments evidence of their veneration
of the `Lord of Day.' Archæologists have ascertained
this by their researches into the world of the
ancient Ph{\oe}nicians, Assyrians, Hittites, and other nations
now passed from earth. A favorite representation of
the sun god among them was the `winged globe,' or
`winged solar disk,'\index{solar disk, the winged} types of which are well preserved
on the lintels of an ancient Egyptian shrine of granite in
the temple at Edfu. In the Holy Scriptures are repeated
allusions to the protecting wings of the Deity, referring
to this frequently recurring sculptured design; and we
know that if his life-giving rays were withheld from the
earth, every form of human activity would speedily come
to an end.

\textbf{The Sun dominates the Planetary System.}\index{sun!ruler}---The sun
is important and magnificent beyond all other objects in
the universe, not only to us, inhabitants of the earth,
but to dwellers on other planets, if such there be. All
these bodies journey round him, obedient to the power
of his attraction. Upon his radiant energies, lavishly
scattered throughout space as light and heat, is dependent,
either directly or indirectly, the existence of nearly every
form of life activity; and the transformation of solar
\DPPageSep{265.png}
energy produces almost every variety of motion upon
the earth, whether animate or inanimate. The more
primitive the civilization, the more apparent is the dependence
of man upon the sun.

\Smaller
Activities in Labrador here pictured are an excellent illustration.
Without the sun's vitalizing action, the trees, whose trunks and
branches furnished the load on the sled, not to say the sled itself,
% Fig 11.1
\begin{figure}[htb!]
  \centering
  \Input{page_256}
  \caption{In Labrador (Activities originating in the Sun)}
\end{figure}
could not have grown. The food, whether animal or vegetable, upon
which the life and energy of man and dog depend, would not have
been possible without the sun. Creatures of land and sea, whose
skins provided the straps by which the sled is drawn, could not long
live without warmth and vitality lavished by the sun. Nor must we
overlook the farther fact pertaining to natural movements and phenomena
of the air; for the sun provides even the breeze to bulge the sail,
and he has raised from the sea and diffused over the land the moisture
which descends as snow, for the sled to slide upon. In the
complicated life of our higher civilization, the sun is still all-powerful,
though the links in the chain of connection are in places concealed.
Our comforts and activities are largely dependent upon heat given out
by burning coal; but it was through the action of the sun's rays that
\DPPageSep{266.png}
forests in an early geologic age could wrest carbon from the atmosphere
and store it in this permanent mineral form, so useful---one might
almost say necessary---in the processes of modern life. In everything
material the sun is our constant and bountiful benefactor.
\Restore

\textbf{Sun's Distance the Unit of Celestial Measurement.}\index{sun!distance of}\index{sun!distance a unit}---The
distance between centers of sun and earth is the measuring
unit of the universe. Although motions and relative
distances of heavenly bodies may be known, still their
true or absolute distances cannot be found with accuracy,
unless the fundamental unit is itself precisely determined.
It is as if one were to try to measure the size of a house
with a lead pencil; it would be possible to find the dimensions
of the house in terms of the lead pencil, but the
actual size of the building would not be known until the
length of the pencil, or unit of measure, had been ascertained.
The distance of the sun is this unit. A method
of finding the distance of the moon has been given, but
the sun's distance is too great to be measured in this way---even
the whole diameter of the earth is not long enough
to form a suitable base for the slender triangle drawn from
its antipodes to the sun.

\Smaller
\index{triangulation}For the proper application of this method of finding distances, the
triangle included between distant object and the two ends of the base
line, must be
% Fig 11.2
\begin{wrapfigure}[13]{o}{0.25\textwidth}
  \centering
  \Input[0.25\textwidth]{page_257}
  \caption{Well-conditioned Triangle}
\end{wrapfigure}
 well-conditioned. Such a triangle is
shown in the figure, in which the width of an
impassable stream is found by measuring on the
left bank a distance nearly equal to the breadth
of the stream itself. An ill-conditioned triangle
is one whose base is very short in comparison
with its other two sides. Such a triangle is shown
on page~\pageref{p235}, where the base (or earth's diameter)
is only $\frac{1}{30}$ of the other sides. Base remaining the
same, the farther away the object, the more ill-conditioned
the triangle. As the sun is nearly 400
times farther than the moon, the relation of base
to other sides is only $\frac{1}{11000}$. The triangle is, therefore, so ill-conditioned
\DPPageSep{267.png}
that this direct method of finding the sun's distance becomes
inapplicable, and other methods are always relied upon.
\Restore

\textbf{Finding the Sun's Parallax.}\index{sun!parallax}\index{parallax|see{sun, parallax}}---On those rare occasions
when Venus, a planet nearer the sun than our earth is,
comes in her path exactly between us and the sun, she
moves like a small black dot across the shining disk.
This happens but twice in each century. Two observers
widely separate on our globe, will see Venus projected
upon different portions of the sun's disk at the same time;
as on page~\pageref{p234}, pin is seen against different parts of scale
when viewed through the two peepholes. So the apparent
path of Venus across the sun will be farther south on the
disk, as seen from northern station; and farther north as
seen from southern one. Difference of the two paths leads
by suitable calculation to a knowledge of the angle which
radius of the earth fills, as seen from the sun. This angle
is called the sun's parallax. Its value at the average distance
of the sun is called the mean parallax. The equatorial
radius of our planet is taken, as the standard, the
same as in the case of the moon; also when the sun is on
the horizon its parallax is a maximum, called the horizontal
parallax. The accepted value of the sun's mean equatorial
horizontal parallax is $8''.8$. This means that the sun is so
remote that if one could visit him and look in the direction
of the earth, our globe would appear to be only $17''.6$
broad, an angle so small as to be invisible to the naked
eye. A telescope magnifying at least four or five diameters
would be necessary to see it.

\textbf{The Sun's Distance.}\index{sun!distance of}---The sun's parallax and the length
of earth's radius are data for a calculation by trigonometry,
giving the distance of the sun equal to 93,000,000
miles. Also this important element may be found by
\textit{aberration}. Knowing the velocity of light, it is easy to
calculate the speed which the earth must have in order to
\DPPageSep{268.png}
produce the known amount of aberration of the stars,
called the constant of aberration. So it is found that the
earth's actual velocity is something over $18\frac{1}{2}$~miles in a
second. From this the length of the circumference of the
orbit traversed by the earth in $365\frac{1}{4}$~days or one year is
readily found, and from that the diameter of the orbit, the
half of which is the mean distance of the sun. There are
many other and more complicated methods of obtaining
the distance of the sun, and they all agree within a small
percentage of error. Subtracting $0''.01$ from the parallax
is equivalent to increasing the sun's distance about 105,000
miles, and \textit{vice versa}.

% Fig 11.3
\begin{figure}[hbt!]
  \centering
  \Input{page_259}
  \caption{As Distance from shade is to Size of Image, so is Sun's Distance to his Diameter}
\end{figure}

\Smaller
\textbf{To measure the Size of the Sun.}\label{p259}\index{sun!dimensions}---Knowing the distance of the sun,
it is very easy to observe and calculate his real dimensions. The method
is similar to that by which the size of the moon was measured; and different
only because of the superior intensity of the sun's light. Instead
\DPPageSep{269.png}
of looking directly at the sun, simply look at the image produced by the
sun's rays through a tiny aperture. Every one has noticed sunlight
filtering into a darkened room through chinks between the slats and
frame of a blind or shutter. Oftentimes a series of oval disks may
be seen on the floor. Their breadth depends upon (\textit{a})~the diameter
of the sun, and (\textit{b})~their distance from the shutter. Each oval disk
is a distorted solar image. If a sheet of paper is held at right angles
to the direction of the sun, the oval disk becomes circular, and its
diameter can be measured. But as the paper is carried toward the
shutter, notice that the disk grows smaller and smaller. So you must
measure its distance from the shutter also. Select a time when the
sun is not exactly facing a window, but is a little to the right or left of
it, though not more than an hour in either direction. On closing the
shutters, and turning the slats, the chain of disks on the floor will usually
become visible. Examine them carefully when projected on a small
white card, and select the one which has the sharpest outline. Or, the
blinds may be thrown open, and sunlight admitted through a pin-hole
in the shade, as in last illustration. Attach a sheet of white paper to
the cover of a book; so support it that the surface of the paper shall
be at right angles to the line from book to sun. With a sharply-pointed
pencil, mark two short parallel lines on the paper, a little farther apart
than the diameter of the bright disk. Move the paper back until the
sun's image just fills the space between the two lines. Measure distance
between lines; also with a non-elastic cord, measure distance
from shade to paper on the book. This completes the observation.

\textbf{Calculating the Observation.}---As in calculating the size of the moon
when its distance is known, so in computing the dimensions of the
sun, only the `rule of three' is necessary. On 22d~May, 1898, size of
a pin-hole image of sun was measured and found to be 1.175~in. in
diameter. Distance between the card on which the image fell and
the aperture in shade was 10~ft.\, 5.4~in. So the proportion is---
\[
125.4\: :\: 1.175\: ::\: 93,000,000\: :\: x.
\]

The value of $x$ comes out 871,000 miles, or about $\frac{1}{140}$ part too great.
But this amount of error is to be expected, because the method is a
crude one. Notice, however, its exactness in principle. To convey
an adequate idea of the sun's tremendous proportions is practically
impossible.
\Restore

\textbf{How Astronomers measure the Sun.}\index{sun!dimensions}---The principle of
their method is exactly the same as that just illustrated;
and their results are more accurate only because their
instruments are more delicate, and training in the use
\DPPageSep{270.png}
of them thorough and complete. The latest and best
value of the sun's diameter is 865,350 miles.

\Smaller
The best method utilizes an instrument called the heliometer\index{heliometer}, or sun
measurer. It is a telescope of medium size, mounted equatorially; but
the essential point of difference is in the object glass, \textit{AB}, which is
divided exactly in the middle. Accurate mechanical devices are provided
by which \textit{B} can be slipped
sidewise relatively to \textit{A}, as in
the lower figure, and the precise
amount of the motion recorded.
Before the halves of the glass
are moved apart, the sun's image
% Fig 11.4, 5
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \begin{minipage}{0.25\textwidth}
    \centering
    \Input[0.4\textwidth]{page_261a}
    \caption{Divided Object Glass of Heliometer}
  \end{minipage}
  \hfill
  \begin{minipage}{0.3\textwidth}
    \centering
    \Input{page_261b}
    \caption{Images of Sun in Heliometer}
  \end{minipage}
  \index{heliometer}
\end{wrapfigure}
is a single, very bright disk, like
the left hand of the three
here shown. Turn the screw
separating the halves of the
glass, and overlapping images appear, as in the middle figure; and by
turning it far enough, the two images of the sun may be brought into
exact exterior contact, as in the right hand of the three images.
Final calculation of the sun's diameter is a tedious and complicated
process, because a great variety of conditions and corrections must be
taken into account; but the heliometer is the most accurate measuring
instrument employed by modern astronomers. The limit of
accuracy of measurement with the heliometer is an angle no larger
than that which a baseball would fill at New York as seen from
Chicago.
\Restore

\textbf{The Sun is a Sphere.}\index{sun!spherical}---As the sun turns round on his
axis, equatorial diameters are measured in every direction.
As they do not differ appreciably from the polar diameter,
the figure of the sun is a sphere. His real diameter is not
subject to change; but as already shown, the sun's apparent
diameter varies from day to day, in exact proportion
to our change of distance from him. The mean value is
almost $32'\, 0''$ (according to Auwers\index{Auwers, A. (ow´verz), Ger.\ ast.}, $31'\, 59''.26$).

\Smaller
The actual diameter of the sun is difficult to determine, for a variety
of reasons. The heat of his rays disturbs the atmosphere through
which they travel, so that his outline, or limb, is rarely seen free from a
quivering or wave-like motion. Another reason is irradiation, a physiological
effect by which bright objects always seem larger than they really
\DPPageSep{271.png}
are. Irradiation increases as brightness of the object exceeds that of
the background against which it is seen. Error in our knowledge of the
sun's diameter is probably about $\frac{1}{1000}$ part of the whole, or about $2''$.
At the distance 93,000,000 miles, $1''$ of arc is equivalent to 450~miles,
so that the amount of uncertainty in the diameter of the sun is about
900~miles.
\Restore

\textbf{The Sun's Volume, Mass, and Density.}\index{sun!volume}\index{sun!mass}\index{sun!density}---As the sun's
diameter is nearly 110 times greater than that of the
earth, his volume is almost 1,300,000 times greater, because
volumes of spheres vary as cubes of their diameters.
A method of measuring the mass of the sun is given on
page~\pageref{p386a}. To put it simply, the sun's mass is found by
measuring the force of his attraction. If sun and earth
are at the same distance from a given body, the sun will
attract it 330,000 times more powerfully than the earth
does. Sun's weight, in other words, is 330,000 times as
great as earth's. A body falling freely under the influence
of the sun's attraction would on reaching him have a
velocity of 383~miles a second. As the sun is 1,300,000
times greater in volume than the earth, evidently he must
be much less dense than our globe; and his component
materials, bulk for bulk, must be about one fourth lighter
than those of the earth. As compared with water, the sun
is rather less than $1\frac{1}{2}$ times as dense.

\textbf{Gravity at the Sun's Surface.}\index{sun!gravity at surface}---The weight of the
earth, it will be remembered, is $6 × 10^{21}$ tons. But the
sun weighs 330,000 times as much,---a numerical result
which the human mind is utterly powerless to grasp.
Another comparison will help to fix relative proportions
in memory. Many planets are vastly larger and more massive
than the earth. But if all the planets of the solar
system and their accompanying retinues of satellites were
fused together into a single ball, it would weigh but $\frac{1}{750}$ as
much as the sun. So vast are the dimensions of our central
luminary that the force
% Fig 11.6
\begin{wrapfigure}[19]{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_263}
  \caption{Viewing the Surface of the Sun}
\end{wrapfigure}
of gravity at the surface is not
\DPPageSep{272.png}
so great as his prodigious mass would seem to indicate:
it is only $27\frac{2}{3}$~times as great as gravity at the surface
of the earth. A
body would fall vertically
444~feet in
the first second.
Recall the agile
athlete who, when
transferred to the
moon, executed a
record jump of
39~feet: if at the
sun, he would find
his movements
hampered by a
bodily weight of two
tons, and his `running
high jump,'
if possible at all,
could not exceed
three inches. On the sun, the pendulum of an ordinary
mantel clock would quiver or oscillate so rapidly that its
vibrations could not easily be counted. For every tick of
the escapement here, there would be five at the sun.

\Smaller
\textbf{How to observe the Sun.}\index{sun!observing}---Unless the telescope is provided with a
special eyepiece, called a helioscope\index{helioscope}, it is dangerous to look at the sun
directly, because heat rays coming through the dense colored glass covering
the eyepiece are very harmful to the delicate rods of the retina.
Besides this, the colored glass is liable to be broken suddenly by the
intense heat. If such accident happens while the eye is at the telescope,
a dark spot in the retina is pretty sure to result; and it will remain
permanently insensitive---an extreme case of `over-exposure.'
Rather look at the sun's surface indirectly, by projection, as in the picture.
To the telescope tube attach a cardboard screen, two or three feet
square, and fill the chinks around the tube with cloth or paper. This
large screen tightly fastened to the tube, is very necessary to keep
\DPPageSep{273.png}
direct light of the sun from falling upon the sheet of paper below, on
which the sun's image is projected. This sheet may be held in the
hand; but it is better to attach it to a light frame, which slides along a
stick firmly screwed to the side of the telescope tube. Then the paper
% Fig 11.7
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.55\textwidth]{page_264}
  \caption{Photosphere (photographed by Janssen)}
  \index{Janssen, P.~J.~C.\ (1823--1907), Fr.\ ast.}\index{photography!of sun}
  \index{photosphere}
\end{wrapfigure}
may be kept always at
right angles to the axis
of the telescope; and
spots may be made to
look larger or smaller by
merely sliding the frame
toward or from the eyepiece.
Careful focusing
is important, and probably
it will be necessary to refocus
every time the distance
between paper and
eyepiece is changed.
Ten or twelve persons
can readily observe sun
spots in this way at the
same time, and without
the slightest danger or
inconvenience. Surface
mottlings and faculæ\index{faculæ|see{sun, faculæ}}\index{sun!faculæ}, or
white spots, are finely
seen. If the telescope is
a large one, the eyepiece
should occasionally be
taken out and cooled;
but even a spyglass will
gather enough light to
show the spots and other
details of the sun's surface.

\textbf{The Photosphere.}\index{photosphere}\index{sun|see{photosphere}}---The photosphere is that mottled exterior of the sun
which radiates its light. The photographic picture\index{photography!of sun} above shows its general
texture. The blurring is a real phenomenon. This rice-grain\index{sun!rice grains} structure can
nearly always be seen even with moderate telescopic power, because the
grains are about 500~miles across. Under the best conditions of vision,
and great increase of power, the grains subdivide into granules. Floating
above the photosphere, and quite numerous around the sun's limb,
may usually be seen a number of irregularly connected whitish spots, or
patches, called faculæ\index{sun!faculæ}. It is certain that some of the faculæ are elevations,
because they have been seen projecting beyond the edge of the
disk. As will be shown farther on, the faculæ extend in zones all the
\DPPageSep{274.png}
way across the sun; but they are more obvious at the limb, because
general illumination of the photosphere in that region is less, owing to
greater thickness of solar atmosphere through which rays from the
photosphere must pass.
\Restore

% Fig 11.8
\begin{wrapfigure}[17]{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_265}
  \caption{Sun Spot highly magnified (Secchi)}
  \index{sun!spots}\index{Secchi, A.\ (seck´key) (1818--78), It.\ ast.}
\end{wrapfigure}

\textbf{Sun Spots.}\index{sun!spots}---Immense dark spots are frequently seen on
the photosphere\index{photosphere}. Generally they have a dark center,
called the umbra, and a
somewhat lighter fringe, called the
penumbra, which is
darker near its outer
edge, lighter toward
the umbra, and often
shows a thatch-work
structure, as in Secchi's\index{Secchi, A.\ (seck´key) (1818--78), It.\ ast.}
drawing (also
page~\pageref{p11}). Of widely
varying shapes and
sizes, they are usually
nearly circular at the
middle stage of existence,
though more
irregular at beginning
and end.

\Smaller
The dark umbra is not all equally dark; at times faint patches or
grains of luminous matter appear to float above the darker region underneath.
Also sometimes appear tiny round spots, darker than the umbra,
known as nuclei---perhaps openings into still greater depths; for
the spots themselves nearly always appear like depressions in the photosphere\index{photosphere},
and on several occasions have been seen as actual notches
at the edge of the sun, as in Figure~\ref{fig11.9}. There is good
evidence, however, that many of them are not depressions. If a spot
is as large as 27,000 miles in diameter, it can be seen without a telescope
as a very minute black speck. Occasionally spots are even larger
than this, and 50,000 miles is a size not unknown. The largest sun spot
on record was observed in 1858; it was nearly 150,000 miles in breadth
and covered about $\frac{1}{35}$ of the whole surface of the sun.

\textbf{Veiled Spots.}\index{sun!veiled spot}---Veiled spot is the name given to hazy, darkish
patches appearing now and then upon all parts of the solar disk, even
\DPPageSep{275.png}
close to the poles. They have been seen to change their ill-defined
outlines very rapidly. Not extensively observed as yet, they are nevertheless
regarded as kin to ordinary spots, only that the forces producing
them are not intense enough to disrupt the photosphere. Faculæ are
often seen above them.
\Restore

% Fig 11.9
\begin{figure}[hbt!]
  \centering
  \Input{page_266}
  \caption{Many Spots are seen as Depressions at the Sun's Limb}
  \label{fig11.9}
\end{figure}
\textbf{Formation and End of Spots.}---Each spot or group of
spots has its independent method of formation. Perhaps
very gradual, through many weeks, spots have yet been
known to attain full proportions in a few hours. When
completed, they are roughly circular; but as their end
draws near, the surrounding matter seems to approach and
crowd upon the umbra, as if to tumble pell-mell into its
cavernous depths. Very likely this is what actually happens.
Often tongue-like encroachments of the penumbra
force themselves across the umbra (illustrated in process
on page~\pageref{p11}); and this usually indicates the beginning of a
rapid decline and disappearance. The chasm seems to be
filled; and only a slightly disturbed surface (surrounded by
faculæ or white spots, which soon disperse) remains for a
brief time to indicate very indefinitely the place where
the spot existed. Sun spots are easiest of all solar phenomena
to observe. Sometimes exceptional disturbance
sets up a motion so rapid and violent that vast changes
have been seen within a few minutes' time, even while
the observer was watching.

\textbf{Duration and Distribution of Spots.}---Often spots are
carried across the face of the sun in its rotation, and they
become elliptical by foreshortening as they approach the
\DPPageSep{276.png}
edge and disappear. Figure~\ref{fig11.10} shows how
this takes place. If a spot lasts a fortnight or more, it will
again come into view when the sun's rotation shall have
carried it halfway round. On reappearing at the eastern
limb, a spot is elliptical and very narrow at first, and gradually
% Fig 11.10
\begin{figure}[hbt!]
  \centering
  \Input{page_267a}
  \caption{The Same Spot near Sun's Center and Edge}
  \label{fig11.10}
\end{figure}
it seems to broaden into its actual shape on facing
the earth more and more squarely. The spots are, on an
average, two or three months in duration, though very
often lasting only a week, or perhaps even a few days or
hours. The longest on record lasted 18 months, in the
years 1840 and 1841. Spots do not appear on every part
of the sun's disk, but they are nearly always confined to
zones on both sides of the solar equator, extending from
latitude 5° to 30°. The spots are most numerous in solar
latitude 15°, both north and south, and a few more are seen
in the northern than the southern hemisphere.

% Fig 11.11
\begin{figure}[hb!]
  \centering
  \Input[\textwidth]{page_267b}
  \caption{Apparent Motion of Spots across the Sun}
\end{figure}

\Smaller
The sun's equator is tilled about 7° to the ecliptic, so that the spot
zones appear sometimes straight and sometimes curved on the sun's
disk, as the four figures show, for different seasons of the year.
\DPPageSep{277.png}
Early in March the sun's south pole, and early in September his north
pole, is turned farthest toward us. The axis of the sun, if prolonged
northward, would cut the celestial sphere near Delta Draconis. In
April the sun's axis is inclined about 25° west of the hour circle passing
through his center; in October, about the same amount to the east of it.
\Restore

\textbf{Periodicity of the Sun Spots.}---Spots are not always
equally numerous on the surface of the sun. At times
they may be counted by hundreds, and again days, and
even weeks, will elapse without a single spot being visible.
A well-established period is now recognized. Spots diminish
in number slowly, all the while appearing at lower and
lower latitudes on the sun, and they pass through a minimum
at about latitude 5° both north and south. Then
rather suddenly there is an outbreak of spots, in latitude
about 30° on both
sides of the sun's
equator, followed by
a growth in number
and size of the spots
to a maximum, after
which again comes
the decline in number,
size, and latitude. As a new outbreak in high latitudes
usually begins about two years before final disappearance
of the zones of low latitude, it follows that near minimum
the spots, although few in number, are distributed in four
narrow belts, two of low and two of high latitude. The
complete round,
% Fig 11.12
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.6\textwidth]{page_268}
  \caption{Curve of Sun Spots and Magnetic Declination}
\end{wrapfigure}
or spot period, is eleven years and one
month in duration. From minimum to maximum is usually
about five years, and from maximum to minimum about six
years. The fluctuation in latitude is called Spoerer's\index{Spoerer, F.~W.~G.\ (1822--95), Ger.\ ast.} `law
of zones.'\index{zones, Spoerer's law of} Regarding as determinant of the true period,
not merely the total number of spots, but the number
as affected by the law of zones, the true sun-spot cycle
\DPPageSep{278.png}
appears to be about fourteen years long, because a new
zone breaks out in high latitudes while the old one still
exists near the equator. Neither the cause underlying the
law of zones, nor the reason for the spot period itself, is
known. Probably the latter is due to the outbreak of
exceptional eruptive forces held in check during seasons of
few spots. A minimum occurred in 1901, and a maximum
in 1905. Underlying the ordinary spot period is another
cycle about 35 years in duration.

\Smaller
\textbf{Do the Spots affect the Earth?}\index{earth!affected by sun spots}\index{magnetic disturbances}---When sun spots are most numerous,
displays of the aurora borealis are most frequent and brilliant, and the
effects of magnetic storms are most strongly exhibited by fluctuations
of magnetic needles
% Fig 11.13
\begin{wrapfigure}[15]{o}{0.5\textwidth}
  \centering
  \Input[0.4\textwidth]{page_269}
  \caption{Zones of Invisible Faculæ, 7th August, 1893 (photographed by Hale)}\index{Hale, G. E., Dir.\ Carnegie Solar Obs.}\index{sun!faculæ}
  \index{photography!of sun}\index{spectroheliogram, spectroheliograph}
\end{wrapfigure}
delicately mounted in observatories. Wolfer's\index{Wolfer, A., Dir.\ Obs.\ Zurich}
diagram opposite shows how closely spot activity kept time with fluctuations
of magnetic declination during the years 1886--96. Even in periods
of largest and most numerous spots, the amount of heat received from
the sun is not a thousandth part lessened, and any effect of periodicity
of the spots upon the weather is too slight to be detected.
\Restore

\label{p269} \textbf{Faculæ.}\index{sun!faculæ}---On the bright surface of the sun may nearly
always be seen still brighter specks or streaks, many
thousand miles in length,
and much larger than
any of our continents.
Such faculæ were discovered
by Hevelius\index{Hevelius, J.\ (1611--87), Ger.\ ast.}, at
Danzig, about the middle
of the 17th century.
They are supposed to
be elevated regions of
the surface, crests of
luminous matter protruding
through the general
and denser level of the
photosphere. The faculæ
are very numerous around the spots. The sun's atmosphere
\DPPageSep{279.png}
absorbs a large percentage of its own light, so that
the illumination of the disk diminishes gradually toward
the edge all around. On this account the faculæ are better
seen near the edge; but they exist in belts all the way
across the sun's disk, and can be so photographed at any
time by the spectroheliograph\index{spectroheliogram, spectroheliograph} (described in a later section),
although they are invisible to ordinary vision. These
invisible faculæ are most abundant in the sun-spot zones.
There is evidence that some faculæ are clouds of incandescent
calcium\index{calcium!in sun}, an element strongly marked in the sun. The
invisible faculæ appear to be related to the prominences
projected against the photosphere.

\textbf{The Sun's Rotation on his Axis.}\index{sun!rotation}---The spots which last
longest help most in ascertaining the time required by
the sun in turning round once on his axis. A large number
of observations have shown that a long-lived spot near
the sun's equator, starting from the center, will pass from
east to west all the way round and return to the center in
$27\frac{1}{2}$ days. But as the earth will meanwhile have moved
eastward also, the sun's period of rotation, as referred to
the stars, is $25\frac{1}{4}$ days. This is the length of the true, or
sidereal period. The exterior of the sun is not rigid, as
the earth appears to be; and it is found that spots remote
from the equator give a longer period of rotation the
higher their latitude. At latitude $45$°, the period of the
sun's rotation is about two days longer than on the equator.
At latitude $75$°, the rotation period, as found by Dunér\index{Duner@{Dunér, N.~C., Dir.\ Obs.\ Upsala}} with
the spectroscope, is $38\frac{1}{2}$ days. Also Young\index{Young, C.~A.\ (1834--1908), Am.\ ast.}, Crew\index{Crew, H., Prof.\ Northwestern Univ.}, and
others have verified the rotation in this manner in the
equatorial regions. The cause of acceleration at the
equator has not yet been discovered.

\Smaller
The faculæ\index{sun!faculæ} appear to have a different law of rotation from that
governing the spots; for no matter what their latitude, they go round
in less time than spots. From careful measures of numerous lines in
\DPPageSep{280.png}
the solar spectrum, Jewell\index{Jewell, L.~E., Am.\ physicist} has found that acceleration of the sun's
equator is greatest for the higher or outer parts of the solar atmosphere,
and that the difference between the rotation periods of the sun's outer
and inner atmosphere amounts to several days.

\textbf{The Spectroscope.}\index{spectroscope}---Place a prism in the path of a slender beam of
sunlight. It will be refracted out of a straight course, and will emerge
as a colored band. The light is all refracted, but it is not refracted
equally; the red is bent least, and the violet most. The many-colored
image produced in this manner is called a spectrum\index{spectrum}. This unequal
refraction, and decomposition of white light into its primary colors is
called dispersion. Upon it depend the principles of spectrum analysis\index{spectrum!analysis},
which is a study of the nature and composition of luminous bodies
by means of the light which they emit. Usually the spectroscope consists
of four parts: (1)~a very narrow slit \textit{S} through which the beam
% Fig 11.14
\begin{figure}[hbt!]
  \centering
  \Input{page_271}
  \caption{Illustration: A Single-prism Spectroscope in Outline}
  \label{p271}\index{spectroscope}
\end{figure}
of light is admitted, (2)~a collimator\index{collimator}, \textit{A}, or small telescope at whose
focus the slit is placed, (3)~a prism, \textit{P}, or a closely ruled surface, which
effects the dispersion necessary to produce a spectrum, (4)~a view
telescope, \textit{BE}, for studying optically the different regions of the spectrum.
In researches of the present day, in which photography\index{photography!of sun} plays
an important part, the spectroscope is usually constructed so that the
eyepiece can be removed, and a plate-holder substituted in its place.
Spectra can then be photographed, and afterward examined at leisure.
The illustration \vpageref{p272a} shows a modern spectroscope as
adapted for photographic work. Rays enter the upper tube on the left.

\textbf{Continuous Spectrum and Fraunhofer Lines.}\index{Fraunhofer lines}\index{spectrum!continuous}---Place a candle before
the slit, and a continuous spectrum is produced. A continuous spectrum
is one which is crossed by neither bright nor dark lines; the
colors from red to violet blend insensibly from one to the other in
succession. Replace the candle by a beam of sunlight, and observe
\DPPageSep{281.png}
the difference: at first sight the spectrum appears to be continuous,
but closer observation immediately shows that the band of color is
crossed at right angles by a multitude of fine dark lines, of different
widths and intensities, and seemingly without order of arrangement.
\Restore

\label{p272}This spectrum is a discontinuous spectrum\index{spectrum!discontinuous}. The dark
lines are called Fraunhofer lines\index{Fraunhofer lines}, from Fraunhofer, who
% Fig 11.15
\begin{figure}[hbt!]
  \centering
  \Input{page_272}
  \caption{Brashear's Universal Spectroscope (arranged for Photographic Research)}
  \label{p272a}
  \index{Brashear, J. A.}\index{spectroscope}
\end{figure}
first made a chart of their position in the prismatic spectrum.
He designated the more strongly marked lines by
the first letters of the alphabet, the \textit{A} line being in the
red, and the \textit{H} line in the violet. Their character and
position in the spectrum are highly significant; for they
indicate the chemical elements of which luminous bodies,
especially the sun, are composed.
\DPPageSep{282.png}

% Fig 11.16
\begin{figure}[hbt!]
  \centering
  \Input{page_273a}
  \caption{A Diffraction Spectroscope in Outline}\index{diffraction!spectroscope}
  \index{spectroscope}
\end{figure}
\textbf{Normal Solar Spectrum.}\index{spectrum!normal solar}---If the spectrum is formed by
passing the rays through a prism, as in the illustration,
(page~\pageref{p271}), relative position of the dark lines will vary with
the substance composing the prism \textit{P}; the amount of dispersion
in different parts of the spectrum varies with the
material of the prism. Another method of producing the
spectrum is therefore employed: by reflecting the sun's
rays from a grating, \textit{A}, accurately ruled with a diamond
point upon polished speculum metal, thousands of lines to
the inch, a diffraction spectrum\index{diffraction!spectrum} is formed. In this case
dispersion is entirely independent of the material of the
grating; and the spectrum is called the \textit{normal solar spectrum},
because the amount of dispersion of the rays is
proportional to their wave length.

% Fig 11.17
\begin{figure}[hbt!]
  \centering
  \Input{page_273b}
  \caption{Normal and Prismatic Spectra of Equal Length (Middle of both Spectra at \textit{D})}
  \label{fig11.17}
\end{figure}
\Smaller
The diagram gives a comparison of the two types of spectrum. The
middle of the spectrum is practically coincident with the yellow \textit{D} lines
of sodium. As referred to the normal spectrum, the red end of a prismatic
\DPPageSep{283.png}
spectrum is very much compressed; and its violet end similarly
expanded. The finest gratings are ruled with a dividing engine perfected
by Rowland\index{Rowland, H.~A.\ (r\=o´land) (1848--1901), Am.\ physicist}. The precision of its working is such that the number of
parallel lines which can be ruled on a plate of metal an inch square
exceeds 20,000; but one tenth this number is a good working limit.
\Restore

\textbf{High Power Spectroscopes.}\index{spectroscope}---The length of the spectrum
varies with the degree of dispersion. It is evident that
the greater the dispersion, the more the dark lines will be
spread out lengthwise in the spectrum, and separated from
each other. It is as if magnifying power were increased.
Consequently the higher the dispersion, the greater the
number of dark lines which can be seen and photographed.

\Smaller
When a greater degree of dispersion is required than one prism will
produce, it is usual to employ an arrangement of many prisms, as shown
in the figure. Light comes
from the object glass of the
collimator on the left, and
passes round through several
prisms successively, dispersion
becoming greater and
greater, as indicated by the
gradually widening white
band, which finally passes
into the observing telescope
on the right. When prisms
and their accompanying
small telescopes
% Fig 11.18
\begin{wrapfigure}[20]{o}{0.55\textwidth}
  \centering
  \Input[0.5\textwidth]{page_274}
  \caption{A High Power Prism Spectroscope}\index{spectroscope}
\end{wrapfigure}
are rigidly
secured to the great tube in
place of the eyepiece ordinarily
used with it, such a
combination of the two instruments
is often called a
telespectroscope\index{telespectroscope}. In the
diffraction spectroscope, increase
of power is obtained
by passing to the spectrum of a higher order, which is obtained by
tilting the grating at an angle suitable to the order (second, third, or
fourth) of spectrum desired. In all cases, the higher the degree of
dispersion, the fainter becomes the spectrum in every part. So that
a practical limit is soon reached.
\Restore
\DPPageSep{284.png}

\textbf{Principles of Spectrum Analysis.}\index{spectrum!analysis}---In 1858 Kirchhoff\index{Kirchhoff, G.~R.\ (keerk´hof) (1824--87), Ger.\ physicist}
reduced to the following compact and comprehensive form
the three principles underlying the theory of spectrum
analysis: (1)~Solid and liquid bodies, also gases under
high pressure, give, when incandescent, a continuous spectrum.
(2)~Gases under low
pressure give a discontinuous
spectrum, crossed by bright
lines whose number and position
in the spectrum differ
according to the substances
vaporized. (3)~When white
light passes through a gas,
this medium absorbs rays of identical wave length with
those composing its own bright-line spectrum. Therefore
dark lines or bands exactly replace the characteristic bright
lines in the spectrum of the gas itself. This principle,
theoretically correct, is easily illustrated and verified
experimentally. These three fundamental principles fully
account for the discontinuous spectrum of the sun, and
the multitude of dark Fraunhofer lines\index{Fraunhofer lines} which cross it.

% Fig 11.19, 20
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.5\textwidth}
    \centering
    \vspace{2ex}
    \Input {page_275a}
    \caption{Slit and the Comparison Prism}\index{prism, comparison}
    \index{slit!spectroscope}
  \end{minipage}
  \hfill
  \begin{minipage}{0.4\textwidth}
    \centering
    \Input {page_275b}
    \caption{Course of Rays in Comparison Prism}
  \end{minipage}
\end{figure}

\Smaller
\textbf{Photographing the Sun's Spectrum.}\index{photography!of sun}\index{spectrum!solar}\index{sun|see{spectrum, solar}}---The principles of spectrum
analysis just enunciated indicate clearly how to ascertain the elements
composing the sun. The process is one of mapping
or photographing the lines in the solar spectrum,
and alongside of it in succession the spectra
of terrestrial elements whose existence in the sun
is suspected. This is effected by means of the
comparison prism, \textit{ab}, shown above. It covers part
of the slit, $m$. Sun's rays come from \textit{B}, pass into
the comparison prism, are totally reflected, and pass
through the slit (downward in the adjacent figure).
Thus they appear to come from \textit{A}, the same as rays
from the vaporized substance under examination;
and as both sets of rays then make the optical circuit
of the spectroscope side by side, the field of view embraces solar
spectrum and spectrum of the terrestrial substance, also side by
\DPPageSep{285.png}
side. Direct comparison line for line is thereby greatly facilitated.
Rowland\index{Rowland, H.~A.\ (r\=o´land) (1848--1901), Am.\ physicist} of Baltimore and Higgs\index{Higgs, G., Eng.\ physicist} of Liverpool have achieved very
marked success in photographing the sun's spectrum. The
illustration \vpageref{p276} shows a very small part of that spectrum,
known as the `Great G group,' highly amplified, from a photograph
% Fig 11.21
\begin{figure}[hbt!]
  \centering
  \Input{page_276}
  \caption{Great G Group of Solar Spectrum (photographed by Higgs)}
  \label{p276}\index{spectrum!solar}
\end{figure}
by the latter. These lines are in the indigo. Many hundreds of the
dark lines in the sun's spectrum are caused by absorption in our
atmosphere. They are called telluric lines\index{telluric lines}, and variation in their
number and intensity affords an excellent method of finding the
amount of aqueous vapor in the atmosphere, as Jewell\index{Jewell, L.~E., Am.\ physicist} and others
have shown.
\Restore

\textbf{Elements already recognized in the Sun.}\index{sun!elements}\index{sun!metals}\index{sun!constitution}---This process
of comparison of the solar spectrum with spectra of terrestrial
elements has been carried so far that about 40 of these
substances are now known to exist in the sun. Among
them are (according to Rowland and others):---
\begin{center}
\TableSize
\begin{tabular}{@{} ll@{\qquad} ll@{\qquad} ll}
  (Al) &amp; Aluminium &amp; (H)  &amp; Hydrogen  &amp; (Ag) &amp; Silver    \\
  (Cd) &amp; Cadmium   &amp; (Fe) &amp; Iron      &amp; (Na) &amp; Sodium    \\
  (Ca) &amp; Calcium   &amp; (Mg) &amp; Magnesium &amp; (Ti) &amp; Titanium  \\
  (C)  &amp; Carbon    &amp; (Mn) &amp; Manganese &amp; (V)  &amp; Vanadium  \\
  (Cr) &amp; Chromium  &amp; (Ni) &amp; Nickel    &amp; (Y)  &amp; Yttrium   \\
  (Co) &amp; Cobalt    &amp; (Sc) &amp; Scandium  &amp; (Zn) &amp; Zinc      \\
  (Cu) &amp; Copper    &amp; (Si) &amp; Silicon   &amp; (Zr) &amp; Zirconium
  \index{aluminum in sun}%
  \index{cadmium in sun}%
  \index{calcium!in sun}%
  \index{carbon!in sun}%
  \index{chromium in sun}%
  \index{cobalt in sun}%
  \index{copper in sun}%
  \index{hydrogen!in sun}%
  \index{iron!in sun}%
  \index{magnesium!in sun}%
  \index{manganese in sun}%
  \index{nickel in sun}%
  \index{scandium in sun}%
  \index{silicon in sun}%
  \index{silver in sun}%
  \index{sodium!in sun}%
  \index{titanium in sun}%
  \index{vanadium in sun}%
  \index{yttrium in sun}%
  \index{zinc in sun}%
  \index{zirconium in sun}%
\end{tabular}
\end{center}

The certainty with which an element is recognized depends
upon two things: (\emph{a})~the number of coincidences of
spectral lines, (\emph{b})~the intensity of the lines. Calcium ranks
first in intensity, but iron has by far the greatest number
of lines, with more than 2000 coincidences. All told, it
may be said that iron, calcium, hydrogen, nickel, and sodium
\DPPageSep{286.png}
are the most strongly indicated. Runge\index{Runge, C.\ (roong´eh), Ger.\ physicist} has found certain
evidence of oxygen in the sun\index{oxygen in sun}. Chlorine and nitrogen,
abundant elements on the earth, and gold, mercury, phosphorus,
and sulphur are not indicated in the solar spectrum\index{chlorine!not in sun}\index{nitrogen!not in sun}.

\textbf{Sun-spot Spectrum.}\index{spectrum!solar}---If the spectrum of the sun itself
is complicated, that of a spot is even more so. In it are
multitudes of fine dark lines, indicating a greater degree
of gaseous absorption than prevails on the sun generally.

\Smaller
A few of the Fraunhofer lines\index{Fraunhofer lines} in the ordinary solar spectrum are
not only deepened in intensity, but broadened out in the spot spectrum,
as shown in the illustration. The dark belt running lengthwise through
the middle is the
% Fig 11.22
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.6\textwidth]{page_277}
  \caption{Thickened Lines of Spot Spectrum}\index{spectrum!sun spot}
\end{wrapfigure}
spectrum of the
umbra, and above
and below it are
spectra of both
sides of the penumbra,
much less
dark. Thickening
of the lines is most
marked in the umbra,
and gradually
diminishes on both
sides to the edges
of the penumbra.
Not infrequently
these heavily thickened lines are pierced in the middle by a narrow
bright line, called a `double reversal.' Always this is true of the \textit{H}
and \textit{K} bands in the spot spectrum. Spectra of many spots strengthen
the view that the spots are themselves depressions. Occasionally it
happens that there is a violent motion, either toward or from us, of the
gases above a spot; this produces in the spectrum a marked distortion
or branching of the dark lines. By measuring the amount and direction
of this distortion, it can be calculated whether the gases were
rushing toward or from us, and at what speed. On rare occasions
these velocities have been as great as 200 or even 300 miles per second.
The simple principle by which this is done is known as `Doppler's
principle\index{Doppler's principle}.' It is explained on page~\pageref{p432}.

\textbf{The Bolometer.}\index{bolometer}\index{bolometer|see{spectro-bolometer}}---With rise in its temperature, a metal becomes a
poorer conductor of electricity; with loss of heat, it conducts electricity
better. Iron at 300° below centigrade zero is nearly as perfect
\DPPageSep{287.png}
an electrical conductor as copper at ordinary temperatures. Upon the
application of this important relation depends the principle of the
bolometer. Its distinctive feature is a tiny strip of platinum leaf, looking
much like a fine hair or coarse spiderweb. It is about $\frac{1}{4}$~inch long,
$\frac{1}{500}$~inch broad, and so thin that a pile of 25,000 such strips would be
only an inch high. This bolometer strip is connected into an electric
circuit, and it is then carried slowly along the region of the infra-red
spectrum, and kept parallel to the Fraunhofer lines. So sensitive is
this instrument that the inconceivably slight change of temperature
of only the one-millionth of a degree of the centigrade scale may be
indicated.
\Restore

\textbf{Infra-red of the Solar Spectrum.}\index{spectrum!solar}---Beneath and beyond
the red in the solar spectrum is an extensive region of dark
bands wholly invisible to the human eye; nevertheless it
has been photographed\index{photography!of sun} with certainty. But the actinic or
% Fig 11.23
\begin{figure}[hbt!]
  \centering
  \Input{page_278}
  \caption{Invisible Heat Spectrum (photographed by Langley)}
  \index{Langley, S.~P.\ (1834--1906), Am.\ ast.\ and physicist}
\end{figure}
chemical intensity is very feeble in this region, so that it is
difficult to photograph directly. Langley\index{Langley, S.~P.\ (1834--1906), Am.\ ast.\ and physicist}, by means of an
ingenious automatic process, in conjunction with his bolometer,
or spectro-bolometer\index{spectro-bolometer}, has photographed the sun's
heat spectrum in a form comparable with the normal spectrum.
The above illustration represents its dark bands.
The length of the invisible spectrum is extraordinary, being
10~times that of the sun's luminous spectrum, which would
be represented on the same scale by a trifle more than the
diameter of a lead pencil to the left of \textit{A}.

\Smaller
\textbf{Ultra-violet of the Solar Spectrum.}\index{spectrum!solar}---When we pass to higher regions
of the sun's spectrum known as the violet, the light intensity is
rapidly weakened, so that the lines become invisible to the eye. Photographs\index{photography!of sun}
of this region can, however, be taken, because the chemical
intensity is great. In this manner, photographic maps of the invisible
\DPPageSep{288.png}
ultra-violet spectrum were made by Cornu\index{Cornu, M. A. (1841--1902), Fr.\ physicist}, and their length is many
times that of the visible spectrum. Just where the ultra-violet spectrum
really ends is not known, as the farther region of it appears to terminate
abruptly in consequence of absorption by the earth's atmosphere.

\textbf{How to distinguish True Solar from Telluric Lines.}\index{telluric lines}---Dark lines in
the solar spectrum being produced by absorption in our own atmosphere,
as well as in that of the sun, it is important to have some method
of distinguishing between them. One way is as follows, employing
Doppler's principle\index{Doppler's principle}. Arrange the spectroscope so that sunlight may
fall upon a small oscillating mirror, which reflects into the slit alternately
rays from the east and the west limb. On account of the sun's
rotation, the east limb is coming toward us; so the truly solar lines
in its spectrum will be displaced toward the violet. Similarly, those
of the west limb will lie toward the red, because that limb is going
from us. As the mirror oscillates, Fraunhofer lines\index{Fraunhofer lines} caused by solar
absorption will themselves vibrate forth and back, as if the spectrum
were being shaken; but dark lines due to absorption by our atmosphere
will remain all the time immovable---a method due to Cornu.
\Restore

\textbf{Absorption by Solar Atmosphere.}\index{atmosphere!of sun}\index{sun!absorption by its atmosphere}\index{sun|see {atmosphere, of sun}}---Absorption by the
sun's own atmosphere not only reduces the amount of sunlight
received by the earth,
% Fig 11.24
\begin{wrapfigure}{o}{0.4\textwidth}
  \centering
  \Input[0.4\textwidth]{page_279}
  \caption{Solar Disk much brighter at the Center than near the Limb}
  \label{fig11.24}
\end{wrapfigure}
but also changes its character.
Langley\index{Langley, S.~P.\ (1834--1906), Am.\ ast.\ and physicist} has ascertained
that if this atmosphere
possessed no absorbing
property, the sun would
shine two or three times
brighter than it now does,
and with a bluish color
resembling that of the
electric arc light.

\Smaller
Project the sun's entire image
on a screen, as if looking for
spots; quite marked is the difference
between the intensity
of light at center of disk and
at its edge. Try the experiment
illustrated in Figure~\ref{fig11.24}.
Where the sun's image falls upon a screen, puncture it
in two places, so that two pencils of sunlight may pass through and
\DPPageSep{289.png}
fall upon a second screen. As one of these comes from the edge of the
solar disk, and the other from its center, their difference in intensity is
rendered very obvious. It can be measured by a photometer. The
sun's disk is only two fifths as bright close to the limb as at the center.
This comparison relates only to rays by which we see in the red and
yellow part of the spectrum. If a similar comparison is made for blue
and violet rays, by which the photographic plate is affected, absorption
is very much greater; photographically, the light at the edge of
the sun's disk is only one seventh as strong as at the center. This
renders it difficult to photograph the entire sun with but a single exposure,
so as to show an even disk; for if the exposure is short enough
for the bright center, the image is very faint at the border.
\Restore

\textbf{The Chromosphere and Prominences.}\index{chromosphere, solar}\index{prominences}---Above and everywhere
surrounding the sun's bright surface is a gaseous
envelope, called the chromosphere. First seen during the
total solar eclipses of 1605 and 1706 as an irregular rose-tinted
fringe, analysis of the light shows that it is mainly
composed of glowing hydrogen, although sodium, magnesium,
and other metals are present. Depth of the chromosphere
is not everywhere the same, and it varies between
5000 and 10,000 miles. Projected up through the chromosphere,
but connected with it, are the fiery-red, cloud-shaped
prominences or protuberances. It was first found
that they are not lunar appendages, because the moon was
seen to pass gradually over them during a total eclipse.
Afterward the spectroscope verified this inference by
showing that their light is due chiefly to incandescent
hydrogen. Also there are the $H$ and $K$ lines, indicating
vapor of calcium; and a bright yellow line, $D_{3}$, due to
helium\index{helium}, an element not known on the earth till discovered
in 1895 by Ramsay\index{Ramsay, W., Prof.\ Univ.\ Col.\ London}, but long known by its line to
exist in the sun, whence its name. It is a very light gas
obtained from a mineral called uraninite\index{uraninite}. The prominences
are now photographed every clear day by means
of the spectroheliograph\index{spectroheliogram, spectroheliograph}. This ingenious instrument furnishes
in a few seconds a complete picture of the prominences
\DPPageSep{290.png}
all the way round the sun's limb, which by the
older methods of observing the protuberances piecemeal
would require hours to make. Prominences cannot be
observed by the telescope alone without the spectroscope,
except during eclipses of the sun. They are most abundant
over the sun's equator and the zones of greatest
spottedness on either side of it; but while spots are never
seen beyond latitude
45°, prominences
have been observed
in all latitudes, even
up to the sun's poles.
They are least numerous
about latitude
65°.

\Smaller
\textbf{The Spectroheliograph.}\index{spectroheliogram, spectroheliograph}---Young\index{Young, C.~A.\ (1834--1908), Am.\ ast.}
in 1870 was the
first to photograph\index{photography!of sun} a solar
prominence. No very
decided success was attained
until about 20 years
afterwards, by the use of
sensitive dry plates exposed
in the spectroscope.
By the addition of suitable
accessory apparatus---mainly
a second slit with
the means of moving
both slits automatically,---the
spectroscope is converted
into a spectroheliograph.
This remarkable
instrument, as devised and employed by Hale\index{Hale, G. E., Dir.\ Carnegie Solar Obs.} and built by Brashear\index{Brashear, J. A.},
is depicted in the above illustration. A similar instrument with which
almost identical results are obtained has been devised and used by
Deslandres\index{Deslandres, H.\ (day-londr´), ast.\ Meudon Obs.}, formerly of the Paris Observatory.
\Restore

\textbf{Classification of the Prominences.}\index{prominences}---The number, height,
and variety of forms of prominences are very great. They
\DPPageSep{291.png}
are seen at every part
% Fig 11.25
\begin{wrapfigure}[27]{o}{0.6\textwidth}
  \centering
  \Input[0.6\textwidth]{page_281}
  \caption{The Spectroheliograph (Hale)}\index{Hale, G. E., Dir.\ Carnegie Solar Obs.}\index{spectroheliogram, spectroheliograph}
\end{wrapfigure}
of the sun's limb, being most abundant
in an equatorial zone about 90° in breadth. Beyond
latitude 45° north and south, there is a marked falling off to
about 65°, followed by a renewed frequency in the region
of both poles. The average height of the prominences is
about 25,000 miles, or about three times the diameter of
the earth. Occasionally prominences start up to a height
exceeding 100,000 miles, as indicated on the colored plate
at page~\pageref{plateII}; and the greatest heights ever observed were
300,000 and 350,000 miles, approaching half the sun's
diameter. The latter was observed by Young\index{Young, C.~A.\ (1834--1908), Am.\ ast.}, 7th October,
1880. Frequently protuberances are prominently
developed at exactly opposite points on the sun's disk.

\Smaller
As to form and structure, prominences are divided into two classes:
eruptive or metallic, and cloud-like, quiescent prominences of hydrogen
(see Figure~\ref{fig11.28}). The former generally appear like brilliant jets, or separate
filaments, varying rapidly in form and brightness. The spectrum of
eruptive prominences shows the presence of a large number of metallic
vapors. For the most part they are observed near the spot zones only,
and never very near the poles of the sun. The velocity of detached
filaments often exceeds 100~miles in a second of time, and on rare occasions
it is four or five times as swift. Frequently prominences form
exactly over spots. Quiescent ones are usually of enormous size laterally,
and in appearance they are a close counterpart of terrestrial cirrus
and stratus clouds. Changes in them are not as a rule rapid, and near
the sun's poles they have been known to last nearly a month without
much change of form. Tacchini\index{Tacchini, P.\ (1838--1905), It.\ ast.} of Rome was a most persistent observer
of prominences.
\Restore

\textbf{Calcium Flocculi.}\index{calcium!flocculi}\index{flocculi}\index{calcium!in sun}\index{sun|see{calcium}}---%
By means of an improved and enlarged
spectroheliograph attached to the Yerkes telescope
(page~\pageref{p15}), Professor Hale has secured the remarkable
photograph shown on page~\pageref{p283}, representing the
calcium clouds, or \textit{flocculi}, as he names them. They are
revealed only in a spectroheliogram\index{spectroheliogram, spectroheliograph}, being wholly invisible
to direct observation or by means of ordinary photography\index{photography!of sun}.
\DPPageSep{292.png}
%[Blank Page]
\DPPageSep{293.png}
% Fig 11.28
\begin{Plate}
  \Input[\textwidth] {plate_v}
  \caption{Solar Prominences (drawn by Trouvelot, from Annals of Harvard College Observatory)}
  \label{fig11.28}\index{Harvard College!obs.}\index{prominences}\index{Trouvelot, L. (1827--92), Fr.\ ast.}
\end{Plate}
\DPPageSep{294.png}
There are other types of flocculi due to hydrogen
which are usually dark, and are found to have only a general
resemblance in form to the bright calcium flocculi.
Also iron flocculi have been obtained. It is apparent from the illustration
that incandescent calcium is pretty evenly
\begin{figure}[hbt!]
  \centering
  \Input{page_283}
  \caption{The Sun---Spectroheliogram of the Calcium Flocculi (1904)}
  \label{p283}
\end{figure}
and very prominently distributed over the entire surface
of the sun, network fashion, from pole to pole. This significant
work is being continued at the Carnegie Solar
Observatory\index{Carnegie Solar Obs.} in California.


\textbf{The Envelopes of the Sun.}\index{sun!envelopes}---The interior of the sun is
\DPPageSep{295.png}
probably composed of gases, in a state quite unfamiliar to
us, on account of intense heat and compression due to solar
gravity. In consistency they may perhaps resemble tar or
pitch. A series of layers, or shells, or atmospheres surround
the main body of the sun. The illustration, Figure~\ref{fig11.29}, has been
conceived by Trouvelot\index{Trouvelot, L. (1827--92), Fr.\ ast.} to show the condition of things
at the sun's surface and just beneath it. Although the
view is a theoretical one, it has been made up from a reasonable
% Fig 11.29
\begin{figure}[hbt!]
  \centering
  \Input{page_284}
  \caption{Atmosphere of the Sun in Ideal Section (from \textit{Bulletin Astronomique})}
  \label{fig11.29}
  \index{Bulletin Astronomique (Paris monthly)}
\end{figure}
interpretation of all the facts. Proceeding from
the outside inward, we meet first the very thin shell called
the chromosphere\index{chromosphere, solar}\index{sun|see{chromosphere, solar}}, probably about 5000 miles in thickness.
Immediately underneath is the photosphere\index{photosphere}, made up of
filaments due to the condensation of metallic vapors. The
outer ends of these filaments form the granular structures
which we see upon the sun generally, and their light shines
through the chromosphere. Between them and the chromosphere
is an envelope thinner still, not over 700~miles in
thickness, and represented by the darker shaded upper
side of the photosphere. It is called the reversing layer\index{reversing layer}.\index{sun|see{reversing layer}}
In this gaseous envelope takes place that absorption which
gives rise to the Fraunhofer lines\index{Fraunhofer lines}. Where undisturbed by
eruptions from beneath, the filaments of the photosphere
are radial; but where such eruptions take place, producing
under certain conditions the spots, these filaments are
\DPPageSep{296.png}
swept out of their normal vertical lines, as shown, forming
the penumbra of the spot as seen from our point of
view. From the outer surface of the body of the sun
proper (which we never see) rise vapors of hydrogen and
various metals of which the sun is composed. Numbers
of these eruptive columns are shown. They are spread
into masses of cloud-like forms composed of metallic vapors
underneath the photosphere. As these columns grow
in number and stress becomes more and more intense,
outbursts through the photospheric shell take place, giving
rise to phenomena known as sun spots and protuberances.
Naturally such eruptions would be more violent at
one time than at another, and we might expect them to
occur periodically, just as we observe the spots actually
do. Still above the chromosphere and prominences is the
corona\index{corona}, not an atmosphere, properly speaking, but a luminous
appendage of the sun (not shown in this illustration)
whose light is of a complex character, and about which
relatively little is known, because it can be seen only during
total eclipses of the sun. Illustrations of it are given
in the next chapter, with theories of its constitution.

\textbf{Light and Brilliance of the Sun.}\index{sun!light of}\index{sun!brilliance of}---It is not easy to convey,
in words or figures, any idea of the amount of light
given out by the sun, since the figures expressed in `candle
power,' or in terms of the ordinary gas burner, or even the
arc light, are so enormous as really to be beyond our comprehension.
Indeed, any of these artificial illuminations,
even the most brilliant electric light, if placed between the
eye and the sun, seems black by comparison. The sun is
nearly four times brighter than the brightest part of the
electric arc. By an experiment at a steel works in Pennsylvania,
Langley\index{Langley, S.~P.\ (1834--1906), Am.\ ast.\ and physicist} compared direct sunlight with the blinding
stream of molten metal from a Bessemer converter; and
although absolutely dazzling in its brightness, sunlight
\DPPageSep{297.png}
was found to be more than 5000 times brighter. The
amount of light received from the sun is equal to that from
600,000 full moons.

\textbf{The Sun's Heat at the Earth.}\index{sun!heat}\index{heat|see{sun, heat}}---Although difficult to give
an idea of the sun's light, much more so is it to convey an
adequate notion of his enormous heat. So great is that
heat, even at our vast distance from the sun, that it exceeds
intelligible calculation. The unit of heat is called the calorie\index{calorie defined},
and it signifies the amount of heat required to raise the temperature
of a kilogram of water one degree of the centigrade
scale. The number of calories received each minute
upon a square meter of the earth's surface has been repeatedly
measured, and found to be 37, neglecting the
considerable portion which is absorbed by our atmosphere.
No variation in this amount has yet been detected; so that
37~calories per square meter per minute is termed the \textit{solar
constant}\index{solar constant}\index{sun|see{solar constant}}. With the sun in the zenith, his heat is powerful
enough to melt annually a layer of ice on the earth nearly
200~feet in thickness. Or if we measure off a space five
feet square, the energy of the sun's rays, when falling vertically
upon it, is equivalent to one horse power, or the
work of about five men. Upon the deck of a steamer on
tropical oceans there falls enough heat to propel it at about
10~knots, if only that heat could be fully utilized. Several
attempts have been made to employ solar heat directly for
industrial purposes, and Ericsson\index{Er´icsson, J.\ (1803--89), Swed.-Am.\ eng.}, the great Swedish engineer,
and Mouchot\index{Mouchot, A.\ (moo-show´), Fr.\ phys.} built solar engines. The sun's gaseous
envelope, too, absorbs heat. Frost\index{Frost, E. B., Prof.\ Univ.\ Chicago} has shown that all
parts of the disk radiate uniformly, and that we should
receive 1.7 times more heat, if the solar atmosphere were
removed.

\textbf{The Sun's Heat at the Sun}.---The intensity of heat,
like that of light, decreases as the square of the distance
from the radiating body increases. Therefore, the amount
\DPPageSep{298.png}
of heat radiated by a given area of the sun's surface must
be about 46,000 times greater than that received by an
equal area at the distance of the earth.

\Smaller
One square meter of that surface radiates heat enough to generate
more than 100,000 horse power, continuously, night and day. Imagine
a solid cylinder of ice, nearly three miles in diameter and as long as the
distance from the earth to the sun. The sun emits heat sufficient to
melt this vast column in a single second of time; in eight seconds it
would be converted into steam. Were the sun no farther from us than
the moon, not only would his vast globe fill the entire sky, but his overpowering
heat would vaporize the oceans, and speedily melt the solid
earth itself. To investigate this inconceivable outlay of heat, to determine
the laws of its radiation and its effects upon the earth, and to
theorize upon the method by which this heat is maintained, are among
the most important and practical problems of the astronomy of the
present day. Whether the amount of heat given out by the sun is a
constant quantity, or whether it varies from year to year or from century
to century, is not yet determined. The temperature\index{sun!temperature} of the sun is
very difficult to ascertain. Widely different estimates have been made.
Probably 16,000° to 18,000° Fahrenheit is near the truth. But no
artificial heat exceeds 4000° F.
\Restore

\textbf{How the Sun's Heat is maintained.}\index{sun!maintenance}---The sun's heat
cannot be maintained by the combustion of carbon, for
although the vast globe were solid anthracite, in less than
5000 years it would be burned to a cinder. Heat, we
know, may result from sudden impact, as the collision
of bodies. According to one theory, the sun's heat may be
maintained by the impact of falling meteoric matter, and
very probably this accounts for a small fraction; but in
order that all the heat should be produced in this manner,
an amount of matter equal to a hundredth part of the
earth's mass would have to fall upon the sun each year
from the present distance of the earth. This seems very
unlikely. Only one possible explanation remains: if the
sun is contracting upon himself, no matter how slowly,
gases composing his volume must generate heat in the
process\index{sun!contraction of}. The eminent German physicist, von Helmholtz\index{Helmholtz@v.\ Helmholtz, H.~L.~F.\ (1821--94), Ger.\ physicist}
\DPPageSep{299.png}
first proposed this theory of maintenance about 1850, and
it is now universally accepted. So enormous is the sun
that the actual shortening of his diameter (the only dimension
we can measure) need take place but very slowly. In
fact; a contraction of only six miles per century would fully
account for all the heat given out by the sun. But six
miles would subtend an angle of only $\frac{1}{75}$ of a second
of arc at the sun, and this is very near the limit of
measurement with the most refined instruments. So it is
evident that many centuries must elapse before observation
can verify this theory.

\textbf{The Past and Future of the Sun.}\index{sun!past and future of}---Accepting the
theory that the sun's heat is maintained by gradual
shrinkage of his volume, he must have been vastly larger
in the remote past, and he will become very much reduced
in size in the distant future. If we assume the rate of
contraction to remain unchanged through indefinite ages,
it is possible to calculate that the earth has been receiving
heat from the sun about 20,000,000 years in the past;
also, that in the next 5,000,000 years, he will have shrunk
to one half his present diameter. For 5,000,000 years additional,
he might continue to emit heat sufficient to maintain
certain types of life on our earth. A vast period of
30,000,000 to 40,000,000 years, then, may be regarded as
the likely duration, or life period, of the solar system, from
origin to end. Their heat all lost by radiation, the sun
and his family of planets might continue their journey
through interstellar space as inert matter for additional
and indefinite millions of years.
\DPPageSep{300.png}


\Chapter{XII}{Eclipses of Sun and Moon}

\index{eclipses, solar|(}%
\index{solar eclipses|see{eclipses, solar}}%
\index{lunar eclipses|see{eclipses, lunar}}%
In earliest ages, every natural event was a mystery.
Day and night, summer and winter, and the most
ordinary occurrences filled whole nations with wonder,
and fantastic explanations were given of the simplest
natural phenomena. But when anything happened so
strange, and even frightful, as the total darkening of the
sun in the daytime, it is scarcely matter for surprise that
fear and superstition ran riot. Some nations believed
that a vast monster was devouring the friendly sun, and
barbarous noises were made to frighten him away. For
ages the sun was an object of worship, and it was but
natural that his darkening, apparently inexplicable, should
have brought consternation to all beholders. Among
uncivilized peoples, the ancient view regarding eclipses
prevails to the present day.

\Smaller
\textbf{Remarkable Ancient Eclipses.}\index{eclipses, solar}\index{eclipses, solar!ancient}---The earliest mentioned solar eclipse
took place in \BC~776, and is recorded in the Chinese annals\index{Chinese annals}. During
the next hundred years several eclipses were recorded on Assyrian tablets\index{Assyria!tablets}
or monuments. On 28th May, \BC~585, took place a total eclipse
of the sun, said to have been predicted by Thales\index{Thales (\BC~600), Gk.\ phil.}, which terminated a
battle between the Medes and Lydians. This eclipse has helped to
fix the chronology of this epoch. So, too, a like eclipse, 3d August,
\BC~431, has established the epoch of the first year of the Peloponnesian
war; and the eclipse of 15th August, \BC~310, is historically known as
`the eclipse of Agathocles\index{Agathocles (\BC~320), eclipse of},' because it took place the day after he had
invaded the African territory of the Carthaginians, who had blockaded
him in Syracuse: `the day turned into night, and the stars came out
everywhere in the sky.' Also a few solar eclipses are connected with
\DPPageSep{301.png}
events in Roman history. The first historic reference to the corona\index{corona},
or halo of silvery light which seems to encircle the dark eclipsing moon,
occurs in Plutarch's description of the total eclipse\index{eclipses, solar!total} of 20th March, \AD~71.
Although it must have been frequently seen, there is no subsequent
mention of it till near the end of the 16th century. The few eclipses
recorded in this long interval have little value, scientific or otherwise,
except as they have helped modern astronomers to ascertain the motion
of the moon.
\Restore

\textbf{The Cause of Solar Eclipses.}\index{eclipses, solar!causes of}---Any opaque object interposed
between the eye and the sun will cause a solar
eclipse; and it will
be total
% Fig 12.1
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.54\textwidth]{page_290}
  \caption{How Eclipses of Sun and Moon take Place}
  \label{p290}
\end{wrapfigure}
provided the
angle filled by the
object is at least as
great as that which
the sun itself subtends;
that is, about
one half a degree.
Every one recognizes
the shadow of
the eagle flying over
the highway, and the
cloud's dark shadow
moving slowly across
the landscape, as produced
by the interposition
of a dark
body between sun
and earth. To the
eager spectators on
the towers of Notre
Dame, Paris, 21st
October, 1783, there
appeared a novel sort of solar eclipse, caused by the drifting
between them and the sun of the balloon in which
\DPPageSep{302.png}
were M.~Pilâtre\index{Pilâtre de Rozier, J.~F.\ (pee-l\u ottr´ d\u uh-ro-ze-\=a´) (1756--85), Fr.\ aeronaut} and the Marquis
d'Arlandes\index{d'Arlandes, F. L. (där-lond´) (1742--1809), Fr.\ marquis}. And just as when the
eye is placed below the eagle, or
behind the cloud, or beneath the
balloon, an apparent but terrestrial
eclipse of the sun is seen, just so
when the moon comes round between
earth and sun a real or astronomical
eclipse of the sun takes
place. But the great advantage of
the latter comes from the fact that
the moon, the eclipse-producing
body, is very much farther away
than cloud, and eagle, and balloon
are,---beyond the atmosphere of the
earth, at a distance relatively very
great and comparable with that of
the sun itself. It is a striking fact
that the sun, about 400 times broader
than the moon, happens to be about
400 times farther away, so that sun
and moon both appear to be of
nearly the same size in the heavens.
A slight variation of our satellite's
size or distance might have made that
impressive phenomenon, the sun's
total eclipse, forever impossible.

\textbf{The Shadows of Heavenly Bodies.}\index{shadows of heavenly bodies}---As
every earthly object, when in
sunshine, casts a shadow of the
same general shape as itself, so do
the
% Fig 12.2
\begin{wrapfigure}[40]{o}{0.36\textwidth}
  \centering
  \Input[0.36\textwidth]{page_291}
  \caption{Slender Shadows of Earth and Moon}
  \label{p291}\index{shadows of heavenly bodies}
\end{wrapfigure}
celestial bodies of our solar system.
All these, whether planets or
satellites, are spherical; and as they
\DPPageSep{303.png}
are smaller than the sun, it is evident that their shadows
are long, narrow cones stretching into space and always
away from that central luminary. Evidently, also, the
length of such a shadow depends upon two things,---the
size of the sphere casting it, and its distance from the
sun. The average length of the shadow of the earth is
857,000 miles; of the moon, 232,000 miles. Each is at
times about $\frac{1}{60}$ part longer or shorter than these mean
values, because our distance from the sun varies $\frac{1}{60}$ part
from the mean distance. So far away is the sun that the
shadows of earth and moon are exceedingly long and
slender. To represent them in their true proportions is
impossible within the limits of a small page like this. In
the illustration just given, however, attempt is made to
give some idea of these slender shadows; but even there
they are drawn five times too broad for their length. The
shadow cast by a heavenly body is a cone, and is often
called the umbra, or dense shadow, because the sun's light
is wholly withdrawn from it. Completely surrounding the
umbra is a less dense shadow, from which, as the figure
on page~\pageref{p290} shows, the sun's light is only partly excluded.
This is called the penumbra; and it is a hollow frustum
of a cone, whose base is turned opposite to the base of the
umbra. Both umbra and penumbra sweep through space
with a velocity exceeding 2000~miles an hour; and they
trail eastward across our globe. The way in which they
strike its surface gives rise to different kinds of solar
eclipse, known as partial\index{eclipses, solar!partial}, annular\index{eclipses, solar!annular}, and total\index{eclipses, solar!total}.

\Smaller
\textbf{True Proportions of Earth's and Moon's Orbits.}---Even more difficult
is it to represent the sizes and distances of sun, earth, and moon, in their
true relative proportions on paper. It is easy, however, to exhibit them
correctly in a medium-sized lot. Cut out a disk one foot in diameter to
represent the sun. Pace off 107~feet from it, and there place an ordinary
shot, $\frac{1}{10}$~inch in diameter, to represent the earth. At a distance of
$3\frac{1}{3}$~inches from the shot, place a grain of sand, or a very small shot, to
\DPPageSep{304.png}
represent the moon. Then not only will the sizes of sun, earth, and
moon, be exhibited in true proportion, but the dimensions of earth's and
moon's orbits will be correctly indicated on the
same scale. Every inch of this scale corresponds
to 72,000 miles in space.
\Restore

% Fig 12.3, 4
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.4\textwidth}
    \centering
    %\vspace{5ex}
    \Input {page_293a}
    \caption{Sun not in Plane of Moon's Orbit---Eclipses Impossible}
  \end{minipage}
  \hfill
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input[\textwidth]{page_293b}
    \caption{Sun in Plane of Moon's Orbit---Eclipses Inevitable}
  \end{minipage}
  \label{p293}
\end{figure}

\textbf{The Nodes of the Moon's Orbit.}\index{moon!nodes}---Once
every month---that is, every time
the moon comes to the phase called
new---there would be an eclipse of the
sun, were it not that the moon's path
about the earth, and that of the earth
about the sun are not in the same plane,
but inclined to each other by an angle
of $5\frac{1}{7}$°. When our satellite comes round
to conjunction or new moon, she usually
passes above or below the sun, which
therefore suffers no eclipse. Two
opposite points on the celestial sphere where the plane of
moon's orbit crosses ecliptic are called the moon's nodes.
Indeed, the term \textit{ecliptic}\index{ecliptic!origin of} had its
origin from this condition: it is
the plane near to which the moon
must be in order that eclipses
shall be possible.

\Smaller
The figures should make this clear.
The sun is where the eye is, and the
disk held at arm's length represents the
lunar orbit, the earth being at its center.
When held at the side, with the wrist
bent forward, the moon's shadow falls
far below the earth, and an eclipse is
impossible. Now carry the disk slowly
to the position of the second figure,
gradually straightening out the wrist,
and taking care to keep plane of disk
always parallel to its first position: moon's orbit is now seen edge on,
and when new moon occurs, an eclipse of the sun is inevitable.
\DPPageSep{305.png}
% Fig 12.5
\begin{figure}[b]
  \centering
  \Input{page_294}
  \caption{Solar Ecliptic Limit, both East and West of Moon's Ascending Node}
  \index{moon!nodes}\index{ecliptic limit!solar}
\end{figure}

\textbf{Solar Ecliptic Limit.}\index{ecliptic limit!solar}---As a solar eclipse cannot take place unless
some part of the moon overlaps the sun's disk, it is clear that the
apparent diameters of these two bodies must affect the distance of the
sun from the moon's node, within which an eclipse is possible. This
distance is called the solar ecliptic limit, and the figure illustrates it on
both sides of the ascending node. From the new moon at the center
to the farther new moon on either side is an arc of the ecliptic about
18° long. This is the value of the solar ecliptic limit. It is not a constant
quantity, but is greatest when perigee and perihelion occur at the
same time. As our satellite may reach the new-moon phase at any
time within this limit, and may therefore eclipse the sun at any distance
less than 18° from the moon's node, all degrees of solar eclipse
are possible. They will range from the merest notch cut out of the
sun's disk when he is remote from the node, to the central (annular
or total) eclipse when he is very near the node.
\Restore

\textbf{Two Solar Eclipses Certain Every Year.}\index{eclipses, solar!number in year}---As the solar
ecliptic limit is 18° on both sides of the moon's node, it is
plain that an eclipse of the sun of greater or less magnitude
is inevitable at each node, every year. For the
entire arc of possible eclipse is about 36°, and the sun
requires nearly 37~days to pass over it. If, therefore, new
moon occurs just outside of the limit west of the node (as
on the right in the figure just given), in $29\frac{1}{2}$~days she will
have made her entire circuit of the sky, and returned to
the sun. An eclipse (partial) at this new moon is certain,
because the sun can have advanced only a few degrees
east of the node, and is well within the limit. One solar
eclipse is therefore certain at each node every year.

\Smaller
If new moon falls just within the limit west of the node, two partial
solar eclipses are certain at that node; also two are possible in like
manner at the opposite node. Even a fifth solar eclipse in a calendar
\DPPageSep{306.png}
year may take place in extreme cases. For if the sun passes a node
about the middle of January, causing two eclipses then, two may also
happen in midsummer; and the westward motion of the node makes
the sun come again within the west limit in the month of December,
with a possibility of a fifth solar eclipse before the calendar year is out.
As two lunar eclipses also are certain in this period, the greatest possible
number of eclipses in a year is seven. But this happens only once
in about three centuries, the next occasion being the year 1935. The
number of eclipses in a year is commonly four or five.
\Restore

\textbf{Partial Solar Eclipses.}\index{eclipses, solar!partial}---When the moon comes almost
between us and the sun, she cuts off only a part of the
solar light, and a partial eclipse takes place.

% Fig 12.6
\begin{figure}[hbt!]
  \centering
  \Input{page_295}
  \caption{Solar Eclipse of 1887 (photographed in T\=oky\=o, Japan) \textit{Exposure of the maximum phase immediately above was too long and the negative was solarized}}
  \label{fig12.6}
\end{figure}

\Smaller
This happens when the sun is some distance removed from the node
of the lunar orbit. Figure~\ref{fig12.6} shows several advancing
and retreating stages of a partial eclipse. The degree of obscuration
is often expressed by digits, a digit being the twelfth part of the
sun's diameter. When there is a partial eclipse, it is only the moon's
penumbra which strikes the earth, consequently the partial eclipse will
be visible in greater or less degree from a large area of the earth's surface,
perhaps 2000 miles in breadth, if measured at right angles to the
shadow, but often double that width on the curving surface of our
\DPPageSep{307.png}
globe. This will be near the north pole or the
south pole according as the center of the moon
passes to the north or south of the center of the
sun. About 90 partial eclipses of the sun occur in
a century.
\Restore

\textbf{Annular Eclipses.}\index{eclipses, solar!annular}---If the sun is very
near the moon's node when our satellite
becomes new, clearly the moon must then
pass almost exactly
% Fig 12.7
\begin{wrapfigure}[19]{o}{0.25\textwidth}
  \centering
  \Input[0.25\textwidth]{page_296a}
  \caption{Annular Eclipse}
\end{wrapfigure}
between earth and
sun. If at the same time she is in apogee,
her apparent size is a little less than that
of the sun. Then her conical shadow
does not quite reach the surface of the
earth, and a ring of sunlight is left, surrounding
the dark moon completely. This
is called an annular eclipse because of the annulus, or
bright ring of sunlight still left shining.

\Smaller
Its greatest possible breadth
is about $\frac{1}{20}$ the sun's apparent
diameter. This ring may last
nearly $12\frac{1}{2}$~minutes under the
most favorable circumstances,
though its average duration is
about one third of that interval.
The illustration shows the
ring at five different phases.
Nearly 90 annular eclipses of
the sun take place every century.
These phenomena are
now recognized to be of exceptional
value, that of 10th
November, 1901, having added
appreciably to our knowledge
of the reversing layer (page~\pageref{p299}).
Only two annular
eclipses visit the United States
during the rest of the twentieth
century: 7th April, 1940, and
10th May, 1994.\index{eclipses, solar!dates of}
\Restore
\DPPageSep{308.png}

% Fig 12.8
\begin{wrapfigure}[16]{i}{0.4\textwidth}
  \centering
  \Input[0.325\textwidth]{page_296b}
  \caption{Phases of the Annulus (reduced from a Daguerreotype by Alexander)}
  \index{Alexander, S. (1806--83), Am.\ ast.}
\end{wrapfigure}
\textbf{Total Solar Eclipses.}\index{eclipses, solar!total}---Most impressive and important
of all obscurations of heavenly bodies is a total eclipse of
the sun. It takes place when the lunar shadow actually
reaches the earth as in the illustration. While the moon
passes eastward, approaching gradually the point where
she is exactly between us and the sun, steadily the darkness
deepens for over an hour, as more and more sunlight
is withdrawn. Then quite suddenly the darkness of
late twilight comes on, when the moon
reaches just the point where she first shuts
off completely the light of the sun. At
that instant, the solar corona\index{corona} flashes out,
and the total eclipse begins. The observer
is then inside the umbra, and totality lasts
only so long as he remains within it.
Total eclipses are sometimes so dark that
observers need artificial light in making
their records. In consequence of the motion
of the moon, the tip\break
\vspace{-\baselineskip}
%[** TN: Hack to place two wrapfigures in one paragraph]

% Fig 12.9
\begin{wrapfigure}{o}{0.25\textwidth}
  \centering
  \Input[0.25\textwidth]{page_297}
  \caption{Total Eclipse}\index{eclipses, solar!total}
\end{wrapfigure}
\noindent of the lunar
shadow, or umbra, makes a path or trail
across the earth, and its average breadth
is about 90~miles. The earth by its rotation
is carrying the observer eastward in
the same direction that the shadow is going. If he is
within the tropics, his own velocity is nearly half as great
as that of the shadow, so that it sweeps over him at cannon-ball
speed, never less than 1000 miles an hour. As an
average, the umbra will require less than three minutes to
pass by any one place, but the extreme length of a total
solar eclipse is very nearly eight minutes. Few have,
however, been observed to exceed five minutes in duration;
and no eclipses closely approaching the maximum duration
occur during the next $2\frac{1}{2}$~centuries. Total eclipses occurring
near the middle of the year are longest, if at the
\DPPageSep{309.png}
same time the moon is near perigee, and their paths fall
within the tropics. Always after total eclipse is over, the
partial phase begins again, growing smaller and smaller
and the sun getting continually brighter, until last contact
when full sunlight has returned. Nearly 70 total eclipses
of the sun take place every century. If the atmosphere
is saturate with aqueous vapor, weird color effects ensue,
by no means overdrawn in the frontispiece. \label{p298}

\Smaller
\textbf{The Four Contacts.}\index{contacts!in eclipses}---As the moon by her motion eastward overtakes
the sun, an eclipse of the sun always begins on the west side of the
solar disk. First contact occurs just before the dark moon is seen to
begin overlapping the sun's edge or limb. Theoretically the absolute
first contact can never be observed; because the instant of true contact
has passed, a fraction of a second before the moon's edge can be seen.
First contact marks the beginning of partial eclipse. If the eclipse is
total or annular, a long partial eclipse precedes the total or annular phase.
At the instant this partial eclipse ends, the total or annular eclipse
begins; and this is the time when second contact occurs. Usually
second contact will follow first contact by a little more than an hour.
If the eclipse is total, second contact takes place on the east side of the
sun; if annular, on the west side. Following second contact, by a very
few moments at the most, comes third contact: in the total eclipse, it
occurs at the sun's west limb; in the annular eclipse, at the east limb.
Students should represent the contacts by a diagram. Then from third
contact to last contact is a partial eclipse, again a little more than an
hour in duration---the counterpart of the partial eclipse between first
and second contacts. Fourth or last contact takes place at the instant
when the moon's dark body is just leaving the sun, and the interval between
first and fourth contacts is usually about 3 hours. If the eclipse
is but partial, only two contacts, first and last, are possible.
\Restore

\textbf{Young's Reversing Layer.}\index{reversing layer}\index{Young, C.~A.\ (1834--1908), Am.\ ast.}---According to the principles
of spectrum analysis, a gas under low pressure gives a
discontinuous spectrum composed of characteristic bright
lines. As the dark lines of the solar spectrum are produced
by absorption in passing through the atmosphere of the
sun, it occurred to Young that a total eclipse afforded an
opportunity to observe the bright-line spectrum of this
atmosphere by itself. Following is his description of this
\DPPageSep{310.png}
phenomenon, as seen for the first time in Spain, during
the total eclipse of 1870:---

\Smaller\label{p299}
`As the moon advances, making narrower and narrower the remaining
sickle of the solar disk, the dark lines of the spectrum for the most part
remain sensibly unchanged\ldots. But the moment the sun is hidden,
through the whole length of the spectrum, in the red, the green, the
violet, the bright lines flash out by hundreds and thousands, almost
startlingly; as suddenly as stars from a bursting rocket head, and as
evanescent, for the whole thing is over within two or three seconds. The
layer seems to be only something under a thousand miles in thickness.'
A like observation has been made on several occasions, and during the
eclipse of 1896 and later eclipses the bright lines have been successfully
photographed. This stratum of the solar atmosphere, known as
Young's reversing layer, is probably about 700~miles in thickness.
\Restore

\textbf{The Solar Corona.}\index{corona}---The corona is a luminous radiance
seen to surround the sun during total eclipses. The strong
illumination of our atmosphere precludes our seeing it at
all other times. The corona, as observed with the telescope,
is composed of a multitude of streamers or filaments,
often sharply defined, and sometimes stretching out into
space from the disk of the sun millions of miles in length.
For the most part these streamers are not arranged radially,
and often the space between them is dark, close down to
the disk itself. The general light of the corona averages
about three times that of the full moon; but the amount of
this light varies from one eclipse to another, just as the
form and dimensions of the streamers do. The coronal
light, very intense close to the sun, diminishes rapidly outward
from the disk, so that the object is a very difficult
one to photograph distinctly in every part on a single
plate. The corona appears to be at least triple; there are
polar rays nearly straight, inner equatorial rays sharply
curved, and often outer equatorial streamers, perhaps connected
in origin with the zodiacal light. The last are not
visible at every eclipse, and they were first successfully
\DPPageSep{311.png}
photographed in India during the total eclipse of 1898.
Recent photographs of the corona show no variation in
form from hour to hour. As yet no theory of this
marvelous object explains the phenomena satisfactorily.
Neither a magnetic theory advanced by Bigelow\index{Bigelow, F. H., U. S. Weather Bureau}, nor a
mechanical one by Schaeberle\index{Schaeberle, J.~M.\ (sheb´bur-ly), Am.\ ast.}, has successfully predicted
its general form. The brighter filaments may be due to
electric discharges. Total eclipses permit only a few
hours' advantageous study of the corona, in a century.

\textbf{The Spectrum of the Corona.}\index{corona!spectrum}\index{spectrum|see{corona, spectrum}}---Our slight knowledge of
the corona is for the most part based on evidence furnished
by the spectroscope.

\Smaller
Its light gives a faint continuous spectrum, showing incandescent
liquid or solid matter; and a superposed spectrum of numerous bright
lines indicating luminous gases, among them hydrogen. Also, in the
violet and ultra-violet
% Fig 12.10
\begin{wrapfigure}[17]{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_300}
  \caption{Corona of 1871 (Lord Lindsay)}\index{corona}
  \index{Lindsay, Lord, Scot.\ noble and ast.}
\end{wrapfigure}
are numerous bright lines. But the characteristic
line of the coronal spectrum
is a bright double one in the
green, often called the `1474
line,' erroneously, and now
known as 5303.7. Calcium
and helium are not present.
The bright lines are mainly due
to a supposed element called
`coronium'\index{coronium} existing in a gaseous
form in the corona, only
recently recognized on the
earth. Also there are dark
lines, indicating much reflected
sunlight, possibly coming from
meteoric matter surrounding
the sun. Deslandres\index{Deslandres, H.\ (day-londr´), ast.\ Meudon Obs.}, by photographing
on a single plate
the spectrum of the corona on
opposite sides of the sun, obtained a displacement of its bright line,
snowing that eastern filaments are approaching the earth, and western
receding from it; and the calculated velocities indicate that the corona
revolves with the sun\index{corona!rotation}. Independent proof of the solar origin of the
corona is thus afforded.
\Restore
\DPPageSep{312.png}

% Fig 12.11, 12
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.49\textwidth}
    \centering
    \vspace{2ex}
    \Input {page_301a}
    \caption{Corona of 1882 (Schuster and Wesley)}
    \label{p301}\index{Schuster, A., Prof.\ Victoria Univ.}
    \index{Wesley, W.~H., Libr.\ Roy.\ Ast.\ Soc.}
  \end{minipage}
  \hfill
  \begin{minipage}{0.49\textwidth}
    \centering
    \Input {page_301b}
    \caption{Corona of 1893 (Deslandres)}\index{Deslandres, H.\ (day-londr´), ast.\ Meudon Obs.}
  \end{minipage}
\end{figure}

% Fig 12.13, 14
\begin{figure}[ht!]
  \centering
  \begin{minipage}{0.49\textwidth}
    \centering
    \Input[0.95\textwidth]{page_302a}
    \caption{Corona of 1878 (Harkness)}
    \label{p302}\index{Harkness, W.\ (1837--1903), Am.\ ast.}
  \end{minipage}
  \hfill
  \begin{minipage}{0.49\textwidth}
    \centering
    \Input {page_302b}
    \caption{Corona of 1889 (Pritchett)}\index{Pritchett, H.~S., Am.\ ast.}
  \end{minipage}
\end{figure}

\textbf{Periodicity of the Corona.}\index{corona!periodicity}---At no two eclipses of the
sun is the corona alike. How rapidly it varies is not yet
found out, but observations
of the total eclipse
of 1893 showed that the
corona was exactly the
same in Africa as when
photographed in Chile
$2\frac{1}{2}$~hours earlier. Slow
periodic variations are
known to take place,
seeming to follow the
11-year cycle of the spots
on the sun. At the time
of maximum spots, the
corona is made up of an
abundance of short, bright, and interwoven streamers,
rather fully developed all around the sun, as in these
three photographs (India
1871, Egypt 1882, and
Africa 1893). At or near
the sun-spot minimum,
on the other hand, the
corona is unevenly developed:
there are beautiful,
short, tufted
streamers\index{corona!streamers} around the
solar poles, and outward
along the ecliptic extend
the streamers, millions
of miles in length, as
pictured in the photographs
%(\vpageref*{p302})
of total eclipses in the United States in
1878 and 1889. A similar form was repeated in the eclipse
\DPPageSep{313.png}
of 1900, so the cycle is established; but no sufficient explanation
of this periodicity of the corona has yet been given.

\textbf{Important Modern
Eclipses of the Sun.}\index{eclipses, solar!dates of}---Not
until the European
eclipse of 1842 did the
true significance of circumsolar
phenomena
begin to be appreciated.
In the eclipses of 1851
and 1860 it was proved
that prominences and
corona belong to the sun,
and not to the moon.
Just after the eclipse of
1868 (India) was made
the important discovery that prominences can be observed
at any time without an eclipse by means of the spectroscope.
In 1869 (United
States), bright lines were
found in the spectrum of
the corona\index{corona!spectrum}, one line in
the green showing the
presence of an element
not then known on the
earth, and hence called
\textit{coronium}\index{coronium}. In 1870
(Spain), the reversing
layer\index{reversing layer} was discovered, and
in 1878 (United States),
a vast extension of the
coronal streamers about
11~million miles both east and west of the sun (shown
above only in part). In 1882 (Egypt), the spectrum of the
\DPPageSep{314.png}
corona was first photographed; and in 1889 (California),
fine detail photographs of the corona were obtained. In
1893 (Africa), it was shown that the corona probably
rotates bodily with the sun; in 1896 (Nova Zembla), actual
spectrum photographs of the reversing layer established its
existence conclusively; and in 1898 (India), the long ecliptic
streamers of the corona were for the first time successfully
photographed. In 1900 (the southern United States,
Spain, Algiers, and Tripoli) periodicity in the form of
the corona for the epoch of minimum spots was definitely
ascertained; in 1901 (Mauritius, Sumatra, and Singkep),
the new gases argon, neon, krypton, and xenon were revealed
in the sun's chromosphere; and in 1905 (Spain,
Tunis, Tripoli, and Egypt), periodicity in the form of the
corona for the epoch of maximum spots was finally established.
Numerous observations have been made tending
to show that certain streamers of the corona are intimately
associated with adjacent sunspots and prominences; also
that other streamers seem to partake in part of the nature
of electric discharges.

\Smaller
\textbf{Observations during Total Eclipses.}---Observations of importance
at future eclipses are as follows, in large part photographic:---

1. Contacts and photographs for correcting the tables of the moon's
motion.

2. Spectrum of the `flash' at the beginning and end of totality.

3. Spectrum of the corona in different regions near the moon's limb---for
its rotation\index{corona!rotation} and constitution.

4. Photographs of the corona, with varied exposure in different
parts---correctly timed, if possible, at all distances from the moon's
limb.

5. Polarization and photometry of the corona.

6. Measurement of its heat radiations with the bolometer.

7. Observations of the shadow bands, just before, after, and during
totality.

8. Electrical conditions of the air.
\DPPageSep{315.png}

9. Terrestrial magnetic currents.

10. Temperature, barometric pressure, and direction of the wind.
\Restore

\textbf{Important Future Eclipses.}\index{eclipses, solar!prediction of}\index{eclipses, solar!dates of}---Total eclipses of the sun
in the coming quarter century are for the most part visible
in foreign lands. The paths of very few cross the United
States. Following are dates of important eclipses, regions
of general visibility, and approximate duration of the total
phase:---
\begin{center}
\TableSize
\begin{tabular}{llc}
                     &amp;                               &amp; min. \\
1907, January 14     &amp; Turkestan and Mongolia        &amp; 2 \\
1912, October 10     &amp; Ecuador and Brazil            &amp; 2 \\
1914, August 21      &amp; Norway, Sweden, and Russia    &amp; 2 \\
1916, February 3     &amp; Colombia and Guadeloupe       &amp; 3 \\
1918, June 8         &amp; Oregon to Florida             &amp; 2 \\
1919, May 29         &amp; Brazil, Liberia, and Congo    &amp; 7 \\
1922, September 21   &amp; West Australia and Queensland &amp; 6 \\
1923, September 10   &amp; Lower California and Mexico   &amp; 4 \\
1925, January 24     &amp; Duluth to New Haven, Conn.    &amp; 2 \\
1926, January 14     &amp; Sumatra and Borneo            &amp; 4 \\
1927, June 29        &amp; England, Norway, and Lapland  &amp; 1 \\
1929, May 9          &amp; Sumatra and the Philippines   &amp; 5 \\
1932, August 31      &amp; James Bay, Quebec, and Maine  &amp; 2 \\
\end{tabular}
\end{center}

% Fig 12.15
\begin{figure}[hbt!]
  \centering
  \Input[0.7\textwidth]{page_304}
  \caption{Earth's Shadow and Penumbra in Section}
  \index{shadows of heavenly bodies}
\end{figure}\index{eclipses, solar|)}

Exact times and circumstances of all these eclipses are
\DPPageSep{316.png}
regularly published in the Nautical Almanacs, issued by
the English, German, French, and American governments
(p.~\pageref{p170}). The great total eclipses of 1955 (Luzon) and
1973 (Sahara) will be $7\frac{1}{2}$~minutes in duration, the longest
for a thousand years.

\textbf{Eclipses of the Moon.}\index{moon|see{eclipses, lunar}}\index{eclipses, lunar}---As all dark celestial bodies cast
long, conical shadows in space, any non-luminous body
passing into the shadow of another is necessarily darkened
or eclipsed thereby. When, in her journey round our earth,
the moon comes exactly opposite the sun, or nearly so, she
% Fig 12.16, 17
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.4\textwidth}
    \centering
    \Input {page_305a}
    \caption{Lunar Eclipse of $10\frac{1}{2}$ Digits}
  \end{minipage}
  \hfil
  \begin{minipage}{0.4125\textwidth}
    \centering
    \Input {page_305b}
    \caption{Lunar Eclipse one Digit short of Totality}
  \end{minipage}\index{eclipses, lunar}
\end{figure}
passes through our shadow. Then a lunar eclipse takes
place. Refer to illustrations given on pages \pageref{p290} and \pageref{p291}:
clearly, a lunar eclipse can happen only when the moon
is full, or at opposition. There is not an eclipse of the
moon every month, because unless she is near the plane
of the ecliptic, that is, near her node at the time, she
will pass above or below the earth's shadow. There are
partial eclipses of the moon as well as of the sun; but in
this case the eclipse is partial because the moon passes
only through the edge of our shadow (lower orbit in the
illustration opposite), and so is not wholly darkened. The
eclipse may be total, however (upper of the three orbits),
without our satellite passing directly through the center of
the earth's shadow, because that shadow, where the moon
\DPPageSep{317.png}
passes through it, is nearly three times the moon's own
diameter. A lunar eclipse is always visible to that entire
hemisphere of our globe turned moonward at the time.
The total phase lasts nearly two hours, and the whole
eclipse often exceeds three hours in duration.

\Smaller
The magnitude of a lunar eclipse is often expressed by digits, that
is, the number of twelfths of the moon's diameter which are within the
earth's umbra. The last illustrations show different magnitudes of
lunar eclipse; note the roughness of the terminator. Also the same
thing may be expressed decimally, an eclipse whose magnitude is 1.0
occurring when the moon enters the dark shadow for a moment, and at
once begins to emerge.

\textbf{Diameter of the Earth's Shadow.}\index{shadows of heavenly bodies}---As the mean distance of our
satellite is 239,000 miles, the earth's shadow must extend into space
beyond the moon a distance equal to the moon's distance subtracted
from the length of the shadow, or 618,000 miles. The diameter of the
earth's shadow where the moon traverses it during a lunar eclipse may,
therefore, be found from the proportion
\[
857,000 : 7900 :: 618,000 : x.
\]
This gives 5700 miles, or $2\frac{2}{3}$ times the moon's diameter. As our satellite
moves over her own diameter in about an hour, a central eclipse
may last about four hours, from the time the moon first begins to enter
shadow to the time of complete emersion from it.

\textbf{Lunar Ecliptic Limit.}\index{ecliptic limit!lunar}---As our satellite revolves round us in a plane
inclined to the ecliptic, it is evident that there must be a great variety
% Fig 12.18
\begin{figure}[hbt!]
  \centering
  \Input{page_306}
  \caption{Lunar Ecliptic Limit West of Moon's Ascending Node}
  \index{ecliptic limit!lunar}
\end{figure}
of conditions under which eclipses of the moon take place. All depends
upon the distance of the center of the earth's shadow from the node of
the moon's orbit at the time of full moon. The illustration helps to
make this point plain. It shows a range in magnitude of eclipse, from
the total and central obscuration (on the left), to the circumstances
which just fail to produce an eclipse (on the right). The arc of the
\DPPageSep{318.png}
ecliptic, about 12° long, included between these two extremes, is called
the lunar ecliptic limit. It varies in length with our distance from the
sun; evidently the farther we are from the sun, the larger will be the
diameter of the earth's shadow. Also the lunar ecliptic limit varies
with the moon's distance from us; because the nearer she is to us, the
greater the breadth of our shadow which she must traverse. Inside of
this limit, the moon may come to the full at any distance whatever from
the nodes. Clearly there is a limit of equal length to the east of the
node also; and the entire range along the ecliptic within which a lunar
eclipse is possible is nearly 25°. As the sun (and consequently the
earth's shadow) consumes about 26~days in traversing this arc, there is
an interval of nearly a month at each node, or twice a year, during
which a lunar eclipse is possible.
\Restore

\textbf{The Moon still Visible although Eclipsed.}\index{eclipses, lunar!moon visible during}---Usually the
moon, although in the middle of the earth's shadow where
she can receive no direct
% Fig 12.19
\begin{wrapfigure}{o}{0.3\textwidth}
  \centering
  \Input[0.3\textwidth]{page_307}
  \caption{Total Lunar Eclipse, 3d September, 1895 (photographed by Barnard)}
  \index{Barnard, E. E., Prof.\ Univ.\ Chicago}\index{eclipses, lunar!total}
\end{wrapfigure}
light from the sun, is nevertheless
visible because of a faint, reddish brown illumination.
Probably this is due to light refracted through the earth's
atmosphere all around the sunrise and sunset line. Atmosphere
absorbs nearly all the bluish
rays, allowing the reddish ones to pass
quite freely.

\Smaller
\index{eclipses, lunar!dates of}Naturally, if this belt of atmosphere were perfectly
clear, the darkened portion of the moon
might be plainly visible as in the picture of
the eclipse of 1895 (page~\pageref{p308}), while if it were
nearly filled with cloud, very little light could
pass through and fall upon the moon; so that
when she had reached the middle of the
shadow, she would totally disappear. Accordingly
there are all variations of the moon's
visibility when totally eclipsed; in 1848, so
bright was it that some doubted whether there
really was an eclipse; while in 1884 the coppery
disk of the moon disappeared so completely
that she could scarcely be seen with the telescope. In September 1895
the moon, even when near the middle of our shadow, gave light enough
to enable Barnard to obtain this photograph of the total eclipse, by
making a long exposure, which accounts for the stars being trails
instead of mere dots; for the clockwork was made to follow the moving
\DPPageSep{319.png}
moon. Total lunar eclipses are of use to the astronomer in measuring
the variation of heat radiated at different phases of the eclipse.
Also the occultations of faint stars can be accurately observed, as the
moon's disk passes over them; and by combining a large number of
these observations at widely different parts of the earth, the moon's size
and distance can be more precisely ascertained. The total eclipses of
our satellite in 1888, 1895, and 1898 were successfully utilized in this
manner. By consulting the almanac, the times of the phases of lunar
eclipses can be ascertained; also the regions of the globe where they
may be visible. But these phenomena cannot be observed very accurately,
because the earth's penumbra is never sharply defined on the moon.
% Fig 12.20
\begin{figure}[hbt!]
  \centering
  \Input{page_308}
  \caption{Lunar Eclipse just before Totality, observed at Amherst College, 10th March, 1895}
  \label{p308}
  \index{Amherst College!lunar eclipse at}
\end{figure}

\textbf{Relative Frequency of Solar and Lunar Eclipses.}\index{eclipses, lunar!frequency of}\index{eclipses, solar!frequency of}---Draw lines tangent
to sun and earth, as in next figure. An eclipse of the moon takes place
whenever
% Fig 12.21
\begin{wrapfigure}[9]{i}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_309}
  \caption{More Solar than Lunar Eclipses}
\end{wrapfigure}
our satellite, near $M'$, passes into the dark shadow cone. On
the other hand, when near $M$, a solar eclipse happens if the moon
touches any part of the earth's shadow cone extended sunward from
\DPtypo{E}{$E$}.
As the breadth of this shadow cone is greater at $M$ than at $M'$, obviously
the moon must pass within it more often at $M$; that is,
eclipses of the sun are more frequent than eclipses of the moon. Calculation
shows that the relative frequency is about as 4 to 3. This
\DPPageSep{320.png}
means simply with reference to the earth as a whole. If, however, we
compare the relative frequency of solar and lunar eclipses visible in a
given country, it will be found that lunar eclipses are much more often
seen than solar ones. This is
because some phase of every
lunar eclipse is visible from
more than half of our globe,
while a solar eclipse can be seen
from only that limited part of
the earth's surface which is
traversed by the moon's umbra and penumbra. If we consider the
narrow trail of the umbra alone, a total solar eclipse will be visible from
a given place only once on the average in 350~years.

\textbf{Eclipse Seasons.}\index{eclipse seasons}---It has been shown that eclipses of sun and moon
can happen only when the sun is near the moon's node. Were these
points stationary, it is clear that eclipses would always take place near
the same time every year. But the westward motion of the nodes is
such that they travel completely round the ecliptic in $18\frac{2}{3}$~years. The
sun, then, does not have to go all the way round the sky in order to
return to a node; and the interval elapsing between two consecutive
passages of the same node is only $346\frac{2}{3}$~days. This is called the eclipse
year. Eclipses at a given node, then, happen nearly three weeks
earlier each calendar year. The midyear eclipses of 1899 took place
in June, of 1900 and 1901 in May. Each passage of a node marks
the middle of a period during which the sun is traveling over an arc
equal to double the ecliptic limit. No eclipse can happen except at
these times. They are, therefore, called \textit{eclipse seasons}. As the solar
ecliptic limit exceeds the lunar, so the season for eclipses of the sun
exceeds that for lunar eclipses: the average duration of the former is
37~days, and of the latter 23.
\Restore

\textbf{Recurrence and the Saros.}\index{eclipses, solar!prediction of}\index{eclipses, solar!recurrence}\index{eclipses, lunar!recurrence}\index{Saros, cycle of eclipses}---Ever since the remote age
of the Chaldeans, \BC~700, has been known a period called
the saros, by which the return of eclipses can be roughly
predicted. The length of the saros is $6585\frac{1}{3}$ days, or 18
years $11\frac{1}{3}$~days. At the end of this period, the centers of
sun and moon return very nearly to their relative positions
at the beginning of the cycle; also certain technical conditions
relating to the moon's orbit and essential to the
accuracy of the saros are fulfilled. Solar and lunar eclipses
are alike predictable by it.
\DPPageSep{321.png}

\Smaller
A total eclipse of the sun occurred in the southern United States,
28th May, 1900; and reckoning forward from that date by means of the
saros, we might predict the eclipses of 8th June, 1918, and 19th June,
1936. But only in a general way; if the precise circumstances of the
eclipse are required, and the places where it will be visible, a computation
must be made from the Ephemeris, or Nautical Almanac. Mark
the effect of the one third day in the saros: the eclipse at each recurrence
falls visible about 120° of longitude farther west; in 1900 visible
in the United States, in 1918 on the Pacific Ocean, in 1936 in central
Asia. A period of 54~years 1~month 1~day, or three times the length of
the saros, will therefore bring a return of an eclipse in very nearly the
same longitude, but its track will always be displaced several hundred
miles in latitude. For example, the total eclipse of 8th July, 1842, was
observed in central Europe; but its return, 9th August, 1896, fell visible
in Norway. About 70 eclipses usually take place during a saros, of
which about 40 are eclipses of the sun, and 30 of the moon.

\textbf{Life History of an Eclipse.}\index{eclipses, solar!life history of}---As to eclipses in their relation to the
saros, every eclipse may be said to have a life history. Whatever its
present character, whether partial, total, or annular, it has not always
been so in the past, nor will its character continue unchanged in the
indefinite future. New and very small partial eclipses of the sun are
born at the rate of about four every century; they grow to maturity as
total and annular eclipses, and then decline down their life scale as
merely partial obscurations, becoming smaller and smaller until even
the moon's penumbra fails to touch the earth, and the eclipse completely
disappears. For a lunar eclipse, this long cycle embraces nearly 900
years, that is, the number of returns according to the saros is almost
50; but solar eclipses, for which the ecliptic limit is larger, will return
nearly 70 times, and last through a cycle of almost 1200 years.

\textbf{Occultations of Stars and Planets by the Moon.}\index{occultations}---Closely allied to
eclipses are the phenomena called occultations. When the moon comes
in between the earth and a star or planet, our satellite is said to occult
it. There are but two phases, the disappearance and the reappearance;
and in the case of stars, these phases take place with startling suddenness.
Disappearances between new and full, and reappearances between full
and new, are best to observe, because they take place at the dark edge
or limb of the moon. When the crescent is slender, a very small telescope
is sufficient to show these interesting phenomena for the brighter
stars and planets. Occultations of the Pleiades are most interesting and
important. Many hundreds of occultations of stars are predicted in the
Nautical Almanac each year. Occultations of the major planets are
very rare.
\Restore
\DPPageSep{322.png}


\Chapter{XIII}{The Planets}\index{planets}

Tethered by an overmastering attraction to the
central and massive orb of the solar system are a
multitude of bodies classified as planets. Next
beyond the moon, they are nearest to us of all the heavenly
spheres, and telescopes have on that account afforded
astronomers much knowledge concerning them. But before
presenting this we first consider their motions, and the
aspects and phases which they from time to time exhibit.

\Section{Motions---Classification---Aspects---Phases}

\textbf{Apparent Motions of the Planets.}\index{planets!apparent motions}---Watch the sky from
night to night. Nearly all the bright stars, likewise the
faint ones, appear to be fixed on the revolving celestial
sphere; that is, they do not change their positions with
reference to each other. But at nearly all times, one or
two bright objects are visible which evidently do not belong
to the great system of the stars considered as a whole;
these shift their positions slowly from week to week, with
reference to the fixed stars adjacent to them. The most
ancient astronomers detected these apparent motions, and
gave to such bodies the general name of planets; that is,
wanderers. Their movements among the stars appear to
be very irregular---sometimes advancing toward the east,
then slowing down and finally remaining nearly stationary
for different lengths of time, and again retrograding, that
\DPPageSep{323.png}
is, moving toward the west. But their advance motion
always exceeds their motion westward, so that all, in greater
or less intervals, journey completely round the heavens.
None of the brighter ones are ever found outside of the
zodiac; in fact, Mercury, which travels nearest to the edge
of this belt, is always about two moon breadths within it.
A study of the apparent motions of all the planets reveals
a great variety of curves. If the motions of the planets
could be watched from the sun, there would be no such
complication of figures; for they exist only because we
observe from the earth, itself one of the planets, and continually
in motion as the other sun-bound bodies are.

\textbf{Planets' Motions explained by the Epicycle.}\index{epicycle}\index{planets!motion (in epicycle)}---The irregular
motions of the
planets among the
stars were ingeniously
explained
by the
% Fig 13.1
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.6\textwidth]{page_312}
  \caption{A Planet's Motion in the Epicycle}\index{epicycle}
  \index{planets!motion (in epicycle)}
\end{wrapfigure}
ancient
astronomers from
the time of Hipparchus\index{Hipparchus (\BC~140), Gk.\ ast.} (\BC~130)
onward, by means
of the epicycle.
A point which
moves uniformly
round the circumference
of a small
circle whose center
travels uniformly
round the periphery of a large one, is said to
describe an epicycle.

\Smaller
The figure should make this plain: the center, \textit{c}, of the small circle,
called the epicycle, moves round the center \textit{t} of the large circle, called
the \textit{deferent}\index{deferent circle}; and at the end of each 24th part of a revolution, it occupies
\DPPageSep{324.png}
 successively the points 1, 2, 3, 4, 5, and so on. But while $c$ is moving
to 1, the point $a$ is traversing an arc of the deferent equal to $a_1b_1$.
By combination of the two motions, therefore, the point $a$ will traverse
the heavy curve, reaching the points indicated by $b_1$, $b_2$, $b_3$, $b_4$, $b_5$, when
$c$ arrives at corresponding points 1, 2, 3, 4, 5. In passing from $b_2$ to
$b_4$ the planet will turn backward, or seem to describe its retrograde
arc among the stars. By combining different rates of motion with circles
of different sizes, it was found that all the apparent movements of
the planets could be almost perfectly explained. This false system\index{Ptolemaic system},
advanced by Ptolemy (\AD~140)\index{Ptolemy@Ptolemy, C. (tol´-em-mi) (\AD~140), Alex.\ ast.} in his great work called the \textit{Almagest}\index{Almagest|see{Ptolemy}}\index{Ptolemy@Ptolemy, C. (tol´-em-mi) (\AD~140), Alex.\ ast.!Almagest},
was in vogue until overthrown by Copernicus\index{Copernicus, N. (1473-1534), Ger.\ ast.} on the publication of his
great work \textit{De Revolutionibus Corporum Coelestium} in 1543.
\Restore

\textbf{Naked-eye Appearance of the Planets.}---Mercury\index{Mercury!naked-eye appearance}\index{planets!naked-eye appearance} can
often be seen in all latitudes of the United States by
looking just above the eastern horizon before sunrise
(in August, September, or October), or just above the
western horizon after sunset (in February, March, or
April). In these months the ecliptic stands at a very
large angle with the horizon, and Mercury will appear as
a rather bright star in the twilight sky, always twinkling
violently. Venus\index{Venus!naked-eye appearance}, excepting sun and moon the brightest
object in the sky, is known to everybody. She is always so
much brighter than any of the other planets that she cannot
be mistaken---either easterly in the early mornings or
westerly after sunset, according to her orbital position relatively
to the earth. Usually, when passing near the sun,
Venus cannot be seen because the sun overpowers her
rays. During periods of greatest brilliancy, however,
Venus is not difficult to see with the naked eye when near
the meridian in a clear blue sky. Mars\index{Mars!naked-eye appearance}, when visible, is
always distinguishable among the stars by a brownish
red color. Distance from both earth and sun varies so
greatly that he is sometimes very faint, and again when
nearest, exceedingly bright. Jupiter\index{Jupiter!naked-eye appearance} comes next to Venus
in order of planetary brightness. Though much less bright
than Venus, he is still brighter than any fixed star. Saturn\index{Saturn!naked-eye appearance}
\DPPageSep{325.png}
is difficult to distinguish from a star, because he shines
with about the order of brightness of a first magnitude
star. His light has a yellowish tinge, and by looking
closely, absence of twinkling will be noticed. Unless very
near the horizon, none of the planets except Mercury ever
twinkle; and this simple fact helps to distinguish them
from fixed stars near them. Uranus\index{Uranus!naked-eye appearance}, just on the limit of
visibility without the telescope may be seen during spring
and summer months, if one has a keen eye and knows
just where to look. Also Vesta\index{Vesta, small planet}, one of the small planets,
may at favorable times be seen without a telescope. Neptune
is never visible without optical aid.

\textbf{Convenient Classifications of the Planets.}\index{planets!classifications}---Neither apparent
motion, nor naked-eye appearance, however, affords
any basis for classification of the planets. But distance
from the sun and size do. In order of distance, succession
of the eight principal planets with their symbols is as
follows, proceeding from the sun outward:---

$\mercury$ Mercury, $\venus$~Venus, $\earth$~Earth, $\mars$~Mars, $\jupiter$~Jupiter,
$\saturn$~Saturn, $\uranus$~Uranus, $\neptune$~Neptune. Of these, Mercury and
Venus, whose orbits are within the earth's, are classified as
inferior planets\index{planets!inferior}, and the other five from Mars to Neptune,
as superior planets\index{planets!superior}. In the same category would be included
the ring of asteroids, or small planets, between Mars
and Jupiter. The real motions of the planets round the
sun are counter-clockwise, or from west toward east.

Also the planets are often conveniently classified in
three distinct groups:---

(I) The inner or terrestrial planets, Mercury, Venus,
Earth, Mars\index{planets!terrestrial}; also the unverified intramercurian bodies\index{planets!intramercurian}.

(II) The asteroids\index{asteroids}, or small planets, sometimes called
planetoids, or minor planets\index{planets!small}\index{planets!minor}.

(III) The outer or major planets, Jupiter, Saturn,
Uranus, Neptune\index{planets!major}\index{planets!exterior}.
\DPPageSep{326.png}

\Smaller
In this classification the zone of asteroids forms a definite line of
demarcation; but the basis is chiefly one of size, for all the terrestrial
planets are very much smaller than the outer or major planets. Here
may be included also the zodiacal light\index{zodiacal light}, and the \textit{gegenschein}\index{gegenschein (gay´gen-shine)}, both faint,
luminous areas of the nightly sky. Probably their light is mere sunlight
reflected from thin clouds of meteoric matter entitled to consideration
as planetary bodies, because, like the planets, each particle must
pursue its independent orbit round the sun. All the planetary bodies
of whatever size, together with their satellites, the sun itself, and multitudes
of comets and meteors, are often called the solar system\index{solar system!described}.
\Restore

\textbf{Configurations of Inferior Planets.}\index{planets!inferior, configuration}\index{planets!configurations}---In consequence of
their motions round the central orb, Mercury\index{Mercury!conjunctions} and Venus\index{Venus!conjunctions}
% Fig 13.2
\begin{figure}[hbt!]
  \centering
  \Input[0.7\textwidth]{page_315}
  \caption{Aspects of Inferior and Superior Planets}
  \label{p315}\index{planets!aspects}\index{planets!superior}\index{planets!inferior}
\end{figure}
regularly come into line with earth and sun, as illustrated
in above diagram. If the planet is between us and the
sun, this configuration is called \textit{inferior conjunction}\index{conjunction!planets'}\index{planets!conjunction}; \textit{superior
conjunction}, if the planet is beyond that luminary.
At inferior conjunction, distance from earth is the least
possible; at superior conjunction, the greatest possible.
On either side of inferior conjunction the inferior planets
attain greatest brilliancy\index{Mercury!greatest brilliancy}\index{Venus!greatest brilliancy}; with Mercury this occurs about
three weeks, and with Venus about five weeks, preceding
and following inferior conjunction. For many days near
\DPPageSep{327.png}
this time, Venus is visible in the clear blue even at midday;
but in a dark sky her radiance is almost dazzling,
and with every new recurrence she deceives the uneducated
afresh.

\Smaller
Near her western elongation, in 1887--88, many thought she was the
`Star of Bethlehem'; and in 1897 multitudes in New England gave
credence to a newspaper story that the brilliant luminary was an electric
light attached to a balloon sent up from Syracuse, and hauled down
slowly every night about 9~\PM\ The following are times of greatest
brilliancy of Venus:---

Elongation east, and visible after sunset: May, 1908; Jan., 1910;
Aug., 1911; Mar., '13; Oct., '14; May, '16; Dec., '17; Aug., '19.

Elongation west, and visible before sunrise: Jan., 1907; Aug., 1908;
Mar., 1910; Oct., '11; June, '13; Jan., '15; Aug., '16; Mar., '18; Oct., '19.
\Restore

\textbf{Greatest Elongation of Inferior Planets.}\index{Mercury!greatest elongation}\index{Venus!greatest elongation}\index{planets!elongation}---An inferior
planet is at greatest elongation when its angular distance
from the sun, as seen
from
% Fig 13.3
\begin{wrapfigure}[18]{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_316}
  \caption{Inferior Planets at Greatest Elongation East (after Sunset in Spring)}
  \label{p316}
\end{wrapfigure}
the earth, is as great
as possible. The following
illustrations help to
make these points clear.
The earth is at the eye
of the observer, and a
thin disk about 18~inches
in diameter, and held
about one foot from the
eye, represents the plane
of the orbits of the inferior
planets. They
travel round with the
arrows, passing superior
conjunction when farthest away from the eye, and therefore
of their smallest apparent size. Coming round to
greatest elongation, they are nearer and larger, and their
phase is that of the quarter moon. The angle between
\DPPageSep{328.png}
Venus and the sun is then 47°. Mercury at a like phase
may be as much as 28° distant; but his orbit is so eccentric
that if he is near perihelion at the same time, he
may be only 18° from the sun.

\Smaller
Passing on to inferior conjunction, the phase is a continually
diminishing crescent, of a gradually increasing diameter, as shown.
The figure \vpageref{p316} represents
the apparent position of the orbits
(relative to horizon) when
the greatest eastern elongations
occur in our springtime.
The observer is looking west
at sunset, and the planets at
elongation shine far above the
horizon in bright twilight, and
are best and most conveniently
seen. When greatest elongations
west of the sun occur,
one must look eastward for
them, before sunrise, as in the
adjacent illustration (autumn
inclination to east horizon).
The ancients early knew that
Venus in these two relations
was one and the same planet;
but they preserved the poetic distinction of a double name,---Phosphorus
for the morning star, and Hesperus for the evening.
\Restore

\textbf{Configurations of Superior Planets.}\index{planets!superior, configuration}\index{planets!configurations}---By virtue of the
position of superior planets outside our orbit, they may
recede as far as 180° from
% Fig 13.4
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_317}
  \caption{Inferior Planets at Greatest Elongation West (before Sunrise in Autumn)}
\end{wrapfigure}
the sun. Being then on the
opposite side of the celestial sphere, they are said to be in
opposition\index{opposition of planets}\index{planets!opposition} (page~\pageref{p315}). When in the same part of the
zodiac with the sun, they are in conjunction\index{conjunction!planets'}. Halfway
between these two configurations a superior planet is in
quadrature\index{planets!quadrature}\index{quadrature|see{planets, qudrature}}; that is, an elongation of 90° from the sun.
Opposition, conjunction, and quadrature usually refer to
the ecliptic, and the angles of separation are arcs of
celestial longitude, nearly. Sometimes, however, it is
\DPPageSep{329.png}
necessary to use \textit{conjunction in right ascension}\index{conjunction!in right ascension}. Inferior
planets never come in opposition or even quadrature, because
their greatest elongations are much less than 90°.

\textbf{The Phases of the Planets.}\index{planets!phases}---Some of the planets, as
observed with the telescope, are seen to pass through all
the phases of the moon. Others are seen at times to
resemble certain lunar phases; while still others have no
% Fig 13.5
\begin{figure}[hbt!]
  \centering
  \Input{page_318}
  \caption{Phases and Apparent Size of the Planet Mercury}
  \label{p318}
\end{figure}
phase whatever. To the first class belong the inferior
planets, Mercury\index{Mercury!phase} and Venus\index{Venus!phase}. On approaching inferior
conjunction, their crescent becomes more and more
slender, like that of the very old moon when coming to
new; while from inferior conjunction to superior conjunction,
they pass through all the lunar phases from new to
full. As in the case of the moon, the horns of the crescent
are always turned from the sun (toward it, as seen in
the inverting telescope). When near their greatest elongation,
the phase of these planets is that of the moon at
quarter. One of Galileo's\index{Galile´i, G. (1564--1642), It.\ ast.} first discoveries with the first
astronomical telescope, in 1610, was the phase of Venus.
None of the superior planets can pass through all the
phases of the moon, because they never can come between
us and the sun.

\Smaller
The degree of phase which they do experience, however, is less in
proportion as their distance beyond us is greater. Mars, then, has the
greatest phase. At quadrature the planet is gibbous, about like the moon
three days from full. Mars\index{Mars!phase} appears at maximum phase in Figure~\ref{fig13.35}.
But at opposition, his disk\index{planets!disk of}, like that of all other planets,
appears full. Some of the small planets, too, give evidence of an
appreciable phase: not that it can be seen directly, for their disks are
\DPPageSep{330.png}
too small, but by variation in the amount of their light from quadrature
to opposition, as Parkhurst has determined. Jupiter at quadrature
has a slight, though almost inappreciable, phase\index{Jupiter!phase}. Other exterior
planets---Saturn\index{Saturn!phase}, Uranus, and Neptune---have practically none.

\textbf{Loop of a Superior Planet's Apparent Path Explained.}\index{planets!superior, loop of path}\index{planets!loop of path}---Refer to the
figure. The largest ellipse, \textit{ABCD}, is the ecliptic. Intermediate ellipse
is orbit of an exterior planet; and smallest ellipse is the path of earth
% Fig 12.6
\begin{figure}[hbt!]
  \centering
  \Input{page_319}
  \caption{To explain Formation of Loop in Exterior Planet's Path}
\end{figure}
itself. A planet when advancing always moves in direction \textit{GH}. The
sun is at \textit{S}. When earth is successively at points marked 1, 2, 3, 4, 5,
6, 7 on its orbit, the outer planet is at the points marked 1, 2, 3, 4, 5, 6, 7
on the middle ellipse. So that the planet is seen projected upon the
sky in the directions of the several straight lines. These intersect
the zone \textit{F, G, H, J,} of the celestial sphere in the points also marked
upon it 1, 2, 3, 4, 5, 6, 7, and among the stars of the zodiac. Following
them in order of number, it is evident that the planet advances
from 1 to 3, retrogrades from 3 to 5, and advances again
from 5 to 7. Also its backward motion is most rapid from 3 to 4,
when the planet is near opposition, and its distance from earth is the
least possible. In general, the nearer the planet to earth, the more
extensive its loop.
\Restore

\textbf{A Planet when Nearest Retrogrades.}\index{planets!retrograde motion}---First consider the
inferior planets of which Venus may be taken as the type.
Fixed stars are everywhere round the outer ring, representing
the zodiac (\vpageref*{p320}). Within are two large arrows flying
in the counter-clockwise direction in which the planets
really move round the sun. Earth's orbit is the outer circle
in the left-hand figure, and the dotted circle within is
the orbit of Venus. As Venus moves more swiftly than
\DPPageSep{331.png}
the earth does, evidently the latter may be regarded as
stationary, and Venus as moving past it at the upper part
of the orbit, where inferior conjunction takes place. But
Venus in this position appears to be among the stars far
beyond the sun, consequently her real motion forward seems
to be motion backward among the stars, as indicated by
% Fig 12.7 a, b
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.48\textwidth}
    \centering
    \Input{page_320a}
    \caption{Inferior Planets retrograde at Inferior Conjunction}
  \end{minipage}
  \hfill
  \begin{minipage}{0.48\textwidth}
    \centering
    \Input{page_320b}
    \caption{Superior Planets retrograde at Opposition}
  \end{minipage}
  \caption{All Planets retrograde when nearest to, and advance when farthest from, the Earth}
  \label{p320}\index{planets!retrograde motion}
\end{figure}
the right-hand arrow at the bottom. Next, consider the
exterior planet, of which Mars may be taken as the type.
In the right-hand figure, inner circle is orbit of earth, and
outer, orbit of Mars; and as earth moves more swiftly than
Mars, earth may be regarded as the moving body and Mars
as stationary. In the upper part of the figure occurs opposition,
and earth overtakes Mars and moves on past him.
But Mars is seen among the stars above and beyond it, and
evidently his apparent motion is westerly, or retrograde,
in the direction of the small arrow at the top of the figure.
Thus is reached the conclusion that the \textit{apparent motion
of all the planets, whether inferior or superior, is always
retrograde when they are nearest the earth}.

\textbf{A Planet when Farthest Advances.}---Return to the inferior
\DPPageSep{332.png}
 planet Venus, and the left-hand figure; when
farthest she is in the lower part of her orbit, and her
apparent position is among the stars still farther below,
west or to the left of the sun. Advance or eastward motion
in orbit, then, appears as advance motion forward
among the stars. Seemingly, Venus is moving toward the
sun, and will soon overtake and pass behind him. Now the
exterior planet again. Assuming Mars to remain stationary
in the position of the black dot in lower part of orbit,
earth (in upper part of orbit, where distance between the
two is nearly as great as possible) moves eastward in the
direction of the arrow through it. As a consequence of
this motion, then, Mars seems to travel forward on the
opposite or lower side of the celestial sphere (in the direction
of a very minute arrow near the bottom of the figure).
Thus is reached this general conclusion: \textit{The apparent
motion of all the planets, whether inferior or superior, is
always retrograde when they are nearest the earth, and
advance or eastward when farthest from it}.

\Section{Orbits---Elements---Periods---Laws of Motion}

\textbf{The Four Inner or Terrestrial Planets.}\index{orbit (planetary)}\index{planets!terrestrial}---On page~\pageref{p322}
are charted the orbits of the four inner planets, Mercury,
Venus, earth, and Mars. Observe that while Venus and
the earth move in paths nearly circular, with the sun very
near their center, orbits of Mercury and Mars are both
eccentrically placed. So nearly circular are the orbits of
all planets that, in diagrams of this character, they are
indicated accurately enough by perfect circles. Orbits
having a considerable degree of eccentricity are best represented
by placing the sun a little at one side of their
center.

\Smaller
The double circle outside the planetary orbits represents the ecliptic,
graduated from 0° eastward, or counter-clockwise, around to 360° of
\DPPageSep{333.png}
longitude, according to the signs of the zodiac, as indicated; the vernal
equinox, or the first point of the sign Aries corresponding to 0°.
Small black dots on each orbit represent positions of the planets at
intervals of ten days, zero for each planet being at longitude 180°. All
the planets travel round the sun eastward, or counter-clockwise, as
% Fig 12.8
\begin{figure}[hbt!]
  \centering
  \Input{page_322}
  \caption{Illustration: Orbits and Heliocentric Movements of the Four Terrestrial Planets}
  \label{p322}%
  \index{Mercury!orbit}%
  \index{Venus!orbit}%
  \index{earth!orbit}%
  \index{Mars!orbit}%
  \index{planets!heliocentric movements}%
  \index{planets!orbits}%
\end{figure}
indicated by arrows. In order to find the distance of any planet from
earth, or from any other at any time, first find the position of the two
planets in their respective orbits by counting forward or backward from
the dates given for each planet on the corners outside the chart, when
they are at longitude 180°. Then with a pair of dividers the distance
may be found from the scale of millions of miles underneath.

\textbf{The Four Outer and Major Planets.}---On page~\pageref{p323} is a chart of the orbits
of the four outer planets, Jupiter, Saturn, Uranus, and Neptune. Observe
\DPPageSep{334.png}
that these orbits are all sensibly circular and concentric, except
that of Uranus, the center of which is slightly displaced from the sun.
The double outer circle represents the ecliptic, the same as in the
diagram \vpageref{p322}. The small black dots on the orbits of
Jupiter and Saturn represent the positions of these planets at intervals
% Fig 12.9
\begin{figure}[hbt!]
  \centering
  \Input{page_323}
  \caption{Orbits and Heliocentric Movements of the Four Greater Planets}
  \label{p323}%
  \index{Jupiter!orbit}%
  \index{Saturn!orbit}%
  \index{Uranus!orbit}%
  \index{Neptune!orbit}%
  \index{planets!heliocentric movements}%
  \index{planets!orbits}%
\end{figure}
a year in length; and similarly, the positions of Uranus and Neptune
are indicated at 10-year intervals; the zero in every case being coincident
with longitude 180°. The distance of these planets from each
other, or from the earth at any time, may be found in the same way as
described \vpageref{p322} for the inner planets.
\Restore

\textbf{True Form of the Planetary Orbits.}---Were it possible
to transport our observatory and telescope from earth to
\DPPageSep{335.png}
each of the planets in turn, and then repeat the measures
of the sun's diameter with great refinement, just as
we did from the earth (page~\pageref{p136}), we should reach a result
precisely similar in every case. So the conclusion is, that
the orbits of all the planets are ellipses, so situated in
% Fig 12.10
\begin{figure}[hbt!]
  \centering
  \Input{page_324}
  \caption{Planetary Orbits having Greater Inclinations to the Ecliptic}
  \index{planets!orbits}
\end{figure}
space that the sun occupies one of the foci of each ellipse.
None of them would lie in the same plane that the earth
does, but each planet would have an ecliptic of its own, in
the plane of which its orbit would be situated.

\textbf{Inclination and Line of Nodes.}%
%\index{planets!nodes}\index{nodes|see{planets!nodes}}
\index{planets!inclination}\index{planets!nodes}---The orbits of all the
great planets, except Mercury, Venus, and Saturn, are
inclined to the ecliptic less than 2°. Saturn's inclination
is $2\frac{1}{2}$°\index{Saturn!inclination}, that of Venus $3\frac{2}{5}$°\index{Venus!inclination}, and Mercury's 7°\index{Mercury!inclination}, as in the diagram.
Orbits of the small planets stand at much greater
angles; six are inclined more than 25°, and the average
of the group is about 8°. The two opposite points where
a planet's orbit cuts the ecliptic are called its \textit{nodes}.

\textbf{Eccentricity of their Orbits.}\index{planets!eccentricity}---The eccentricity of Mercury
is $\frac{1}{5}$, of Mars $\frac{1}{11}$, of Jupiter\index{Jupiter!eccentricity}, Saturn, and Uranus about
$\frac{1}{20}$, and of Venus and Neptune very slight. The chief
effect of the eccentricity is to change a planet's distance
from the sun, between perihelion and aphelion; and to
vary the speed of revolution in orbit. On %At top of next
page~\pageref{p325} are eccentricities of the planetary orbits, together
with total variation of distance due to eccentricity.

\Smaller
Some of the small planets have an eccentricity more than double
that of Mercury even, so that their perihelion point is near the orbit
of Mars, while at aphelion they wander well out toward the path of
\DPPageSep{336.png}
Jupiter. The average eccentricity of their orbits is excessive, being
about equal to that of Mercury. The path of Andromache (175) is
very like the orbit of Tempel's comet~\textsc{ii} (page~\pageref{p401}).
\Restore

\begin{table}
\caption{\textsc{Eccentricity and Variation of Distance from the Sun}}
\label{p325}\index{planets!distance}\index{distance|see{planets!distance}}
\begin{center}
\begin{tabular}{ll@{\quad}| rc}
\hline\hline
\multicolumn{2}{m{8em}|}
{\centering\footnotesize\textsc{\rule{0pt}{3.5ex}
    Eccentricity}}
&amp; \multicolumn{2}{m{10em}}
{\centering\footnotesize\textsc{\rule{0pt}{3.5ex}
    Change of Distance due to Eccentricity}}
\\[3ex]  \hline
  Mercury, &amp; 0.2056\rule{0pt}{3ex}
&amp; \multicolumn{1}{@{}l}{\multirow{8}{*}{
    $\left.\begin{array}{r}
      15  \\  1  \\  3  \\  26 \\
      47  \\  90  \\  166  \\  49
    \end{array}\ \right\}$}}
&amp; \multicolumn{1}{@{\quad}l}{\multirow{8}{4em}{\centering Millions of miles}}
\\
  Venus,   &amp; 0.0068 &amp;    &amp;  \\
  Earth,   &amp; 0.0168 &amp;    &amp;  \\
  Mars,    &amp; 0.0933 &amp;    &amp;  \\
  Jupiter  &amp; 0.0482 &amp;     &amp;  \\
  Saturn,  &amp; 0.0561 &amp;     &amp;  \\
  Uranus,  &amp; 0.0464 &amp;     &amp;  \\
  Neptune, &amp; 0.0090 &amp;
\\[1ex]  \hline\hline
\end{tabular}
\end{center}
\index{Mercury!eccentricity}%
  \index{Venus!eccentricity}%
  \index{Earth!eccentricity}%
  \index{Mars!eccentricity}%
  \index{Jupiter!eccentricity}%
  \index{Saturn!eccentricity}%
  \index{Uranus!eccentricity}%
  \index{Neptune!eccentricity}%
  \index{planets!distance}%
\end{table}

\textbf{Synodic Periods.}\index{planets!periods}---Just as with the moon, so each
planet has two kinds of periods. A planet's sidereal
period is the time elapsed while it is journeying once completely
round the sun, setting out from conjunction with
some fixed star and returning again to it. If during this
interval the earth remained stationary as related to the
sun, the times occupied by the planets in traversing the
round of the ecliptic would be their true sidereal periods.
But our continual eastward motion, and the apparent
motion of sun in same direction, makes it necessary to
take account of a second period of revolution---the
synodic period, or interval between successive conjunctions.
If a superior planet, the average interval between
oppositions is also the synodic period. Following are the
\begin{table}[h]
\TableSize
\centering
\caption{\textsc{Synodic Periods}}
\begin{tabular}{m{3cm}@{ }r|m{3cm}@{ }r}
  \hline\hline
  \multicolumn{2}{c|}{\footnotesize\textsc{The Terrestrial Planets}}
   &amp; \multicolumn{2}{c }{\footnotesize\textsc{The Major Planets}}\rule{0pt}{3ex}
   \\[1ex]
   \hline
   Mercury   \dotfill &amp; 116 days
   &amp; Jupiter \dotfill &amp; 399 days\rule{0pt}{3ex}  \\
   Venus     \dotfill &amp; 584 days
   &amp; Saturn  \dotfill &amp; 378 days  \\
   Mars      \dotfill &amp; 780 days
   &amp; Uranus  \dotfill &amp; 370 days  \\
                      &amp;
   &amp; Neptune \dotfill &amp; 368 days \\[1ex]
  \hline\hline
\end{tabular}
\index{Mercury!period}%
  \index{Venus!period}%
  \index{Earth!period}%
  \index{Mars!period}%
  \index{Jupiter!period}%
  \index{Saturn!period}%
  \index{Uranus!period}%
  \index{Neptune!period}%
  \index{planets!periods}%
\end{table}
\DPPageSep{337.png}

The exceptional length of the synodic periods of Venus
and Mars is due to the fact that their average daily motion
is more nearly that of the earth than is the case with any
of the other planets.

\textbf{Sidereal Periods.}\index{planets!periods}---As our earth is a moving observatory,
it is impossible for us to determine the sidereal
periods of the planets directly from observation. But their
synodic periods may be so found; and from them the true
or sidereal periods are ascertained by calculation, involving
only the relation of the earth's (or sun's apparent) motion
to that of the planet. They are as follows:---
\begin{table}[h]
\TableSize
\centering
\caption{\textsc{Sidereal Periods or Periodic Times}}
\begin{tabular}{m{3cm}@{.}r|m{3cm}@{.}r}
  \hline\hline
  \multicolumn{2}{c|}{\footnotesize\textsc{The Terrestrial Planets}}
&amp; \multicolumn{2}{c }{\footnotesize\textsc{The Major       Planets}\rule{0pt}{3ex}}
\\[1ex]   \hline
  Mercury   \dotfill &amp; \dotfill\ $ 88\phantom{\frac{1}{1}}$ days\rule{0pt}{3ex}
&amp; Jupiter   \dotfill &amp; \dotfill\ $ 11         \frac{7}{8} $ years  \\[.5ex]
  Venus     \dotfill &amp; \dotfill\ $225\phantom{\frac{1}{1}}$ days
&amp; Saturn    \dotfill &amp; \dotfill\ $ 29         \frac{1}{2} $ years  \\[.5ex]
  The Earth \dotfill &amp; \dotfill\ $365         \frac{1}{4} $ days
&amp; Uranus    \dotfill &amp; \dotfill\ $ 84\phantom{\frac{1}{1}}$ years  \\[.5ex]
  Mars      \dotfill &amp; \dotfill\ $687\phantom{\frac{1}{1}}$ days
&amp; Neptune   \dotfill &amp; \dotfill\ $165\phantom{\frac{1}{1}}$ years
\\[1ex]  \hline\hline
\end{tabular}
\index{Mercury!period}%
  \index{Venus!period}%
  \index{Earth!period}%
  \index{Mars!period}%
  \index{Jupiter!period}%
  \index{Saturn!period}%
  \index{Uranus!period}%
  \index{Neptune!period}%
  \index{planets!periods}%
\end{table}

Periodic times of the small planets range between $1\frac{3}{4}$
and $8\frac{3}{4}$~years.

\textbf{Kepler's Laws.}\index{planets!laws of}\index{Kepler, J. (1571--1630), Ger.\ ast.!laws}---Kepler, to whom the motions of the
planets were a mystery, nevertheless had discovered in 1619
three laws governing their motions. (I)~the orbit of every
planet is elliptical in form, and the sun is situated at one
of the foci of the ellipse. (II)~The motion of the radius
vector, or line joining the planet to the sun, is such that
it sweeps over equal areas of the ellipse in equal times.
(III)~The squares of the periodic times of the planets
are proportional to the cubes of their average distances
from the sun. Kepler was unable to give any physical explanation
of these laws. He merely ascertained that all
the planets appear to move in accordance with them.
\DPPageSep{338.png}
\begin{table}
\TableSize
\centering
\caption{\textsc{Verification of Kepler's Third Law}}
\begin{tabular}{l| D{!}{}{-1}| D{!}{}{-1}| c}
  \hline\hline
  \multicolumn{1}{m{5em}|}{\footnotesize\centering \textsc{\rule{0pt}{3ex}
    Name of Planet}}
&amp; \multicolumn{1}{m{7em}|}
    {\footnotesize\centering\textsc{\rule{0pt}{3ex}
    Periodic Time (in Days)}}
&amp; \multicolumn{1}{m{11em}|}
    {\footnotesize\centering\textsc{\rule{0pt}{3ex}
    Mean Distance (Earth's Distance = 1)}}
&amp; \multicolumn{1}{m{5em}}{\footnotesize\centering \rule{0pt}{4.5ex}%
    $\frac{\text{\footnotesize\textsc{[Time]    }}^2}
          {\text{\footnotesize\textsc{[Distance]}}^3}$}
\\[3ex]  \hline
  Mercury &amp;    8!7.97 &amp;  0.3!871 &amp; 133,414\rule{0pt}{3ex}  \\
  Venus   &amp;   22!4.70 &amp;  0.7!233 &amp; 133,430  \\
  Earth   &amp;   36!5.26 &amp;  1.0!000 &amp; 133,415  \\
  Mars    &amp;   68!6.95 &amp;  1.5!237 &amp; 133,400  \\
  Ceres   &amp;  168!1.41 &amp;  2.7!673 &amp; 133,408  \\
  Jupiter &amp;  433!2.58 &amp;  5.2!028 &amp; 133,272  \\
  Saturn  &amp; 1075!9.22 &amp;  9.5!388 &amp; 133,400  \\
  Uranus  &amp; 3068!8.82 &amp; 19.1!833 &amp; 133,410  \\
  Neptune &amp; 6018!1.11 &amp; 30.0!551 &amp; 133,403
\\[1ex]  \hline\hline
\end{tabular}
\index{Ceres, first small planet discovered}%
  \index{planets!distance}
\index{Mercury!distance}%
  \index{Venus!distance}%
  \index{Earth!distance}%
  \index{Mars!distance}%
  \index{Jupiter!distance}%
  \index{Saturn!distance}%
  \index{Uranus!distance}%
  \index{planets!distance}%
\end{table}

\Smaller
\textbf{Verification of Kepler's Third Law.}---A half hour's calculation suffices
to prove the truth of this law. The results are shown in the last
column of the following table, where the number in each line was obtained
by dividing the square of the planet's periodic time by the cube
of its mean distance from the sun.

The third law of Kepler, often called the `harmonic law,' is rigorously
exact, only upon the theory that planets are mere particles, or exceedingly
small masses relatively to the sun. On this account the discrepancy
in the last column is quite large, in the case of Jupiter, because
his mass is nearly $\frac{1}{1000}$ that of the sun.
\Restore

\textbf{Mean Distances of the Planets.}\index{planets!distance}---Kepler's third law enables
us to calculate a planet's average distance from the
sun, once its time of revolution is known; for regarding
the earth's period of revolution as unity (one year), and
our distance from the sun as unity, it is only necessary to
square the planet's time of revolution, extract the cube
root of the result, and we have the planet's mean distance
from the sun. For example, the periodic time of Uranus
is 84~years; its square is $7056$; the cube root of which is
$19.18$. That is, the mean distance of Uranus from the sun
is $19.18$ times our own distance from that central luminary.
\DPPageSep{339.png}
Its distance in miles, then, will be $19.18 × 93,000,000$. In
like manner may be found the distances of all the other
planets from the sun; and they are as follows:---
\begin{table}[h]
\TableSize
\centering
\caption{\textsc{Mean Distance from Sun}}
\begin{tabular}{lr|lr}
  \hline\hline
  \multicolumn{2}{c|}{\footnotesize\textsc{The Terrestrial Planets\rule{0pt}{3ex}}}
&amp; \multicolumn{2}{c}{\footnotesize\textsc{The Major Planets}}
\\[1ex]  \hline
$\left.\rule{0pt}{5ex}
\begin{array}{lr@{}l}
  \text{Mercury} \dotfill &amp;  36 &amp;  \\
  \text{Venus}   \dotfill &amp;  67 &amp; \frac{1}{5}  \\
  \text{The Earth}\rule{1em}{0pt} \dotfill &amp;  93  \\
  \text{Mars}     \dotfill &amp; 141 &amp; \frac{1}{2}
\end{array}
\right\}$
&amp; \multicolumn{1}{m{4em}|}{\centering Millions of \\ miles}
&amp;
$\left.
\begin{array}{lr@{}l}
  \text{Jupiter} \dotfill &amp;  483 &amp; \frac{1}{3}  \\
  \text{Saturn}  \dotfill &amp;  886  \\
  \text{Uranus}  \dotfill &amp; 1780  \\
  \text{Neptune}\rule{1em}{0pt} \dotfill &amp; 2790  \\
\end{array}
\right\}$
&amp; \multicolumn{1}{m{4em}}{\centering Millions of \\ miles}
\\  \hline\hline
\end{tabular}
\end{table}

These distances are all represented in true relative proportion
in the figure on page~\pageref{p334}. Scattered over a zone
about 280 millions of miles broad, or $\frac{5}{6}$ of the distance
separating Mars from Jupiter, is the ring of small planets,
or asteroids probably many thousand in number, of which
about 600 have already been discovered.

\textbf{The Nearest and the Farthest Planet.}\index{planets!nearest}\index{planets!farthest}---Mars is often said
to be the nearest of all the planets, because his orbit is so
eccentric that favorable oppositions, as shown later in the
chapter, may bring him within 35,000,000 miles of the earth.
But Venus comes even nearer than that\index{Venus!nearest planet}. Her distance
from the sun subtracted from ours gives 26,000,000 miles
for the average distance of Venus from the earth at
inferior conjunctions; and Venus may approach almost
2,000,000 miles nearer than this, if conjunction comes in
December or January, near earth's perihelion. But we
find that the nearest planet of all is an asteroid discovered
in the year 1898. About one half its orbit lies nearer
the sun than the nearer half of Mars's orbit does; and
once in 30 years it comes to perihelion and opposition at
about the same time. Its distance from us is then less than
\DPPageSep{340.png}
14,000,000 miles. This planet (No.~433) is named Eros\index{Eros}.
Of the known planets the farthest from the earth is Neptune.
So far away is he that we must multiply the least
distance of Venus more than a hundredfold in order to
obtain the distance of Neptune from the earth.

\Smaller
\textbf{Aberration Time.}\index{aberration time}---Knowing the velocity of light by experiment,
and knowing the distances of the planets from us, it is easy to calculate
the time consumed by light in traveling from any planet to the
earth. So distant is Neptune, for example, that light takes about
$4\frac{1}{4}$~hours to reach us from that planet. This quantity is called the
planet's aberration time, or the equation of light. Its value in seconds
for any planet is equal to 499 times the planet's distance from the earth
(expressed in astronomical units).
\Restore

\textbf{Newton's Law of Gravitation.}\index{gravitation!law of}\index{Newtonian law}---Sir Isaac Newton about
1675 simplified the three laws of motion of the planets
into a single law, hence known as the Newtonian law of
gravitation. It has two parts of which the first is this:
that every particle of matter in the universe attracts every
other particle directly as its mass or quantity of matter;
and second, that the amount of this attraction increases
in proportion as the square of the distance between the
bodies decreases. That Kepler's three laws are embraced
in this one simple law of Newton may be shown by a
mathematical demonstration. With a few trifling exceptions,
all the bodies of the solar system move in exact accordance
with Newton's law, whether planets themselves,
their satellites, or the comets and meteors. Newton's law
is often called `The Law of Universal Gravitation,' because
it appears to hold good in stellar space as well as
in the solar system itself.

\textbf{Elements of Planetary Orbits.}\index{orbit (planetary)!elements}\index{planets!orbit elements}---The mathematical quantities
which determine the motion of a celestial body are
called the elements of its orbit. They are six in number,
and they define the size of the orbit, its shape, and its relation
to the circles and points of the celestial sphere.
\DPPageSep{341.png}

%[** TN: In original, these items are hangindented about 4em]
\MyItem
(1) $a$ Mean distance, or half the major axis of the ellipse
in which the planet moves round the sun.

\MyItem
(2) $e$ Eccentricity, or ratio of distance between center and
focus of ellipse to the mean distance.

\MyItem
(3) $\Omega$ Longitude of ascending node, or arc of great circle
between this node and the vernal equinox.

\MyItem
(4) $i$ Inclination of plane of orbit to ecliptic.

\MyItem
(5) $\pi$ Longitude of perihelion, or angle between line of
apsides and the vernal equinox.

\MyItem
(6) $\epsilon$ Longitude of the planet at some definite instant, often
technically called the \textit{epoch}.

\noindent Once the exact elements of an orbit are found, the undisturbed
motion of the body in that orbit can be predicted,
and its position calculated for any past or future time.

\textbf{Secular Variations of the Elements.}\index{orbit (planetary)!secular variations}\index{secular variations}\index{planets!secular variations}---About a century
ago, two eminent mathematical astronomers of France,
La~Grange\index{La Grange, J. L. (l\=a-gr\=onzh´) (1736--1813), Fr.\ math.} and La~Place\index{La Place, P. S. de (lä-plass´) (1749--1827), Fr.\ ast.\ and math.}, made the important discovery
that the action of gravitation among the planets can never
change the size of their orbits; that is, the element $a$, or
the mean distance, always remains the same. As for the
other elements affecting the shape of the orbit and its position
in space, they can only oscillate harmlessly between
certain narrow limits in very long periods of time. These
slow and minute fluctuations of the elements are called
\textit{secular variations;} and they may be roughly represented
by holding a flexible and nearly circular hoop between the
hands, now and then compressing it slightly, also wobbling
it a little, and at the same time slowly moving the arms
one about the other. The oscillatory character of the
secular variations secures the permanence and stability
of our solar system, so long as it is not subjected to perturbing
or destructive influences from without. One who
really wishes fully to understand these complicated relations
\DPPageSep{342.png}
must undertake an extended course of mathematical
study---the only master key to complete knowledge of the
planetary motions.

\Section{Colors---Albedo---Bode's\ Law---Relative Distances}

\textbf{A Planet when Nearest looks Largest.}\index{planets!apparent size}---In proportion
as a planet comes nearer to us, its apparent disk\index{planets!disk of} fills a
% Fig 12.11
\begin{figure}[hbt!]
  \centering
  \Input{page_331a}
  \caption{Variation in Apparent Size of Mars}\index{Mars!variation in size}
\end{figure}
larger angle in the telescope. The two planets, then,
nearest the earth, Venus within our orbit, and Mars without,
must undergo the greatest changes in apparent diameter,
because their greatest
distance is many
times their least. Mars,
at nearest to the earth,
% Fig 12.12
\begin{wrapfigure}[11]{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_331b}
  \caption{Variation in Apparent Size of Venus}\index{Venus!variation in size}\index{Venus!phase}
\end{wrapfigure}
is 35,000,000 miles away;
at farthest, more than
seven times as distant.
This seeming variation
in size is shown in above
figure. The next greatest variation is exhibited by Venus
(lower figure); at superior conjunction her diameter seems
to be only one sixth as great as at inferior conjunction.

\Smaller
The figure illustrates not only this marked increase of her diameter as
she\break
\vspace{-\baselineskip}
%[** TN: Hack to coax two wrapfigures into one paragraph]

\noindent comes toward us, but her phases also. Third in order is Mercury,
\DPPageSep{343.png}
whose diameters at greatest and least distance are about as 1 to 3
(already shown on page~\pageref{p318}).
% Fig 12.13
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_332}
  \caption{Variation in Apparent Size of Jupiter}\index{Jupiter!variation in size}
\end{wrapfigure}
And following Mercury is Jupiter,
whose variations are accurately shown in the adjacent figure. Saturn,
Uranus, and Neptune, too, show fluctuations of the same character,
but much less, because of their very great distance from us. From
conjunction to opposition, the
apparent breadth of Saturn increases
only about one third;
while the similar increase of
Uranus and Neptune is so
slight that a micrometer is
necessary to measure it.

\textbf{Apparent Magnitudes and
Colors of the Planets.}\index{planets!colors}---All
the planets vary in brightness,
as their distance from the sun and the earth varies. Five of
them shine with an average brightness exceeding that of a first
magnitude star. Of these, Venus is by far the brightest, and Jupiter
next, the others following in the order Mars, Mercury, and Saturn.
Uranus is about equivalent to a star of the sixth magnitude. Also a
few of the small planets approach this limit when near opposition. But
Neptune's vast distance from both sun and earth renders him as faint
as an eighth magnitude star, so that he is invisible without at least a
small telescope. The colors of the planets are:
\begin{table}[h]
\TableSize
\centering
\begin{tabular}{l}
Mercury, pale ash; \\
Venus, brilliant straw; \\
Mars, reddish ochre; \\
Jupiter, bright silver; \\
Saturn, dull yellow; \\
Uranus, pale green; \\
Neptune, the same.
\end{tabular}
\index{Mercury!color}%
  \index{Venus!color}%
  \index{Mars!color}%
  \index{Jupiter!color}%
  \index{Saturn!color}%
  \index{Uranus!color}%
  \index{Neptune!color}%
\end{table}

The entire significance of these colors is not yet known; but
apparently they are indicant as to degree and composition of atmosphere
enveloping each.

\textbf{Albedo of the Planets.}\index{planets!albedo}---Albedo is a term used to express the capacity
of a surface, like that of a planet, to reflect light. It is a number
expressing the ratio of the amount of light reflected from a surface to
the amount which falls upon it. By observations of a planet's light
with a photometer, it can be compared with a star or another planet,
and its albedo found by computation. The moon's surface reflects
about $\frac{1}{6}$ the light falling upon it from the sun. The albedo of Mercury\index{Mercury!albedo}
is even less, or $\frac{1}{8}$; but the surface of Venus\index{Venus!albedo} is highly reflective, its albedo
\DPPageSep{344.png}
being $\frac{1}{2}$. The albedo of Mars\index{Mars!albedo} is about $\frac{1}{4}$; that of Saturn\index{Saturn!albedo} and Neptune\index{Neptune!albedo},
about the same as Venus; while the albedo of Jupiter\index{Jupiter!albedo} and Uranus\index{Uranus!albedo} is
the highest of all the planets, or nearly $\frac{2}{3}$. This means that their surfaces
reflect about four times as much light as sandstone does.

% Fig 12.14
\begin{wrapfigure}[39]{o}{0.25\textwidth}
  \centering
  \Input[0.25\textwidth]{page_334}
  \caption{Relative Distances and Orbital Motions of the Planets}
  \label{p334}
\end{wrapfigure}
\textbf{The So-called Law of Bode.}\index{planets!distance}---Titius\index{Titius, J.~D.\ (1726--96), Ger.\ math.} discovered a law which approximately
represents the relative distances of the planets from the sun. It
is derived in this way. Write this simple series of numbers, in which
each except the second is double the one before it: \\
\begin{tabular}{*{7}{c}}
  \makebox[2.5em][c]{ 0} &amp; \makebox[2.5em][c]{ 3}
&amp; \makebox[2.5em][c]{ 6} &amp; \makebox[2.5em][c]{12}
&amp; \makebox[2.5em][c]{24}
&amp; \makebox[2.5em][c]{48} &amp; \makebox[2.5em][c]{ 96}
\end{tabular}

Add 4 to each, giving \\
\begin{tabular}{*{7}{c}}
  \makebox[2.5em][c]{ 4} &amp; \makebox[2.5em][c]{ 7}
&amp; \makebox[2.5em][c]{10} &amp; \makebox[2.5em][c]{16}
&amp; \makebox[2.5em][c]{28}
&amp; \makebox[2.5em][c]{52} &amp; \makebox[2.5em][c]{100}
\end{tabular}

The actual distances of the planets known in the time of Titius
(1766) are as follows (the earth's distance being represented by 10): \\
\begin{tabular}{*{7}{c}}
  \makebox[2.5em][c]{3.9} &amp; \makebox[2.5em][c]{7.2}
&amp; \makebox[2.5em][c]{10} &amp; \makebox[2.5em][c]{15.2}
&amp; \makebox[2.5em][c]{------}
&amp; \makebox[2.5em][c]{52.0} &amp; \makebox[2.5em][c]{95.4}
\\
  \makebox[2.5em][c]{\mercury} &amp; \makebox[2.5em][c]{\venus}
&amp; \makebox[2.5em][c]{\earth} &amp; \makebox[2.5em][c]{\mars}
&amp; \makebox[2.5em][c]{
  $\begin{Bmatrix}
    \text{small}\\
    \text{planets}
  \end{Bmatrix}$ }
&amp; \makebox[2.5em][c]{\jupiter} &amp; \makebox[2.5em][c]{\saturn}
\end{tabular}
\index{Mercury!distance}%
  \index{Venus!distance}%
  \index{Mars!distance}%
  \index{Jupiter!distance}%
  \index{Saturn!distance}%
  \index{Uranus!distance}%
  \index{Neptune!distance}%

Although the law is by no means exact, Bode\index{Bode, J. E., (b\=o´d\u uh) (1747--1826), Ger.\ ast., law of}, a distinguished German
astronomer, promulgated it. On that account it is always called
Bode's law. Except historically, this so-called law is now of no
importance; for its error, when extended to the outer planets, Uranus\index{Uranus!Bode's law}
and Neptune\index{Neptune!Bode's law}, is even greater than in the case of Saturn. But by directing
attention to a break in succession of planets between Mars and
Jupiter, Bode's law led to telescopic search for a supposed missing
body; a search speedily rewarded by discovery of the first four small
planets, \textcircled{\footnotesize 1} Ceres\index{Ceres, first small planet discovered}, \textcircled{\footnotesize 2} Pallas\index{Pallas, small planet}, \textcircled{\footnotesize 3} Juno\index{Juno, small planet}, and \textcircled{\footnotesize 4} Vesta\index{Vesta, small planet}.

\textbf{Relative Distances and Orbital Motions.}\index{planets!distance}---Once the distances of the
planets have been found, measures of their disks with the telescope enable
us to calculate their true dimensions. One need not try to improve
upon Sir John Herschel's\index{Herschel, Sir J.~F.~W.\ (1792--1871), Eng.\ ast.} illustration of the relative distances, sizes, and
motions in the solar system. `Choose any well-leveled field or bowling
green. On it place a globe two feet in diameter; this will represent the
sun; Mercury will be represented by a grain of mustard seed, on the
circumference of a circle 164 feet in diameter for its orbit; Venus a pea,
on a circle of 284 feet in diameter; the earth also a pea, on a circle of
430 feet; Mars a rather large pin's head, on a circle of 654 feet; the
asteroids, grains of sand, in orbits of from 1000 to 1200 feet; Jupiter
a moderate-sized orange, in a circle nearly half a mile across; Saturn a
small orange, on a circle of four fifths of a mile; Uranus a full-sized
cherry or small plum, upon the circumference of a circle more than a
mile and a half; and Neptune a good-sized plum, on a circle about two
miles and a half in diameter\ldots. To imitate the motions of the
\DPPageSep{345.png}
planets, in the above-mentioned orbits, Mercury
must describe its own diameter in 41~seconds;
Venus, in $4\,m.\:14\,s.$; the earth, in $7\,m.$; Mars, in
$4\,m.\:48\,s.$; Jupiter, in $2\,h.\:56\,m.$; Saturn, in $3\,h.\:13\,m.$;
Uranus, in $2\,h.\:16\,m.$; and Neptune, in
$3\,h.\:30\,m.$' A farther and helpful idea of relative
motion of the planets may be obtained from the figure,
in which Mercury's period round the sun is
taken as the unit. While he is moving $360$°, that is
in 88~days, the other planets move over the arcs set
down opposite their distance from the sun. This
makes very apparent how much the motion of planets
decreases on proceeding outward from the sun. If
Neptune moves as an athlete runs, Mercury speeds
round with the celerity of a modern locomotive.
\Restore

\Section{Sizes---Masses---Axial Rotation---Tidal
Evolution}

\textbf{The Size of the Planets.}\index{planets!dimensions}---Regarding
the group of small planets as a dividing
line in the solar system, all planets inside
that group are, as previously said, relatively
small, and all outside it large. The
illustration \vpageref{p335} serves to show this
well, presenting not only the relative sizes
of the planets, but also the relation of
their diameters to the sun's. More particularly
the mean diameters are:---
\begin{center}
\parbox{5em}{\centering Inner Terrestrial Planets}
$\left\{\begin{array}{l@{\ }c@{\ }l}
\text{Mercury,} &amp; \makebox[4em]{\dotfill} &amp; \text{3,000 miles}\\
\text{Venus,  } &amp; \dotfill &amp; \text{7,700 miles}\\
\text{Earth,  } &amp; \dotfill &amp; \text{7,920 miles}\\
\text{Mars,   } &amp; \dotfill &amp; \text{4,200 miles}
\end{array}\right.$
\index{Mercury!diameter}%
  \index{Venus!diameter}%
  \index{Earth!diameter}%
  \index{Mars!diameter}%
\end{center}

Group of small planets: Ceres\index{Ceres, first small planet discovered} the largest, 490
miles in diameter.
\begin{center}
\parbox{5em}{\centering Outer Major Planets}
$\left\{\begin{array}{l@{\ }c@{\ }l}
\text{Jupiter,} &amp; \makebox[4em]{\dotfill} &amp; \text{87,000 miles}\\
\text{Saturn, } &amp; \dotfill &amp; \text{73,000 miles}\\
\text{Uranus, } &amp; \dotfill &amp; \text{32,000 miles}\\
\text{Neptune,} &amp; \dotfill &amp; \text{32,000 miles}
\end{array}\right.$
  \index{Jupiter!diameter}%
  \index{Saturn!diameter}%
  \index{Uranus!diameter}%
  \index{Neptune!diameter}%
\end{center}%
\DPPageSep{346.png}

% Fig 12.15
\begin{figure}[hbt!]
  \centering
  \Input{page_335}
  \caption{Relative Sizes of Planets (Sun's Diameter on Same Scale equals Length of the Cut)}
  \label{p335}\index{planets!relative sizes}
\end{figure}
Other small planets\index{asteroids} whose diameters
have been measured (by Barnard\index{Barnard, E. E., Prof.\ Univ.\ Chicago})
are Pallas\index{Pallas, small planet}, 300~miles; Juno\index{Juno, small planet},
120~miles; Vesta\index{Vesta, small planet}, 240~miles. Probably
none of the others are as
large as Juno, and the average of
recent faint discoveries cannot exceed
20~miles.

\Smaller
\textbf{Masses and Densities of Planets.}\index{planets!masses}\index{planets!densities}---Best
by comparison can some idea of the masses
of the planets be conveyed. Relative
weights of common things are helpful, and
sufficiently precise: Let an ordinary bronze
cent piece represent the earth. So small are
Mercury\index{Mercury!mass} and Mars\index{Mars!mass} that we have no coin
light enough to compare with them; but
these two planets, if merged into a single
one, might be well represented by an old-fashioned
silver three-cent piece; Venus\index{Venus!mass},
by a silver dime; Uranus\index{Uranus!mass}, a silver dollar,
half dollar, and quarter together; Neptune\index{Neptune!mass},
two silver dollars; Saturn\index{Saturn!mass}, eleven silver dollars;
and Jupiter\index{Jupiter!mass}, thirty-seven silver dollars
(rather more than two pounds avoirdupois).
An inconveniently large sum of silver would
be required if this comparison were to be
carried farther, so as to include the sun; for
he is nearly 750 times more massive than
all the planets and their satellites together,
and, on the same scale of comparison, he
would somewhat exceed the weight of the
long ton. In striking contrast with this
vast and weighty globe are the tiny asteroids,
so light that 300 of them have been estimated
to have a mass of only $\frac{1}{3000}$ that of
our earth. If we derive the densities of
planets as usually, by dividing mass by volume,
we find that Mercury\index{Mercury!density} is the densest
of all (one fifth denser than the earth).
Venus\index{Venus!density}, Earth\index{Earth!density}, and Mars\index{Mars!density} come next, the last
\DPPageSep{347.png}
a quarter less dense than our globe. Three of the major planets
have about the same density as the sun himself\index{Jupiter!density}\index{Uranus!density}\index{Neptune!density}; that is, only one fourth
part that of the earth. Saturn's\index{Saturn!density} mean density is the least of all, only
one eighth that of our globe.
\Restore

\textbf{Center of Gravity of the Sun and Jupiter.}\index{Jupiter!center of gravity of sun and}---Though
the sun's mass is vastly greater than that of his entire
retinue of planets put together, he
% Fig 12.xx
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.45\textwidth]{page_336}
  \caption{Jupiter balancing the Sun}
\end{wrapfigure}
is nevertheless forced
appreciably out of the position he would otherwise occupy
by the powerful attraction
of the giant planet
whose mass is $\frac{1}{1047}$ his
own. It is easy to calculate
how much, for the
sun and Jupiter revolve round their common center of
gravity, exactly as if the two vast globes, \textit{S} and \textit{J} were
connected by a rigid rod of steel. But as \textit{S} weighs 1047
times as much as \textit{J}, the center of gravity of the system
is $\frac{1}{1048}$ of the distance between the centers of \textit{S} and
\textit{J}. Now as Jupiter in perihelion makes this distance
460,000,000 miles, the center of gravity is displaced from
\textit{S} toward \textit{J} 440,000 miles. But the radius of the sun is
433,000 miles; so the center of gravity of the Sun--Jupiter
system is never less than 7000 miles outside the solar
orb. And this distance becomes greater as Jupiter recedes
to his aphelion.

\textbf{Axial Rotation of the Planets.}\index{planets!rotation}---The giant planet turns
most swiftly on his axis, for the average period of rotation
of the white belt girdling his equator is only 9\,h.\:$50\frac{1}{3}$\,m.\index{Jupiter!rotation}
But, like the sun, his zones in different latitudes revolve in
different periods, the average of which is about 9\,h.\:$55\frac{1}{2}$\,m.
The period of revolution of the great red spot averages
9\,h.\:55\,m.\:39\,s. Saturn, too, exhibits similar discrepancies,
but the white spots of his equatorial belts gave, in 1893, a
period of 10\,h.\:12\,m.\:53\,s.\index{Jupiter!rotation} There are indications that the
\DPPageSep{348.png}
axial period of Uranus\index{Uranus!rotation} is about the same; but that of
Neptune\index{Neptune!rotation} is unknown. Then comes our earth with its day
of 23\,h.\:56\,m.\:4.09\,s\index{earth!rotation}. Next in order of length is Mars,
whose day is equal to 24\,h.\:37\,m.\:22.7\,s.\index{Mars!rotation}, a constant known
with great precision, because it has been determined by
observing fixed markings upon the surface, and the whole
number of revolutions is many thousand. Following,
though at a long distance, are Mercury and Venus, which
turn round but once on their axes while going once round
the sun. The axial period (sidereal) of the former, then
is 88~days\index{Mercury!rotation}; and of the latter, 225 days\index{Venus!rotation},---the longest
known in the solar system. Her solar day, therefore, is
infinite in duration, and her year and sidereal day are equal
in length. This equality of periods, in both Mercury and
Venus, was undoubtedly effected early in their life history,
through the agency of friction of strong sun-raised tides
in their masses, then plastic.

\Smaller
\textbf{Ellipticity and Axial Inclination of the Planets.}\index{planets!axial inclination}\index{planets!ellipticity}---The disks of
many of the planets do not appear perfectly circular, but exhibit a
degree of flattening at the poles. This is due to rotation about their
axes, the centrifugal force producing an equatorial bulge. In the case
of Jupiter and Saturn, it is so marked as to attract immediate attention
on examining their disks with the telescope. The polar flattening
of Saturn's\index{Saturn!ellipticity} ball is $\frac{1}{9}$ (page~\pageref{p367}), of Uranus\index{Uranus!ellipticity} $\frac{1}{12}$, and of Jupiter $\frac{1}{16}$\index{Jupiter!ellipticity}
(page~\pageref{p363}), these planets being exceptionally large, and their axial
rotation relatively swift. Next comes Mars\index{Mars!ellipticity}, whose polar flattening is
$\frac{1}{190}$, followed by the earth's\index{earth!ellipticity}, $\frac{1}{300}$. The ellipticity of the other planets,
of the satellites, and of the sun itself, is so small as to escape detection.
Inclination of planetary equator to plane of orbit round the sun is excessive
in the case of Uranus\index{Uranus!axial inclination}; also probably in Neptune\index{Neptune!axial inclination}; has a medium
value (about $25$°) for the earth\index{earth!axial inclination}, Mars\index{Mars!axial inclination}, and Saturn\index{Saturn!axial inclination}; and is very slight
for all the other three great planets.
\Restore

\textbf{Librations of the Planets.}\index{planets!libration}---There are librations of
planets, just as there are librations of the moon. But
the only planetary libration we need to consider is libration
in longitude. This is due to the fact that while the planet
\DPPageSep{349.png}
turns with perfect uniformity on its axis, its revolution in
orbit is swifter near perihelion, and slower near aphelion
than the average. The amount of a planet's libration in
longitude, therefore, will depend upon the degree of eccentricity
of its orbit; and it must be taken into account in
finding the true period of the planet's day.

\Smaller
Mercury's libration\index{Mercury!libration} is the greatest of all. His average daily angle of
rotation is about $4$°; but at perihelion he moves round the sun more
than $6$°, and at aphelion rather less than $3$° daily. The effect of libration
is an apparent oscillation of the disk, alternately to the east and
west. Starting from perihelion, the angle of revolution in orbit
gains about $2$° each day on the angle of axial turning; the amount of
gain constantly diminishing, until nearly three weeks past perihelion.
Mercury's libration is then at its maximum, amounting to $23\frac{1}{2}$° at
the center of the disk. In the opposite part of his orbit, the disk
seems to swing as much in the opposite direction, making thus the
extent of the angle of Mercury's libration equal to $47$°. On $\frac{3}{8}$ of
his surface, then, the sun never shines. On $\frac{3}{8}$ it is perpetually
shining, and on $\frac{1}{4}$ there is alternate sunshine and shadow. So, too,
on Mars\index{Mars!libration}, there is an apparent libration of the center of the disk,
though not so large as Mercury's, because his orbit is less elliptical;
and the sun shines on every part of the surface, because the rotation
and revolution periods of Mars are not equal. Still less are the librations
of Jupiter\index{Jupiter!libration} and Saturn\index{Saturn!libration}, their eccentricity of orbit being only
about half that of Mars.
\Restore

\textbf{Tidal Evolution.}\index{evolution, tidal}\index{tidal evolution}---By tidal evolution is meant the distinct
rôle played by tides in the progressive development
of worlds. The term \textit{tide} is here used, not in its common
or restricted sense, applying to waters of the ocean, but to
that periodic elevation of plastic material of a world in its
early stages, occasioned by gravitation of an exterior mass.
Newton's law of gravitation first gave a full explanation
of the rising and falling of ocean tides, but as applied to
motions of planets, it presupposed that all these bodies
were rigid. In 1877, George Darwin\index{Darwin, G.~H., Prof.\ Univ.\ Cambridge, Eng.}, in a series of elaborate
mathematical papers, showed the effect of gravitation
upon these masses in earlier stages of their history, when,
\DPPageSep{350.png}
according to the nebular hypothesis, they were not rigid,
but composed of yielding material. Ocean tides are raised
at the gradual, though almost inappreciable, expense of
earth's energy of rotation. In like manner, earth-raised
tides in the youthful moon continued to check its axial
rotation until that effect was completely exhausted, and
the moon has never since turned on its axis relatively to
the earth. Evidently this effect of tidal friction has been
operant in the case of sun-raised tides upon the planets,---more
powerfully if the planet is nearer the sun; less
powerfully if its mass is great; also less powerfully if its
materials have early become solidified on account of the
planet's small size. Combination of these conditions explains
the present periods of rotation of all the planets:
Mercury and Venus strongly acted upon by the sun, so
that they now and for all time turn their constant face
toward him; earth, also probably Mars, even yet suffering
a very slight lengthening of their day; Jupiter and
Saturn, also probably Uranus and Neptune, still endowed
with swift axial rotation, because of (1)~their massiveness,
and (2)~their vast distance from the center of attraction.

\Section{Transits---Satellites---Atmospheres---Surfaces}

\textbf{Transits of Inferior Planets.}\index{planets!transits}\index{transits of inferior planets}---If either Mercury\index{Mercury!transits} or
Venus\index{Venus!transits} at inferior conjunction is near the node of the orbit,
the planet can be seen to pass across the sun like a round
black spot. This is called a transit. About 13 transits
of Mercury take place every century, the shortest interval
being $3\frac{1}{2}$~years, and the longest 13. They can happen
only in the early part of May and November, because the
earth is then near the nodes of Mercury's orbit. There
are about twice as many transits in November as in May,
because Mercury's least distance from the sun falls near
\DPPageSep{351.png}
the November node. Transits of Venus occur in pairs,
eight years apart; and the intervals between the midway
points of the pairs are alternately $113\frac{1}{2}$ and $129\frac{1}{2}$~years.
June and December are the only possible months for their
occurrence, and a June pair in one century will be followed
by a December pair in the next. Both Mercury
and Venus at transit, being then nearest the earth, their
apparent motion is westerly or retrograde. Consequently
a transit always begins on the east side
of the sun. Duration of transit varies
with the part of the disk upon which
the planet seems to be projected,
whether north or south of the center
or directly over the middle.

% Fig 12.17
\begin{figure}[hbt!]
  \centering
  \Input{page_340}
  \caption{Contacts at Ingress}\index{contacts!in transits}
\end{figure}

\Smaller
\textbf{Contacts at Ingress and Egress.}\index{contacts!in transits}---Hold the
book up south. The white arc in the figure
adjacent will then represent the east limb of
the sun, upon which the planet enters at ingress,
or beginning of transit, as seen in an
ordinary astronomical telescope. Upper part
of figure shows the phase called \textit{external
contact}. Actual geometric contact cannot of
course be observed, because it is impossible
to see the planet until its edge has made a
slight notch into the sun's limb. The observer
catches sight of this as soon as possible,
and records the time as his observation
of external contact. The planet then moves
along to the left, until it reaches the phase
shown at I, a few seconds before internal
contact. The observer must then watch
intently the bright horns, which will soon close in rapidly toward each
other, and finally a narrow filament of light will shoot quickly across
and join the two horns together. This will be internal contact shown
at II. After a few seconds the planet will have advanced to III, well
within the limb of the sun. Then there will be little to observe until
the planet has crossed the solar disk, and is about to present the
phases of egress. These will be exactly similar to those at ingress,
but will take place in reverse order. The atmosphere of Venus (page~\pageref{p348})
\DPPageSep{352.png}
complicates observations of these contacts, and they cannot be
observed within two or three seconds of time.

% Fig 12.18
\begin{figure}[hbt!]
  \centering
  \Input[0.8\textwidth]{page_341}
  \caption{Paths of Transits of Mercury at Ascending and Descending Nodes}
  \index{Mercury!transits}\index{planets!nodes}
\end{figure}
\textbf{Past and Future Transits of Mercury.}\index{Mercury!transits}---Gassendi\index{Gassendi, P.\ (1592--1655), Fr.\ ast.} made the first
observation of a transit of Mercury in 1631. The annexed engraving
shows the paths of Mercury during all transits from 1868 to 1924.
The circle represents the disk of the sun; near the top is north, and
below the right side west. The broken line is part of the ecliptic. Consider
first the November transits. Their dates are: 5th November, 1868;
7th November, 1881; 10th November, 1894; 14th November, 1907; 6th
November, 1914. Mercury is then near ascending node\index{planets!nodes}; and the
paths of these transits are drawn at an ascending angle of about $7$° to
the ecliptic, this being the inclination of Mercury's orbit to that plane.
Dots on these paths show positions at half-hour intervals. Observe
how far apart they are. This is because Mercury is near perihelion,
where swifter motion carries him quickly across the sun. Next, consider
the May transits. They are only three in number in the same
interval, and their dates are: 6th May, 1878; 9th May, 1891; 7th
\DPPageSep{353.png}
May, 1924. They occur near Mercury's descending node, as shown,
that of 1924 being nearly central because Mercury happens to come to
inferior conjunction with the earth, at very nearly the time of reaching
its node. The half-hour dots are nearer together than in November
transits, because Mercury is near aphelion, and consequently his motion
is as slow as possible. The greatest length of a transit of Mercury
is 7\,h.\:50\,m., and the transit of 1924 approaches near this limit.

\textbf{Past and Future Transits of Venus.}---Jeremiah Horrox\index{Horrox, J.\ (1617--41), Eng.\ ast.} made the
first observation of a transit of Venus in 1639. Nearly every century
witnesses a pair of these transits. Below are four disks representing
% Fig 12.19
\begin{figure}[hbt!]
  \centering
  \Input{page_342}
  \caption{Paths of Transits of Venus at Ascending and Descending Nodes}
  \index{Venus!transits}\index{planets!nodes}
\end{figure}
the sun; and upon them are indicated apparent paths of Venus, for
all transits occurring in the 17th to the 21st centuries inclusive. In each
case the top of the disk is north, and the right-hand side west. The
dots show the position of the planet at intervals of fifteen minutes.
Pairs of transits take place at average intervals of $\frac{1}{5}$ centuries; so there
will be no transit of Venus in the 20th century.
\begin{table}[htb]
\centering
\caption{\textsc{Dates of Transits of Venus}}
\index{Venus!transits}
\begin{tabular}{c|c}
  \hline\hline
  \footnotesize\textsc{At the Ascending  Node}\rule{0pt}{3ex}
&amp; \footnotesize\textsc{At the Descending Node}
\\[1ex]
\hline
1631, December 7 &amp; 1761, June 5\rule{0pt}{3ex} \\
%[ It looks like the date-----^ was changed to 3,
%  but that is incorrect; the transit occurred on 6/6 UT.
%  http://www.nao.rl.ac.uk/nao/transit/V_1761/]
1639, December 4 &amp; 1769, June 3 \\
1874, December 9 &amp; 2004, June 8 \\
1882, December 6 &amp; 2012, June 6 \\[1ex]
\hline\hline
\end{tabular}
\end{table}

As is evident from the figure, a pair of transits at ascending node
(1631 and 1639) is followed by a pair at descending node (1761 and
1769), and so on alternately. Southern transits at ascending node
(1639 and 1882) are followed by southern transits at descending node
\DPPageSep{354.png}
(1761 and 2004); and a northern transit at descending node (1769) is
followed by a northern transit at ascending node. Rows of black dots
in contact with each other indicate the chord of the sun's disk traversed
at each transit, as seen from the center of the earth. The greatest
possible length of a transit of Venus is 7\,h.\:58\,m., and the shortest
one ever observed was that of 1874. Transits of Venus are phenomena
of great interest to astronomers, because proximity of the
planet produces a large effect of parallax. By measuring it, her distance
from the earth is found. This tells us the scale on which the
solar system is built, including therefore the length of the unit in
astronomical measures, the sun's mean distance from the earth. The
transits of 1769 and 1882 were visible in the United States. Those of
1874 and 1882 were extensively observed by costly expeditions under
the auspices of the principal governments.
\Restore

\Section{Satellites of the Planets}\index{planets!satellites}

\textbf{Satellites of the Terrestrial Planets.}---The solar system
has this curious and interesting feature, that most of its
chief planets are accompanied by moons or satellites.
Twenty-six are now known. No satellite has yet been
discovered belonging to either of the inferior planets.
There have, however, been many spurious observations of
a supposed satellite of Venus\index{Venus!supposed satellite}. Our earth has but one.
Mars has two satellites\index{Mars!satellites}, discovered by Hall\index{Hall, A.\ (1829--1907), Am.\ ast.} in 1877. They
are about seven miles in diameter, and can, be seen only by
large telescopes under favorable conditions. Phobos, the
inner moon of Mars, is less than 4000 miles from the planet's
surface, and travels round in 7\,h.\:39\,m., a period less than
one third that of Mars' rotation. To an observer on the
planet, Phobos must, therefore, seem to rise in the west
and set in the east. Its horizontal parallax is enormous,
being $21\frac{1}{5}$°. The outer moon, Deimos, is rather more than
12,000 miles from the surface of Mars, and its periodic
time is 30\,h.\:18\,m. As the planet's day is 24\,h.\:37\,m.,
Deimos must consume, allowing for parallax, about $2\frac{1}{2}$
days in leisurely circuiting the Arean sky from horizon
to horizon.
\DPPageSep{355.png}

\textbf{Satellites of the Major Planets.}\index{Jupiter!satellites}---Jupiter has eight
moons\index{Jupiter!satellites}. The four large ones (see table below) were discovered
by Galileo\index{Galile´i, G. (1564--1642), It.\ ast.} in 1610, with the first telescope ever
used astronomically. They move in nearly circular orbits.
The fifth or innermost moon was discovered in 1892 by
Barnard\index{Barnard, E. E., Prof.\ Univ.\ Chicago}. \label{p344} In 1904--1905, Perrine\index{Perrine, C.~D., Dir.\ Argentine Nat.\ Obs.} of the Lick Observatory\index{Lick Observatory}
discovered by means of photography a sixth outer satellite
of Jupiter revolving round him in a period of 251 days;
also a seventh moon, period 260 days. An eighth moon,
also exceedingly faint, was found photographically by
Melotte at Greenwich in 1908, with a period of 830 days.
Saturn\index{Saturn!satellites} is very rich in attendants, having not only the
wonderful rings (quite different from everything else in
the solar system, and undoubtedly made up of an infinity
of small individual bodies or satellites, too small ever to be
separately seen), but in addition ten distinct satellites are
known. Uranus has four moons\index{Uranus!satellites}, and far-away Neptune\index{Neptune!satellite}
has one attendant body.

\textbf{Periods, Transits, Occupations, and Eclipses.}---Table~\ref{ISJ} shows the principal data of the inner satellites of Jupiter.

\begin{table}
\TableSize
\centering
\caption{\textsc{The Inner Satellites of Jupiter}}
\label{ISJ}
\begin{tabular}{r@{\quad}|r| r| *{4}{r@{ }l@{ }} |c}
  \hline\hline
  \multicolumn{1}{m{2.5em}|}{\centering\footnotesize\textsc{Num\-ber}}
&amp; \multicolumn{1}{m{4em}|}{\centering\footnotesize\textsc{Diameter} (miles)}
&amp; \multicolumn{1}{m{6em}|}{\centering\footnotesize\textsc{Distance from Jupiter}\\ (miles)}
&amp; \multicolumn{8}{m{10em}|}{\centering\footnotesize\textsc{Sidereal Period of Revolution}}
&amp; \multicolumn{1}{m{4em}}{\centering\footnotesize\textsc{Mass in Terms of Jupiter}}
\\  \hline
    V &amp;  100 &amp;   112,000 &amp;  0 &amp; d. &amp; 11 &amp; h. &amp; 57 &amp; m. &amp; 22.7 &amp; s. &amp; ? \rule{0pt}{3ex} \\[1ex]
    I &amp; 2500 &amp;   261,000 &amp;  1 &amp;    &amp; 18 &amp;    &amp; 27 &amp;    &amp; 33.5 &amp;    &amp; $\frac{1}{60000}$ \\[1ex]
   II &amp; 2100 &amp;   415,000 &amp;  3 &amp;    &amp; 13 &amp;    &amp; 13 &amp;    &amp; 42.1 &amp;    &amp; $\frac{1}{44000}$ \\[1ex]
  III &amp; 3600 &amp;   664,000 &amp;  7 &amp;    &amp;  3 &amp;    &amp; 42 &amp;    &amp; 33.4 &amp;    &amp; $\frac{1}{11000}$ \\[1ex]
   IV &amp; 3000 &amp; 1,167,000 &amp; 16 &amp;    &amp; 16 &amp;    &amp; 32 &amp;    &amp; 11.2 &amp;    &amp; $\frac{1}{25000}$ \\[1ex]  \hline\hline
\end{tabular}
\index{Jupiter!satellites}
\end{table}

% Fig 13.20
\begin{wrapfigure}[13]{o}{0.3\textwidth}
  \centering
  \Input[0.3\textwidth]{page_345a}
  \caption{Jupiter (Shadow of Satellite in Transit)}
  \index{Jupiter!satellites}
\end{wrapfigure}
\Smaller
So near Jupiter is the fifth satellite that his disk, as seen from the
surface of the satellite, would stretch more than half way from horizon
to zenith. Referring to conditions which produce eclipses of sun and
\DPPageSep{356.png}
moon, illustrated on page~\pageref{p293}, and remembering that the orbits of
the large satellites nearly coincide with the
plane of his path, it is clear that eclipses of
the sun and of Jupiter's moons\index{eclipses of Jupiter's satellites} must occur
every time a satellite goes round the planet.
So there are nearly 9000 eclipses of the
sun and moons annually, from some point
or other of Jupiter's disk. The \textsc{iv} satellite
alone escapes eclipse---about half the time.
When the dark shadow of a satellite is
seen to cross the disk, it is called a transit
of the shadow; and the projection of the
satellite itself on the disk is called a transit of
the satellite.\break
\vspace{-\baselineskip}
%[** TN: Hack to coax two wrapfigures into one paragraph]

\noindent In the opposite part of their
orbits, a satellite's passing behind the disk is called an occultation\index{occultations!Jupiter's satellites};
and its dropping into the planet's shadow is called an eclipse. Eclipses
vary from just a few minutes to nearly five hours in length.
% Fig 13.21
\begin{wrapfigure}[19]{o}{0.2\textwidth}
  \centering
  \Input[0.15\textwidth]{page_345b}
  \caption{}
\end{wrapfigure}
Eclipses,
occultations, and transits are predicted many years in advance in the
\textit{Ephemeris}\index{Ephemeris}, and are very interesting to observe, even with small telescopes.
An opera glass will show at a glance the moons which are not
in transit, occultation, or eclipse. Sometimes all four disappear
for a time.
\Restore

\label{p345} \textbf{Light requires Time to travel.}\index{light!velocity of}---In 1675,
Roemer\index{Roemer, O.\ (reh´mer) (1644--1710), Danish ast.} first suspected this, because he found
that when Jupiter was in opposition, eclipses
of his satellites took place several minutes
earlier than the average, and when in conjunction,
the same amount later. The figure shows
why; for when Jupiter is in conjunction, sunlight
reflected from a satellite must journey an
entire diameter of the earth's orbit farther
than at opposition. Eclipses of all four moons
exhibited the same discrepancy. So the conclusion
was manifest, that light requires a definite time to
travel; and we now know, from elaborate calculations,
that light from these moons travels across the earth's
orbit in 998~seconds. Half this number, or 499, is the
constant factor in `the equation of light.' Its careful
\DPPageSep{357.png}
determination is a matter of great importance, and eclipses
of Jupiter's satellites are now recorded with high accuracy
by the photometer and by means of photography.

\Smaller
\textbf{Physical Peculiarities of Jupiter's Satellites.}\index{Jupiter!satellites}---The first satellite is
not a sphere, but a prolate
ellipsoid, its longer axis being
directed toward the center
% Fig 12.22
\begin{wrapfigure}[11]{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_346}
  \caption{Markings on Jupiter's 3d Satellite (Douglass)}
  \index{Douglass, A.~E., Am.\ ast.}\index{Jupiter!satellites}
\end{wrapfigure}
of
Jupiter---a remarkable peculiarity
discovered by W.~H.\ Pickering\index{Pickering, W.~H., Prof.\ Harv.\ Univ.}
and verified by Douglass\index{Douglass, A.~E., Am.\ ast.}.
Markings, very faint in
character, have been seen upon
all the satellites. By means of
these their periods of axial revolution
are found. Fading out at the edge may be indication that \textsc{iii}
possesses an atmosphere. Satellites \textsc{iii} and \textsc{iv}, also probably \textsc{ii}, turn
around once on their axes while going once around Jupiter, a relation
like that of our moon to the earth. Douglass, from observations of very
narrow belts on \textsc{iii} in 1897, makes its period of rotation 7\,d.\:5\,h. Also he
has published the above sketch-map of the satellite's surface. Near the
poles of \textsc{iii} and \textsc{iv} white spots have been seen by several observers.
Douglass makes the rotation period of \textsc{i} to be 12\,h.\:24\,m.
\Restore

\label{p346} \textbf{Satellites of Saturn.}\index{Saturn!satellites}---Table~\ref{SS} shows the principal data
of the satellites of Saturn.

% 13.8
\begin{table}
\TableSize
\centering
\caption{\textsc{The Satellites of Saturn}}
\label{SS}\index{Saturn!satellites}
\index{Bond, W. C., (1789--1859), Am.\ ast.}
\begin{tabular}{r@{\ }|l|r@{ }r@{ }l|r@{\ }|r|*{3}{r@{ }}r}
\hline\hline
  \multicolumn{1}{m{2em}|}       {\centering \footnotesize \textsc{Num\-ber}}
&amp; \multicolumn{1}{m{6em}|}       {\centering \footnotesize \textsc{Name of Satellite  Name of Discoverer}}
&amp; \multicolumn{3}{m{4.5em}|}     {\centering \footnotesize \textsc{Date of Discovery}}
&amp; \multicolumn{1}{@{}m{3em}@{}|} {\centering \footnotesize \textsc{Diam\-eter}}
&amp; \multicolumn{1}{m{4em}|}       {\centering \footnotesize \textsc{Distance from Saturn}}
&amp; \multicolumn{4}{m{5em}}        {\centering \footnotesize \textsc{Sidereal Period of Revolution}} \\
  \hline
  &amp;  &amp;  &amp;  &amp; &amp; \footnotesize miles\rule{0pt}{2ex}
&amp; \multicolumn{1}{c|}{\footnotesize miles}
&amp; \footnotesize  d. &amp;\footnotesize h. &amp; \footnotesize m.
&amp; \multicolumn{1}{c}{\footnotesize s.}
\\[1ex]
  I &amp; Mimas              &amp; 17 &amp; Sept. &amp; 1789 &amp;  750
&amp;   117,000 &amp;  0 &amp; 22 &amp; 37 &amp; 5.7 \\
    &amp; W. Herschel &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp; \\
    II &amp; Enceladus       &amp; 28 &amp; Aug. &amp;1789  &amp;  800
&amp;   157,000 &amp; 1 &amp; 8 &amp; 53 &amp; 6.9 \\
    &amp; W. Herschel &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp; \\
   III &amp; Tethys        &amp; 21 &amp; Mar. &amp;1684  &amp; 1100
&amp;   186,000 &amp; 1 &amp; 21 &amp; 18 &amp; 25.6 \\
       &amp; J.~D.~Cassini &amp;&amp;&amp;&amp;&amp;&amp;&amp; \\
    IV &amp; Dione         &amp; 21 &amp; Mar. &amp; 1684  &amp; 1200
&amp;   238,000 &amp; 2 &amp; 17 &amp; 41 &amp; 9.3 \\
       &amp; J.~D.~Cassini &amp;&amp;&amp;&amp;&amp;&amp;&amp; \\
     V &amp; Rhea         &amp; 23 &amp; Dec. &amp; 1672  &amp; 1500
&amp;   332,000 &amp;  4 &amp; 12 &amp; 25 &amp; 11.6 \\
       &amp; J.~D.~Cassini &amp;&amp;&amp;&amp;&amp;&amp;&amp; \\
    VI &amp; Titan            &amp; 25 &amp; Mar. &amp; 1655  &amp; 3000
&amp;   771,000 &amp; 15 &amp; 22 &amp; 41&amp; 23.2 \\
       &amp; C.~Huygens &amp;&amp;&amp;&amp;&amp;&amp;&amp; \\
     X &amp; Themis      &amp; 28 &amp; Apr. &amp; 1905  &amp;   40
&amp;   906,000 &amp; 20 &amp; 20 &amp; 24 &amp; \ldots \\
       &amp; W.~H.~Pickering &amp;&amp;&amp;&amp;&amp;&amp;&amp; \\
   VII &amp; Hyperion         &amp; 16 &amp; Sept.&amp; 1848 &amp;  500
&amp;   934,000 &amp; 21 &amp; 6 &amp; 39 &amp; 27.0 \\
       &amp; W.~C.~Bond &amp;&amp;&amp;&amp;&amp;&amp;&amp; \\
  VIII &amp; Iapetus       &amp; 25 &amp; Oct. &amp; 1671  &amp; 2000
&amp; 2,225,000 &amp; 79 &amp; 7 &amp; 54 &amp; 17.1 \\
       &amp; J.~D.~Cassini &amp;&amp;&amp;&amp;&amp;&amp;&amp; \\
    IX &amp; Phoebe      &amp; 14 &amp; Mar. &amp; 1899  &amp;   40
&amp; 8,110,000 &amp; \multicolumn{4}{l}{550.44 days}  \\
       &amp; W.~H.~Pickering &amp;&amp;&amp;&amp;&amp;&amp;&amp; \\[1ex]
\hline\hline
\end{tabular}
\index{Huygens, C.\ (hy´genz) (1629--95), Dutch ast.}%
  \index{Cassini, J.~D.\ (kas-se´ne) (1625--1712), It.-Fr.\ ast.}%
  \index{Pickering, W.~H., Prof.\ Harv.\ Univ.}%
  \index{Di´o-ne, satellite of Saturn}%
  \index{Enceladus, satellite of Saturn}%
  \index{Hype´rion, satellite of Saturn}%
  \index{Iapetus (e-ap´e-tus), satellite of Saturn}%
  \index{Mimas, satellite of Saturn}%
  \index{Phoebe, satellite of Saturn}%
  \index{Rhea, satellite of Saturn}%
  \index{Tethys (teth´iz), satellite of Saturn}%
  \index{Themis, satellite of Saturn}%
  \index{Titan, satellite of Saturn}%
\end{table}
\DPPageSep{358.png}

The orbits of the five inner satellites are circular. The
satellites first discovered are easiest to see, the largest,
Titan\index{Titan, satellite of Saturn}, being nearly always visible even with very small
instruments. Its mass according to Stone is $\frac{1}{4600}$ that of
Saturn. Eclipses and transits of some of the satellites
have occasionally been observed with large telescopes.

\textbf{Satellites of Uranus.}\index{Uranus!satellites}---Table~\ref{SU} shows the principal data
of the satellites of Uranus:---
% 13.9
\begin{table}[h]
\TableSize
\centering
\caption{\textsc{The Satellites of Uranus}}
\label{SU}\index{Uranus!satellites}
\begin{tabular}{r@{\qquad}|cl|r| c*{4}{r@{ }l} }
  \hline\hline
  \multicolumn{1}{m{4em}|}{\centering\footnotesize\textsc{Number}}
&amp; \multicolumn{2}{m{6em}|}{\centering\footnotesize\textsc{Name of Satellite}}
&amp; \multicolumn{1}{m{6em}|}{\centering\footnotesize\textsc{Distance from Uranus} (miles)}
&amp; \multicolumn{9}{m{14em}}{\centering\footnotesize\textsc{Sidereal Period of Revolution}}
\\  \hline
I   &amp;&amp; Ariel   &amp; 120,000 &amp;&amp; 2  &amp; d. &amp; 12 &amp; h. &amp; 29 &amp; m. &amp; 21.1 &amp; s.\rule{0pt}{3ex}\\
II  &amp;&amp; Umbriel &amp; 167,000 &amp;&amp;  4 &amp;    &amp;  3 &amp;    &amp; 27 &amp;    &amp; 37.2 &amp;   \\
III &amp;&amp; Titania &amp; 273,000 &amp;&amp;  8 &amp;    &amp; 16 &amp;    &amp; 56 &amp;    &amp; 29.5 &amp;   \\
IV  &amp;&amp; Oberon  &amp; 365,000 &amp;&amp; 13 &amp;    &amp; 11 &amp;    &amp;  7 &amp;    &amp;  6.4 &amp;   \\[1ex]
\hline\hline
\end{tabular}
\index{Ariel, satellite of Uranus}%
  \index{Umbriel, satellite of Uranus}%
  \index{Titania, satellite of Uranus}%
  \index{Oberon, satellite of Uranus}%
\end{table}

The two inner satellites are about 500 miles in diameter,
and the outer ones are nearly twice as large. For about
thirty years, while the earth is near a line perpendicular
to their orbits, the satellites may always be seen whenever
Uranus is visible. Only great telescopes, however, will
show them. The satellites of Uranus revolve in planes
nearly at right angles to the planet's orbit, and their
motion is retrograde, or from east to west. Ariel\index{Ariel, satellite of Uranus} and
Umbriel\index{Umbriel, satellite of Uranus} were discovered by Lassell\index{Lassell, W.\ (1799--1880), Eng.\ ast.} in 1851; Titania\index{Titania, satellite of Uranus} and
Oberon\index{Oberon, satellite of Uranus}, by Sir William Herschel\index{Herschel, Sir F. W. (1738--1822), Eng.\ ast.} in 1787.

\textbf{Satellite of Neptune.}\index{Neptune!satellite}---Its distance from Neptune is
224,000 miles, the period of revolution 5~d.\ 21~h.\ 3~m., with
motion retrograde. It was discovered by Lassell in 1846,
only a few weeks after the planet itself was found. Probably
Neptune's satellite is about the size of our own moon.
\DPPageSep{359.png}

\Section{Atmospheres of the Planets}\index{planets!atmospheres}

\textbf{Atmosphere of Mercury.}\index{Mercury!atmosphere}---Without much doubt, the
atmosphere of Mercury is inappreciable. His color by
day, when best observable, resembles that of the pale moon
under like conditions. If there is no air, then quite certainly
no water; as evaporation would continue to supply
a slight atmosphere as long as it lasted. The improbability
of an atmosphere surrounding this planet is confirmed
by the argument from the kinetic theory of gases,
already stated (page~\pageref{p244}); for Mercury's mass is too slight
to retain
an envelope of aqueous vapor.

\label{p348}\textbf{Atmosphere of Venus.}\index{Venus!atmosphere}---Observations of Venus when
very near her inferior conjunction prove the existence of
an atmosphere which is thought
to be more dense than ours. The
illustration shows part of the evidence:
Venus is just entering
upon the sun's disk during the
transit of 1882, and sunlight shining
through the planet's atmosphere
illuminates it in a nearly
complete ring surrounding Venus,
which appears dark because her
sunward side is turned away from
us. Also an aureole surrounds
the dark disk when in transit; and
on several occasions when Venus
has passed close above or below
the sun at inferior conjunction, just escaping a transit,
the
% Fig 13.23
\begin{wrapfigure}{o}{0.35\textwidth}
  \centering
  \Input[0.35\textwidth]{page_348}
  \caption{Venus entering the Disk of the Sun in 1882 (Langley)}
  \index{Langley, S.~P.\ (1834--1906), Am.\ ast.\ and physicist}\index{Venus!transits}
\end{wrapfigure}
horns of the atmospheric ring have been observed
almost to meet, forming a nearly complete ring. This
crescent would be little more than a complete semicircle,
if there were no atmosphere.
\DPPageSep{360.png}

\textbf{Atmosphere of Mars.}\index{Mars!atmosphere}---Doubtless a thin atmosphere envelops
this planet, although neither so extensive nor so
dense as our own. While usually cloudless, occasional and
temporary veilings of some of the best known regions of
the planet have been seen. Many careful investigators,
using the spectroscope, have found absorption lines in the
spectrum of Mars thought to be due to neither solar nor
terrestrial atmosphere, indicating water vapor in a gaseous
envelope. Also regular shrinking and subsequent
enlarging of the polar caps\index{Mars!polar caps} are excellent evidence that the
ruddy planet is surrounded by a medium acting as an
agent in the formation and deposition of snow. Changing
intensity of the light, with a change of the planet's
phase also indicates the presence of an atmosphere.
Another important piece of evidence is the discovery of a
twilight arc\index{Mars!twilight arc} of about $12$°, causing a regular increase of the
planet's apparent diameter through the equator, as phase
increases. Quite certainly density of the atmosphere of
Mars cannot exceed one half that of our own, and probably
it is very much less. Referring again to the kinetic
theory of gases, and calculating the critical velocity for
Mars, we find it to be rather more than three miles per
second. Free hydrogen, then, could not be present in his
atmosphere, but other gases might. Campbell\index{Campbell, W. W., Dir.\ Lick Obs.} and Keeler\index{Keeler, J.~E.\ (1857--1900), Am.\ ast.}
have found the spectrum of Mars practically identical with
that of the moon, indicating probably that the spectroscopic
method is inconclusive.

\textbf{Atmosphere of Jupiter and Saturn.}\index{Jupiter!atmosphere}\index{Saturn!atmosphere}---The indications of a
dense and very extended atmosphere encircling Jupiter
are unmistakable:---ceaseless changes in markings called
belts and spots; varying length of the planet's day in different
regions of latitude; absorption shadings in the inferior
portion of Jupiter's spectrum; and withal his giant
mass potent to retain captive all gaseous materials originally
\DPPageSep{361.png}
belonging to him. Probably in point of both depth
and chemical constitution, the atmosphere of Jupiter is
widely diverse from our own; in fact, it is not unlikely
that this great planet may still be in a gaseous condition
throughout. At least the depth of atmosphere must
be reckoned in thousands of miles. Dark bands in the
red may be due to some substance in the planet's atmosphere
not in our own, and possibly metallic. In
nearly every respect the atmosphere of the ball of Saturn
resembles that of Jupiter, but the ring gives every appearance
of being without atmosphere. Saturn's spectrum, too,
is quite the same as Jupiter's, and its intenser absorption
bands indicate a little more plainly the presence of gaseous
elements as yet unrecognized on the earth and in the
sun. Another indication of atmosphere, common to both
these planets, is the shading out or absorption of all markings
at the limb or edge of their disks.

\textbf{Atmosphere of Uranus and Neptune.}\index{Uranus!atmosphere}\index{Neptune!atmosphere}---So remote are
these planets, and so small their apparent disks, that practically
nothing has yet been ascertained concerning their
atmospheres except by the spectroscope. Uranus is bright
enough so that its spectrum shows 10 broad diffused
bands, between \textit{C} and \textit{F}, indicating strong absorption by a
dense atmosphere very different from that of the earth,
as Keeler\index{Keeler, J.~E.\ (1857--1900), Am.\ ast.} has shown. The position of these lines in the
red is sufficient to account for the sea-green tint of the
planet. Neptune's color is almost the same; and its spectrum,
if not so faint, would probably show similar absorption
bands.


\Section{Surfaces of the Planets}\index{planets!surfaces}

% Fig 13.24
\begin{wrapfigure}{o}{0.34\textwidth}
  \centering
  \Input[0.35\textwidth]{page_351}
  \caption{The Zodiacal Light in Tropic Latitudes}
  \label{fig12.24}\index{zodiacal light}
\end{wrapfigure}
\textbf{Zodiacal Light.}\index{zodiacal light}---Interior to the orbit of Mercury, but
possibly stretching out beyond the path of the earth, is
a widely diffused disk of interplanetary particles moving
\DPPageSep{362.png}
round the sun, mildly reflecting its rays to us, and called the
zodiacal light. Douglass\index{Douglass, A.~E., Am.\ ast.} first photographed it in 1901.

\Smaller
Figure~\ref{fig12.24} shows it well---a faintly luminous and ill-defined
triangular area, expanding downward along the ecliptic toward the
western horizon, shortly
after twilight on
clear, moonless nights
from January to April.
Its central region is
brightest and slightly
yellowish. It has suffered
no change for
more than two centuries.
Its spectrum is
short and continuous,
without bright lines,
though possibly a few
faint dark ones are
present. In tropic
latitudes, where the
ecliptic always stands
high above the horizon,
the zodiacal light
can be well seen in
clear skies the year
round. In our middle
latitudes it cannot be
seen early in autumn
evenings, because of
the slight inclination
of the ecliptic to the
horizon, as the next
figure shows: that part
of the zodiacal\break
\vspace{-\baselineskip}
%[** TN: Hack to coax two wrapfigures into one paragraph]

\noindent
% Fig 13.25
\begin{wrapfigure}[11]{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_352a}
  \caption{Why Zodiacal Light is Invisible in our Fall Evenings}
\end{wrapfigure}
light near \textit{a} and above the horizon, \textit{HH}, is lost in
low-lying mist and haze. In autumn it must be looked for in the east
just before dawn, leaning toward the right in our latitudes.

\textbf{The Gegenschein.}\index{gegenschein (gay´gen-shine)}---This is a name of German origin, given to a
zodiacal counterglow discovered by Brorsen\index{Brorsen, T. (1819--93), Ger.\ ast.} in 1854---an exceedingly
faint and evenly diffused nebulous light, nearly opposite the sun, sometimes
slightly south and again somewhat north of the ecliptic. A
bright star or planet near by is sufficient to overmaster its light; even
proximity to the Milky Way obliterates it. Sometimes the gegenschein
\DPPageSep{363.png}
is circular, at others elliptic; and its diameter varies between $3$° and $13$°,
according to Barnard\index{Barnard, E. E., Prof.\ Univ.\ Chicago} and Douglass\index{Douglass, A.~E., Am.\ ast.}. It is best seen in September and
October, in Sagittarius
and Pisces. No satisfactory
theory as to its cause
exists. Very likely the
gegenschein is due to
clouds of small interplanetary
bodies, though
possibly it may be caused
by abnormal refraction in
our atmosphere.
\Restore

\textbf{Surface of Mercury.}\index{Mercury!surface of}---Mercury is so small a planet and
so distant from the earth that the disk is disappointing.
In the northern hemisphere
he is
% Fig 13.26
\begin{wrapfigure}[15]{i}{0.4\textwidth}
  \centering
  \Input[0.4\textwidth]{page_352b}
  \caption{Typical Drawings of Mercury, 1896 (Lowell)}
  \index{Lowell, P., Am.\ ast.}
\end{wrapfigure}
best seen
near greatest elongation
east in spring, and greatest
elongation west in
autumn; because he is
then in the northernmost
part of the zodiac, where
meridian altitude is as
great as possible. Markings
on the surface of
Mercury are described by
Lowell\index{Lowell, P., Am.\ ast.} as less difficult
than those on Venus;
without color, and lines rather than patches; and the fact
that they do not change from hour to hour, nor perceptibly
from day to day, shows that the planet's periods
of rotation and revolution are the same. Above are nine
drawings of the planet in October, 1896; also \vpageref{p353}
Lowell's chart of all that portion of the surface of
Mercury ever visible, amounting to five eighths of the
entire spherical superficies. The surface is probably rough,
\DPPageSep{364.png}
because, like the moon, the amount of light reflected
from a unit of surface increases from crescent phase
to full.

\textbf{Illuminated Hemisphere of Venus.}\index{Venus!illuminated hemisphere}---The unillumined
half of Venus appears to be forever sealed from investigation
by our eyes; but
that part of
% Fig 13.27
\begin{wrapfigure}{i}{0.4\textwidth}
  \centering
  \Input[0.4\textwidth]{page_353a}
  \caption{Chart of All the Visible Surface of Mercury (Lowell)}
  \label{p353}\index{Lowell, P., Am.\ ast.}
\end{wrapfigure}
the sunward
hemisphere turned toward
us has been repeatedly
drawn during the
last 250~years. Only dull,
indefinite markings, or
spots covering large areas
have, however, been seen
until recently. The illustration
below shows the
general nature of markings
drawn by the earlier observers. Frequently the terminator
was irregularly curved, indicating mountains of great
height; and polar caps were depicted. According to recent
observations of Lowell\index{Lowell, P., Am.\ ast.}, however, the disk of Venus is colorless,
and resembles `simply a design in black and white
over which is drawn a brilliant straw-colored veil.' This
\DPPageSep{365.png}
veil is doubtless the planet's atmosphere. No polar caps
were seen.

% Fig 13.28
\begin{figure}[hbt!]
  \centering
  \Input{page_353b}
  \caption{Venus as drawn by Mascari in 1892}
  \index{Mascari, A., ast.\ Catania Obs.}\index{Venus!drawings}
\end{figure}

\Smaller
Markings on the disk, seen and drawn independently by Lowell\index{Lowell, P., Am.\ ast.} and
his assistants, Douglass, See\index{See, T.~J.~J., Am.\ ast.}, and others, are broad belts, not spots.
Three specimen
% Fig 13.29
\begin{wrapfigure}[8]{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_354a}
  \caption{Venus as drawn by Lowell in 1896}\index{Lowell, P., Am.\ ast.}\index{Venus!drawings}
\end{wrapfigure}
drawings are
adjacent. The markings are
mostly great circles on the
planet's surface, and many
of them radiate from a single
center, as the accompanying
chart shows. They
partake of the general brilliance
of the disk, and their
lack of contrast renders them difficult objects, except to observers
trained in visualizing faint planetary detail. Three slight protuberances,
perhaps mountains, were detected on the terminator. Although
these observations were made in the steady air of Flagstaff, Arizona,
there is reason\break
\vspace{-\baselineskip}
%[** TN: Hack to coax two wrapfigures into one paragraph]

% Fig 13.30
\begin{wrapfigure}[15]{o}{0.4\textwidth}
  \centering
  \Input[0.4\textwidth]{page_354b}
  \caption{Chart of Visible Hemisphere of Venus (Lowell)}
  \index{Lowell, P., Am.\ ast.}\index{Venus!chart}
\end{wrapfigure}
\noindent for doubting the reality of such elusive markings,
and many astronomers regard them as optical illusions purely, to be
explained by principles of
physiological optics. Their
existence cannot be accepted
as fact until fully confirmed
by observers in other parts
of the world. Taken in connection
with the practical certainty
of an atmosphere, the
constant aspect of one hemisphere
perpetually toward the
sun is very significant; probably
atmospheric currents
would gradually remove all
water and nearly all moisture
from the sunward hemisphere,
and deposit it as ice
on the dark side of the
planet. This affords a likely
explanation of the so-called phosphorescence of the dark hemisphere;
for a faint light diffused over the unilluminated portion of
the disk has repeatedly been seen by many good observers.
\Restore

\textbf{Surface of Mars in General.}\index{Mars!surface of}---Huygens\index{Huygens, C.\ (hy´genz) (1629--95), Dutch ast.}, in 1659, made
the first sketch of Mars to show definite markings; and in
\DPPageSep{366.png}
1840, Beer\index{Beer, W. (bay´er) (1797--1850), Ger.\ banker and ast.} and Maedler\index{Maedler@v.\ Mædler, J. H. (med´ler) (1794--1874), Ger.\ ast.} drew the
% Fig 13.31
\begin{wrapfigure}[19]{i}{0.3\textwidth}
  \centering
  \Input[0.25\textwidth]{page_355}
  \caption{Mars in 1877 (Green)}\index{Green, N.~E.\ (1823--99), Eng.\ ast.}
\end{wrapfigure}
first chart of the planet.
The two hemispheres exhibit a marked difference in brightness,
the northern being much brighter. Probably it is
land, while the southern is mainly water\index{Mars!water on}; but in general
there is no analogy with the present scattering of land
and water on the earth. Four to eleven is the proportion
here; but on Mars land somewhat
predominates. Probably the waters
have for the most part slight depth.
Extensive regions which change from
yellow, like continents, to dark brown,
are thought to be marshes, varying
depth of water causing the diversity
of color. Mars appears to be so far
advanced in his life history that areas
of permanent water are very limited.
The border of the disk is brighter
than the interior, and changes in apparent
brightness of certain regions
are well established. In considerable
part these depend upon the angle
of vision as modified by axial
turning of the planet. Photographs
of Mars have been taken, but they
show only salient features of the disk. Markings of Syrtis
Major, a well-known region (see fifth figure on page~\pageref{p358})
appear to be vegetation rather than water. Smoothness
of the terminator\index{Mars!terminator}, along which a few projections and
flattenings have been observed, indicates clearly that the
Martian surface is relatively flat, as compared with the
present rugged exterior of earth and moon.

\Smaller
\textbf{Orbits of Earth and Mars.}\index{earth!orbit}\index{Mars!orbit}---Inner circle in next illustration represents
orbit of earth, and outer one orbit of Mars eccentrically placed
in true proportion. Around inner circle are indicated positions of earth
\DPPageSep{367.png}
in different months, and around outer circle are shown the points occupied
by Mars at opposition time in the several years indicated. The
most favorable opposition of Mars, or when that planet is at the minimum
distance of 35,000,000 miles from the earth, can take place only
in August and September, as indicated on right-hand side of diagram.
% Fig 13.32
\begin{figure}[hbt!]
  \centering
  \Input{page_356}
  \caption{Orbits of Mars and Earth, showing Least and Greatest Distances at Opposition}\index{Mars!opposition}
\end{figure}
Similarly on left-hand side the least favorable oppositions occur in those
years when the opposition time falls in February and March. Exact
positions of Mars at recent favorable oppositions are shown at 1877
and 1892. But at opposition, October, 1894, although the planet was
then much farther from earth, still he culminated higher than in 1892;
because the sun crosses the
meridian lower in October than in August.
Higher northern declination enabled the planet to be observed to
greater advantage in 1894 than in 1892, because nearly all the observatories
of the world are located in its northern hemisphere. Subsequent
\DPPageSep{368.png}
favorable oppositions of Mars are July 1907,
September 1909, and August 1924. The
last occurs very near the same position as
1892.
\Restore

\textbf{Polar Caps of Mars.}\index{Mars!polar caps}---These were
discovered by Cassini\index{Cassini, J.~D.\ (kas-se´ne) (1625--1712), It.-Fr.\ ast.} in 1666.
Rather more than a century later,
Sir William Herschel\index{Herschel, Sir F. W. (1738--1822), Eng.\ ast.} first made out
their variation in size with progress
of the seasons on Mars, which are
in general similar to ours, although
longer, because the Arean year is
longer. Near the end of Martian
winter the polar caps are largest,
and they gradually shrink in size
till the end of summer.

\Smaller
This remarkable diminution of the south
polar cap has been repeatedly observed since
Herschel's time, and the illustrations show
its progress during the Martian spring and
summer of 1894. Without much doubt,
this shrinking of the polar cap is due
to melting of snow and ice. But Stoney\index{Stoney, G.~J., Brit.\ physicist},
arguing upon principles outlined on page~\pageref{p244},
concludes that water cannot remain on
Mars; that his atmosphere is mainly nitrogen
and argon, with carbon dioxide, distillation
of the vapor of which toward the poles
alternately may perhaps account for the
phenomena of the caps. The north polar
cap covers the planet's pole of rotation
almost exactly; but the center of the
south is now displaced about 200 miles
from the true pole, and this distance varies
irregularly from time to time. At the
beginning of the summer season of 1892,
the south polar cap was 1200 miles in diameter;
gradually a long, dark line appeared
near the middle, and eventually cut the cap
in two; the edge became notched; dark
\DPPageSep{369.png}
% Fig 13.34 a-f
\begin{figure}[p!]
  \centering
  \subfloat[Top of Fork on left is Fastigium Aryn. Dark Horn nearly central is Margaritifer Sinus]{\Input[0.349\textwidth]{page_358a}}
  \hfil
  \subfloat[Solis Lacus is nearly central. Double Nectar runs to the left from it]{\Input[0.349\textwidth]{page_358b}}

  \subfloat[Seven Canals diverge from Sinus Titanum. Eumenides-Orcus threads Nine Oases]{\Input[0.35\textwidth]{page_358c}}
  \hfil
  \subfloat[The Rectangle is Trivium Charontis. Dark Mare Cimmerium is central.]{\Input[0.35\textwidth]{page_358d}}

  \subfloat[Largest Roundish Area is Hellas. Below Hellas is the pointed Syrtis Major]{\Input[0.35\textwidth]{page_358e}}
  \hfil
  \subfloat[Among Double Canals are Euphrates (nearly vertical), and Asopus perpendicular to it]{\Input[0.35\textwidth]{page_358f}}

  \caption{Mars according to Schiaparelli and Lowell (1877--1894)}
  \label{p358}
  \index{canals of Mars}\index{Mars|see{canals of Mars}}\index{Lowell, P., Am.\ ast.}\index{Mars!markings on}\index{Schiaparelli, G.~V.\ (skap-pa-rell´ly) (1835--1910), It.\ ast.}\index{Solis Lacus on Mars}
\end{figure}%
\DPPageSep{370.png}
spots grew in its central regions, and isolated patches were seen to
separate from the principal mass, and later dissolve and disappear.
The phenomenon was similar in 1894, as Barnard's 12~pictures of
the cap show (page~\pageref{p357}). In three months the cap's diameter had
shrunk to 170~miles, and in eight months it had vanished entirely.
\Restore

\textbf{Canals and Oases of Mars.}\index{canals of Mars}\index{Mars|see{canals of Mars}}\index{Mars!oases}---This diminution of the polar
cap seems to afford a key to the physiographic situation
on Mars; for, coincidently with its shrinking, a strange
system of markings begins to develop, traversing continental
areas in all directions, and forming a network of darkish
narrow lines.

\Smaller
Six engravings \vpageref{p358} exhibit the planet's surface in all longitudes,
and show the canals much intensified. All appear on the flat disk as
either straight or uniformly curving lines; and if transferred to the surface
of a globe,
% Fig 13.33
\begin{wrapfigure}[43]{o}{0.3\textwidth}
  \centering
  \Input[0.25\textwidth]{page_357}
  \caption{Shrinkage and Disappearance of South Polar Cap in 1894 (Barnard in \textit{Popular Astronomy})}
  \label{p357}
  \index{Barnard, E. E., Prof.\ Univ.\ Chicago}\index{Mars!polar caps}
  \index{Popular Astronomy@\emph{Popular Astronomy} (monthly)}
\end{wrapfigure}
they are found to traverse it on arcs of great circles.
Many canals connect with projections of bluish-green regions, which
may be actual gulfs and bays. At numerous intersections with other
canals are oval or circular spots, called oases, many of them appearing
like hubs from which canals radiate as spokes. Their average diameter is
about 130~miles. For example, seven canals converge to Lacus Ph{\oe}nicis.
The most signal marking of this character is in Arean latitude about $30$°
south (shown above middle of the second disk opposite). Though
often called the `oculus,' or eye of Mars, it is now generally known as
Solis Lacus, or Lake of the Sun. Its breadth is 300~miles, and its length
540~miles. Through Solis Lacus run narrow double canals, whose
length is much less than the average. In general the canals average
about 1200~miles; but the longest one is Eumenides-Orcus, whose combined
length is 3500~miles, or nearly equal to the entire diameter of
the planet. Length enhances their visibility, for the average width is
only about 30~miles. Canals were first discovered by Schiaparelli\index{Schiaparelli, G.~V.\ (skap-pa-rell´ly) (1835--1910), It.\ ast.} in
1877. They are bluish-green in color, and have been repeatedly observed
by their discoverer in Italy; Lowell\index{Lowell, P., Am.\ ast.}, in Arizona; Perrotin\index{Perrotin, J.~H.\ (1846--1904), Fr.\ ast.}, in
France; W.~H. Pickering\index{Pickering, W.~H., Prof.\ Harv.\ Univ.}, in South America; astronomers of the Lick
Observatory\index{Lick Observatory}; Wilson\index{Wilson, H.~C., Dir.\ Carleton Col.\ Obs.}, in Minnesota; and Williams\index{Williams, A.~S., Eng.\ ast.}, in England. About
200 have been seen in all. But a steady atmosphere is requisite to
reveal them. Photography has certified the actual existence of some
of the canals.

\textbf{Doubling of the Canals and Oases.}---Lowell thus describes this
marvelous phenomenon:---

`Upon a part of the disk where up to that time a single canal has
been visible, of a sudden, some night, in place of the single canals, are
\DPPageSep{371.png}
perceived twin canals,---as like, indeed, as twins, if not more so, running
side by side the whole length of the original canal, usually for
upwards of a thousand miles, of the same size throughout, and absolutely
parallel to each other. The pair may best be likened to the
twin rails of a railroad track. The regularity of the thing is startling.'

Many double canals are shown in the sixth figure on page~\pageref{p358}. Average
distance between the twin canals is 150 to 200~miles. This phenomenon,
still a mystery, does not appear to be an effect of either
optical illusion or double refraction; but rather a really double existence,
seen only under exceptionally favorable conditions of atmosphere.
More strangely still, the oases too are occasionally seen to be double.

\textbf{Meaning of Canal and Oasis.}---It is the design of physical science
not only to record but to explain appearances; and the canals, whether
double or single, have, to many astronomers who have seen them, a
look of artificiality rather than naturalness. If we accept the former,
the explanation of the canals themselves, advanced by W.~H. Pickering\index{Pickering, W.~H., Prof.\ Harv.\ Univ.}
and reinforced by the argument of Lowell\index{Lowell, P., Am.\ ast.}, seems very plausible:
water is scarce on the planet; with melting of the polar caps, it is gradually
conducted along narrow channels through the middle of the
canals, thereby irrigating areas of great breadth which, with the advance
of the season, become clothed with vegetation. Similarly the
oases; and at our great distance, it is vegetation which, although invisible
in the Arean winter, grows visible as canal and oasis with every
return of spring. The fact that oases are seen only at junctions of
canals, and not elsewhere, greatly strengthens this argument. Of
course, acceptance of this theory implies that Mars in ages past, has
been, and may be still, peopled by intelligent beings; and that continuation
of their existence upon that planet, during secular dissipation of
natural water supply, has rendered extensive irrigation a prime requisite.
For animal life, of types known to us, is dependent upon vegetable life;
which, in turn is conditional upon water distribution, either natural or
artificial. But only by long continued observation of the behavior of
canal and oasis in both hemispheres of Mars, can we hope for a rational
solution of the question of life in another world than ours. In 1905
Molesworth\index{Molesworth, P.~B.\ (1867--1908), Eng.\ ast.} published many fine observations of detail on the surface
of Mars, made in the highly favorable atmosphere of Ceylon.
\Restore

\textbf{Seasonal Changes.}---Striking seasonal changes seen to
keep step with progress of Mars in his orbit, are best exhibited
by direct comparison between drawings at intervals
of several months. Three such are chosen in Figure~\ref{fig13.35}. The
region known as Hesperia is central in all. The first, 7th
\DPPageSep{372.png}
% Fig 13.35 a, b, c
\begin{sidewaysfigure}[p!]
  \begin{minipage}{0.3\textwidth}
    \centering
    \Input{plate_via}
    \caption{\textit{Early Spring.}}
  \end{minipage}
  \hfil
  \begin{minipage}{0.3\textwidth}
    \centering
    \Input{plate_vib}
    \caption{\textit{Early Summer.}}
  \end{minipage}
  \hfil
  \begin{minipage}{0.3\textwidth}
    \centering
    \Input{plate_vic}
    \caption{\textit{Late Summer.}}
  \end{minipage}
  \caption{\textsc{The Planet Mars}, three views, showing changing seasons of Hesperia (\textit{from original drawings by Lowell}).}
  \label{fig13.35}\index{Mars!seasonal changes}\index{Hesperia, on Mars}\index{Lowell, P., Am.\ ast.}
\end{sidewaysfigure}
\DPPageSep{373.png}
%[Blank Page]
\DPPageSep{374.png}
June, 1894, corresponds to early spring on Mars. South
polar snows have just begun to melt. Everywhere encircling
it is the dark area, as if water from the melting of the
cap; for this band follows the cap as it shrinks, becoming
less in width as the cap grows smaller. This is shown
in the middle disk, which corresponds to early summer.
Mark the other changes in the disk: (1)~the general thinning
out of dark areas which on the actual planet are
greenish-blue; (2)~the increase in intensity of reddish
ochre regions through the southern hemisphere, as if the
water had in considerable part evaporated, Hesperia
already beginning to show as an oblique, \textsf{V}-shaped, reddish
marking in the center of the disk; (3)~progress in
development of canals, though not as yet far advanced.
As the planet approaches late summer, in the third drawing,
Hesperia has become a broad cleft through the water
area, three canals are particularly well developed in the
northern hemisphere, and the south polar cap has practically
vanished. In other longitudes like changes went on
simultaneously, and in the same significant and seemingly
obvious direction.

\textbf{Discoveries of Small Planets.}\index{asteroids}\index{planets!small}---In 1800, the closing year
of the eighteenth century, conspicuous absence of a planet
between Mars and Jupiter as required by Bode's law\index{Bode, J. E., (b\=o´d\u uh) (1747--1826), Ger.\ ast., law of}, led to
an association of 24~astronomers intent upon search for
the missing body. Piazzi\index{Piazzi, G.\ (pe-at´si) (1746--1826), It.\ ast.} of Sicily inaugurated the long
list of discoveries by finding the first one on the first night
of the 19th century (1st January, 1801). He called it
Ceres\index{Ceres, first small planet discovered}, that being the name of the tutelary divinity of
Sicily. Three others, named Pallas\index{Pallas, small planet}, Juno\index{Juno, small planet}, and Vesta\index{Vesta, small planet},
were found by 1807, but the fifth was not discovered till
1845.

\Smaller
Since 1847 no year has failed to add at least one to the number, and
in 1892 the increase was 28. The total number is now more than
\DPPageSep{375.png}
600. Of these, 80 were discovered in the United States, mainly by Peters\index{Peters, C.~H.~F.\ (1813--90), Am.\ ast.}
(48) at Clinton, New York, and Watson\index{Watson, J.~C.\ (1838--80), Am.\ ast.} (22) at Ann Arbor, Michigan.
Palisa\index{Palisa, J.\ (pa-le´sa), ast.\ Vienna Obs.}, of Vienna, found no less than 84. In 1891, Wolf\index{Wolf, M., Prof.\ Univ.\ Heidelberg} of Heidelberg
inaugurated discoveries of these bodies by the aid of photography,
and he has discovered over 100 in this manner: a sensitive plate exposed
for two or three hours to a suspected region of sky makes a permanent
record of all the stars as round disks, and of any small planets
as short trails because of their apparent motion during exposure. So
they are discovered about 20-fold more readily than by the old-fashioned
method at the eyepiece of a telescope. Charlois\index{Charlois, A.\ (shar-lwah´), ast.\ Nice Obs.} of Nice has
found over 100 small planets by photography. Many of the more
recent discoveries are yet without names, and are designated by their
number, thus $\Planetoid{331}$;
also by a double letter and year of discovery, as
1897 DE $=\Planetoid{428}$. Probably there are hundreds more, and possibly thousands.
Discoveries are disseminated by Gerrish's\index{Gerrish, W.~P., Am.\ ast.} international code.
\Restore

\textbf{Orbits and Origin of Small Planets.}\index{asteroids}\index{planets!small}---The orbits of
small planets, although linked together inseparably, still
present wide degrees of divergence. They are by no
means evenly distributed: in those regions of the zone
where a simple relation of commensurability exists between
the appropriate period of revolution and the periodic time
of Jupiter, gaps are found, resembling those shown farther
on as existing in the ring of Saturn.

\Smaller
Especially is this true for distances corresponding to one half and one
third of Jupiter's period. Not only are the orbits of small planets far
from concentric, but they are inclined at exceptionally large angles to the
ecliptic, that of Pallas $\Planetoid{2}$ being $35$°. Several groups exist having a
near identity of orbits, one such group including 11~members. Polyhymnia
$\Planetoid{51}$ is much perturbed by the attraction of Jupiter, and its motion
has recently been employed by Newcomb\index{Newcomb, S. (1835--1909), Am.\ ast.} in finding
% Fig 13.36
\begin{wrapfigure}[40]{o}{0.4\textwidth}
  \centering
  \Input[0.36\textwidth]{page_363}
  \caption{Jupiter in 1889 (Keeler)}
  \label{p363}%
  \index{Jupiter!drawings}%
  \index{Keeler, J.~E.\ (1857--1900), Am.\ ast.}
\end{wrapfigure}
anew the mass
of the giant planet, equal to $\frac{1}{1047.35}$ that of the sun. Victoria $\Planetoid{12}$, Sappho
$\Planetoid{80}$, and others, on account of favorable approach to the earth, have been
very serviceable in the hands of Gill\index{Gill, Sir D., Scotch ast.} and Elkin\index{Elkin, W.~L., Dir.\ Yale Obs.} in helping to ascertain
sun's distance from earth. Data concerning orbits of these bodies are
published each year in the \textit{Berliner Astronomisches Jahrbuch}\index{Berliner Astron. Jahrbuch}.
\Restore

Olbers\index{Olbers, H.~W.~M.\ (1758--1840), Ger.\ ast.} early originated the theory, now disproved, that
small planets had their origin in explosion of a single
great planet. Most probably, however, proximity of so
\DPPageSep{376.png}
massive a planet as Jupiter
is responsible for the existence
of a multitude of small
bodies in lieu of one larger
one; for his gravitative action
upon the ring in its early
formative stage, in accordance
with principles of the
evolution of planets, may
readily have precluded ultimate
condensation of the
ring into a separate planet.

\textbf{Surface of Jupiter.}\index{Jupiter!surface}---In a
telescope of even moderate
size, Jupiter appears, as in
this typical view, striped with
many light and dark belts,
of varying colors and widths,
lying across the disk parallel
to each other and to his equator,
or nearly so. They always
appear practically
straight because the plane
of Jupiter's equator always
passes very nearly through
the earth. The belts\index{Jupiter!belts} are not
difficult to see; but the telescope
had been invented 20
years before they were discovered,
at Rome, in 1630.
Usually
the equatorial zone,
about $25$° broad, is lightest in
hue, and almost centrally
through it runs a very narrow
\DPPageSep{377.png}
dark stripe. Larger telescopes reveal a variety of spots
and streaks in this zone, and permanence of markings is
rather the exception than the rule. It appears to be a
region of great physical commotion. Bordering this zone,
on either side, are usually two broad reddish belts, about
$20$° of latitude in width. These are zones of little disturbance,
but the southern one often appears divided.
Just beyond it is the `great
red spot.' Here and there
white cloudlike\DPnote{** Hyphenated elsewhere} masses, near
the edge of the equatorial
zone, appear to flow over into
the red belts as long oblique
streamers, seemingly dividing
these broad zones into two or
three narrow stripes. Farther
from the equator are still other
belts, growing narrower as the
poles are approached, because
curvature of the spherical surface
foreshortens them; and
all around the limb, whether
at poles or equator, the belts
fade into indistinctness. Color
and intensity of the principal
belts are by no means constant,
their hue being at times brownish, copper-colored,
and purple. Of the two hemispheres, the reddish tint of
the southern is rather more pronounced.

\textbf{Jupiter's Great Red Spot.}\index{Jupiter!great red spot}---Probably this gigantic marking,
whose
% 13.37
\begin{wrapfigure}[22]{o}{0.4\textwidth}
  \centering
  \Input[0.4\textwidth]{page_364}
  \caption{Jupiter's Great Red Spot in 1881 and 1885 (Denning)}
  \label{p378}\index{Denning, W.~F., Eng.\ ast.}\index{Jupiter!great red spot}\index{Jupiter!drawings}
\end{wrapfigure}
area exceeds that of our whole earth, has long
been forming; for although it was not certainly seen until
1869, and still more definitely in 1878 first by Pritchett\index{Pritchett, C.~W.\ (1823--1910), Am.\ ast.}, there
are indications that Cassini\index{Cassini, J.~D.\ (kas-se´ne) (1625--1712), It.-Fr.\ ast.}, at Paris, observed it in 1685.
\DPPageSep{378.png}

\Smaller
The illustrations \vpageref{p378} show its appearance in 1881 and 1885.
Breadth of this elliptic marking was about 8000 miles, and length 30,000.
The great red spot has not been uniformly conspicuous, for it nearly
faded out in 1883--84. The year following a white cloud appeared to
cover the middle, making it look like a chain-link. The lowest drawing
(page~\pageref{p363}) shows its appearance in 1889. Now quite invisible, it may
have a periodicity, and again reappear. Cloud markings near it have
been observed to be strikingly repelled. If the spot remained stationary
upon the planet's surface, it might be simply a vast fissure in the
outer atmospheric envelope of Jupiter, through which are seen dense
red vapors of interior strata, if not the planet's true surface; but its
slow drift precludes this theory. No satisfactory explanation of the
great red spot has yet been advanced.
\Restore

\Smaller
\textbf{A Chart of Jupiter.}\index{Jupiter!chart of}---Notwithstanding considerable variations in
detailed appearance of Jupiter's disk, many larger markings present a
% Fig. 13.38
\begin{figure}[hbt!]
  \centering
  \Input{page_365}
  \caption{Approximate Chart of a Portion of Jupiter in 1895 (Henderson)}
  \label{p365}\index{Henderson, A., Eng.\ ast.}\index{Jupiter!chart of}\index{Jupiter!drawings}
\end{figure}
sufficient permanence from month to month to admit of charting.
Such a chart is \vpageref{p365}, on the Mercator projection, and intended
to be accurate as to general features only. Center of the great red
spot is taken as origin of longitudes. The principal belts and the more
important white spots are clearly indicated. From the construction
of many such charts, at intervals of about a year, much can be learned
about the planet's atmosphere, present physical condition, and future
development. As yet photography\index{Jupiter!photography}\index{photography!celestial}, successfully applied by Common\index{Common, A. A. (1841--1903), Eng.\ ast.},
and Russell\index{Russell, H.~C.\ (1836--1907), Eng.\ ast.}, and at the Lick Observatory\index{Lick Observatory}, although showing accurately
a great quantity of detail, including a multitude of white and dark spots,
does not equal the eye in recording finer markings. Length of exposure
and unsteadiness of atmosphere are the chief obstacles. Hough\index{Hough, G.~W.\ (huff) (1836--1909), Am.\ ast.}
\DPPageSep{379.png}
in America and Williams\index{Williams, A.~S., Eng.\ ast.} in England have been constant students of
Jupiter.
\Restore

\textbf{Surface of Saturn.}\index{Saturn!surface}---A telescope of only two inches'
aperture will show the ring of Saturn, also Titan\index{Titan, satellite of Saturn}, his largest
satellite. A four-inch object glass will reveal four other
satellites on favorable occasions. The entire disk appears
as if enveloped in a thin, faint, yellowish veil. At irregular
% Fig 13.xx
\begin{figure}[hbt!]
  \centering
  \Input{page_366}
  \caption{Saturn and his Rings (drawn by Pratt\index{Pratt, H.\ (1838--91), Eng.\ ast.} in 1884)}
  \label{p366}\index{Saturn!drawings}
\end{figure}
intervals belts are seen similar to Jupiter's; but they do not
persist so long, and are much fainter. As a rule Saturn's
equatorial belt is his brightest region, and an olive-green
zone often caps the pole. Excellent photographs\index{photography!celestial}\index{Saturn!photographs} have
been taken at the Lick and Greenwich Observatories\index{Greenwich!Observatory}.

\Smaller
At intervals of nearly 15 years, the belts appear very much curved, as in
the illustration above; because the earth is then about $26$° above or
below the plane of the planet's equator, this being the angle by which
the axis of Saturn is inclined to a perpendicular to its orbit plane. Midway
between these epochs, the belts appear practically curveless, like
Jupiter's, because the plane of Saturn's equator is then passing near the
earth (see drawing opposite on the right). Few bright spots and
\DPPageSep{380.png}
irregularities of marking characterize this planet, and his true period of
rotation is on that account difficult to ascertain. Celestial photography\index{photography!celestial}
% Fig 13.40, 41
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.5\textwidth}
    \centering
    \Input{page_367a}
    \caption{Very Early Drawings of Saturn (in the 17th Century)}
    \index{Saturn!drawings}
  \end{minipage}
  \hfill
  \begin{minipage}{0.4\textwidth}
    \centering
    \Input{page_367b}
    \caption{Saturn in 1891. (Mark the Excessive Polar Flattening)}
    \index{Saturn!drawings}\index{Saturn!polar flattening}
  \end{minipage}
  \label{p367}
\end{figure}
is not yet sufficiently perfected to afford much assistance in recording
the minute
% Fig 13.42
\begin{wrapfigure}[40]{o}{0.3\textwidth}
  \centering
  \Input[0.205\textwidth]{page_368}
  \caption{Phases of the Ring of Saturn}
\end{wrapfigure}
details of so small a disk as Saturn's. With the invention
of more highly sensitive plates, requiring a much shorter exposure,
unavoidable blurring of atmosphere will be less harmful. Numerous
faint and nearly circular dark and white spots or mottlings were
observed on the ball in 1896.
\Restore

\textbf{Saturn's Rings and their Phases.}---Saturn is surrounded
by a series of thin, circular plane rings which generally
appear elliptical in form. To astronomers of the first half
of the 17th century, Saturn afforded much puzzlement,
and they drew the planet in a variety of fanciful forms,
some of which are here shown. Huygens\index{Huygens, C.\ (hy´genz) (1629--95), Dutch ast.} first guessed
the riddle of the rings in 1655. When widely open,
as in 1884 (\vpageref*{p366}), and in 1899 and 1914, a keen-eyed
observer, even with a small telescope, can see faint,
darkish lines or markings near the middle of the ring.
These are divisions of the system, and there are three
complete rings; (\textit{A})~outer bright ring, (\textit{B})~inner bright
ring, (\textit{C})~innermost or crape ring.
\DPPageSep{381.png}

\Smaller
While Saturn moves round the sun, the ring maintains
its own plane constant in direction, just as earth's
equator remains parallel to itself. Consequently the
plane of Saturn's rings sometimes passes through the
earth, sometimes through the sun, and again between
earth and sun. At these times the rings of Saturn
actually disappear from view, or nearly so, as just
illustrated. In the first case, the ring is so thin that
it cannot be seen when the earth is exactly in the
plane of it. In the second, the ring disappears because
the sun is shining on neither side of it, but
only on its edge. The ring may disappear in the
third instance when earth and sun are on opposite
sides of it, and therefore only the unillumined face of
the ring is turned toward us. Disappearances due to
these causes take place about every 15~years, or one
half the periodic time of Saturn, the next occurring
in 1921, as the adjacent figures (for inverting telescopes)
show. Intervals between disappearances are
unequal partly because of eccentricity of Saturn's orbit,
perihelion occurring in 1915 and aphelion in 1929.
\Restore

\textbf{Size and Constitution of the Rings.}---The
dimensions of the ring system are enormous,
especially in comparison with its
thickness, which cannot exceed 100~miles.
Seen edge on, it has the appearance of a
fine and often broken hair line (page~\pageref{p367}).

\Smaller
Outer diameter of outside ring is 173,000 miles,
and its breadth, 11,500 miles. Then comes the
division between the two luminous rings, discovered
by Cassini\index{Cassini, J.~D.\ (kas-se´ne) (1625--1712), It.-Fr.\ ast.} in 1676: its breadth is 2400 miles. Outer
diameter of inner bright ring is 145,000 miles, and its
breadth, 17,500 miles. Next, the innermost or dusky
ring, discovered by Bond\index{Bond, G. P. (1825--65), Am.\ ast.} in 1850: its inner diameter
is 90,000 miles, and its breadth 10,000 miles; and it
joins on the inner bright ring without any apparent
division. So gauzy is it that the ball of Saturn can
be seen directly through it, except at the outer edge.
Characteristic of the inner bright ring is a thickening
of its outer edge,---much the brightest zone of the
ring system. The rings of Saturn are neither solid
\DPPageSep{382.png}
nor liquid, but are composed of enormous clouds or shoals of very small
bodies, possibly meteoric, traveling round the planet, each in an orbit
of its own, as if a satellite. Perhaps they are thousands of miles apart
in space; but so distant is the planet from the earth and so numerous
are the particles that they present the appearance of a continuous solid
ring. Keeler\index{Keeler, J.~E.\ (1857--1900), Am.\ ast.} has demonstrated by the spectroscope this theory of the
constitution of Saturn's rings, showing that inner particles move round
the primary more swiftly than outer ones do, in accord with Kepler's
third law\index{Kepler, J. (1571--1630), Ger.\ ast.!laws}. The periodic time of innermost particles is 5\,h.\:50\.m., or
but little more than half the rotation time of the ball itself, which,
according to some observers, is slightly displaced from the center of
the rings. Not impossibly the ring system is a transient feature, and
may be another satellite in process of formation (page~\pageref{p467}).
\Restore

\textbf{Surface of Uranus and Neptune.}\index{Uranus!surface of}\index{Neptune!surface of}---The great planet
Uranus\index{Uranus!discovery}, the first one ever found with the telescope, was
discovered by Sir William Herschel\index{Herschel, Sir F. W. (1738--1822), Eng.\ ast.}, 13th March, 1781.
Calculation backward showed that this planet had been
observed about 20~times during the century preceding,
and mistaken for a fixed star. So remote is Uranus and
so small the apparent disk that very few observers have
been able to detect anything whatever on his pale green
surface. Some have seen belts resembling those on
Jupiter, others a white spot from which a rotation period
equal to 10~hours was found. More recently the planet
has been sketched by Brenner\index{Brenner, L., ast.\ Obs.\ Lussinpicolo}, from the clear skies of
Istria, and six of his drawings are reproduced \vpageref{p370}.
The markings appear neither numerous nor definite.
If so little is found upon Uranus, vastly less must
be expected from Neptune, and no marking whatever has
yet been certainly glimpsed.

\textbf{The Discovery of Neptune.}\index{Neptune!discovery of}---The discovery of Neptune
was a double one. Early in the nineteenth century it was
found that Uranus was straying
% Fig 13.43
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.6\textwidth]{page_370}
  \caption{Uranus in 1896 (Brenner)}
  \label{p370}
  \index{Brenner, L., ast.\ Obs.\ Lussinpicolo}\index{Uranus!drawings}
\end{wrapfigure}
widely from his theoretic
positions, and the cause of this deviation was for a long
time unsuspected. Two young astronomers, Adams\index{Adams, J. C. (1819--92), Eng.\ ast.} in England,
and Le~Verrier\index{Le Verrier, U. J. J. (l\u uh-vay-rya´) (1811--77), Fr.\ ast.} in France, the former in 1843 and the
\DPPageSep{383.png}
latter in 1845, undertook to find out the cause of this
perturbation, on the supposition of an undiscovered planet
beyond Uranus. Adams\index{Adams, J. C. (1819--92), Eng.\ ast.} reached his result first, and
English astronomers began
to search for the
suspected planet with
their telescopes, by first
making a careful map
of all the stars in that
part of the sky. But
Le~Verrier\index{Le Verrier, U. J. J. (l\u uh-vay-rya´) (1811--77), Fr.\ ast.}, on reaching
the conclusion of his
search, sent his result
to the Berlin observatory, where it chanced that an accurate
map had just been formed of all stars in the suspected
region. On comparing this with the sky, the new planet,
afterward called Neptune, was at once discovered, 23d
September, 1846. It was soon found that Neptune, too,
had been seen several times during the previous half century,
and recorded as a fixed star. The tiny disk, however,
is readily distinguishable from the stars around it, if a
magnifying power of at least 200~diameters can be used.
There are theoretic reasons for suspecting the existence of
two planets exterior to Neptune\index{planets!exterior to Neptune}\index{transneptunian planets}; but no such bodies have
yet been discovered, although search for them has been
conducted both optically and by means of photography.
\DPPageSep{384.png}


\Chapter[Argument for Gravitation]{XIV}{The Argument for Universal Gravitation}\index{gravitation!argument for universal}

So striking a confirmation of Newton's\index{Newton, Sir I. (1642--1727), Eng.\ ast.} law was
afforded by the discovery of Neptune, and so completely
does the universality of that law account for
the motions of the heavenly bodies, and the variety of their
physical phenomena, that the present chapter is devoted
to a partial outline sketch of the argument for universal
gravitation.

\textbf{From Kepler to Newton.}\index{Kepler, J. (1571--1630), Ger.\ ast.}---The great progress made by
Kepler in dealing with the motions of the planets had not
in any proper sense explained those motions; for his three
famous laws merely state \textit{how} the planets move, without
at all touching the reason \textit{why} these laws of their motion
are true. Before this question could be answered, the
fundamental principles of physics, or natural philosophy
as it was called in his day, had to be more fully understood.
These principles concern the state of bodies at
rest and in motion. Meaning of the term \textit{rest} is relative,
and absolute rest is undefinable. Motion\index{motion!defined} is a change of
place; and absolute rest is a state of absence of motion.
Galileo\index{Galile´i, G. (1564--1642), It.\ ast.} early in the 17th century was the first philosopher
who ascertained the laws of motion and wrote them down.
But as they were better formulated by Newton, his name
is always attached to them. They are axioms, an axiom
being a proposition whose truth is at once acknowledged
by everybody, as soon as terms expressing it are clearly
understood. Newton, indeed, in his great work entitled
\DPPageSep{385.png}
the \textit{Principia}\index{Principia@\emph{Principia}, Newton's}, or principles of natural philosophy, called
these laws \textit{Axiomata, sive Leges Motûs}. Antecedent to
proper conception of Newton's law of universal gravitation
must come an understanding of the three fundamental
laws of motion.

\textbf{Newton's First Law of Motion.}\index{Newton, Sir I. (1642--1727), Eng.\ ast.}\index{motion!laws of}---The first law reads as
follows: Every body continues in its state of rest or of
uniform motion in a straight line, except in so far as it
may be compelled by force to change that state. Newton
asserts in this law the physical truth that a state of uniform
motion is just as natural as a state of rest. To one
who has never thought about such things, this is at first
very difficult to realize; because rest seems the natural
state, and motion an enforced one. But difficulty is at
once dispelled, as soon as one begins to inquire into the
causes that stop any body artificially set in motion.

\Smaller
A baseball rolling upon a level field soon stops because, in moving
forward, it must repeatedly rise against the attraction of gravity, in
order to pass over minor obstacles, as grass and pebbles. Also there
is much surface friction. A rifle shot soon stops because resistance of
the air continually lessens its speed, and finally gravity draws it down
upon the earth. A vigorous winter game common in Scotland is called
curling. The curling stone is a smooth, heavy stone, shaped like a
much-flattened orange, and with a bent handle on top. When curling
stones are sent sliding on smooth ice as swiftly as possible, they go for
long distances with but slight reduction of speed, thus affording an
excellent approximation to Newton's first law. But a perfect illustration
is not possible here on the earth. If it were practicable to project
a rifle shot into space very remote from the solar system, it would travel
in a straight path for indefinite ages, because no atmosphere would
resist its progress, and there is no known celestial body whose attraction
would draw it from that path.
\Restore

\textbf{Newton's Second Law of Motion.}\index{Newton, Sir I. (1642--1727), Eng.\ ast.}\index{motion!laws of}---The second law
reads: Change of motion is proportional to force applied,
and takes place in the direction of the straight line in
which the force acts.
\DPPageSep{386.png}

\Smaller
This law is easy to illustrate without any apparatus. Throw a stone
or other object horizontally. Everybody knows that its path speedily
begins to curve downward, and it falls to the ground. From the
smooth and level top of a table or shelf, brush a coin or other small
object off swiftly with one hand: it will fall freely to the floor a few
% Fig 14.1
\begin{figure}[hbt!]
  \centering
  \Input{page_373}
  \caption{Illustrating Newton's Second Law of Motion}
\end{figure}
feet away. Repeat until you find the strength of impulse necessary
to send it a distance of about two feet, then four, then six feet, as in
the picture. With the other hand, practice dropping a coin from the
level of the table, so that it will not turn in falling, but will remain
nearly horizontal till it strikes the floor. Now try these experiments
with both hands together, and at the same time. Repeat until one
coin is released from the fingers at the exact instant the other is
brushed off the table. Then you will find that both reach the floor at
precisely the same time; and this will be true, whether the first coin is
projected to a distance of two feet, four feet, six feet, or whatever the
distance. Had gravity not been acting, the first coin would have
traveled horizontally on a level with the desk, and would have reached
a distance of two feet, or four feet, proportioned to the impulse. What
the second law of motion asserts is this: that the constant force (gravity
in this case) pulls the first coin just as far from the place it would
have reached, had gravity not been acting, as the same force, acting
\DPPageSep{387.png}
vertically and alone, would in an equal time draw it from the state of
rest. Whatever distance the coin is projected, the `change of motion'
is always the vertical distance between the level of table and floor,
that is, `in the direction of the straight line in which the force acts.'
The law holds good just the same, if the coin is not projected horizontally,
provided the floor (or whatever the coin falls on) is parallel
to the surface from which it is projected.
\Restore

\textbf{Newton's Third Law of Motion.}\index{Newton, Sir I. (1642--1727), Eng.\ ast.}\index{motion!laws of}---The third law reads:
To every action there is always an equal and contrary
reaction; or the mutual actions of any two bodies are
always equal and oppositely directed. This law completes
the steps necessary for an introduction to the single
law of universal gravitation, because it deals with mutual
actions between two bodies, or among a system of bodies,
such as we see the solar system actually to be.

\Smaller
To illustrate in Newton's own words: `If you press a stone with
your finger, the finger is also pressed by the stone. And if a horse
draws a stone tied to a rope, the horse (if I may so say) will be equally
drawn back toward the stone; for the stretched rope, in one and the
same endeavor to relax or unstretch itself, draws the horse as much
toward the stone as it draws the stone toward the horse.' Action and
reaction are always equal and opposite.
\Restore

So when one body attracts another from a distance, the
second body attracts with an equal force, but oppositely
directed. If there were two equal, and therefore balanced,
forces acting on but one body, that would be in equilibrium;
but the two forces specified in this third law act
on two different bodies, neither of which is in equilibrium.
Always there are two bodies and two forces acting, and
one force acts on each body. To have a single force is
impossible. There must be, and always is, a pair of
forces equal and opposite. Horse and stone advance as a
unit, because the muscular power of the horse exerted
upon the ground exceeds the resistance of the stone.

\textbf{Transition to the Law of Gravitation.}---Having clearly
\DPPageSep{388.png}
apprehended the meaning of Newton's three laws of
motion, transition to his law of universal gravitation is
easy. The laws of motion, however, must not now be
thought of separately, but all as applying together and at the
same time. First, consider the earth in its orbit. Our globe
has a certain velocity as it goes round the sun; it would
go on forever in space in a straight line, with that same
velocity, except that some deflecting force draws it away
from that line. This change of motion or direction from a
straight line must be proportional to the force producing it,
and the change itself must indicate direction in which
the force acts; also, if there is a force acting from the sun
upon the earth, there must be an equal and oppositely
directed force from the earth upon the sun, for action and
reaction are equal.

Similarly the motion of other planets round the sun; and
Newton's reasoning and mathematical calculations, based
on the laws of Kepler\index{Kepler, J. (1571--1630), Ger.\ ast.!laws}, made it perfectly clear that planetary
motions might be dependent upon a central force
directed toward the sun, the intensity of this force growing
less and less in exact proportion as the square of the
planet's distance grows greater: thus at twice the distance
the intensity is but one fourth as great. By making this
single hypothesis, the meaning of all three laws of Kepler
was perfectly apparent. But could the action of any such
force be proved? If it could, the motions of all the satellites
round their primaries might be accounted for by supposing
a like force emanating from the central planets.
This would mean, too, that the moon must move round us
obedient to a force directed toward the earth, but decreasing
in intensity just as rapidly as square of moon's distance
from our center increases. Can it be that the common
attraction of gravity which draws stones and apples downward
is a force answering to this description? Why
\DPPageSep{389.png}
should it attract only common objects near at hand?
Why may not the realm of this mysterious force extend
to the moon? To the calculation of this problem, Newton
next addressed himself.

\textbf{Gravitation holds the Moon in her Orbit.}\index{gravitation!holds moon in orbit}---If gravity
causes the apple to fall from the tree, the bird when shot
to fall to the ground, and hail to descend from the clouds,
certainly it is possible, thought Newton, that it may hold
the moon in her orbit, by continually bending her path round
the earth. If so, the moon must perpetually be falling
from the straight line in which she would travel, were the
central force not acting. Force can be measured by the
change of place it produces. At the surface of the earth,
about 4000 miles from the center of attraction, bodies fall
16.1~feet in the first second of time. But our satellite is
240,000 miles away, or 60~times more distant. So the
moon, if held by the same attraction, only diminishing
exactly as the square of the distance increases, should fall
away from a straight line
\[
\frac{1}{(60×60)}\text{ of }16.1\text{ feet;}
\]
that is, $\frac{1}{20}$ of an inch. Newton calculated how much
the moon actually does curve away from a tangent to
her orbit in one second, and he found it to be precisely
that amount (page~\pageref{p237}). So the law of gravitation was
immediately established for the moon; and Newton's
subsequent work showed that it explained equally well
the motion of the satellites of Jupiter round their primary,
and the motion of earth and all other planets round the
sun. He found, in fact, that the force acting depends, in
each case, on the product of the masses of the two bodies,
and on the square of the distance between them.

\textbf{Law of Gravitation extends also to the Planets.}\index{gravitation!holds planets in orbit}---Newton
\DPPageSep{390.png}
by no means considered his law of gravitation established,
just because it explained the motion of the moon round
the earth. If the law is universal, it must completely
account for the movements of all known bodies of the
solar system as well. Since the planets travel round the
sun as the moon does round the earth, a force directed
toward the sun must continually be acting upon them.
Is not this the force of gravitation? Recall Kepler's
third law\index{Kepler, J. (1571--1630), Ger.\ ast.!laws}.
% Fig 14.2
\begin{wrapfigure}{o}{0.33\textwidth}
  \centering
  \Input[0.25\textwidth]{page_377}
  \caption{Apparatus to illustrate Curvilinear Motion}
  \label{p377}
\end{wrapfigure}
Newton's calculations from it proved that the
planets fall toward the sun in one second of time through
a space which is less for each planet in exact proportion as
the square of its distance from the sun is greater. Also
Kepler's second law: if the attracting force emanates from
the sun, the planet's radius vector will pass over equal
areas in equal times. On the other hand, it cannot pass
over equal areas in equal times, if the center of attraction
resides in any direction but that of the sun. So Kepler's
second law shows that the force which
attracts the planets is directed toward
the sun. What chance for farther doubt
that this force is the attraction of gravitation
of the sun himself? The farther
Newton's investigations were pushed,
the more striking the confirmation of his
theory. Historically, the three laws of Kepler expressed
the bare facts of planetary motion, and formed the basis
upon which Newton built his law of universal gravitation.
But once this general law was established, it was seen
that Kepler's laws were immediate consequences of the
Newtonian law,---merely special cases of the general
proposition.

\Smaller
\textbf{Curvilinear Motion due to a Central Attracting Force.}\index{orbit (planetary)!experimental}\index{motion!curvilinear}---A facile
form of apparatus will help to make clear the motion of a body in
arcs of conic sections under influence of a central attracting force, and
\DPPageSep{391.png}
to impress it upon the mind. A glass plate about 18~inches in diameter
is leveled (\vpageref*{p377}); and through a central hole projects
the conical pole-piece of a large electro-magnet. Smoke the upper
face of the glass plate evenly with lampblack. Connect battery circuit,
and the apparatus is ready for experiment. Project repeatedly across
the
% Fig 14.3
\begin{wrapfigure}[16]{o}{0.4\textwidth}
  \centering
  \Input[0.4\textwidth]{page_378}
  \caption{Experimental Orbits actually obtained with this Apparatus}
  \index{orbit (planetary)!experimental}
\end{wrapfigure}
plate at different velocities a small
bicycle ball of polished steel, aimed a
little to one side of the pole-piece. It
is convenient to blow the ball out of a
stout piece of glass tubing, held in the
plane of the plate. The ball then
leaves its trace upon the plate, as this
figure shows; and the form of orbit is
purely a question of initial velocity.
Lowest speed gives a close approach
to the ellipse with the pole-piece at
one of its foci; friction of the ball in
the lampblack will reduce the velocity
so that the ball is likely to be drawn
in upon the center of attraction, on
completing one revolution. A higher speed gives the parabola, whose
form is also somewhat modified by unavoidable lessening of the ball's
velocity; and still higher initial velocities produce the two hyperbolas,
\textit{C} and \textit{D}. This ingenious experiment is due to Wood\index{Wood, R.~W., Johns Hopkins Univ.}. The true form
of all these curves is given on page~\pageref{p397}.
\Restore

\textbf{Mutual Attractions.}---One farther step had to be taken,
to apply Newton's third law of motion to the case of sun,
moon, and planets. This law states that whenever one
body exerts a force upon another, the latter exerts an
equal force in the opposite direction upon the first. Earth,
then, cannot attract moon without moon's also attracting
earth with an equal force oppositely directed. Sun cannot
attract earth unless earth also attracts sun in a similar
manner. So, too, the planets must attract each other;
and if they do, their motions round the sun must be
mutually disturbed, in accordance with the second law of
motion. Kepler's laws\index{Kepler, J. (1571--1630), Ger.\ ast.!laws}, then, must need some slight
change to fit them to the actual case of mutual attractions.
But it was known from observation that the planets deviate
\DPPageSep{392.png}
slightly from Kepler's laws in going round the sun. The
question, then, arose whether deviations really observed
are precisely matched by calculated attractions of planets
upon each other. Newton could not answer this question
completely, because the mathematics of his day was insufficiently
developed; but over and over again, refined
observations of moon and planets since his time have been
compared with theories of their movements founded on
Newton's law of universal gravitation, as interpreted by
the higher mathematics of a later day, until the establishment
of that law has become complete and final. Essentially
everything is accounted for. And unexpected and
triumphant verification came with the discovery of Neptune\index{Neptune!discovery of}
in 1846; for this proved that the law of mutual
attractions was capable, not only of explaining the motions
of known bodies, but of pointing out an unknown planet
by disturbance it produced in the motion of a known and
neighboring one.

\textbf{Earth and Moon revolve round their Common Center of
Gravity.}\index{gravity!common center of}---It has been said that the moon revolves round
the earth. This statement needs modification, and it
admits of ready illustration. Strictly speaking, the moon
revolves, not round the earth, but round the center of
gravity
% Fig 14.4
\begin{wrapfigure}[20]{o}{0.5\textwidth}
  \centering
  \Input[0.45\textwidth]{page_380}
  \caption{Motion of Earth's Center of Gravity}
  \label{p380}
\end{wrapfigure}
of earth and moon considered as a system or unit.
And as moon's attraction for earth is equal to earth's
for moon, the center of our globe must revolve round that
center of gravity also.

\Smaller
Cut a cardboard figure like that \vpageref{p380}---exact
size inessential.
Its center of gravity will lie somewhere on the line joining the
centers of the two disks, and is easily found by trial, puncturing the card
with a pin until point is found where disks balance each other, and
gravity has no tendency to make the card swing round. This point
will be the center of gravity. Around it describe a circle passing
through center of large disk; and from the same center describe also
an arc passing through center of smaller disk. Twirl the card round
\DPPageSep{393.png}
its center of gravity, by means of a pencil or penholder; or the card
may be projected into the air, spinning horizontally, and allowed to fall
to the floor: these circular
arcs, then, represent paths in
space actually traversed by
centers of earth and moon.
\label{p380a} To find where center of gravity
of earth--moon system lies
in the real earth, recall that
the mass of our globe is $81$
times that of the moon.
Moon's center is therefore $81$
times as far from center of
gravity of the system as
earth's center is. This places
the common center at a continually
shifting point always
within the earth, and at an
average distance of 1000 miles
below that place on its surface
where the moon is in
the zenith. That the earth
really does swing round in
this monthly orbit nearly
6000 miles in diameter is a fact readily and abundantly verified by
observation.
\Restore

\textbf{The Newtonian Law of Universal Gravitation.}\index{Newton, Sir I. (1642--1727), Eng.\ ast.}\index{gravitation!law of}\index{Newtonian law}---If this
attraction for common things, possessed by the earth and
called gravity, extends to the moon; if the same force,
only greater on account of greater mass of central body,
controls the satellites of Jupiter in their orbits; if the
same attraction, greater still on account of the yet greater
mass of the sun, holds all the planets in their paths
around him, may it not extend even to the stars? But
these bodies are so remote that excessive diminution of
the sun's gravitation, in accordance with the law of inverse
squares, would render that force so weak as to be unable
to effect any visible change in their motion, even in thousands
of years. As observed with the telescope, motions
\DPPageSep{394.png}
of certain massive stars relatively near each other do,
however, uphold the Newtonian law. No reason, therefore,
exists for doubting its sway throughout the whole universe
of stars. If we pass from the infinitely great to
the infinitely little, dividing and subdividing matter, as far
as possible, each particle still has weight, and therefore
must possess power of attraction. Gravity, then, attracts
each particle to the earth, and in accordance with the
third law of motion, each particle must attract the earth
in turn and equally. So the gravitation of earth and
moon, for example, is really the mutual attraction of all the
particles composing both these bodies. In its universality,
then, this simple but all-comprehensive law may finally be
written: \textit{Every particle of matter in the universe attracts
every other particle with a force exactly proportioned to
the product of the masses, and inversely as the square of
the distance between them.}

\textbf{Curvilinear Motion: No Propelling Force needed.}\index{motion!curvilinear}---Newton's
theory amounts simply to this: Granted that
planets and satellites were in the beginning set in motion
(it does not now concern us in what manner), then the
attraction of gravitation---of the sun for all the planets
and of each planet for its satellites---completely accounts
for the curved forms of their orbits, and for all their
motions therein. It may be supposed that the state of
motion was originally impressed upon these bodies by
a projectile force, or that their present motions are a
resultant inheritance from untold ages of development
of the solar system from the original solar nebula, in
accordance with the working of natural laws. Once set
in motion, however, Newton's theory suffices to show that
there is no propelling or other force always pushing from
behind, nor is the action of any such force at all necessary
to keep them going. Once started with a certain velocity,
\DPPageSep{395.png}
the uninterrupted working of gravitation maintains every
body continually in motion round its central orb. In one
part of its elliptic path, a planet, for example, may recede
from the sun, but the sun again pulls it back; afterward it
again recedes, but equally again it returns, perihelion and
aphelion perpetually succeeding each other. Gravitation
alone explains perfectly and completely all motions known
and observed.

\textbf{Why the Earth does not fall into the Sun.}\index{earth!why it does not fall into the Sun}---Draw
several arrows tangent to the ellipse at different points,
to show in each case the direction
% Fig 14.5
\begin{wrapfigure}{o}{0.4\textwidth}
  \centering
  \Input[0.35\textwidth]{page_382}
  \caption{Earth is never moving directly towards the Sun}
\end{wrapfigure}
in
which earth is going when at that
point. From these points of tangency
draw dotted lines toward that focus
where the sun is, to represent direction
in which gravitation is acting. It is
apparent that the planet is never moving
directly toward the sun, but always
at a very large angle with the radius vector; greatest at
perihelion, \textit{B}, and aphelion, \textit{D}, where it becomes a right
angle. There the sun is powerless either to accelerate or
retard. According to Kepler's second law\index{Kepler, J. (1571--1630), Ger.\ ast.!laws}, velocity in orbit
is continually increasing from aphelion to perihelion, because
gravitation is acting at an acute angle with the direction
of motion \textit{A}. Therefore earth's motion is all the time
accelerated, until it reaches perihelion. Here velocity is a
maximum, because the sun's attraction has evidently been
helping it along, ever since leaving aphelion. Gravitation
of the sun, too, has increased, exactly as the square of the
planet's distance has decreased. Calculating these two
forces at perihelion, it is found that earth's velocity makes
the tendency to recede even stronger than the increased
attraction of the sun; so that our planet is bound to pass
quickly by its nearest point to the sun, and recede again
\DPPageSep{396.png}
to aphelion. On reaching its farthest point, relation of
the two forces is reversed; velocity has been diminishing
all the way from perihelion, because gravitation is acting
at an obtuse angle with direction of motion, \textit{C}. The earth
is all the time retarded, gravitation holding it back, until
at aphelion its velocity is so much lessened that even the
enfeebled attraction of the sun overpowers it, and therefore
begins to draw the earth toward perihelion again.
So all the planets are perpetually preserved (1)~against
falling into the sun, and (2)~against receding forever
beyond the sphere of his attraction. At points where
both these catastrophes at first seem most likely to occur,
direction of planet's motion is always exactly at right
angles to the attracting force; thus is assured that curvature
of orbit requisite to carry it farther away from the
sun in the one case, and in the other to bring it back
nearer to him.

\Smaller\textbf{Strength of the Sun's Attraction.}\index{sun!strength of attraction}---It was shown, on page~\pageref{p144} that
the earth, in traveling $18\frac{1}{2}$~miles, is bent from a truly straight course
only one ninth of an inch by the sun's attraction. So it might seem
that the force is not very intense after all. But by calculating it and
converting it into an equivalent strain on ordinary steel, it has been
found that a rod or cylinder of this material 3000 miles in diameter
would be required to hold sun and earth together, if gravitation were to
be annihilated. Or, if instead of a solid rod, the force of attraction
were to be replaced by heavy telegraph wires, the entire hemisphere of
the earth turned toward the sun would need to be thickly covered with
them,---about 10 to every square inch of surface. But the necessity
for this vast quantity of so strong a material as steel becomes apparent
on recalling that the weight of the earth is six sextillions of tons, while
the weight of the sun is more than 330,000 times greater; and the stress
between them is equal to the attraction of sun and earth for each
other. Gravitation in the solar system must be thought of as producing
stresses of this character between all bodies composing it, and
taken in pairs; stress between each pair being proportional to the
product of their masses, and varying inversely as the square of the distance
separating them varies. Sun disturbs the moon's elliptic motion
greatly, and even Venus, Mars, and Jupiter perturb it perceptibly.
\Restore
\DPPageSep{397.png}

\label{p384}\textbf{What is Gravitation?}\index{gravitation!law of}---Distinction is necessary between
the terms \textit{gravity} and \textit{gravitation}\index{gravity!distinct from gravitation}. On page~\pageref{p88} it was shown
that gravity diminishes from pole to equator, on account
of (1)~centrifugal force of earth's rotation, and (2)~oblateness
of earth, or its polar flattening, by which all points
on the equator are further from the center than the poles
are. Earth's attraction lessened in this manner is called
gravity. Gravitation, on the other hand, is the term used
to denote cosmic attraction in accordance with the Newtonian
law, between all bodies of the universe taken in
pairs, and depending solely upon the product of the masses
of each pair and the distance which separates them. Do
not make the mistake of saying that Newton discovered
gravity, or even gravitation; for that would be much like
saying that Benjamin Franklin discovered lightning. Men
had always seen and known that everything is held down
by a force of some sort, and had recognized from the
earliest times that bodies possess the property called
weight. What Newton did do, however, was to discover
the universality of gravitation, and the law of its action
between all bodies: upon all common objects at the surface
of the earth; upon the moon revolving round us; and upon
the planets and comets revolving round the sun. This
cardinal discovery is the greatest in the history of astronomy.
Great as it is, however, it is not final; for Newton
did not discover, nor did he busy himself inquiring, \textit{what}
gravitation is. Indeed, that is not yet known. We only
know that it acts instantaneously over distances whether
great or small, and in accordance with the Newtonian law;
and no known substance interposed between two bodies
has power to interrupt their gravitational tendency toward
each other. How it can act at a distance, without contact
or connection, is a mystery not yet fathomed.

\textbf{Weighing a Planet that has a Satellite.}\index{planets!mass found (by satellite)}---If a planet has
\DPPageSep{398.png}
a satellite, it is easy to find the mass, or quantity of matter
in terms of sun's mass. First observe mean distance of
satellite from its primary, and then find the time of revolution.
Cube the distance of any planet from the sun, and
divide by square of periodic time; the quotient will be
the same for every planet, according to Kepler's third law\index{Kepler, J. (1571--1630), Ger.\ ast.!laws}.
Also cube the distance of any satellite of Saturn from the
center of the planet, and divide by the square of its time
of revolution: the quotient will be the same for every satellite,
if distances and periodic times have been correctly
measured. Do the same for satellites of other planets,---Mars,
Jupiter, Uranus, and Neptune. The quotients will
be proportional in each case to mass of central body in
terms of the sun; in the case of Saturn, for example, the
quotient for each satellite will be $\frac{1}{3501}$ that for sun and
planets. The sun, then, is 3501 times more massive than
Saturn\index{Saturn!mass}, as found by A.~Hall\index{Hall, A., Jr., Am.\ ast.}, Jr. Similarly may be found
the mass of any other planet attended by a satellite. It
is not necessary to know the mass of the satellite, because
the principle involved is simply that of a falling body; and
we know, in the case of the earth, that a body weighing
100~pounds or 1000 pounds will fall no swifter than one
which weighs only 10~pounds. By the same method, too,
binary stars are weighed (page~\pageref{p454}), when their distances
from each other and times of revolution become known.

\textbf{Weighing a Planet that has No Satellite.}\index{planets!mass found (without satellite)}---This is a
much more difficult problem; fortunately only two large
planets without satellites are known,---Mercury and Venus.
Their masses can be ascertained only by finding what disturbances
they produce in the motions of other bodies near
them. The mass of Venus, for example, is found by the
deviation she causes in the motion of the earth. The mass
of Mercury is found by the perturbing effect upon Encke's
comet, which often approaches very near him. The Newtonian
\DPPageSep{399.png}
 law of gravitation forms the basis of the intricate
calculations by which the mass is found in such a case.
But the result is reached only by a process of tedious computation
and is never certain to be accurate. Much more
precise and direct is the method of determining a planet's
mass by its satellite.

\Smaller
\index{Mars!mass}The vast difference between the two methods was illustrated at the
Naval Observatory, Washington, 1877, shortly after the satellites of
Mars were discovered. The mass of that planet, as previously estimated
from his perturbation of the earth, was far from right, although
it had cost months of figuring, based upon years of observation. Nine
days after the satellites were first seen, a mass of Mars very near the
truth was found by only a half hour's facile computation.
\Restore

\label{p386a} \textbf{Weighing the Sun.}\index{sun!mass}---In weighing the planets, the sun
is the unit. Our next inquiry is, what is the sun's own
weight? How many times does the
mass of the sun exceed
that of the earth? Evidently the law of gravitation
% Fig 14.6
\begin{wrapfigure}{o}{0.33\textwidth}
  \centering
  \Input[0.3\textwidth]{page_386}
  \caption{To explain the Direct and the Opposite Tides}
  \label{p386}
\end{wrapfigure}
will afford an answer to this question
if we compare the attraction of sun
with that of earth at equal distances.
At the surface of the earth a body
falls 16.1~feet in the first second of
time. Imagine the sun's mass all concentrated
into a globe the size of the
earth: how far would a body on its
surface fall in the first second? First
recall how far the earth falls toward
the sun (or deviates from a straight
line) in a second: it was found to be
0.0099~feet (page~\pageref{p144}). This is deflection
produced by the sun at a distance
of 93,000,000 miles. But we desire to know how far the
earth would fall in a second, were its distance only 4000
miles from the sun's center; that is, if it were 23,250 times
\DPPageSep{400.png}
nearer. Obviously, as attraction varies inversely as the
square of the distance, it would fall $0.0099 × [23.250]^{2}$,
or 5,351,570 feet. But we saw that the earth's mass
causes a body to fall 16.1~feet in the first second; therefore
the sun's mass is nearly 332,000 times greater than
that of the earth.

\textbf{Gravitation explains the Tides.}\index{gravitation!explains tides}\index{tides!explained by gravitation}---According to the
law of gravitation, the attraction of moon and earth is
mutual; moon attracts earth as well as earth attracts
moon. Earth, then, may be considered also as traveling
round the moon (page~\pageref{p380a}). Therefore, earth falls toward
moon, just as moon in going round earth is continually
dropping from the straight line in which it would move,
if gravitation were not acting. Imagine the earth made
up of three parts (\vpageref*{p386}), independent and free
to move upon each other: (\textit{a})~the waters on the side toward
the moon; (\textit{b})~the solid earth itself; (\textit{c})~the waters on the
side away from the moon. In going round moon or sun,
these three separate bodies would fall toward it, through
a greater or less space according to their individual distance
from sun or moon. Waters of the opposite tide,
therefore, would fall moonward or sunward through the
least distance, waters of the direct tide through the greatest
distance, and the earth itself through an intermediate
distance. The resultant effect would be a separation from
earth of the waters on both near and further sides of it.
As, however, the real earth and the waters upon it are not
entirely independent, but only partially free to move relatively
to each other, the separation actually produced takes
the form of a tidal bulge on two opposite sides. These
are known as the direct and the opposite tides.

\textbf{Tides raised by the Sun.}---Besides our satellite the only
other body concerned in raising tides in the waters of the
earth is the sun. Newton demonstrated that the force
\DPPageSep{401.png}
which raises tides is proportional to the difference of
attractions of the tide-raising body on two opposite sides
of the earth. Also he showed that this force becomes less
as the cube of the distance of tide-producing body grows
greater. It is, therefore, only a small portion of the whole
attraction, and the sun tide is much exceeded by that of the
moon. To ascertain how much: first as to masses merely,
supposing their distances equal, sun's action would be
% Fig 14.7, 8
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.33\textwidth}
    \centering
    \vspace{0.2cm}
    \Input{page_388a}
    \caption{Spring Tide at Full Moon}
  \label{p388}
  \end{minipage}
  \hfil
  \begin{minipage}{0.33\textwidth}
    \centering
    \Input{page_388b}
    \caption{Spring Tide at New Moon}
  \end{minipage}
\end{figure}
$26\frac{1}{2}$~million times that of moon, because his mass is
$81 × 332,000$ times greater. But sun's distance is also
390~times greater than the moon's; so that
\[
  \frac{26\frac{1}{2} \text{ millions}}{(390)^3}
\]
expresses the ratio of sun tide to moon tide, or about the
relation of 2 to 5.

%\label{p388}
\textbf{Sun Tides and Moon Tides combined.}---As each body
produces both a direct and an opposite tide, it is clear that
very high tides must be raised at new moon and at full
moon, because sun and moon and earth are then in line.
\DPPageSep{402.png}
These are spring tides (or high-rising tides), occurring, as
the figures \vpageref{p388} show, twice every lunation. Similarly
is explained the formation of lesser tides, called neap
tides, which occur at the moon's first and third quarters.
Instead of conspiring together to raise tides, the attraction
of the sun acts athwart the moon's, so that the resultant
neap tides are raised by the difference of their attractions,
instead of the sum. Both relations of sun, moon, and
% Fig 14.9, 10
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.48\textwidth}
    \centering
    % \vspace{5ex}
    \Input{page_389a}
    \caption{Neap Tide at First Quarter}
  \end{minipage}
  \hfil
  \begin{minipage}{0.48\textwidth}
    \centering
    \Input{page_389b}
    \caption{Neap Tide at Last Quarter}
  \end{minipage}
\end{figure}
earth producing such tides are shown. Considering only
average distances of sun and moon, spring tides are to
neap tides about as 7 to 3. For the earth generally,
highest and lowest spring tides must occur when both sun
and moon are nearest the earth; that is, when the moon
at new or full comes also to perigee, about the beginning
of the calendar year. The complete theory of tides can
be explained only by application of the higher mathematics.
But the law of gravitation, taken in connection
with other physical laws, fully accounts for all observed
facts; so that the tides form another link in the chain
of argument for universal gravitation.
\DPPageSep{403.png}

\textbf{The Cause of Precession.}\index{equinoxes!precession}\index{precession}---Precession and its effect upon
the apparent positions of the stars have already been described
and illustrated in Chapter~\textsc{vi}. This peculiar behavior
of the earth's equator is due to the gravitation of sun
and moon upon the bulging equatorial belt or zone of the
earth, combined with the centrifugal force at the earth's
equator. As equator stands at an inclination to ecliptic,
this attraction tends, on the whole, to pull its protuberant
ring toward the plane of the ecliptic itself. But the earth's
turning on its axis prevents this, and the resultant effect is
a very slow motion of precession at right angles to the
direction of the attracting force, similar to that exemplified
by attaching a small weight to the exterior ring of a
gyroscope. Three causes contribute to produce precession:
if the earth were a perfect sphere, or if its equator
were in the same plane with its path round the sun (and
with the lunar orbit), or if the earth had no rotation on
its axis, there would be no precession. The action of
forces producing precession is precisely similar to that
which raises the tidal wave; and, accordingly, solar precession
takes place about two fifths as rapidly as that produced
by the moon. The slight attraction of the planets
gives rise to a precession $\frac{1}{450}$ that of sun and moon.

\Smaller
\textbf{Nutation of the Earth's Axis.}\index{nutation}---Nutation is a small and periodic
swinging or vibration of the earth's poles north and south, thereby
changing declinations of stars by a few seconds of arc. The axis of
our globe, while traveling round the pole of the ecliptic, $A$, has a slight
oscillating motion across the circumference of the circle described by
precession. So that the true motion of the pole does not take place
along $pp'$, an exact small circle around $A$ as a pole, but along a wavy
arc as shown in next illustration. The earth's pole is at $P$ only at a
% Fig 14.11
\begin{figure}[hbt!]
  \centering
  \Input[0.8\textwidth]{page_391}
  \caption{Illustrating Motion of the Celestial Pole by Nutation}
  \index{nutation}
\end{figure}
given time. This \textit{nodding} motion of the axis, and consequent undulation
in the circular curve of precession, is called nutation. The
period of one cross oscillation due to lunar nutation is $18\frac{3}{5}$~years, so
that the number of waves around the entire circle is greatly in excess
of the proportion represented in the figure. In reality there are nearly
\DPPageSep{404.png}
1400 of them. Just as the celestial equator glides once round on the
ecliptic in 25,900 years, as a result of precession, so the moon's orbit
also slips once round the ecliptic in $18\frac{3}{5}$~years, thereby changing
slightly the direction of moon's attraction upon the equatorial protuberance
of our earth, and producing nutation.
\Restore

When Newton\index{Newton, Sir I. (1642--1727), Eng.\ ast.} had succeeded in proving that his law of
universal gravitation accounted not only for the motions of
the satellites round the planets, for their own motions
round the sun, for the rise and fall of the tides, and for
those changes in apparent positions of the stars occasioned
by precession and nutation, evidence in favor of
his theory of gravitation became overwhelming, and it was
thenceforward accepted as the true explanation of all celestial
motions.
\DPPageSep{405.png}


\Chapter{XV}{Comets and Meteors}\index{comets}\index{meteors}

Comets, as well as other unusual appearances in the
heavens, were construed by very ancient peoples
into an expression of disapproval from their deities.
`Fireballs flung by an angry God,' they were for centuries
thought to be `signs and wonders,---a sort of celestial
portent of every kind of disaster. The downfall of Nero
was supposed to be heralded by a comet; and for centuries
the densest superstition clustered about these objects.

\textbf{True Theory of Comets not Modern.}\index{comets!superstitions}---Chaldean stargazers\index{Chaldean view of comets}
were apparently the sole ancient nation to regard
comets as merely harmless wanderers in space. The
Pythagoreans\index{Pythagoras (\BC~530), Gk.\ phil.} only, of the old philosophers, had some
general idea that they might be bodies obeying fixed laws,
returning perhaps at definite intervals.

\Smaller
Seneca held this view, and Emperor Vespasian attempted to laugh
down the popular superstitions. But in those days, far-seeing utterances
had little effect upon a world full of obstinate ignorance. Some
of the old preachers proclaimed that comets are composed of the sins
of mortals, which, ascending to the sky, and so coming to the notice of
God, are set on fire by His wrath. Texts of Scripture were twisted
into apparent proofs of the supernatural character of comets, and for
seventeen centuries beliefs were held that fostered the worst forms of
fanaticism. Copernicus\index{Copernicus, N. (1473--1534), Ger.\ ast.}, of course, refused to regard comets as supernatural
warnings, but the 16th century generally accepted their evil
omen as a matter of course. By the middle of the 17th century came
the dawn of changing views, although even as late as the end of that
century, knowledge of the few facts known about comets was kept so
far as possible from students in the universities, that their religious
beliefs might not be contaminated.
\Restore
\DPPageSep{406.png}

But credence began to be given to the statements of
Tycho Brahe\index{Tycho Brahe (1546--1601), Danish ast.} and Kepler\index{Kepler, J. (1571--1630), Ger.\ ast.} that comets were supralunar, or
beyond the moon, and perhaps not so intimately concerned
in `war, pestilence, and famine'
as had been believed.
Newton\index{Newton, Sir I. (1642--1727), Eng.\ ast.} farther demonstrated
that comets are as obedient to
law as planets; and with his
authoritative statements came
the full daylight of the modern
view.

\textbf{Discoveries of Comets.}\index{comets!discoveries}---Comets
are nearly all discovered
by apparent motion
among the stars. The illustration
shows the field of view of
% Fig 15.1
\begin{wrapfigure}[13]{o}{0.35\textwidth}
  \centering
  \Input[0.325\textwidth]{page_393a}
  \caption{A Comet is discovered by its Motion}
\end{wrapfigure}
a telescope, in which appeared
each night two faint objects. Upper one remained
stationary among the stars, but lower one was recognized
as a comet because it moved,
as the arrow shows, and was
seen each night farther to
the right. A century ago,
Caroline Herschel\index{Herschel, Miss C.~L.\ (1750--1848), Eng.\ ast.} in England,
and Messier\index{Messier, C.\ (mes´se-\=a) (1730--1817), Fr.\ ast.} in France,
were the chief discoverers of
comets. Pons\index{Pons, J.~L.\ (1761--1831), Fr.\ ast.} discovered 30
comets in the first quarter of
the 19th century.

\Smaller
Among other noteworthy European
`comet-hunters' during the
middle and latter half of this century
were Brorsen\index{Brorsen, T. (1819--93), Ger.\ ast.}, Donati\index{Donati@Dona´ti, G. B. (1826--73), It.\ ast.}, and
Tempel\index{Tempel, E.~W.~L.\ (1821--89), Ger.\ ast.}. In America, Swift\index{Swift, L., Am.\ ast.},
Brooks\index{Brooks, W. R., Dir.\ Obs.\ Geneva}, and Barnard\index{Barnard, E. E., Prof.\ Univ.\ Chicago} have been preëminently successful. Between
them and several other astronomers, both at home and abroad, the
\DPPageSep{407.png}
entire available night-time sky is parceled out for careful telescopic
search, and it is not likely that many comets, at all within the range\break
\vspace{-\baselineskip}
%[** TN: Hack to place two wrapfigures in one paragraph]

% Fig 15.2
\begin{wrapfigure}[18]{i}{0.5\textwidth}
  \centering
  \Input[0.45\textwidth]{page_393b}
  \caption{Early View of Donati's Comet (1858)}
  \index{Donati's comet (of 1858)}
\end{wrapfigure}
\noindent of visibility from the earth, escape their
critical gaze. Sweeping for comets is
an attractive occupation, but one requiring
close application and much
patience. Large and costly instruments
are by no means necessary. Messier\index{Messier, C.\ (mes´se-\=a) (1730--1817), Fr.\ ast.}
discovered all his comets with a spyglass
of $2\frac{1}{2}$~inches diameter, magnifying
only five times; and the name of
Pons\index{Pons, J.~L.\ (1761--1831), Fr.\ ast.}, the most successful of all comet-hunters,
a doorkeeper at the observatory
of Marseilles, is now more famous
in astronomy than that of Thulis\index{Thulis, M.\ (tu-lee´) (1750--1805), Fr.\ ast.}, the
then director of that observatory, who
taught and encouraged him.
\Restore

% Fig 15.3, 4
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.48\textwidth}
    \centering
    %\vspace{5ex}
    \Input {page_394a}
    \caption{Telescopic comet without and with nucleus}
  \end{minipage}
  \label{p394}
  \hfill
  \begin{minipage}{0.48\textwidth}
    \centering
    \Input {page_394b}
    \caption{Halley's Comet (1835)}
    \index{Halley, E.@Halley, E.\ (1656--1742), Ast.\ Roy.}\index{Astronomer Royal|see{Halley, E.}}
  \end{minipage}
\end{figure}

\textbf{Their Appearance.}\index{comets!appearance}---Usually a
comet has three parts. The
\textit{nucleus} is the bright, star-like
point which is the kernel, the true, potential comet.
Around this is spread the \textit{coma}\index{comets!coma}, a sort of luminous fog,
shading from the nucleus\index{comets!nucleus}, and
forming with it the \textit{head}\index{comets!head}. Still
beyond is the delicate \textit{tail}\index{comets!tail},
stretching away into space.
And this to the world in general
is the comet itself, though
always the least dense of the
whole. Sometimes entirely
wanting, or hardly detectible,
the tail is again an extension
millions of miles long.
Although usually a single
brush of light, comets have
been seen with no less than
six tails.
\DPPageSep{408.png}

\textbf{Changes in Appearance.}\index{comets!changes}---With increase in a comet's
speed on approaching the sun and its state of excitation,
part tidal and part perhaps
% Fig 15.5
\begin{wrapfigure}{o}{0.45\textwidth}
  \centering
  \Input[0.4\textwidth]{page_394c}
  \caption{Head of Donati's Comet (1858)}
  \index{Donati's comet (of 1858)}
\end{wrapfigure}
electrical, its appearance
changes accordingly. When
remote from the sun, comets are
never visible except by aid of a
telescope, and their appearance
is well shown \vpageref{p394};
but on approaching
nearer the sun, a nucleus will
often develop and throw off jets
of luminosity toward the sun,
sometimes curving round and
opening like a fan. On rare
occasions the comet will become
so brilliant as to be visible in
broad daylight. After growth
of the \textit{coma} comes development
of the tail; and this showy
appendage sometimes reaches
stupendous lengths, even so
great as sixty millions of miles,
growing often several million
miles in a day.

\textbf{Development and Direction of
Tail.}\index{comets!tail}---It is not a correct analogy
that the tail streams out
behind like a shower of sparks
from a rocket.
% Fig 15.6
\begin{wrapfigure}[29]{o}{0.4\textwidth}
  \centering
  \Input[0.35\textwidth]{page_395}
  \caption{Tail always point away from the Sun}\index{comets!tail}
\end{wrapfigure}
There is no
medium to spread the tail; for there is no material substance
like air in interplanetary space, and therefore nothing
to sweep the tail into the line of motion. Explanation
of the backward sweep of the tail, nearly always away
from the sun, as in above diagram, is found in the fact that
\DPPageSep{409.png}
while the comet is attracted, the tail is strongly repelled by
the sun. Rapid growth of tail upon approaching the sun is
explainable in this way: the comet as a solid is attracted;
but when it comes near enough to be partly dissipated into
vapor, the highly rarefied gas is so repelled that gravitation
is entirely overcome, and the tail streams visibly away from
the sun. Probably electrical repulsion and perhaps also the
direct pressure of sunlight are concerned. As the comet
recedes, the great heat diminishes; and the tail becomes
smaller, because less material is converted into vapor.

\textbf{Types of Cometary Tails.}\index{comets!tail}---Bredichin\index{Bredichin, T. A. (1831--1904), Russ.\ ast.} divides tails of
comets into three types: (1)~those absolutely straight in
space, or nearly so, like the
tail of the great comet of
1843; (2)~tails gently curved,
like the broad streamer of
Donati's comet of 1858\index{Donati's comet (of 1858)} (page~\pageref{p20});
(3)~short bushy tails,
curving sharply round from
the comet's nucleus, as in
Encke's\index{Encke, J.~F.\ (eng´k\u uh) (1791--1865), Ger.\ ast.} comet. The origin
of tails of the first type is
related to ejections of hydrogen\index{comets!constitution},
the lightest element
known, and the sun's repulsive
force is in this case 14
times stronger than his gravitative
attraction. The slightly
curved tails of the second type are due to hydrocarbons\index{hydrocarbons, in comets}
repelled with a force somewhat in excess of solar gravity.
In producing the sharply curved tails of the third type,
the sun's repellent energy is about one fifth that of his
gravity, and these tails are formed from emanations of still
heavier substances, principally iron\index{iron!in comets} and chlorine\index{chlorine!in comets}.
\DPPageSep{410.png}


\Smaller
This theory permits a complete explanation of a comet's possessing
tails of two different types; or even tails of all three distinct types.
An excellent photograph of comet Rordame-Quénisset\index{Rordame, A., Am.\ ast.}\index{Quenisset@{Quénisset, F.\ (kay-nis´say), Fr.\ ast.}} (1893) showed
four tails, which subsequently condensed into a single one. Evidently
the ejections may be at different times connected with hydrogen, hydrocarbon,
or iron, or any combination of these, according to the chemical
composition of substances forming the nucleus.
\Restore

% Fig 15.7
\begin{figure}[hbt!]
  \centering
  \centering
  \begin{minipage}{0.5\textwidth}
    \centering
    \Input[0.65\textwidth]{page_396}
    \caption{Types of Cometary Tails (Bredichin)}\index{comets!tail}
  \end{minipage}
  \hfil
% Fig 15.8
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input{page_397}
    \caption{Form of Cometary orbits}
    \label{p397}
  \end{minipage}
\end{figure}

\textbf{Observations for an Orbit.}\index{comets!observations}\index{comets!orbit}---As soon as a new comet is
discovered, its position among the stars is accurately observed
at once. On subsequent
evenings, these observations
are repeated; and after
three complete observations have
been obtained, the precise path
of the comet can generally be
calculated. This path will be
one of the three conic sections:
(1)~if it is an ellipse, the comet
belongs to the class of periodic
comets, and the length of its
period will be greater as the
eccentricity of orbit is greater;
(2)~if the path is a parabola, the
comet will retreat from the sun along a line nearly parallel
to that by which it came in from the stellar depths;
(3)~if a hyperbola, the paths of approach to and recession
from the sun will be widely divergent.

\textbf{Cometary Orbits.}---Some comets are permanent members
of the solar system, while others visit us but once. Three
forms of path are possible to them,---the \textit{ellipse}\index{ellipse!comet orbit}, the
\textit{parabola}\index{parabola!comet orbit}, and the \textit{hyperbola}\index{hyperbola!comet orbit}. With a path of the first type
only can the comet remain permanently attached to the
sun's family. The other two are open curves, as in above
diagram; and after once swinging closely round the sun,
and saluting the ruler of our solar system, the comet then
plunges again into unmeasured distances of space.
\DPPageSep{411.png}

\Smaller
Whether or not an orbit is a closed or open curve depends entirely
upon velocity\index{comets!velocity}. If, when the comet is at distance unity, or 93,000,000
miles from the sun, its speed exceeds 26~miles a second, it will never
come back; if less, it will
return periodically, after wanderings
more or less remote.
Very often the velocity of a
comet is so near this critical
value, 26~miles a second, that
it is difficult to say certainly
whether it will ever return or
not. Many comets, however,
do make
% Fig 15.9
\begin{wrapfigure}[26]{o}{0.6\textwidth}
  \centering
  \Input[0.55\textwidth]{page_398}
  \caption{A Projectile's Path is a Parabola}
  (From an Instantaneous Photograph by Lovell)
  \index{Lovell, J. L., photographer}
\end{wrapfigure}
periodical visits
which are accurately foretold.
The form, and position of
their orbits show in numerous
instances that these
comets were captured by
planetary attraction, which
has reduced their original
velocity below 26~miles a second,
and thus caused them
to remain as members of the
solar system indefinitely, and
obedient to the sun's control.

\label{p398} \textbf{A Projectile's Path is a
Parabola.}\index{parabola!comet orbit}---This proposition,
demonstrated mathematically
from the laws of motion, is excellently verified by observation of the
exact form of curves described by objects thrown high into the air.
Resistance of the atmosphere does not affect the figure of the curve
appreciably, unless the velocity is very swift. A `foul ball' frequently
exhibits the truth of this proposition beautifully, in its flight from the
bat, high into the air, and then swiftly down to the `catcher,' whom
the photograph shows in the act of catching the ball, though somewhat
exaggerated in size. The horizontal line above the parabola is
called the \textit{directrix}\index{directrix of parabola}, and the vertical line through the middle of the
parabola is its \textit{axis}. One point in the axis, called the \textit{focus}, is as far
below the vertex as the directrix is above it. This curve has a number
of remarkable properties, one of which is that every point in the curve
is just as far from the focus as it is perpendicularly distant from the
directrix (shown by equality of the dotted lines). Another property,
very important and much utilized in optics, is this: from a tangent at
the point of the parabola, the line from this point to the focus makes
\DPPageSep{412.png}
the same angle with the tangent that a line drawn from the point of
tangency parallel to the axis does. According to this property, parallel
rays all converge to the focus of a reflector (page~\pageref{p196}).
\Restore

\textbf{Direction of their Motion.}\index{comets!motion}---Unlike members of the solar
system in good and regular planetary standing, comets
move round the sun, some in the same direction as the
planets; others revolve just opposite, that is, from east
to west. The planes of cometary orbits, too, lie in all directions---their
paths may be inclined as much as $90$° to
the ecliptic. A comet can be observed from the earth,
and its position determined, only while in that part of its
orbit nearer the sun. Generally this is only a brief interval
relatively to the comet's entire period, because motion
near perihelion is very swift. It is doubtful whether any
comet has ever been observed farther from the sun than
Jupiter.

\textbf{Dimensions of Comets.}\index{comets!dimensions}---Nucleus and head or \textit{coma} of
a comet are the only portions to which dimension can
strictly be assigned. There are doubtless many comets
whose comæ are so small that we never see them---probably
all less than 15,000 miles in diameter remain undiscovered.
The heads of telescopic comets vary from about
25,000 to 100,000 miles in diameter; that of Donati's comet\index{Donati's comet (of 1858)}
of 1858 was 250,000 miles in diameter, and that of the
great comet of 1811, the greatest on record, was nearly five
times as large. Tails of comets are inconceivably extensive,
short ones being about 10,000,000 miles long, and the
longest ones (that of the comet of 1882, for example) exceeding
100,000,000. To realize this prodigious bulk, one must
remember that if such a comet's head were at the sun, the
tail would stretch far outside and beyond the earth.

\textbf{The Periodic Comets.}\index{comets!periodic}---Comets moving round the sun
in well-known elliptic paths are called periodic comets.
About 30 such are now known, with periods less than 100
\DPPageSep{413.png}
years in duration, the shortest being that of Encke's\index{Encke, J.~F.\ (eng´k\u uh) (1791--1865), Ger.\ ast.} comet
($3\frac{1}{3}$~years), and the longest that of Halley's\index{Halley, E.@Halley, E.\ (1656--1742), Ast.\ Roy.} (about 76~years).
Nearly all of these bodies are invisible to the naked eye,
and only about half of them have as yet been observed at
more than a single return. Nearly as many more comets
travel in long oval paths, but their periods are hundreds or
even thousands of years long, so that their return to perihelion
has not yet been verified.

% Fig 15.10
\begin{figure}[p!]
  \centering
  \Input[\textwidth]{page_401}
  \caption{Jupiter's Family of Comets. (From Professor Payne's \textit{Popular Astronomy)}}
  \label{p401}
  \index{Barnard, E. E., Prof.\ Univ.\ Chicago}%
  \index{Biela@v.\ Biela, W. (b\=e´lä) (1782--1856), Aus. officer}%
  \index{Blanpain, M. (1779--1843), Fr.\ ast.}%
  \index{Brooks, W. R., Dir.\ Obs.\ Geneva}%
  \index{Denning, W.~F., Eng.\ ast.}%
  \index{Popular Astronomy@\emph{Popular Astronomy} (monthly)}%
  \index{D'Arrest, H.~L.\ (där-rest´) (1822-75), Ger.\ ast.}%
  \index{De Vico, F.\ (1805--48), It.\ ast.}%
  \index{Encke, J.~F.\ (eng´k\u uh) (1791--1865), Ger.\ ast.}%
  \index{Faye, H.~A.~E.~A.\ (fy) (1814--1902), Fr.\ ast.}%
  \index{Finlay, W.~H., ast.\ Capetown Obs.}%
  \index{Holmes, E., Eng.\ ast.}%
  \index{Jupiter!family of comets}%
  \index{Lexell, A.~J.\ (1740--84), Swed.\ math.}%
  \index{Payne, W.~W., Am.\ ast.}%
  \index{Pigott, E.\ (1768--1807), Eng.\ ast.}%
  \index{Spitaler, R., ast.\ Prague Obs.}%
  \index{Swift, L., Am.\ ast.}%
  \index{Tempel, E.~W.~L.\ (1821--89), Ger.\ ast.}%
  \index{Tuttle, H.~P.\ (1839--92), Am.\ ast.}%
  \index{Wolf, R.\ (1816--93), Ger.\ ast.}%
\end{figure}

\textbf{Planetary Families of Comets.}\index{comets!families}---When periodic comets
are classified according to distance from the sun at their
aphelion, it is found that there is a group of several corresponding
to the distance of each large outer planet from
the sun. Of these, the Jupiter family of comets is the
most numerous, and the orbits of many of them are excellently
shown \vpageref{p401}. Without much
doubt, these comets originally described open orbits, either
parabolas or hyperbolas; but on approaching the sun, they
passed so near Jupiter that he reduced their velocity below
the parabolic limit, and they have since been forced to
travel in elliptical orbits, having indeed been captured by
the overmastering attraction of the giant planet. While
Jupiter's family of comets numbers 18, Saturn similarly
has 2, Uranus 3, and Neptune 6.

\textbf{Groups of Comets.}\index{comets!groups}---Vagaries in structure of comets
prevent their identification by any peculiarities of mere
physical appearance. Identity of these bodies then, or
the return of a given comet, can be established only by
similarity of orbit. In several instances comets have made
their appearance at irregular intervals, traveling in one
and the same orbit. They could not be one and the same
comet; so these bodies pursuing the same track in the
celestial spaces are called groups of comets.

\Smaller
The most remarkable of these groups consists of the comets of 1668,
1843, 1880, 1882, and 1887, all of which travel \text{tandem}\index{comets!tandem} round the sun.
\DPPageSep{414.png}
\DPPageSep{415.png}
Probably they are fragments of a comet, originally of prodigious size
but disrupted by the sun at an early period in its history; because the
perihelion point is less than 500,000 miles from the sun's surface. At
this distance an incalculably great disturbing tidal force would be exerted
by the sun upon a body having so minute a mass and so vast a
volume; and separate or fragmentary comets would naturally result.
\Restore

\textbf{Number of Comets.}\index{comets!number}---In the historical and scientific
annals of the past, nearly 1000 comets are recorded. Of
these about 100 were reappearances; so that the total number
of distinct comets known and observed is between 800
and 900.

\Smaller
During the centuries of the Christian era preceding the eighteenth, the
average number was about 30 each century; but nearly all these were
bright comets, discovered and observed without telescopes. As telescopes
came to be used more and more, 70 comets belong to the eighteenth
century, and nearly 300 to the
% Fig 15.11
\begin{wrapfigure}[14]{o}{0.33\textwidth}
  \centering
  \Input[0.3\textwidth]{page_402}
  \caption{Cheseaux's Multi-tailed Comet (1744)}
  \label{p402}
\end{wrapfigure}
nineteenth. Of this last number, less
than one tenth could have been discovered
with the naked eye; so that the
number of bright comets appears to
vary but little from century to century.
The number of telescopic comets found
each year is on the increase, because
more observers are engaged in the
search than formerly, and their work is
done in accordance with a carefully
organized system. About seven comets
are now observed each year. Fewer
are found in summer, owing to the
short nights. During the 2000 years---although
but `a minute in the probable
duration of the solar system'---the
comets coming within reach of the sun must be counted by thousands;
for it is probable that about 1000 comets pass within visible
range from the earth every century. It is not, however, likely that
more than half of these can ever be seen.

\textbf{Remarkable Comets before 1850.}---Comets of immense proportions
have visited our skies since the earliest times. Others having singular
characteristics must be mentioned also. Halley's\index{Halley, E.@Halley, E.\ (1656--1742), Ast.\ Roy.} comet is famous
because it was the first whose periodicity was predicted. This was in
1704, but the verification did not take place till 1759, again in 1835,
\DPPageSep{416.png}
again in 1910, and it will reappear in 1986. The comet of 1744
(\vpageref*{p402}) had a fan-shaped, multiple tail. The great comet of 1811
was one of the finest of the 19th century, and its period is about 3000
years in duration. In 1818 Pons\index{Pons, J.~L.\ (1761--1831), Fr.\ ast.} discovered a very small comet, which
has become famous because of the short period of its revolution round
the sun---only $3\frac{1}{3}$~years. This fact was discovered by Encke\index{Encke, J.~F.\ (eng´k\u uh) (1791--1865), Ger.\ ast.}, a great
German astronomer, and the comet is now known as Encke's comet. It
has been seen at every return to perihelion, three times every ten years.
Up to 1868, the period of Encke's comet was observed to be shortening,
by about $2\frac{1}{2}$~hours, at each return; and this diminution led to the hypothesis
of a resisting medium in space---not well sustained by more
recent investigations. Encke's comet is inconspicuous, has
% Fig 15.12
\begin{wrapfigure}{o}{0.45\textwidth}
  \centering
  \Input[0.4\textwidth]{page_403}
  \caption{Biela's Double Comet (1845--46)}
\end{wrapfigure}
exhibited
remarkable eccentricities of form and structure, and is now invisible
without a telescope. Returns are in 1895, 1901, and 1911. The great
comet of 1843, perhaps the most remarkable of all known comets, was
visible in full daylight, and at perihelion the outer regions of its coma
must have passed within 50,000 miles of the surface of the sun---nearer
than any known body. At perihelion, its motion was unprecedented in
swiftness, exceeding 1,000,000 miles an hour. Its period is between 500
and 600 years.

\textbf{The Lost Biela's Comet.}---Montaigne\index{Montaigne, M.\ (1716--85), Fr.\ ast.} at Limoges, France, discovered
in 1772 a comet which was seen again by Pons in 1805, and then
escaped detection until 1826, when it
was rediscovered and thought to be
new by an Austrian officer named Biela
  \index{Biela@v.\ Biela, W. (b\=e´lä) (1782--1856), Aus. officer},
by whose name the comet has since
been known. He calculated its orbit,
and showed that the period was $6\frac{1}{2}$
years. At reappearance in 1845--46,
it was seen to have split into two
unequal fragments, as in the illustration,
and their distance apart had
greatly increased when next seen in
1852. At no return since that date has Biela's comet been seen; and
the showers of meteors observed near the end of November in 1872,
1885, and 1892, are thought to be due to our earth passing near the
orbit of this lost body, and to indicate its further, if not complete disintegration\index{comets!disintegration}.
These meteors are, therefore, known as the Bielids\index{Bielids (be´lidz), meteors}; also
Andromedes\index{Andromedes, meteors}, because they appear to come from the constellation
of Andromeda. During the shower of 1885, on the 27th of November,
a large iron meteorite fell, and was picked up in Mazapil, Mexico.
Without doubt it once formed part of Biela's comet.

\textbf{Remarkable Comets between 1850 and 1875.}\index{comets!remarkable}---In 1858 appeared
Donati's comet\index{Donati's comet (of 1858)}, which attained its greatest\index{comets!greatest} brilliancy in October, having
\DPPageSep{417.png}
a tail $40$°
% Fig 15.13
\begin{wrapfigure}[19]{o}{0.4\textwidth}
  \centering
  \Input[0.4\textwidth]{page_404}
  \caption{Donati's Triple-tailed Comet of 1858}
  \index{Donati's comet (of 1858)}
\end{wrapfigure}
 long, sharply curved, and $8$° in extreme breadth. Also there
were two additional tails, nearly straight, and very long and narrow,
as shown in the following illustration. Its orbit is elliptic, with a
period of nearly 2000 years. In 1861 appeared another great comet.
Its tail was fan-shaped, with six distinct emanations, all perfectly
straight. The outer ones attained the enormous apparent length of
nearly $120$°, and were very divergent, owing to immersion of the earth
in the material of the tail to a
depth of 300,000 miles. This comet
also travels round the sun in an
elliptic path, with a period exceeding
400 years. The next fine comet
appeared in 1874, and is known as
Coggia's\index{Coggia, G.\ (ko´jha), ast.\ Obs.\ Marseilles} comet. Its nucleus was
of the first magnitude, and its tail
$50$° in length, and very slightly
curved. Coggia's comet was the
first of striking brilliancy to which
the spectroscope was applied, and
it was found that its gaseous surroundings
were in large part composed
of hydrogen compounded
with carbon. Coggia's comet, when
far from perihelion, presented an
anomalous appearance, well shown
in the opposite illustration---a
bright streak immediately following
the nucleus and running through the middle of the tail. When nearer
the sun, this streak was replaced by the usual dark one. No sufficient
explanation of either has yet been proposed. The orbit of Coggia's
comet is an ellipse of so great eccentricity that this body cannot
reappear for thousands of years.

\textbf{Remarkable Comets between 1875 and 1890.}\index{comets!remarkable}---Only two require
especial mention, the first of which was discovered in 1881, and was a
splendid object in the northern heavens in June of that year. It was
similar in type to Donati's comet of 1858, and was the first comet ever
successfully photographed. In 1882 there were two bright comets, one
of them in many respects extraordinary. So great was the intrinsic
brightness that it was observed with the naked eye, close alongside
the sun. Indeed, it passed between the earth and the sun, in actual
transit; and just before entering upon the disk, the intrinsic brightness
of the nucleus was seen to be scarcely inferior to that of the sun itself.
It was a comet of huge proportions. Its tail stretched through space
over a distance exceeding that of the sun from the earth, and parts of
\DPPageSep{418.png}
its head passed within 300,000 miles of the solar surface, at a speed
of 200~miles a second. Probably this near approach explains what was
seen to take place on recession from the sun---the breaking up of the
comet's head into several separate nuclear masses, each pursuing an
independent path. Also this comet's tail presented a variety of unusual
phenomena, at one time being single and nearly straight, while again
there were two tails slightly curved.
Besides this, its coma was surrounded
by an enormous sheath or
envelope several million miles long,
extending toward the sun.

\textbf{Remarkable Comets since 1890.}\index{comets!remarkable}---No
very bright comet appeared
between 1882 and 1901; but the
Brooks\index{Brooks, W. R., Dir.\ Obs.\ Geneva} comet of 1893, although a
faint one and at
% Fig 15.14
\begin{wrapfigure}[18]{o}{0.4\textwidth}
  \centering
  \Input[0.4\textwidth]{page_405}
  \caption{Drawings of Coggia's Comet (1874)}
  \index{Coggia, G.\ (ko´jha), ast.\ Obs.\ Marseilles}
\end{wrapfigure}
no time visible to
the naked eye, is worthy of note
because of some remarkable photographs
of it obtained by Barnard\index{Barnard, E. E., Prof.\ Univ.\ Chicago}.
The illustration (\vpageref*{p406}) is reproduced
from one of them, and
enlarged from the original negative.
Changes in this comet were rapid
and violent, and the tail appeared
broken and distorted, like `a torch
flickering and streaming irregularly
in the wind.' Ejections of matter from the comet's nucleus may have
been irregular or it may have encountered some obstacle which shattered
it---perhaps a swarm of meteors. A bright southern comet with
a double tail 7° long was seen in 1901, and another in 1907. A brilliant
comet with a tail 25° long appeared early in 1910, and Halley's\index{Halley, E.@Halley, E.\ (1656--1742), Ast.\ Roy.} returned
the same year, though fainter than was expected (see page~\pageref{p420}).
\Restore

\textbf{When will the Next Comet come?}\index{comets!next to come}---If a large bright comet
is meant, the answer must be that astronomers cannot tell.
One may blaze into view at almost any time. During the
latter half of the 19th century, bright comets came to perihelion
at an average interval of about eight years. New
though faint comets are discovered very frequently. Of
the lesser and fainter periodic comets, several return nearly
every year; but they are for the most part telescopic, and
\DPPageSep{419.png}
rarely attract the attention of any one save the astronomers.

% Fig 15.15
\begin{figure}[hb!]
  \centering
  \Input{page_406}
  \caption{Brooks's Comet of 1893 (photographed by Barnard)}
  \label{p406a}
  \index{Barnard, E. E., Prof.\ Univ.\ Chicago}\index{Brooks, W. R., Dir.\ Obs.\ Geneva}
\end{figure}

\label{p406} \textbf{Light of Comets.}\index{comets!light}---The light of comets is dull and feeble,
and not always uniform. When in the farther part of
their orbits, comets seem to shine only
by light reflected from the sun; and
that is why they so soon become invisible,
on going away from perihelion.
They are then bodies essentially dark
and opaque. But with approach toward
the sun, the vast increase in brightness,
often irregular, is due to light
emitted by the comet itself, and it is
this intrinsic brightness of comets,
that, for the most part, makes them
the striking objects they are. In some
manner not completely understood, radiations
of the sun act upon loosely compacted
materials of the comet's head,
producing a luminous condition which,
in connection with the repulsive force
exerted by that central orb gives rise to
all the curious phenomena of the heads
and tails of comets.

\textbf{Chemical Composition.}\index{comets!chemical composition}---Through
analysis of the light of comets by the
spectroscope, it is known that the chief
element in their composition is carbon\index{carbon!in comets},
combined with hydrogen; that is, hydrocarbons\index{hydrocarbons, in comets}.
The elements so far found are
few. Sodium\index{sodium!in comets}, magnesium\index{magnesium!in comets}, and iron\index{iron!in comets} were
found in the great comet of 1882; also nitrogen, and
probably oxygen. It is not certain that the spectrum of
a comet remains always the same; perhaps there are
\DPPageSep{420.png}
rapid changes on approaching the sun. The faint continuous
spectrum, a background for brighter lines in the blue,
green, and yellow, is reflected sunlight.

\Smaller
The illustration shows a part of the spectrum of the comet of 1882,
with the Fraunhofer lines \textit{G, h, H, K,} and others, whose presence distinctly
confirms this hypothesis. The spectra of between 20 and 30
comets have been observed in all, and they appear to have in general
very nearly the same chemical composition.
% Fig 15.16
\begin{figure}[hbt!]
  \centering
  \Input[\textwidth]{page_407}
  \caption{Spectrum of Comet of 1882 (Sir William Huggins)}
  \index{Huggins, W.\ (1824--1910), Eng.\ ast.}
\end{figure}

\textbf{Photographing Comets.}\index{comets!photography}---The light of a comet is usually feeble, at
least so far as the eye is concerned, and its actinic power is even less.
How then can a comet be photographed? Evidently in one of two
ways only. Either the photographic plate must be very sensitive, or
the exposure must be very long. Before invention of the modern
sensitive dry plate, it had been found impossible to photograph comets.
The first photograph of a comet was made by Henry Draper\index{Draper, H. (1837--82), Am.\ ast.}, who
photographed the comet of 1881. Since 1890 many faint comets have
been successfully photographed at the Lick Observatory\index{Lick Observatory}, and elsewhere,
by the use of very sensitive plates and a long exposure. Figure~\ref{p408}
shows a photograph of Gale's\index{Gale, W.~F., Australian ast.} comet (1894), in which the exposure
was prolonged to 1\,h.\:0\,m. The comet was moving rapidly, and
as the clockwork moving the telescope was made to follow the comet
accurately, all stars adjacent to it appear upon the photograph, not as
points of light, but as parallel trails of equal length. Henry\index{Henry, Paul (ong-ree´) (1848--1905), Fr.\ ast.}\index{Henry, Prosper (ong-ree´) (1849--1903), Fr.\ ast.} and Wilson\index{Wilson, H.~C., Dir.\ Carleton Col.\ Obs.}
have met with equal success.
\Restore

\textbf{Comets discovered during Eclipses.}\index{comets!discoveries}---Probably more
than one half of all comets coming within range of
visibility from earth remain undiscovered, because of the
overpowering brilliancy of the sun. Ought not, then, new
comets to be discovered during total eclipses of the sun?
This has actually happened on at least two such occasions,
and a like appearance has been suspected on two more.
\DPPageSep{421.png}

\Smaller
During the total eclipse of the 17th of May, 1882, observed in Egypt,
Schuster\index{Schuster, A., Prof.\ Victoria Univ.} photographed a new comet alongside the solar corona, as
shown on page~\pageref{p301}. This comet was named for Tewfik\index{Tewfik (teff´ik) (1852--92), Egypt.\ khedive}, who was then
khedive. Also another comet was similarly photographed, but joining
immediately upon the streamers of the corona, during
the total eclipse of the 16th of April, 1893, by Schaeberle\index{Schaeberle, J.~M.\ (sheb´bur-ly), Am.\ ast.}
in Chile. Both of these comets were new discoveries,
and neither of them has since been seen. As there is
but one observation of each, nothing is known about
their orbits round the sun, nor whether they will ever
return.
\Restore

% Fig 15.17
\begin{figure}[hbt!]
  \centering
  \Input{page_408}
  \caption{Gale's Comet of 1894 (photographed by Barnard)}
  \label{p408}
  \index{Barnard, E. E., Prof.\ Univ.\ Chicago}\index{Gale, W.~F., Australian ast.}
\end{figure}
\textbf{Mass and Density.}\index{comets!mass}\index{comets!density}---So small are the masses
of comets that only estimates can be given as
compared with the mass of the earth. Comets
have in certain instances approached very near
to lesser bodies of the solar system; but while
cometary orbits and motions have been greatly
disturbed thereby, no change has been observed
in the motion of satellites or other
bodies near which a comet has passed. So
this mass must be slight. Probably no comet's
mass is so great as the $\frac{1}{100000}$ part of the
earth's; but even if only one third of this, it
would still equal a ball of iron 100~miles in
diameter. If the mass of comets is so small,
while their volume is so vast, what must be
the density of these bodies? For the density
is equal to the mass divided by the volume,
and comets must, therefore, be exceedingly
thin and tenuous. On those rare occasions
when stars have been observed through the
tail of a comet, although it may be millions
of miles in thickness, still no diminution of the star's
luster has been perceived. Even through the denser coma
the light of a star passes undimmed; though the star's
image, if very near the comet's nucleus, may be rendered
\DPPageSep{422.png}
somewhat indistinct. The air pump is often used to produce
an approach to a perfect vacuum; but in a cubic
yard of such vacuum there would be many hundred times
the amount of matter in a cubic yard of a comet's head.

\textbf{Passing through a Comet's Tail.}\index{comets!earth passes through}---Curious as it may
seem, these enormous tails are in actual mass so slight
that thrusting the hand into their midst would bring no
recognition to the sense of touch. Collision would be
much like an encounter with a shadow. Comets' tails
are excessively airy and thin, or, as Sir John Herschel\index{Herschel, Sir J.~F.~W.\ (1792--1871), Eng.\ ast.}
remarks, possibly only an affair of pounds or even ounces.

\Smaller
The mass of a comet's head may be large or small; it may not be
more than a very large stone, or in the case of the larger comets it is
perfectly possible that the mass of the head should be composed of an
aggregation of many hundreds or even thousands of small compact
% Fig 15.18
\begin{figure}[hbt!]
  \centering
  \Input{page_409}
  \caption{Earth about to pass through Tail of Comet of 1861}
\end{figure}
bodies, stony and metallic. Usually the speed is so great that the
comet itself would be dissipated into vapor on experiencing the shock
of collision with any of the planets. In at least two instances it is
known that the earth actually passed through the tail of a comet, once
on 30th June, 1861. The figure shows positions of sun (\textit{S}), head of
comet (\textit{c}), and earth (\textit{t}), just before our planet's plunge into the diaphanous
tail. But we came through without being in the least conscious
of it, except from calculations of the comet's position.
\Restore

\textbf{Collision with a Comet.}\index{comets!collision}---As the orbits of comets lie at all
possible inclinations to the earth's path, or ecliptic, and as
the motion of these erratic bodies may be either direct or
retrograde, evidently it is entirely possible that our planet
may some time collide with a comet, because these bodies
\DPPageSep{423.png}
exist in space in vast numbers. As but one collision is
likely to take place every 15,000,000 years, the chances
are immensely against the happening of such an event in
our time, and comets are not dangerous bodies. `If one
should shut his eyes and fire a gun at random in the air,
the chance of bringing down a bird would be better than
that of a comet of any kind striking the earth.'

\Smaller
However, should the head of a large comet collide squarely with our
globe---the consequences might be inconceivably dire: probably the
air and water would be instantly consumed and dissipated, and a considerable
region of the earth's surface would be raised to incandescence.
But consequences equally malign to human interests might result from
the much more probable encounter of the earth's atmosphere with
solid particles of a large hydrocarbon comet: it might well happen that
diffusion of noxious gases from sudden combustion of these compounds
would so vitiate the atmosphere as to render it unsuitable for breathing.
In this manner, while the earth itself, its oceans, and even human habitations,
might escape unharmed, it is not difficult to see how even a
brush from the head of a large comet might cause universal death to
nearly all forms of animal existence.

\textbf{Origin of Comets.}\index{comets!origin}---The origin of comets is still shrouded in mystery.
Probably they have come from depths of the sidereal universe,
and so are entirely extra-solar in origin. Arriving apparently from
all points of space in their journey from one star to another, they
wheel about the sun somewhat like moths round a candle. Sometimes,
as already shown, they speed away in a vast ellipse, with the promise
of a future visit, though at some date which cannot be accurately
assigned. Sometimes they continue upon interstellar journeys of such
vast parabolic dimensions, perhaps round other suns, that no return
can ever be expected. Probably the comets are but chips in the workshop
of the skies, mere waste pieces of the stuff that stars are made of.
It has been urged, too, that some comets may have originated in vaporous
materials ejected by our own sun, or the larger planets of our
system; but here we tread only the vast fields of mere conjecture,
tempting, though unsatisfying.
\Restore

\textbf{Disintegration of Comets.}\index{comets!disintegration}---Every return to perihelion
appears to have a disintegrating effect upon a comet.
In a few cases this process has actually been taking
place while under observation; for example, the lost
\DPPageSep{424.png}
Biela's comet\index{Biela@v.\ Biela, W. (b\=e´lä) (1782--1856), Aus. officer} in 1846, the great comet of 1882, and
Brooks's comet\index{Brooks, W. R., Dir.\ Obs.\ Geneva} of 1889, the heads of which were seen
either to divide or to be divided into fragments. Groups
of comets probably represent a more complete disintegration.

\Smaller
For example, the comets of 1843, 1880, 1882, and 1887 travel tandem\index{comets!tandem},
and originally were probably one huge comet. In the case of still other
comets, this disintegration has gone so far that the original cometary
mass is now entirely obliterated. Instead of a comet, then, there
exists only a cloud of very small fragments of cometary matter, too
small, in fact, to be separately visible in space. Such interplanetary
masses, originally single comets of large proportions, have by their
repeated returns to the sun been completely shattered by the oft-renewed
action of disrupting forces; and all that is now left of them is
an infinity of meteoric particles, trailing everywhere along the original
orbit. The astronomer becomes aware of the existence of these small
bodies only when they collide with our atmosphere, sometimes penetrating
even to the surface of the earth itself.
\Restore

\textbf{Meteors, Shooting Stars, and Meteorites.}\index{meteors}\index{meteorites}\index{shooting stars!see {meteors}}---Particles of
matter thought to have their origin in disintegrated comets,
and moving round the sun in orbits of their own, are
called \textit{meteors}. In large part, our knowledge of these
bodies is confined to the relatively few which collide with
the earth. The energy of their motion is suddenly converted
into heat on impact with the atmosphere, and friction
in passing swiftly through it. As a rule, this speedily
vaporizes their entire substance, the exterior being brushed
off by the air as soon as melted, often leaving a visible train
in the sky. The luminous tracks pass through the upper
atmosphere, few if any meteors appearing at greater
heights than 100~miles, and few below 30~miles. These
paths, if very bright, can be recorded with great precision
by photography as Wolf\index{Wolf, M., Prof.\ Univ.\ Heidelberg}, Barnard\index{Barnard, E. E., Prof.\ Univ.\ Chicago}, and Elkin\index{Elkin, W.~L., Dir.\ Yale Obs.} have done.
As the speed of meteors through the air is comparable with
that of our globe round the sun, we know that their motion
is controlled by the sun's attraction, not the earth's.
\DPPageSep{425.png}

\Smaller
Very small meteors, sometimes falling in showers, are frequently
called \textit{shooting stars}, but the late Professor Newton's\index{Newton, H.~A.\ (1830--96), Am.\ ast.} view is gradually
gaining ground, that there is no definite line of distinction. The
shooting stars are thought to be very much smaller than meteors,
because they are visible for only a second or two, and disappear
completely at much greater heights than the meteors do. Many
millions of them collide with our atmosphere every day, and are
quickly dissipated. Although the average of them are not more massive
than ordinary shot, their velocity is so great that all organic beings,
without the kindly mantle of the air (were it possible for such to live
without it) would be pelted to death. If a meteor passes completely
through the atmosphere, and reaches the surface of the earth, it becomes
known as a meteorite. Many thousand pounds of such interplanetary
material have been collected from all parts of the earth,
and the specimens are jealously preserved in cabinets and museums,
the most complete of which are in London\index{British Museum meteorites}, Paris\index{Paris!Museum, meteorites}, and Vienna\index{Vienna, meteorites}. Remarkable
collections in the United States are at Amherst College\index{Amherst College!meteorite collection},
Harvard\index{Harvard College!meteorite collection} and Yale Universities\index{Yale University, meteorites}, the National Museum\index{U.~S., National Museum, meteorites} at Washington,
and the museums of Chicago and New York.

\textbf{Meteors most Abundant in the Morning.}\index{meteors}---Run rapidly in a rainstorm:
the chest becomes wetter than the back, because
of advance
of the body to meet the drops. In like manner, the forward or advance
hemisphere of the earth, in its motion round the sun, is pelted by more
meteors than any other portion. As every part of the earth is turned
toward the radiant during the day of 24~hours, it is obvious that
the most meteors will be counted at that hour of the day when the
dome of the sky is nearly central around the general direction of our
% Fig 15.19
\begin{wrapfigure}[12]{o}{0.6\textwidth}
  \centering
  \Input[0.6\textwidth]{page_412}
  \caption{When Meteors are most Abundant}\index{meteors}
\end{wrapfigure}
motion about the sun; in other words, when apex of earth's way is
nearest to the zenith. Recalling
the figures on pages \pageref{p134}--\pageref{p135},
it is apparent that this takes
place about sunrise; and in
the adjacent illustration,
where the sun is above the
earth, and illuminating the
hemisphere \textit{abd}, it is sunrise
at \textit{d}, and the earth is speeding
through space in the direction
\textit{dp}, indicated by the great arrow. So the hemisphere \textit{adc} is
advancing to meet the meteors which seem to fall from the directions
\textit{ggg}. If we suppose meteoric particles evenly distributed throughout
the shoal, the number becoming visible by collision with our atmosphere
will increase from midnight onward to six in the morning, provided
the season is such that dawn does not interfere. From noon at
\DPPageSep{426.png}
\textit{a} to sunset at \textit{b}, there would be a gradual decrease, with the fewest
meteors falling from the directions $fff$, upon the earth's rearward
hemisphere, \textit{abc}. Also, as to time of the year, it is well known that our
globe encounters about three times as many shooting stars in passing
from aphelion to perihelion as from perihelion to aphelion.
\Restore

\textbf{Radiant Point.}\index{radiant, meteoric}---On almost any clear, moonless night,
especially in April, August, November, and December, a
few moments of close watching
% Fig 15.20
\begin{wrapfigure}[14]{i}{0.5\textwidth}
  \centering
  \Input[0.4\textwidth]{page_413}
  \caption{To Illustrate the Radiant Point}
\end{wrapfigure}
will show one or more
shooting stars. Ordinarily, they appear in any quarter of
the sky; and on infrequent occasions they streak the
heavens by hundreds and thousands, for hours at a time,
as in November of 1799 and 1833. These are known as
meteoric showers. Careful watching has revealed the very
important fact, that practically all the luminous streaks of
a shower, if prolonged backward, meet in a small area
of the sky which is fixed among the stars. Arrows in the
following figure represent the visible paths of 20~meteors,
and the direction of their flight. It is clear that lines drawn
through them will nearly all
strike within the ring. This
area is technically known as
the radiant point, or simply
the radiant. Divergence
from it in every direction is
only apparent---a mere effect
of perspective, proving that
meteors move through space
in parallel lines. The radiant
is simply the vanishing point.
Notice that the luminous
paths are longer, the farther they are from the radiant; if
a meteor were to meet the earth head on, its trail would
be foreshortened to a point, and charted within the area of
the radiant itself. About 300 such radiant points are now
\DPPageSep{427.png}
known, of which perhaps 50 are very well established.
The constellation in which the radiant falls gives the
name to the shower; so there are Leonids and Perseids,
Andromedes and Geminids, and the like.

\Smaller
\textbf{List of Principal Meteor Showers.}\index{meteors}---In table~\ref{tab15.1} is given
a short list of the chief meteoric displays of the year, according to
Denning\index{Denning, W.~F., Eng.\ ast.}, a prominent English authority:---
% Table 15.1
\begin{table}[h]
\centering
\caption{\textsc{Annual Showers of Meteors}}
\label{tab15.1}
\begin{tabular}{l@{}| r@{ }l@{ }r@{ }l@{\,}| r@{ }r|cl@{ }rc| c}
  \hline\hline
  \multirow{2}{*}{\centering\footnotesize\textsc{\rule{0pt}{4ex}%
    Name of Shower\ }}
&amp; \multicolumn{6}{c|}{\centering\footnotesize\textsc{\rule{0pt}{3ex}%
    Position of Radiant}}
&amp; \multicolumn{4}{c|}{
  \multirow{2}{6em}{\centering\footnotesize\textsc{\rule{0pt}{3ex}%
    Date of Maximum}}}
&amp; \multirow{2}{5em}{\centering\footnotesize\textsc{\rule{0pt}{3ex}%
    Duration in Days}}
\\[1ex]  \cline{2-7}
  &amp; \multicolumn{4}{c|}{\centering\footnotesize\textsc{\rule{0pt}{3ex}%
  R.~A.}}
  &amp; \multicolumn{2}{c|}{\centering\footnotesize\textsc{Decl.}} &amp;&amp;&amp;&amp;&amp; \\[1ex]  \hline
  Quadrantids \dotfill    &amp;\ 15 &amp; h.&amp; 19 &amp; m.&amp;\ N.&amp; 53°
&amp;\ \ &amp; Jan.  &amp;  2 &amp;&amp;  \phantom{0}2\rule{0pt}{3ex}  \\

  Lyrids \dotfill         &amp; 17 &amp;   &amp; 59 &amp;   &amp; N.&amp; 32\phantom{°}
&amp;&amp; April &amp; 18 &amp;&amp;  \phantom{0}4  \\

  Eta Aquarids \dotfill   &amp; 22 &amp;   &amp; 30 &amp;   &amp; S.&amp;  2\phantom{°}
&amp;&amp; May   &amp;  2 &amp;&amp;  \phantom{0}8  \\

  Delta Aquarids \dotfill &amp; 22 &amp;   &amp; 38 &amp;   &amp; S.&amp; 12\phantom{°}
&amp;&amp; July  &amp; 28 &amp;&amp;  \phantom{0}3  \\

  Perseids \dotfill       &amp;  3 &amp;   &amp;  4 &amp;   &amp; N.&amp; 57\phantom{°}
&amp;&amp; Aug.  &amp; 10 &amp;&amp; 35  \\

  Orionids \dotfill       &amp;  6 &amp;   &amp;  8 &amp;   &amp; N.&amp; 15\phantom{°}
&amp;&amp; Oct.  &amp; 19 &amp;&amp; 10  \\

  Leonids \dotfill        &amp; 10 &amp;   &amp;  0 &amp;   &amp; N.&amp; 23\phantom{°}
&amp;&amp; Nov.  &amp; 13 &amp;&amp;  \phantom{0}2  \\

  Andromedes \dotfill     &amp;  1 &amp;   &amp; 41 &amp;   &amp; N.&amp; 43\phantom{°}
&amp;&amp; Nov.  &amp; 26 &amp;&amp;  \phantom{0}2  \\

  Geminids \dotfill       &amp;  7 &amp;   &amp; 12 &amp;   &amp; N.&amp; 33\phantom{°}
&amp;&amp; Dec.  &amp;  7 &amp;&amp; 14
\\[1ex]  \hline\hline
\end{tabular}
\index{Geminids, meteors}%
  \index{Andromedes, meteors}%
  \index{Leonids, meteors}%
  \index{Orionids, meteors}%
  \index{Perseids, meteors}%
  \index{Lyrids, meteors}%
  \index{Quadrantids, meteors}%
  \index{Aquarids, Delta, Eta, meteors}%
  \index{meteors}%
\end{table}

\noindent When more than one radiant falls in any constellation, the usual
designation of the nearest star is added, to distinguish between them.
\Restore

\textbf{Paths of Meteors.}\index{meteors}---Repeated observation of the paths
of meteors belonging to any particular radiant soon establishes
the fact that showers recur at about the same time
of the year. Also in a few instances the shower is very
prominently marked at intervals of a number of years.
So it has become possible to predict showers of meteors,
which on several occasions have been signally verified.
Conspicuously so is the case of the shower of November,
1866, which came true to time and place; but the prediction
\DPPageSep{428.png}
of a like shower in 1899--1900 was only partly verified.
The periodic time of these meteors is $33\frac{1}{4}$~years.

% Fig 15.21
\begin{figure}[hbt!]
  \centering
  \Input{page_415}
  \caption{Orbit of Comet I (1866) and of the November Meteors}
  \label{p415}\index{Leonids, meteors}
\end{figure}

\Smaller
The position of their radiant among the stars, and the direction in
which the meteors are seen to travel, has afforded the means of calculating
the size and shape of their orbit, and just where it lies in space.
Figure~\ref{p415} shows the orbit of the Leonids\index{Leonids, meteors}, or November meteors, as
related to the paths of the planets, and it is evident that these bodies,
although they pass at a distance
of 100,000,000 miles from the
sun at their perihelion, recede
about $16\frac{2}{3}$~years later to a distance
greater than that of Uranus.
They are not aggregated
at a single point in their orbit,
but are scattered along a considerable
part of it, called the
`Gem of the ring.' As the
breadth of the gem takes more
than two years to pass the perihelion
point, which nearly coincides
with the position of the
earth in the middle of November,
there will usually be two or
three meteoric showers at yearly
intervals, while the entire shoal
is passing perihelion. Failure
of this shower is probably due
to planetary perturbations and
secular dissipation of this meteoric
stream.
\Restore

% Fig 15.22
\begin{figure}[hbt!]
  \centering
  \Input[0.75\textwidth]{page_416}
  \caption{Perihelion Parts of Orbits of the August and November Meteor-showers}
  \label{p416}
\end{figure}

\textbf{Meteoric Orbits in Space.}\index{Uranus!meteors near}\index{meteors}---But
it must not be inferred
from the figure here
given that the Leonids\index{Leonids, meteors}
travel in the plane of the
planetary orbits; for, at the time when their distance
from the sun is equal to that of the planetary bodies,
they are really very remote from all the planets except
the earth and Uranus. This is because of the large angle
\DPPageSep{429.png}
of 17° by which the orbit of the November meteors
is inclined to the ecliptic. It stands in space as %the adjacent
Figure~\ref{p416} shows, being the lower one of the two orbits
whose planes are cut off. Similarly, the upper and nearly
vertical plane represents the position in space of another
meteoric orbit, which intersects our path about 10th
August. This shower is therefore known as the August
shower; also these meteors are often called Perseids.
\DPPageSep{430.png}

\Smaller
As shown by the arrows, both the Perseids\index{Perseids, meteors} and the Leonids\index{Leonids, meteors} travel
oppositely to the planets; so that their velocity of impact with our
atmosphere is compounded of their own velocity and the earth's also.
This average speed for the Leonids, about 45~miles per second, is
great enough to vaporize all meteoric masses within a few seconds;
so it is unlikely that a meteoric product from the Leonids will ever be
discovered. Impact velocity of the Andromedes\index{Andromedes, meteors} is very much less,
because they overtake the earth. In the case of meteorites, the velocity
of ground impact probably never exceeds a few hundred feet per second,
so great is the resistance of the air; and several meteoric stones which
fell in Sweden, 1st January, 1869, on ice a few inches thick, rebounded
without either breaking it or being themselves broken.
\Restore

\textbf{Connection between Comets and Meteors.}\index{comets!connection with meteors}---Not long
after the important discovery of the motion of meteors in
regular orbits, an even more significant relation was ascertained:
that the orbits of the Perseids\index{Perseids, meteors} and the Leonids\index{Leonids, meteors}
are practically identical with the paths in which two comets
are known to travel. The orbit of the Leonids is coincident
with that of Tempel's comet (1866 \textsc{i}), and the Perseids
pursue the same track in space with Swift's comet (known
as 1862 \textsc{iii}). The latter has a period of about 120~years,
and recedes far beyond the planet Neptune. So do the
meteors traveling in the same track. They are much
more evenly distributed all along their path than the
Leonids are; and no August ever fails of a slight sprinkle,
although the shorter nights in our hemisphere often interfere
with the display.

\textbf{What are Meteors?}\index{meteors}---Several other meteor swarms and
comets have been investigated with a like result; so the
conclusion is now well established that these meteors, and
probably all bodies of that nature, are merely the shattered
residue of former comets. This important theory is confirmed,
whether we look backward in the life of a comet,
or forward: if backward, comets are known to disintegrate,
and have indeed been `caught in the act'; if forward, our
expectation to find the disruption farther advanced in the
\DPPageSep{431.png}
case of some comets and meteors than others is precisely
confirmed by the facts regarding different showers. Then,
too, as will be shown in a later paragraph, the spectra
of meteorites vaporized and photographed in our laboratories
are practically identical with the spectra of the
nuclei of comets. The conclusion is, therefore, that these
latter are nothing more than a compact swarm or shoal
of meteoric particles, vaporized in their passage through
space, under conditions not yet fully understood. The
practical identity of composition between comets and
meteors had long been suspected, but it was not completely
confirmed until 27th November, 1885, when meteorites
which fell to the earth from a shower of Bielids\index{Bielids (be´lidz), meteors} were
picked up in Mexico, and chemical and physical investigation
established their undoubted nature as originally part
of the lost Biela's comet.\index{Biela@v.\ Biela, W. (b\=e´lä) (1782--1856), Aus. officer}

\textbf{Falls of Meteorites.}\index{meteorites!falls of}---In general the meteorites are
divided into two classes: meteoric stones and meteoric
irons. Falls of the stony meteorites have been much
oftener seen than actual descents of masses of meteoric
iron. The most remarkable fall ever seen took place on
10th May, 1879, in Iowa, the heaviest stone weighing 437
pounds. This is two thirds the weight of the largest
meteoric stone ever discovered, though not actually seen
to fall. It was found in Hungary in 1866, and is now part
of the Vienna collection\index{Vienna, meteorites}. The iron masses are often much
heavier: the `signet' meteorite, a complete ring found in
Tucson, Arizona, and now in the United States National
Museum\index{U.~S., National Museum, meteorites} at Washington, weighs 1400 pounds; a Texas
meteorite, now part of the Yale collection\index{Yale University, meteorites}, weighs 1635
pounds; and a Colorado meteorite in the Amherst\index{Amherst College!meteorite collection} collection
weighs 437 pounds. But although the cabinets contain
hundreds of specimens of meteoric irons, only eight or
ten have actually been seen to fall.
\DPPageSep{432.png}

\Smaller
Of these, the largest one fell in Arabia in 1865, and its weight is 130
pounds. It is now in the British Museum\index{British Museum meteorites}. The average velocity of
meteors is 35 miles per second. Their visibility begins at an altitude
of about 70~miles, and they fade out at half that height. The work
done by the atmosphere in suddenly checking their velocity appears in
large part as heat which fuses the exterior to incandescence, and leaves
them, when cooled, thinly encrusted as if with a dense black varnish.
The iron meteorites, not reduced by rust, are invariably covered with
deep pittings or thumb marks. Meteorites are always irregular in form\index{meteorites!form irregular},
never spherical; and the pittings are in part due to impact of minute
aerial columns which resist their swift passage through the air.
\Restore

\textbf{Analysis of the Meteorites.}\index{meteorites!analysis}---Meteoric iron is an alloy,
containing on the average ten per cent of nickel, commingled
with a much smaller amount
% Fig 15.23
\begin{wrapfigure}[16]{o}{0.4\textwidth}
  \centering
  \Input[0.3\textwidth]{page_419}
  \caption{Widtmannstättian Figures}\index{Widmannstättian (vid-m\u on-stet´y\u an) figs.}
\end{wrapfigure}
of cobalt, copper, tin, carbon, and a
few other elements. Meteoric iron
is distinguishable from terrestrial
irons by means of the `Widmannstättian
figures\index{Widmannstättian (vid-m\u on-stet´y\u an) figs.},' which etch themselves
with acids upon the polished
metallic surface---a test which rarely
fails. The illustration shows these
figures of their true size, as it was
made from a transfer print from the
actual etched surface of a meteorite
in the Amherst\index{Amherst College!meteorite collection} collection. In meteoric
stones, chemical analysis has revealed the presence
of about one third of all the elemental substances
recognized in the earth's crust; among them the elements
found in meteoric irons, also sulphur, calcium, chlorine,
sodium, and many others.

\Smaller
The minerals found in meteoric stones are those which abound in
terrestrial rocks of igneous or volcanic origin, like traps and lavas.
Carbon\index{meteorites!carbon in}\index{carbon!in meteorites} sometimes is found in meteorites as diamond\index{diamond in meteorites}. The analysis
of meteorites has brought to light a few compounds new to mineralogy,
but has not yet led to the discovery of any new element; and the study
\DPPageSep{433.png}
of meteorites is now the province of the crystallographer, the chemist,
and the mineralogist, rather than the astronomer. Even the most
searching investigation has so far failed to detect any trace of organic
life in meteorites.
\Restore

Occlusion\index{occlusion of gases} is the well-known property of a metal, particularly
iron, by which at high temperatures it absorbs
gases, and retains them until again heated red hot. Hydrogen\index{hydrogen!in meteorites},
carbonic oxide, and nitrogen\index{nitrogen!in meteorites} are usually present in
iron meteorites as occluded gases, also, in very small quantities,
the light gas, newly discovered, called helium\index{helium!in meteorites}. In
1867, during a lecture on meteors by Graham\index{Graham, T., (graim) (1805--69), Scot.\ chem.}, a room
in the Royal Institution, London, was lighted by gas
brought to earth in a meteorite from interplanetary space.
We have now traversed the round of the solar system; it
remains only to consider the bodies of the sidereal system,
and the views held by philosophers concerning the progressive
development of the material universe.
\label{p420}
\begin{figure}[hbt!]
  \centering
  \Input{page_420}
  \caption{Halley's Comet, May, 1910 (from a photograph by Ellerman in the Hawaiian Islands)}
\end{figure}
\DPPageSep{434.png}


\Chapter{XVI}{The Stars and the Cosmogony}\index{cosmogony}\index{stars}

Our descriptions of heavenly bodies thus far have concerned
chiefly those belonging to the solar system.
We found distance growing vast beyond the power
of human conception, as we contemplated, first the neighborly
moon, then the central orb of the system 400 times
farther away, and finally Neptune, 30 times farther than
the sun,---not to say some of the comets whose paths
take them even remoter still. But outside of the solar
system, and everywhere surrounding it, is a stellar universe\index{universe!stellar}
the number of whose countless hosts is in some sense a
measure of their inconceivable distance from our humble
abode in space.

\textbf{The Sidereal System.}\index{sidereal system}---All these bodies constitute the
sidereal system, or the stellar universe. It comprises stars
and nebulæ; not only those which are visible to the naked
eye, but hundreds of thousands besides, so faint that their
existence is revealed only by the greatest telescopes and
the most sensitive photographic plates. Remoteness of
the stars at once forbids supposition that they are similar
in constitution to planets, shining by light reflected from
the sun as the moon and planets do. Even Neptune, on the
barriers of our system, is too faint for the naked eye to
grasp his light. But the nearest fixed star is about 9000
times more distant. So the very brightness of the lucid
stars leads us to suspect that they at least must be self-luminous
like the sun; and when their light is analyzed
\DPPageSep{435.png}
with the spectroscope, the theory that they are suns\index{stars!are suns} is
actually demonstrated. It is reasonable to conclude, then,
that the sun himself is really a star, whose effulgence, and
importance to us dwellers on the earth, are due merely to
his proximity. The figure below will help this conception:
for if we recede from the sun even as far as Neptune, his
disk will have shrunk almost to a point, though a dazzling
one. Were this journey to be continued to the nearest
star, our sun would have dwindled to the insignificance
of an ordinary star.

\textbf{The Magnitudes of Stars.}\index{stars!magnitudes of}---While stars as faint as the
sixth magnitude can just be seen by the ordinary eye on
a clear dark night, still
other and fainter stars can
be followed with the telescope
far beyond this
limit,
% Fig 16.24
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.55\textwidth]{page_422}
  \caption{Our Sun but a Brilliant Star as seen from Neptune}
  \index{Neptune!sun seen from}
\end{wrapfigure}
to the fifteenth magnitude
and even farther
by the largest instruments.
Division into magnitudes,
although made arbitrarily,
is a classification warranted
by time, and use
of many generations of
astronomers. Brightness
of stars decreases in geometric
proportion as the
number indicating magnitude
increases; the constant
term being $2\frac{1}{2}$. Thus,
an average star of the first magnitude is $2\frac{1}{2}$ times brighter
than one of the second magnitude; a second magnitude
star gives $2\frac{1}{2}$ times more light than one of the third magnitude,
and so on. At the observatory of Harvard College\index{Harvard College!obs.},
\DPPageSep{436.png}
Pickering\index{Pickering, E. C., Dir.\ Harv.\ Coll.\ Obs.}, its director, has devoted many years to determination
of stellar magnitudes with the meridian photometer,
a highly accurate instrument of his devising, by which
the brightness of any star at culmination may be compared
directly with Polaris as a standard. Brightest of all the
stars is Sirius\index{Sirius}, and as no others are so brilliant, strictly
he ought perhaps to be the only first magnitude star. But
many fainter than Sirius are ranked in this class, three
of them so bright that their stellar magnitude is negative,
as below. Decimal fractions express all gradations of
magnitude. Even the surpassing brilliancy of the sun
can be indicated on the same scale; the number $-25.4$
expresses his stellar magnitude\index{sun!stellar magnitude}.

\textbf{The Brightest Stars.}\index{stars!brightest}---Twenty stars are rated of the
first magnitude; half of them are in the northern hemisphere
of the sky. They are given in Table~\ref{p423}.
% Table 16.1
\begin{table}[htb]
\TableSize
\centering
\caption{\textsc{The Brightest Stars}}
\index{Achernar ($\alpha$ Eridani)}\index{Aldeb´aran}\index{Altair}\index{Anta´res ($\alpha$ Scorpii)}\index{Arcturus}\index{Betelgeux (bet-el-gerz´)}
\label{p423}
\begin{tabular}{r@{\qquad}|r@{\qquad}|cl}
  \hline\hline
  \multicolumn{1}{m{4em}|}{\centering\footnotesize\textsc{
    Order of Brightness}}
&amp; \multicolumn{1}{m{5em}|}{\centering\footnotesize\textsc{
    Stellar Magnitude}}
&amp; \multicolumn{2}{m{12em}}{\centering\footnotesize\textsc{
    Stars' Names}}
\\  \hline
1 &amp; $-1.4$ &amp;&amp; $\alpha$ Canis Majoris (\textit{Sirius})\rule{0pt}{3ex}  \\
2 &amp; $-0.8$ &amp;&amp; $\alpha$ Argûs (\textit{Canopus}) *          \\
3 &amp; $-0.1$ &amp;&amp; $\alpha$ Centauri *                            \\
4 &amp; 0.1    &amp;&amp; $\alpha$ Aurigæ (\textit{Capella})          \\
5 &amp; 0.2    &amp;&amp; $\alpha$ Boötis (\textit{Arcturus})            \\
6 &amp; 0.2    &amp;&amp; $\alpha$ Lyræ (\textit{Vega})               \\
7 &amp; 0.3    &amp;&amp; $\beta$  Orionis (\textit{Rigel})              \\
8 &amp; 0.4    &amp;&amp; $\alpha$ Eridani (\textit{Achernar}) *         \\
9 &amp; 0.5    &amp;&amp; $\alpha$ Canis Minoris (\textit{Procyon})      \\
10&amp; 0.7    &amp;&amp; $\beta$  Centauri *                            \\
11&amp; 0.9    &amp;&amp; $\alpha$ Orionis (\textit{Betelgeux})          \\
12&amp; 0.9    &amp;&amp; $\alpha$ Crucis *                              \\
13&amp; 0.9    &amp;&amp; $\alpha$ Aquilæ (\textit{Altair})           \\
14&amp; 1.0    &amp;&amp; $\alpha$ Tauri (\textit{Aldebaran})            \\
15&amp; 1.1    &amp;&amp; $\alpha$ Virginis (\textit{Spica})             \\
16&amp; 1.2    &amp;&amp; $\alpha$ Scorpii (\textit{Antares})            \\
17&amp; 1.2    &amp;&amp; $\beta$  Geminorum (\textit{Pollux})           \\
18&amp; 1.3    &amp;&amp; $\alpha$ Piscis Australis (\textit{Fomalhaut}) \\
19&amp; 1.3    &amp;&amp; $\alpha$ Leonis (\textit{Regulus})             \\
20&amp; 1.4    &amp;&amp; $\alpha$ Cygni (\textit{Deneb})                \\[1ex]
\hline\hline
\multicolumn{4}{c}{* Invisible in our middle northern latitudes.}
   \index{Fomalhaut (f\=o´mal-\=o)}%
  \index{Pollux ($\beta$ Geminorum)}%
  \index{Regulus ($\alpha$ Leonis)}%
  \index{Rigel ($\beta$ Orionis)}%
  \index{Spica ($\alpha$ Virginis)}%
  \index{Deneb@Deneb, ($\alpha$ Cygni)}%
  \index{Centauri, Alpha}%
  \index{Cano´pus ($\alpha$ Argûs)}%
  \index{Capella}%
  \index{Sirius}%
\end{tabular}
\end{table}

These stars culminate at different altitudes varying
with their declination, and at different times throughout
\DPPageSep{437.png}
the year, which you may find from charts of the constellations
(pp.\ \pageref{plateIII}--\pageref{plateIV}).

\textbf{Number of the Stars.}\index{stars!number of}---Besides twenty stars of the first
magnitude, not only are there nearly six thousand of
lesser magnitude visible to the naked eye, likewise many
hundreds of thousands visible in telescopes of medium
size, but also millions of stars revealed by the largest
telescopes. From careful counts, partly by Gould\index{Gould, B.~A.\ (1824--96), Am.\ ast.}, the
number of stars of successive magnitudes is found to increase
nearly in geometric proportion, as shown in Table~\ref{tab16.2}.

% Table 16.1
\begin{table}
\TableSize
\centering
\caption{}
\label{tab16.2}
\begin{tabular}{l@{ }cr c@{\hspace{3em}} r@{ }cr}
  1st &amp; magnitude &amp;   20 &amp;   &amp;  6th &amp; magnitude &amp;    5000 \\
  2d  &amp;  \Ditto   &amp;   65 &amp;   &amp;  7th &amp;  \Ditto   &amp;  20,000 \\
  3d  &amp;  \Ditto   &amp;  200 &amp;   &amp;  8th &amp;  \Ditto   &amp;  68,000 \\
  4th &amp;  \Ditto   &amp;  500 &amp;   &amp;  9th &amp;  \Ditto   &amp; 240,000 \\
  5th &amp;  \Ditto   &amp; 1400 &amp;   &amp; 10th &amp;  \Ditto   &amp; 720,000
\end{tabular}
\end{table}

Any glass of two inches aperture should show all these
stars. But in order to discern all the uncounted millions
of yet fainter stars, we need the largest instruments, like
the Lick\index{Lick telescope} and the Yerkes telescopes\index{Yerkes, C. T. (yer´kez) (1837--1905), Am.\ patron!telescope}. Their approximate
number has been ascertained not by actual count, but
by estimates based on counts of typical areas scattered
in different parts of the heavens. The number of stars
within reach of our present telescopes perhaps exceeds
125 millions. But the telescope by itself, no matter
how powerful, is unable to detect any important difference
between these faint and multitudinous luminaries; seemingly
all are more alike than peas or rice grains to the
naked eye. There is good reason for believing that the
dark or non-luminous stars are many times more numerous
than the visible ones, and modern research has made the
existence of many such invisible bodies certain.

\textbf{Total Light from the Stars.}\index{stars!light from}---Argelander\index{Argelander, F. W. A. (1799--1875), Ger.\ ast.}, a distinguished
German astronomer, made a catalogue and chart
of all the stars of the northern hemisphere increased by
\DPPageSep{438.png}
an equatorial belt, one degree in width, of the southern
stars. His limit was the $9\frac{1}{2}$~magnitude, and he recorded
rather more than 324,000 stars in all. Accepting a sixth
magnitude star as the standard, and expressing in terms of
it the light of all the lucid stars registered by Argelander,
they give an amount of light equivalent to 7300 sixth
magnitude stars. But calculation proves also that the
telescopic stars of this extensive catalogue yield more than
three times as much light as the lucid ones do. The stars,
then, we cannot see with the naked eye give more light
than those we can, because of their vastly greater numbers.
If, now, we suppose the southern heavens to be
studded just as thickly as the northern, there would be in
the entire sidereal heavens about 600,000 stars to the
$9\frac{1}{2}$~magnitude; and their total light has been calculated
equal to $\frac{1}{80}$ that of the average full moon.

\Smaller
\textbf{Colors of the Stars.}\index{stars!colors}---A marked difference in color characterizes
many of the stars. For example, the polestar and Procyon are white,
Betelgeux\index{Betelgeux (bet-el-gerz´)} and Antares\index{Anta´res ($\alpha$ Scorpii)} red, Capella\index{Capella} and Alpha Ceti yellowish, Vega
and Sirius\index{Sirius} blue. Among the telescopic stars are many of a deep blood-red
hue; variable stars\index{variable stars} are numerous among these. In observing true
stellar colors, the objects should be high above the horizon, for the
greater thickness of atmosphere at low altitudes absorbs abundantly the
bluish rays, and tends to give all stars more of an orange tint than they
really possess. Colors are easier to detect in the case of double stars
(page~451), because the components of many of these objects exhibit
complementary colors\index{double stars!colored}\index{stars|see{double stars}}; that is, colors which produce white light when
combined. If components of a `double' are of about the same magnitude,
their color is usually the same; if the companion is much fainter,
its color is often of complementary tint, and always nearer the blue end
of the spectrum. Complementary colors are better seen with the stars
out of focus. Following are a few of these colored double stars:---
\begin{center}
\begin{tabular}{ r@{ }l@{ }l *{2}{r@{}l@{ }l} }
  $\eta$   &amp; Cassiopeiæ, &amp; yellow and purple,
&amp; 4&amp;  &amp; mag.&amp; 7&amp; \footnotesize $\frac{1}{2}$&amp; mag.
\\
  $\gamma$ &amp; Andromedæ,  &amp; orange and green,
&amp; 3&amp; \footnotesize $\frac{1}{2}$ &amp;  &amp; 5&amp;\footnotesize$\frac{1}{2}$ &amp;
\\
  $\iota$  &amp; Cancri,       &amp; orange and blue,
&amp; 4&amp; \footnotesize $\frac{1}{2}$ &amp;  &amp; 6
\\
  $\alpha$ &amp; Herculis,     &amp; orange and green,
&amp; 3&amp;  &amp;  &amp; 6
\\
  $\beta$  &amp; Cygni,        &amp; yellow and blue,
&amp; 3&amp;  &amp;  &amp; 7
\end{tabular}
\end{center}
\DPPageSep{439.png}

There is some evidence that a few stars vary in color in long periods
of time; for example, two thousand years ago Sirius\index{Sirius} was a red star,
now it is bluish white. Any significance of color as to age or intensity
of heat is not yet recognized; rather is it probably due to variant composition
of stellar atmospheres.\index{atmosphere!of stars}
\Restore

\textbf{Star Catalogues and Charts.}\index{stars!catalogues and charts}---When you consult a
gazetteer you find a multitude of cities set down by name.
Corresponding to each is its latitude, or distance from
the equator, and its longitude, or arc distance on the
equator, measured from a departure point or prime meridian.
These arcs are measured on the surface of our
earth. Turning, then, to the map, you find the city in
question, and perhaps many neighboring ones set down in
exact relation to it. Precisely in a similar manner all the
brighter stars of the sky are registered in their true relations
one to another, on charts and photographic plates.
These will be accurate enough for many purposes, but not
for all. When a higher precision is required, one must
consult those gazetteers of the sky known as star catalogues.
Set down in them will be found the coördinates
of a star; that is, its right ascension and declination, the
counterparts of terrestrial longitude and latitude. But we
shall soon observe this peculiar difference between longitude
on the earth and right ascension in the sky: the star's right
ascension will (in nearly all cases) be perpetually increasing,
while the longitude of a place remains always the
same. This perpetual shifting of the stars in right ascension
is mostly due to precession. It is as if Greenwich or
Washington were constantly traveling westward, but so
slowly that only in 26,000 years would it have traveled all
the way round the globe.

\textbf{Precession and Standard Catalogues.}\index{precession!effects of}---It was Hipparchus\index{Hipparchus (\BC~140), Gk.\ ast.}
(\BC~130) who first discovered this perpetual and apparent
shifting of all the stars. And partly for this reason he
\DPPageSep{440.png}
made a catalogue (the first one ever constructed) of 1080
stars, so that the astronomers coming after him might, by
comparing his map and catalogue with their own, discover
what changes, if any, are in progress among the
stellar hosts. No competitor appeared in the field, until
the 15th century, when the second catalogue was constructed,
by Ulugh-Beg\index{Ulugh-Beg (1394--1449), Arab.\ ast.} (\AD~1420), an Arabian astronomer.
Since his day vast improvements have been made
in methods of observing the stars, and in calculating
observations of them. There are now about 100 large
catalogues of stars, constructed by astronomers of both
hemispheres; and the place of every star in the entire
celestial sphere revealed by telescopes of medium dimension
will soon be determined with astronomical precision.
Several of the larger government observatories prepare a
catalogue of stars every year from their observations; and
these again are combined into other and more accurate
catalogues (called standard catalogues), especially of the
zodiacal stars. These afford average or mean positions of
stars for the beginning of a particular year, called the
epoch of the catalogue. Positions for any given dates are
obtained by bringing the epoch forward, and farther correcting
for precession, aberration, and nutation (pages~130,
164, and 390). The mean position so corrected becomes
the apparent place. The chief American authorities on
standard stellar positions are Newcomb\index{Newcomb, S. (1835--1909), Am.\ ast.}, Boss\index{Boss, L., Dir.\ Dudley Obs.}, and Safford\index{Safford, T.~H.\ (1836--1901), Am.\ ast.}.

% Fig 16.2
\begin{figure}[p!]
  \centering
  \Input{page_428}
  \caption{The Vicinity of $\eta$ Carinæ (Eta Argûs), \AR\  10\,h.\:41\,m., Decl.\ S.\,59° (photographed by Bailey with the Bruce Telescope, 1896. Exposure 4~hours)}
  \label{p428}
  \index{Argus@Argûs, Eta, nebula}\index{Bailey, S. I., Am.\ ast.}
  \index{Bruce telescope}\index{Carina, Eta}
\end{figure}

\Smaller
\textbf{Photographic Charts of the Entire Heavens.}\index{astrographic charts}---On proposal of David
Gill\index{Gill, Sir D., Scotch ast.}, her Majesty's astronomer at the Cape of Good Hope\index{Cape of Good Hope!Obs.}, an international
congress of astronomers met at Paris in 1887, and arranged for
the construction of a photographic chart of the entire heavens. The
work of making the charts has been allotted to 18 observatories, one
third of which are located in the southern hemisphere. They are
equipped with 13-inch telescopes, all essentially alike; and exposures
are of such length as to include all stars to the 14th magnitude, probably
more than 50 millions in all. Stars to the 11th magnitude inclusive
(about 2,000,000) are to be counted and their positions measured and
\DPPageSep{441.png}
\DPPageSep{442.png}
catalogued. Each photograph covers an area of four square degrees;
and as duplicate exposures are necessary, the total number of plates
will be not less than 25,000. The entire expense of this comprehensive
map of the stars will exceed \$2,000,000. The observatories of the
United States have taken no part in this coöperative programme; but
by the liberality of Miss Bruce\index{Bruce, C. W. (1816--1900), Am.\ patron}, the Observatory of Harvard College\index{Harvard College!obs.},
which has a station in Peru also, has undertaken independently to chart
in detail the more interesting regions of the entire heavens, with the
Bruce photographic telescope, a photographer's doublet consisting of
four lenses, each 24 inches in aperture. A section of a recent chart
obtained with this great instrument is shown opposite. The plates are
$14 × 17$ inches; about two thousand will be required to cover the entire
sky. On the original plate of which the illustration is part were counted
no less than 400,000 stars. Also Kapteyn\index{Kapteyn, J.~C., Univ.\ Groningen} has measured and catalogued
about 300,000 stars on plates taken at Capetown\index{Cape of Good Hope!Obs.}.
\Restore

\textbf{Proper Motions of the Stars.}\index{stars!proper motions}---If Ptolemy\index{Ptolemy@Ptolemy, C. (tol´-em-mi) (\AD~140), Alex.\ ast.} or Kepler\index{Kepler, J. (1571--1630), Ger.\ ast.}
or any great astronomer of the past were alive to-day,
and could look at the stars, and constellations as he did in
his own time, he would be able to discern no change whatever
in either the brightness of the stars or their apparent
positions relatively to each other. Consequently they seem
to have been well named \textit{fixed stars}. If, however, we compare
closely the right ascensions and declinations of stars
a century and a half ago with their corresponding
% Fig 16.3
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.6\textwidth]{page_430}
  \caption{Ursa Major now, and after 400 Centuries}\index{Dipper}\index{Ursa Major}
\end{wrapfigure}
positions
at the present day, we find that very great changes are
taking place; but these changes relatively to the imaginary
circles of the celestial sphere are in the main due to precessional
motion of the equinox. A star's annual proper
motion in right ascension is the amount of residual change
in its right ascension in one year, after allowance for aberration,
and motion of the equinox. The proper motion in
declination may be similarly defined. Proper motion is
simply an angular change in position athwart the line of
vision, and may correspond to only a small fraction of the
star's real motion in space.

\Smaller
As a whole, proper motion of the brighter stars exceeds that of
the fainter ones, because they are nearer to us; and proper motion is a
\DPPageSep{443.png}
combined effect of the sun's motion in space and of the stars among
each other. Ultimately these two effects can be distinguished. Still,
even the largest proper motion
yet known, that of an
orange yellow star of the
eighth magnitude in the southern
constellation of Pictor, is
not quite $9''$; and about
two centuries must elapse
before it would seem to be
displaced so much as the
breadth of the moon. The
average proper motion of
first magnitude stars is about
$0''.25$; and of sixth magnitude
stars, only one sixth
as great. Among European
astronomers Auwers\index{Auwers, A. (ow´verz), Ger.\ ast.} has contributed
most to these critical studies, and Porter\index{Porter, J.~G., Dir.\ Cincinnati Obs.} in America has
published a catalogue of proper motions.
\Restore

\textbf{Secular Changes in the Constellations.}\index{constellations}\index{stars!secular changes}---The accumulated
proper motion of the stars of a given asterism will
hardly change its naked-eye appearance appreciably within
2000 years. But when intervals of 15 to 20 times greater
are taken, the present well-known constellation figures
will in many cases be seriously distorted.

\Smaller
Particularly is this true of Cassiopeia\index{Cassiopeia}, Orion\index{Orion@Ori´on}, and Ursa Major\index{Ursa Major}. In
the left-hand diagram above is shown the present asterism of the Dipper\index{Dipper},
to each star of which is attached an arrow indicating the direction and
amount of its proper motion in about 400 centuries. The companion
diagram at the right is a figure of the same constellation (according
to Proctor\index{Proctor, R.~A.\ (1837--88), Am.\ ast.}) after that interval has elapsed: though much distorted, it
would be recognized as Ursa Major still. As indicated by the direction
of the arrows, the extreme stars, Alpha and Eta, seem to move almost
in the opposite direction from the others, and observations with the
spectroscope confirm this result. As the spectra of the five intermediate
stars are quite identical, it is likely that they originally formed part of
a physically connected system. Most of the brighter stars of the
Pleiades\index{Pleiades (ple´ya-deez)} are also moving in one and the same direction, and this community
of proper motion has received the name star drift\index{stars!drift}.
\Restore
\DPPageSep{444.png}

\textbf{Apex of the Sun's Way.}\index{earth!path in space}\index{sun!way (apex)}---When riding upon the rear
platform of a suburban electric car, where the ties are not
covered under, observe that they seem to crowd rapidly
together as the car swiftly recedes from them. If possible
to watch from the front platform, precisely the opposite
effect
% Fig 16.4
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.55\textwidth]{page_431}
  \caption{Earth's Helical Path in Space}\index{earth!path in space}
\end{wrapfigure}
will be noticed: the ties seem to open out and separate
from each other just as rapidly. In like manner
the stars in one part of the celestial sphere, when taken by
thousands, are found to have a common element of proper
motion inward toward a center or pole; while in the
opposite region, they seem to be moving radially outward\index{stars!motion in line of sight},
as if from the hub and along the spokes of a wheel.
This double phenomenon is explained by a secular motion\index{sun!secular motion}
of the sun through space, transporting his entire family of
planets, satellites, and comets along with him. This hub
or pole toward which the
solar system is moving is
called the \textit{sun's goal}\index{goal, sun's}, or \textit{the
apex of the sun's way}; and
determinations by L.~Struve\index{Struve, L., Dir.\ Kharkov Obs.},
Boss\index{Boss, L., Dir.\ Dudley Obs.}, Porter\index{Porter, J.~G., Dir.\ Cincinnati Obs.}, and Dyson\index{Dyson, F.~W., Eng.\ ast.}
make it practically coincident
with the star Vega\index{Vega}.
Similarly the point from
which we are receding is
known as the \textit{sun's quit}\index{quit, sun's},
and it is roughly a point halfway between Sirius and
Canopus\index{Cano´pus ($\alpha$ Argûs)}. So vast is this orbit of the sun that no deviation
from a straight line is yet ascertained, although our motion
along that orbit is about 12 miles every second.

\Smaller
This result is verified both by discussion of proper motions, and
by finding the relative movement of stars `fore and aft' by means of
the spectroscope. As yet, however, there is no indication of a `central
sun\index{sun!central},' a favorite hypothesis in the middle of the 19th century. This
\DPPageSep{445.png}
motion of the sun does not interfere with the relations of his family
of planets to him; but simply makes them describe, as in the figure
just given, vast spiral circumvolutions through interstellar space.
\Restore

\textbf{Stellar Motions in the Line of Sight.}\label{p432}\index{motion!of stars in sight line}---From a bridge
spanning a rivulet, whose current is uniform, we observe
chips floating by, one every 15~seconds. Ascending the
stream, we find their origin: an arithmetical youth on the
bank has been throwing them into mid-stream at regular
intervals, four chips to the minute. We interfere with his
programme only by asking him first to walk down stream
for two minutes, then to return at the same uniform speed;
and to repeat this process several times, always taking
care to throw the chips at precisely the same intervals as
before. Returning to the bridge to observe, we find the
chips no longer pass at intervals of 15~seconds as at first;
but that the interval is less than this amount while the
boy who tosses them is walking down stream, and greater
by a corresponding amount while he is going in the opposite
direction. By observing the deviation from 15~seconds,
the speed at which he walks can be found. Similarly
with the motions of stars toward or from the earth; the
boy is the moving star, and the chips are the crests of
light waves emanating from it. When the star is coming
nearer, more than the normal number of waves reach us
every second, and a given line in the star's spectrum is
displaced toward the violet. Likewise when a star is
receding, the same line deviates toward the red. This
effect was first recognized in 1842 by Doppler\index{Doppler, C.\ (1803--53), Ger.\ physicist}, from whom
comes the name `Doppler's principle.\index{Doppler's principle}' Research of this
character is an important part of the programme at Greenwich\index{Greenwich!Observatory}
(\vpageref*{p433}), and at the Yerkes Observatory\index{Yerkes, C. T. (yer´kez) (1837--1905), Am.\ patron!observatory} (page~\pageref{p7}).

\Smaller
The spectral observation is an exceedingly delicate one; but by
measuring the degree of displacement of stellar lines, as compared with
the same lines due to terrestrial substances artificially vaporized (titanium
is often used), the motions of many hundred stars have been
\DPPageSep{446.png}
% Fig 16.5
\begin{Plate}
  \Input[\textwidth]{page_433}
  \caption{The Royal Observatory, Greenwich. W.~H.~M. Christie, F.R.S., Astronomer Royal}

\legend{Founded by \textsc{Charles the Second} in 1675, for the main purpose of advancing our knowledge of the movements of the heavenly
bodies, in order to improve the means of finding the position of ships at sea. The work of the Royal Observatory now
includes many other important lines as well.}
  \label{p433}
  \index{Astronomer Royal|see{Christie, Sir W.~H.~M.}}\index{Christie, Sir W.~H.~M., Ast.\ Royal}\index{Charles II (1630--85), Eng.\ king}\index{navigation!astronomy of}
\end{Plate}%
\DPPageSep{447.png}
ascertained. The limit of accuracy is a fraction of a kilometer per
second. The observed radial velocities of stars not situated at the
poles of the ecliptic, or near them, require a correction depending on
the earth's orbital motion round the sun. So accurate, indeed, have
these measurements become that the velocity of the earth in its orbit has
been ascertained with such precision as to give a new and trustworthy
value for the sun's parallax and its distance from the earth. The radial
velocities of many stars are found to vary slowly, in some cases appearing
to indicate orbital motion of their own.
\Restore

\textbf{Motion of the Solar System by Radial Velocities.}\index{stars!motion in line of sight}---The
early years of the 20th century saw the inception of a comprehensive
plan for applying measures of radial velocity
to solving the problem of the sun's motion in space---its
precise direction and its exact velocity. By coöperation
of many observatories possessing very powerful spectroscopes---Pulkowa\index{Pulkowa (pul-ko´va) Obs.}
in Russia, Potsdam in Germany, Cambridge
in England, also among others the Lick\index{Lick Observatory} and Yerkes
Observatories\index{Yerkes, C. T. (yer´kez) (1837--1905), Am.\ patron!observatory} in America,---the spectra of stars in all regions
of the northern heavens are systematically recorded
by photography\index{photography!spectra}. Also the southern stars were included
by the Mills Expedition sent out in 1903 from the Lick
Observatory to Santiago, Chile. Preliminary discussion of
the line-of-sight measures confirms the result already given
(page~431) for the apex of the sun's way\index{sun!way (apex)} (the star Vega),
and the sun's velocity about 12~miles per second. The
average velocity of stars so far observed is about 20~miles
per second; but a few have been discovered with a motion
three or four fold greater.

\textbf{Relation of Brightness to Distance of the Stars.}\index{stars!brightness related to distance}---Were
the stars all of the same real size and brightness, their
apparent magnitudes, combined with their direction from
us, would make it possible to state their precise arrangement
throughout the celestial spaces. But all assumptions
of this character are unfounded, and lead to erroneous
conclusions. The very little yet known about the real distances
\DPPageSep{448.png}
of the stars and their motions, when taken in connection
with their apparent magnitudes, proves conclusively
that many of the fainter stars are relatively near the solar
system; also that several of the brighter stars are exceedingly
remote, and therefore exceptionally large and massive.
Apparent brightness, therefore, is no certain criterion of
distance. This subject of investigation is so vast and
intricate that very little headway has yet been securely
made. What we really know may be put in a single brief
sentence: Only as a very general rule is it true that the
brighter stars are nearer and larger than the great mass
of fainter ones; and to this rule are conspicuous and important
exceptions. Our knowledge is rather negative than
positive; and we may be certain that (1)~the stars are far
from equally distributed throughout space, and (2)~they
are far from alike in real brightness and dimensions.

\textbf{How Stellar Distances are found.}\index{distance!stars}\index{stars!distances, how found}---Recall the instance of
the earth and moon (page~\pageref{p237a}): we found the moon's distance
from us by measuring her displacement among the
stars, as seen from two observatories at the ends of a diameter
of our globe, or as near its extremities as convenient.
But this earth is so small, that, as seen from a star, even its
entire diameter would appear as an infinitesimal; we must
therefore seek another base line. Only one is feasible;
and although 25,000 times greater, still it is hardly long
enough to be practicable.

\Smaller
Imagine the earth replaced by a huge sphere, whose circle equals
our orbit round the sun. From the ends of a diameter, where we are
at intervals of six months, we may measure the displacement of a star,
just as we measured the
% Fig 16.6
\begin{wrapfigure}[36]{o}{0.6\textwidth}
  \centering
  \Input[0.6\textwidth]{page_436}
  \caption{The Nearest Star describes the Largest Apparent Ellipse among the Farthest Stars}\index{distance!stars}
\end{wrapfigure}
displacement of the moon from the two observatories.
We find, then, that half this displacement represents the
star's parallax\index{stars!parallax}, just as half the moon's displacement gave the lunar
parallax. And just as in the case of moon, sun, and planets we employ
the term \textit{diurnal parallax}, so in the case of stars we call \textit{annual
parallax}\index{parallax!annual} the angle at the star subtended by the radius of earth's orbit.
Measurement of a star's annual parallax is one of the exceedingly difficult
\DPPageSep{449.png}
problems that confront the practical astronomer; so small is the
angle that its measurement is much as if a prisoner who could only look
out of the window of his cell were given instruments of utmost precision
and compelled to ascertain
the distance of a
mountain 20~miles away.

\textbf{A Star's Parallactic Ellipse.}\index{ellipse!parallactic}\index{parallactic ellipse, star's}\index{stars!parallax}---Stand
a book on
the table, and place the eye
about two feet from the side
of it. Hold the point of a
pen or pencil steadily, at
distances of about 5, 10,
and 20 inches from the eye,
and between it and the
book. For each position of
the pencil move the head
around in a nearly vertical
circle about two inches in
diameter, noticing in each
case the size of the circle
which the pen point appears
to describe where projected
on the book. This conclusion
is quickly reached:
the farther the pencil from
the eye, the smaller this circle.
Now imagine the eye
replaced by the earth in its
orbit (as at the bottom of
the diagram), the pencil by
the three stars shown, and
the book by the farthest
stars. Evidently the earth
by traveling round the sun
makes the stars appear to describe
elliptic orbits whose
size is precisely proportioned inversely to their distance from the solar
system. The eccentricity of the parallactic ellipse of a star is exactly
the same as that of its aberration ellipse already figured on page~\pageref{p164}:
a star at the pole of the ecliptic describes a circle, and those situated
in the ecliptic simply oscillate forth and back in a straight line. Stars
in intermediate latitudes describe ellipses whose eccentricities are dependent
upon their latitude. There are these two important differences:
\DPPageSep{450.png}

 (1)~in the aberration ellipse\index{aberration!ellipses}, the star is always thrown $90$°
forward of its true position, while in the parallactic ellipse, it is just $180$°
displaced; (2)~the major axis of the aberration ellipse is the same for
all stars, but in the parallactic ellipse its length varies inversely with
the distance of the star. Measurement of the major axis of this ellipse
affords the means of ascertaining how far away the star is, because the
base line is the diameter of the earth's orbit. This is called the \textit{differential
method}, because it determines, not the star's absolute parallax,
but the difference between its parallax and that of the remotest star,
assumed to be zero. Researches on stellar distances have been prosecuted
by Gill\index{Gill, Sir D., Scotch ast.} at Capetown and Elkin\index{Elkin, W.~L., Dir.\ Yale Obs.} at Yale Observatory with a high
degree of accuracy by the heliometer\index{heliometer}.

\textbf{The Distance of 61 Cygni.}\index{Cygni 61}\index{distance!stars}---The star known as 61~Cygni has
become famous, because it is the first star whose distance was ever
measured. This great
% Fig 16.7
\begin{wrapfigure}[15]{o}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_437}
  \caption{Bessel's Measures of Distance of 61 Cygni}
  \index{Cygni 61}
\end{wrapfigure}
step in our knowledge of the sidereal universe
was taken about 1840 by the eminent German astronomer Bessel\index{Bessel, F. W. (1784--1846), Ger.\ ast.},
often called the father of practical astronomy, because he introduced
many far-reaching improvements conducing to higher accuracy in
astronomical methods and results. This star is a double star, standing
at an angle with the hour circle (north-south), as the diagram shows.
Two small stars are in the same field of view, \textit{a} and \textit{b}, nearly at right
angles in their direction from the double star; and Bessel had reason
for believing that they were
vastly farther away than 61
Cygni itself. So at opposite
seasons of the year he measured
with the heliometer the
distances between each of
the components of 61~Cygni
and both the stars \textit{a} and \textit{b}.
What he found on putting
his measures together was
that these apparent distances
change in the course of the
year; and that the nature of
the change was exactly what
the star's position relatively to the ecliptic led him to expect. The
measured amount of that change, then, was the basis of calculation of
the star's distance from our solar system. Within recent years photography
has been successfully applied to researches of this character,
with many advantages, including increased accuracy of the results
obtained.

\textbf{Illustration of Stellar Distances.}\index{stars!distances illustrated}\index{distance!stars}---The nearest of all the fixed
stars is Alpha Centauri\index{Centauri, Alpha}, a bright star of the southern hemisphere. Its
\DPPageSep{451.png}
parallax\index{stars!parallax} is $0''.75$, and it is 275,000 times more distant from our solar
system than the sun is from the earth. But there is little advantage in
repeating a mere statement of numbers like this. Try to gain some
conception of its meaning. First, imagine the entire solar system as
represented by a tiny circle the size of the dot over this letter \textit{i}\DPtypo{}{.}
Even the sun itself, on this exceedingly reduced scale, could not be
detected with the most powerful microscope ever made. But on the
same scale the vast circle centered at the sun and reaching to Alpha
Centauri would be represented by the largest circle which could be drawn
on the floor of a room 10~feet square. Or the relative sizes of spheres
may afford a better help. Imagine a sphere so great that it would
include the orbits of all the planets of the solar system, its radius being
equal to Neptune's distance from the sun. Think of the earth in comparison
with this sphere. Then conceive all the stars of the firmament as
brought to the distance of the nearest one, and set in the surface of a
sphere whose radius is equal to the distance of that star from us. So
vast would this star sphere be that its relation to the sphere inclosing
the solar system would be nearly the same as the relation of this latter
sphere to the earth. When studying the sun and the large planets, it
seemed as if their sizes and distances were inconceivably great; but
great as they are, even the solar system itself is as a mere drop to the
ocean, when compared with the vastness of the universe of stars.
\Restore

\iffalse
[Handwritten sidenote:
Parsec = Distance at which semi-diameter of earth's orbit subtends angle of $1''$.
1 Parsec = 3.26 light years = $1.9 × 10^{13}$ miles (Approx.).
1 Light yr. = 63000 Mean solar distances ]
\fi

\textbf{The Unit is the Light Year.}\index{light year, unit of distance}\index{unit!of celestial distance}---In expressing intelligently
and conveniently a distance, the unit must not be taken too
many times. We do not state the distance between New
York and Chicago in inches, or even feet, but in miles.
The earth's radius is a convenient unit for the distance of
the moon, because it has to be taken only 60 times; but
it would be very inconvenient to use so small a unit in
stating the distances of the planets. By a convention of
astronomers, the mean radius of our orbit round the sun is
the accepted unit of measure in the solar system. Similarly
the adopted unit of stellar distance is, not the distance
of any planet nor the distance of any star, but the distance
traveled by a light wave in a year. This unit is called
the \textit{light year}.

% Table 16.3
\begin{table}
\footnotesize
\centering
\caption{\textsc{Stellar Distances and Parallaxes}}
\label{tab16.3}
\renewcommand{\arraystretch}{1.2}
\makebox[0pt][c]{%
\begin{tabular}{l|r|rr|lrr|c|c|r@{}l|rc}
  \hline \hline
  \multirow{2}{7em}{\centering\footnotesize\textsc{
    Star's Name}}
&amp; \multirow{2}{1.8em}{\rule{10pt}{0pt}\rotatebox{90}{\centering\footnotesize\textsc{
    Magnitude}}}
&amp; \multicolumn{5}{m{8em}|}{\centering\footnotesize\textsc{
    Approximate [1900.0]}}
&amp; \multirow{2}{3.5em}{\centering\footnotesize\textsc{Proper Motion}}
&amp; \multirow{2}{1.8em}{\rule{7pt}{0pt}\rotatebox{90}{\centering\footnotesize\textsc{
    Parallax}}}
&amp; \multicolumn{4}{m{8em}}{\centering\footnotesize\textsc{
    Distance in---}}
\\[2ex]
\cline{3-7}\cline{10-13}
&amp;&amp; \multicolumn{2}{m{2.5em}|}{\centering\footnotesize\textsc{
    R.~A.}}
&amp; \multicolumn{3}{m{4.5em}|}{\centering\footnotesize\textsc{
    Decl.}}
&amp;&amp;&amp; \multicolumn{2}{m{3em}|}{\centering\footnotesize\textsc{
    Light Years}}
&amp; \multicolumn{2}{m{4.5em}}{\centering\footnotesize\textsc{
    Trillions of Miles}}
\\[2ex]  \hline
&amp; &amp; {\footnotesize h.} &amp; {\footnotesize m.}
&amp; &amp; {\footnotesize $\circ$} &amp; {\tiny $\prime$}
&amp; {\tiny $\prime\prime$} &amp; {\tiny $\prime\prime$} &amp; &amp;
\\
$\alpha$ Centauri \dotfill &amp; $-0.1$ &amp; 14 &amp; 33
&amp; S. &amp; 60 &amp; 25 &amp; 3.67 &amp; 0.75 &amp;   4 &amp; $\frac{1}{3}$ &amp; 25
\\
61 Cygni \dotfill  &amp; 6.1 &amp; 21 &amp; 2
&amp; N. &amp; 38 &amp; 15 &amp; 5.16 &amp; 0.45 &amp;   7 &amp; $\frac{1}{5}$ &amp; 43
\\
Sirius \dotfill &amp; $-1.4$ &amp;  6 &amp; 41
&amp; S. &amp; 16 &amp; 35 &amp; 1.31 &amp; 0.38 &amp;   8 &amp; $\frac{1}{2}$ &amp; 50
\\
Procyon \dotfill &amp; 0.5 &amp; 7 &amp; 34
&amp; N. &amp;  5 &amp; 29 &amp; 1.25 &amp; 0.27 &amp;  12 &amp;&amp;  71
\\
Altair \dotfill &amp; 0.9 &amp; 19 &amp; 46
&amp; N. &amp;  8 &amp; 36 &amp; 0.65 &amp; 0.20 &amp;  16 &amp;&amp;  94
\\
o$^2$ Eridani \dotfill &amp; 4.4 &amp; 4 &amp; 11
&amp; S. &amp;  7 &amp; 48 &amp; 4.05 &amp; 0.19 &amp;  17 &amp;&amp; 100
\\
Groombridge 1830 &amp; 6.5 &amp; 11 &amp; 47
&amp; N. &amp; 38 &amp; 30 &amp; 7.65 &amp; 0.13 &amp;  25 &amp;&amp; 147
\\
Vega \dotfill &amp; 0.2 &amp; 18 &amp; 34
&amp; N. &amp; 38 &amp; 41 &amp; 0.36 &amp; 0.12 &amp;  27 &amp;&amp; 158
\\
Aldebaran \dotfill &amp; 1.0 &amp; 4 &amp; 30
&amp; N. &amp; 16 &amp; 18 &amp; 0.19 &amp; 0.10 &amp;  32 &amp;&amp; 191
\\
Capella \dotfill &amp; 0.1 &amp;  5 &amp;  9
&amp; N. &amp; 45 &amp; 54 &amp; 0.43 &amp; 0.10 &amp;  32 &amp;&amp; 191
\\
Polaris \dotfill &amp; 2.1 &amp;  1 &amp; 23
&amp; N. &amp; 88 &amp; 46 &amp; 0.05 &amp; 0.07 &amp;  47 &amp;&amp; 276
\\
Arcturus \dotfill &amp; 0.2 &amp; 14 &amp; 11
&amp; N. &amp; 19 &amp; 41 &amp; 2.00 &amp; 0.02 &amp; \ 160 &amp;&amp; \quad 950
\\[1ex]  \hline \hline
\end{tabular}}
   \index{Aldeb´aran}%
  \index{Altair}%
  \index{Arcturus}%
  \index{Centauri, Alpha}%
  \index{Capella}%
  \index{Polaris}%
  \index{Vega}%
  \index{Sirius}%
  \index{Procyon}%
  \index{Cygni 61}%
  \index{distance!stars}%
  \index{Groombridge, S.\ (1755--1832), Eng.\ ast.}%
  \index{stars!distances}%
  \index{stars!parallax}%
\renewcommand{\arraystretch}{1}
\end{table}

\Smaller
The velocity of light is 186,300 miles per second, and it travels from
the sun to the earth in 499 seconds. The light year is equal to
\DPPageSep{452.png}
$63,000 × 93,000,000$ miles, because the number of seconds in a year is
about $499 × 63,000$; or, the light year is equal to $5 \frac{7}{8}$~trillion miles.
Obviously, as stellar parallax has a definite relation to distance, parallax
must be related to the light year also: the distance of a star whose
parallax is $1''$ is about $3\frac{1}{4}$ light years. So that, if we divide $3\frac{1}{4}$ by the
parallax (in seconds of arc), we shall have the star's distance in light
years.
\Restore

\textbf{Distances of Well-known Stars.}\index{distance!stars}\index{stars!distances}---Although the parallaxes
of hundreds of stellar bodies have been measured,
only about 50 are regarded as well known. Twelve are
given in Table~\ref{tab16.3}, together with their corresponding
distance in light years.

Most of these are bright stars, but a considerable number
of faint stars have large parallaxes also. Relative distances
and approximate directions from the solar system are shown
in next illustration, for a few of the nearer and best determined
\DPPageSep{453.png}
stars. The scale is necessarily so small that even
the vast orbit of Neptune has no appreciable dimension.
The outer circle corresponds nearly to a parallax $0.''1$.
The distances of many stars have been ascertained by
Sir Robert Ball\index{Ball, Sir R. S., Dir.\ Obs.\ Cambridge, Eng.}; also in America by Flint\index{Flint, A.~S., Am.\ ast.}.

% Fig 16.8
\begin{figure}[hbt!]
  \centering
  \Input{page_440}
  \caption{Distances of Stars from the Solar System in Light Years (according to Ranyard and Gregory)}
  \index{Gregory, R.~A., Eng.\ ast.}%
  \index{Ranyard, A.~C.\ (1845--94), Eng.\ ast.}%
  \index{Sirius}\index{stars!distances}%
\end{figure}

% Table 16.4
\begin{table}
\TableSize
\centering
\caption{}
\index{Aldeb´aran}\index{Altair}\index{Arcturus}
\label{tab16.4}
\begin{tabular}{l@{.}r| l@{.}r}
  \multicolumn{2}{@{}c@{}}{\rule{.5\textwidth}{0pt}}
&amp; \multicolumn{2}{@{}c@{}}{\rule{.5\textwidth}{0pt}} \\[-3ex]
  \multicolumn{2}{c|}{\footnotesize\textsc{Sirian Stars}}
&amp; \multicolumn{2}{c }{\footnotesize\textsc{Solar Stars}} \\
  Procyon   \dotfill &amp; \dotfill\   25
&amp; Aldebaran \dotfill &amp; \dotfill\   70 \\
  Altair    \dotfill &amp; \dotfill\   25
&amp; Pollux    \dotfill &amp; \dotfill\  170 \\
  Sirius    \dotfill &amp; \dotfill\   40
&amp; Polaris   \dotfill &amp; \dotfill\  190 \\
  Regulus   \dotfill &amp; \dotfill\  110
&amp; Capella   \dotfill &amp; \dotfill\  220 \\
  Vega      \dotfill &amp; \dotfill\ 2050
&amp; Arcturus  \dotfill &amp; \dotfill\ 6200
   \index{Pollux ($\beta$ Geminorum)}\index{Regulus ($\alpha$ Leonis)} \index{Aldeb´aran}\index{Altair}\index{Arcturus}\index{Capella}\index{Polaris}\index{Procyon}\index{Sirius}\index{Vega}\index{Sirian stars}\index{solar stars}
\end{tabular}
\end{table}

\Smaller
\textbf{Dimensions of the Stars.}\index{stars!dimensions}---After we had found the distance of the
sun and measured the angle filled by his disk, it was possible to calculate
his true dimensions. But this simple method is inapplicable to the
stars, because their distances are so vast that no stellar disk subtends
an appreciable angle. Indirect means must therefore be employed to
ascertain their sizes; and it cannot be said that any method has yet
yielded very satisfactory results. Combining known distance with
apparent magnitude, Maunder\index{Maunder, E.~W., ast.\ Obs.\ Greenwich} has calculated the absolute light-giving
power of the following stars, that of the sun being unity, as shown in Table~\ref{tab16.4}.
%\Restore
\DPPageSep{454.png}

%\Smaller
But these are far from indicating their real magnitudes; for amount of
light is dependent upon intrinsic brightness of the radiating surface,
as well as its extent. Among the giant stars are Arcturus, possibly a
hundredfold the sun's diameter; also Vega\index{Vega} and Capella\index{Capella}, likewise much
larger than the sun. Algol\index{Algol}, too, must have a diameter exceeding a
million miles, and its dark companion (page~\pageref{p450}) is about the size of
the sun---results reached by means of the spectroscope, which measures
the rate of approach and recession of Algol when the invisible attendant
is in opposite parts of its orbit. The law of gravitation gives the mass
of the star and size of its orbit, so that the length of the eclipse tells
how large the dark, eclipsing body must be.
\Restore

% Fig 16.9
\begin{figure}[hbt!]
  \centering
  \Input[\textwidth]{page_442}
  \caption{Secchi's Four Types of Stellar Spectra}
  \label{p442}\index{Secchi, A.\ (seck´key) (1818--78), It.\ ast.}\index{Capella}\index{Sirius}\index{Schjellerup, H.~C.~F.~C.\ (1827--87), Danish ast.}\index{spectrum!stellar}
\end{figure}

\textbf{Types of Stellar Spectra.}\index{spectrum!stellar}\index{stars!constitution}---Sir William Huggins\index{Huggins, W.\ (1824--1910), Eng.\ ast.} in 1864
first detected lines indicating the vapor of hydrogen\index{hydrogen!in stars}, calcium,
iron, and sodium in the atmospheres of the brighter
stars. Stellar spectra have been classified in a variety of
ways, but the division into four types, proposed in 1865 by
Secchi\index{Secchi, A.\ (seck´key) (1818--78), It.\ ast.}, has obtained the widest adoption. They are illustrated
\vpageref{p442}:---

Type I is chiefly characterized by the breadth and intensity
of dark hydrogen lines; also a decided faintness or
entire lack of metallic lines. Stars of this type are very
abundant. They are blue or white; Sirius\index{Sirius}, Vega\index{Vega}, Altair\index{Altair},
and numerous other bright stars belong to this type, often
called Sirian stars\index{Sirian stars}, a class embracing perhaps more than
half of all the stars.

Type II is characterized by a multitude of fine dark, metallic
lines, closely resembling the solar spectrum. They are
yellowish like the sun; Capella\index{Capella} and Arcturus (page~\pageref{p445})
illustrate this type, often called the solar stars\index{solar stars}, which are
rather less numerous than the Sirian stars. According to
\DPPageSep{455.png}
recent results of Kapteyn\index{Kapteyn, J.~C., Univ.\ Groningen}, absolute luminous power of
first type stars exceeds that of second type stars seven-fold;
and stars least remote from the sun are mostly of
the second type.

Type III is characterized by many dark bands, well defined
on the side toward the blue, and shading off toward
the red end of the spectrum---a `colonnaded spectrum,'
as Miss Clerke\index{Clerke, A,~M.\ (1842--1907), Eng.\ ast.} very aptly terms it. Orange and reddish
stars, and a majority of the variables, fall into this category;
Alpha Herculis, Mira\index{Mira}, and Antares\index{Anta´res ($\alpha$ Scorpii)} are examples of
this type.
\DPPageSep{456.png}
Type IV is characterized by dark bands, or flutings as
they are often technically called, similar to those of the
previous type, only reversed as to shading---well defined
on the side toward the red, and fading out toward the blue.
Stars of this type are few, perhaps 50 in number, faint,
and nearly all blood-red in tint. Their atmospheres contain
carbon\index{carbon!in stars}.

Type V has been added to Secchi's\index{Secchi, A.\ (seck´key) (1818--78), It.\ ast.} classification by
Pickering\index{Pickering, E. C., Dir.\ Harv.\ Coll.\ Obs.}, and is characterized by bright lines. From two
French astronomers who first investigated objects of this
class, they are known as Wolf\index{Wolf, C., Prof.\ Univ.\ Paris}-Rayet\index{Rayet, G.\ (ry-\=a´), Univ.\ Bordeaux} stars. They are all
near the middle of the Galaxy, and their number is about
70. They are a type of stellar objects quite apart by
themselves, of which Campbell\index{Campbell, W. W., Dir.\ Lick Obs.} has made an especial
study. Many objects called planetary nebulæ\index{nebulae!planetary} yield a
spectrum of this type.

A classification by Vogel\index{Vogel, H.~C. (1841--1907), Ger.\ ast.} combines Secchi's types III
and IV into a single type. It is not yet determined
whether these differences of spectra are due to different
stages of development, or whether they indicate real differences
of stellar constitution. Most likely they are due to
a combination of these causes.

\Smaller
\textbf{How a Star's Spectrum is commonly photographed.}\index{photography!spectra}\index{spectrum!stellar}---The light of
a fixed star comes to the earth from a definite point on the dome of the
sky, so that
% Fig 16.10
\begin{wrapfigure}[18]{o}{0.45\textwidth}
  \centering
  \Input[0.4\textwidth]{page_444}
  \caption{Spectra of Stars in Carina (Pickering) (Exposure 2 h.\ 20 m.)}
  \label{p444}\index{Pickering, E. C., Dir.\ Harv.\ Coll.\ Obs.}
  \index{Carina, Eta!spectra}\index{spectrum!stellar}
\end{wrapfigure}
a stellar image, when produced by the object glass of a
telescope, is also a point. Now suppose that a glass prism is attached
to the telescope in front of its objective, as was first done in 1824, by
Fraunhofer\index{Fraunhofer@v.\ Fraunhofer, J. (frown´h\=o-fer) (1787--1826)}, and consider what takes place; the light of the star first
passes through this prism, called the `objective prism,' and then
through the object glass, which brings the rays all to a focus. The
star's image, however, is no longer a point, but spread out into a line,
made up of many colors from red to violet. It is at this focus that
the sensitive dry plate is inserted, and allowed to remain until the exposure
is judged sufficient to produce the desired impression. Perhaps
three hours are necessary; and during all this time the adjustment of the
photographic telescope is so maintained that when the plate is developed,
the spectra of all the stars will appear, not as lines, but as tiny
\DPPageSep{457.png}
rectangular patches, or bits of ribbon with light stripes across them. A
25th part of such a negative is pictured \vpageref{p444}, as obtained with the Bache\index{Bache, A. D. (b\=ach) (1806--67), Am.\ physicist}
telescope of the Boyden\index{Boyden, U. A. (1804--79) Am.\ engineer and patron} Observatory,
by exposure in 1893 to the stars of
the constellation Carina. On it were
1000 spectra sufficiently distinct for
classification.

%\label{p444}
\textbf{The Draper Catalogue.}\index{Draper catalogue, star spectra}---With
an identical instrument, similarly
equipped with prisms, stellar spectrum
photography has been vigorously
conducted at Harvard College
Observatory\index{Harvard College!obs.} since 1886. The prisms
are mounted with their edges east
and west; and the clock motion is
regulated according to the degree of
dispersion employed, as well as the
magnitude and color of the stars
in the photographic field. Upon a
single plate are often many hundred
spectra; and in studying them, the
great advantage of such close juxtaposition is at once apparent. For
example, the spectra of about 50~stars in the Pleiades\index{Pleiades (ple´ya-deez)} show at a
glance practical identity of chemical composition. These researches,
conducted under the superintendence of Edward C. Pickering\index{Pickering, E. C., Dir.\ Harv.\ Coll.\ Obs.},
at the
charges of a fund provided by Mrs.~Draper\index{Draper, H. (1837--82), Am.\ ast.!Mrs.\ H.} as a memorial to her
husband, gave to astronomers in 1890 the `Draper Catalogue of stellar
spectra,' including more than 10,000 stars down to the eighth magnitude.
Nearly all the tedious and time-consuming labor of examining the
plates was performed by Mrs.\ Fleming\index{Fleming, Mrs.~W.~P., Am.\ ast.}, Miss Maury\index{Maury, Miss A.~C., Am.\ ast.}, and others. This
comprehensive system of registering spectra naturally paved the way
for a more detailed classification of the stars than Secchi's\index{Secchi, A.\ (seck´key) (1818--78), It.\ ast.}; and with
subsequent work
% Fig 16.11
\begin{wrapfigure}[40]{o}{0.3\textwidth}
  \centering
  \Input[0.1125\textwidth]{page_445}
  \caption{Part of the Photographic Spectrum of Arcturus (Sir Norman Lockyer)}
  \index{Arcturus}\index{spectrum}\index{Lockyer, Sir J.~N., Eng.\ ast.}
  \label{p445}
\end{wrapfigure}
at the same observatory, has led to their division into
about 20 groups. Also the peculiarities of spectra have led to the
detection of numerous variable stars\index{variable stars}, and several new\index{stars!new} or temporary
stars\index{stars!temporary} (page~\pageref{p448}).
\Restore

\Smaller
\textbf{Stellar Spectra of High Dispersion.}\index{spectrum!stellar}---Vega is the first star whose
spectrum was successfully photographed by Henry Draper\index{Draper, H. (1837--82), Am.\ ast.} in 1872.
Brightest stars afford sufficient light for the photography of their
spectra, even after a high degree of dispersion by a train of several
prisms, or by a diffraction grating. Multitudes of lines are thus recorded,
especially in stars of the solar type. A part of the photographic
spectrum of Arcturus is shown \vpageref{p445}, almost a duplicate
of the solar spectrum. In addition to the fine results obtained at
\DPPageSep{458.png}
Cambridge by Pickering\index{Pickering, E. C., Dir.\ Harv.\ Coll.\ Obs.}, and at South Kensington by Sir
Norman Lockyer\index{Lockyer, Sir J.~N., Eng.\ ast.}, must be mentioned those of Vogel\index{Vogel, H.~C. (1841--1907), Ger.\ ast.} and
Scheiner\index{Scheiner, J., ast.\ Potsdam Obs.} at Potsdam, near Berlin; and of Deslandres\index{Deslandres, H.\ (day-londr´), ast.\ Meudon Obs.} at
Paris, who has lately detected in the spectrum of Altair\index{Altair} a
series of fine, bright, double lines, bisecting the dark hydrogen
and other bands. He regards them as indication that
this star is enveloped by a gaseous medium like that of the
solar chromosphere.
\Restore

\textbf{Variable Stars.}\index{variable stars}\index{stars|see{variable stars}}---A star whose brightness has
been observed to change is called a variable star,
or simply a `variable.' About 3000 such objects
are now recognized. This change may be either
an increase or a decrease; and it may take place
either regularly or irregularly. Other classes of
variables rise and fall in different ways: some exhibiting
several fluctuations of brightness in every
complete period (like Beta Lyræ\index{Lyræ!beta}, a well known
variable with a period of 12\,d.\:21\,h.\:47.4\,m., whose
spectrum presents a complexity of hydrogen\index{hydrogen!in stars}\index{stars!constitution}
lines and helium bands\index{helium!in stars}); some in simple periods
only a few hours (the shortest at present known
is $\omega$~Centauri 91,~$6\frac{1}{5}$~h.); others changing slowly
through several months. In general the last,
which are usually reddish in tint, change as
rapidly when near minimum as when near maximum,
their light-curves being like deep waves
with sharp crests. Astronomers term these `Omicron
Ceti variables\index{Omicron (o-mi´kron) Ceti variables},' after the type star of this
name, also known as Mira\index{Mira}, or `the marvelous,'
whose variability has been known for three centuries.
Their average period is about a year, and
perhaps half of the recognized variables are of
this type. Allied to them are the temporary stars\index{stars!temporary}
described in a subsequent section. Of a type
whose variation is the reverse of Mira are the
\DPPageSep{459.png}
`Algol\index{Algol} variables,' about 20 in number, whose light suddenly
drops at regular intervals, as if some invisible body
were temporarily to intervene.

\Smaller
Knowledge of the variable stars has been greatly advanced by the
labors of Chandler\index{Chandler, S. C.@Chandler, S. C., ed.\ \emph{Astron. Jour.}} and Sawyer\index{Sawyer, E.~F.,  Am.\ ast.}, of Cambridge. Chandler's catalogues
contain about 500 classified variables. Such an object, previously without
a name, is designated by letters R, S, T, U, and so on, in order
of discovery in the especial constellation where found. The average
range in recently discovered variables is less than one magnitude.

\textbf{Distribution and Observation of Variables.}\index{variable stars!distribution and observing}---As to their distribution
over the heavens, variable stars are most numerous in a zone inclined
about $18$° to the celestial equator, and split in two near where the cleft
in the Galaxy occurs. Almost all the temporary stars\index{stars!temporary} are in this duplex
region. A discovery of much significance was made by Bailey\index{Bailey, S. I., Am.\ ast.}, in 1896,
of an exceptional number of variables among the components of stellar
clusters, more than 100 being found among the stars of a single
cluster; and the mutations of magnitude are marked within a few hours.
Variables are most interesting objects, and observations of great value
may be made by amateurs. First the approximate times of greatest or
least brightness must be ascertained; these are given each year in the
`Companion' to \textit{The Observatory} (edited by Lewis and published at
Greenwich), and in \textit{Popular Astronomy}\index{Popular Astronomy@\emph{Popular Astronomy} (monthly)} (issued monthly by Wilson\index{Wilson, H.~C., Dir.\ Carleton Col.\ Obs.}
at Northfield, Minnesota). In Table~\ref{tab16.5} are a few variables, easily found
from star charts.

% Table 16.5
\begin{table}
\centering
\caption{\textsc{Variable Stars}}
\label{tab16.5}
\renewcommand{\arraystretch}{1.2}
\makebox[0pt][c]{%
\begin{tabular}{l|rr|lrr|c|c@{ }c@{ }c|c}
  \hline\hline
  \multirow{2}{7em}{\centering\footnotesize\textsc{
    Star's Name}}
&amp; \multicolumn{5}{m{8em}|}{\centering\footnotesize\textsc{
    Position (1900.0)\rule{0pt}{3ex}}}
&amp; \multicolumn{4}{m{8em}|}{\centering\footnotesize\textsc{
    Variation\rule{0pt}{3ex}}}
&amp; \multirow{2}{4em}{\centering\footnotesize\textsc{
    Type of Variable}}
\\[1ex]
\cline{2-10}
&amp; \multicolumn{2}{m{3em}|}{\centering\footnotesize\textsc{
    R.~A.\rule{0pt}{3ex}}}
&amp; \multicolumn{3}{m{4em}|}{\centering\footnotesize\textsc{
    Decl.\rule{0pt}{3ex}}}
&amp; \multicolumn{1}{m{3.5em}|}{\centering\footnotesize\textsc{
    Period\rule{0pt}{3ex}}}
&amp; \multicolumn{3}{m{4em}|}{\centering\footnotesize\textsc{
    Range\rule{0pt}{3ex}}} &amp;
\\[1ex]  \hline
&amp; {\footnotesize h.} &amp; {\footnotesize m.}
&amp;    &amp; {\footnotesize $\circ$} &amp; {\tiny $\prime$}
&amp; {\footnotesize Days} &amp; \multicolumn{3}{c|}{\footnotesize Magnitude}
\\
Omicron Ceti \dotfill   &amp;  2 &amp; 14 &amp; S. &amp;  3 &amp; 26
&amp; 331              &amp; 1.7 &amp; to &amp; 9.5 &amp; Mira.
\\
Beta Persei \dotfill    &amp;  3 &amp;  2 &amp; N. &amp; 40 &amp; 34
&amp; $2\frac{7}{8}$   &amp; 2.3 &amp; to &amp; 3.5 &amp; Algol.
\\
Zeta Geminorum  &amp;  6 &amp; 58 &amp; N. &amp; 20 &amp; 43
&amp; $10\frac{1}{7}$  &amp; 3.7 &amp; to &amp; 4.5 &amp;
\\
R Leonis  \dotfill      &amp;  9 &amp; 42 &amp; N. &amp; 11 &amp; 54
&amp; 313              &amp; 5.2 &amp; to &amp; 10  &amp;
\\
Delta Libræ \dotfill &amp; 14 &amp; 56 &amp; S. &amp;  8 &amp;  7
&amp; $2\frac{1}{3}$   &amp; 5   &amp; to &amp; 6.2 &amp; Algol.
\\
Alpha Herculis \dotfill &amp; 17 &amp; 10 &amp; N. &amp; 14 &amp; 30
&amp; $90\pm$          &amp; 3.1 &amp; to &amp; 3.9 &amp; Irregular.
\\
X Sagittarii \dotfill   &amp; 17 &amp; 41 &amp; S. &amp; 27 &amp; 48
&amp; 7                &amp; 4   &amp; to &amp; 6   &amp;
\\
Beta Lyræ \dotfill   &amp; 18 &amp; 46 &amp; N. &amp; 33 &amp; 15
&amp; 12.9             &amp; 3.4 &amp; to &amp; 4.5 &amp;
\\
Delta Cephei \dotfill   &amp; 22 &amp; 25 &amp; N. &amp; 57 &amp; 54
&amp; $5\frac{1}{3}$   &amp; 3.7 &amp; to &amp; 4.9 &amp;
\\[1ex]
\hline\hline
\end{tabular}}
\index{Lyræ!beta}%
  \index{Mira}%
  \index{Omicron (o-mi´kron) Ceti variables}%
  \index{variable stars}%
  \index{Algol}%
\renewcommand{\arraystretch}{1}
\end{table}
\DPPageSep{460.png}

A small telescope or opera glass is a distinct help in observing a
variable. When its brightness is changing, repeated comparison and
careful record of its magnitude with that of other stars in the same
field, will make it possible to ascertain the time of maximum or minimum.
Such observations are of use to the professional investigator of
periods of variable stars. Hagen's\index{Hagen, J.~G., Dir.\ Vatican Obs.\ Rome} new atlas is a great assistance.
\Restore

\textbf{Temporary Stars, or New Stars.}\index{stars!temporary}\index{stars!new}---A variable star which,
usually in a few weeks' time, vastly increases in brightness,
and then slowly wanes and disappears entirely, or nearly
so, is called a temporary star. Accounts of several such
are contained in ancient historical records. In the Chinese
annals\index{Chinese annals} is an allusion to such an outburst in Scorpio\index{Scorpio!new star in}, \BC~134;
it was observed by Hipparchus\index{Hipparchus (\BC~140), Gk.\ ast.}, and led to his construction
of the first known catalogue of stars, made with reference
to the detection of similar phenomena in the future.
Tycho Brahe\index{Tycho Brahe (1546--1601), Danish ast.} carefully observed a remarkable object of
this class near Cassiopeia\index{Cassiopeia}, which, in the latter part of 1572,
surpassed the brightness of Jupiter, was for a while visible
in broad daylight, and, in a year and a half, had completely
disappeared. In 1604--5 a new star of equal brightness
was seen by Kepler\index{Kepler, J. (1571--1630), Ger.\ ast.} in Ophiuchus\index{Ophiuchus (oph-i-\=u´kus), Kepler's star in}; it also disappeared.
None were recorded in the 18th century. Similar objects
appeared and passed through like stages near our own
day in---
\begin{center}
\TableSize
\index{Andromeda!new star in}
\begin{tabular}{l}
  1866 in Corona Borealis\index{Corona Borealis!nova};\\
  1876 in Cygnus;\\
  1885 in the Great Nebula in Andromeda;\\
  1891--92 in Auriga;\index{Auriga}\\
  1901 in Perseus.
\end{tabular}
\index{Perseus (per´suce)}\index{Cygnus!nova of, in 1876}
\end{center}
Such a star is often called \textit{Nova}, with the genitive of its
constellation added, as Nova Cygni. Temporary stars
remain unchanged in apparent position during their great
fluctuations of brightness, and no new star has been found
to have a measurable parallax. Probably Nova Andromedæ
was connected with the nebula in which it appeared. The
new stars of 1866 and 1892, after dropping to a low telescopic
\DPPageSep{461.png}
magnitude, had a secondary rise in brightness,
though not to their original magnitude, after which they
faded to their present condition as very faint telescopic
objects. Nova Aurigæ\index{Auriga} has become a faint nebulous
star. \label{p448} Thorough search by Mrs.\ Fleming\index{Fleming, Mrs.~W.~P., Am.\ ast.} of the photographic
charts and spectrum plates of the Harvard College
Observatory\index{Harvard College!obs.}, obtained in both hemispheres, has led to the
detection of many new stars that would otherwise have
escaped observation. Among them are Nova Normæ\index{Norma!new star in}
(1893) and Nova Aquilæ (1899).

\Smaller
\textbf{The New Star in Perseus.}\index{Perseus (per´suce)}\index{stars!new}---The most brilliant temporary star\index{stars!temporary} of
modern times appeared in the constellation Perseus in February, 1901.
At maximum on the 23d, it outshone Capella\index{Capella}. Its waning light
exhibited many unusual fluctuations of brightness. In August, 1901, a
nebula surrounding it was discovered; and a month later, certain wisps
of this nebulosity appeared to have moved bodily, at a speed seventy-fold
greater than ever previously observed in the stellar universe.
This unprecedented appearance is best explained by the meteoritic
hypothesis\index{meteoritic theory} of Sir Norman Lockyer\index{Lockyer, Sir J.~N., Eng.\ ast.}, according to which a vast nebulous
region has been invaded, not by one, but by many meteor swarms,
under conditions such that the effects of collision vary greatly in intensity.
The result of the most violent collision was the new star Nova
Persei itself, and the least violent occurred subsequently in other parts
of the disturbed nebula, almost immeasurably removed. Thus there
is no necessity of supposing actual motion through space at velocities
heretofore unobserved and inconceivably high.

\textbf{Spectra of New Stars.}\index{spectrum!stellar}\index{stars!new}---The spectroscope has proved itself a powerful
adjunct in the observation of temporary stars. First employed on
the Nova of 1866, it demonstrated the presence of incandescent hydrogen\index{hydrogen!in stars}.
Nova Cygni, ten years later, gave a similar spectrum, added to
which were the lines of helium\index{helium!in stars}, long known in the sun, but only in 1895
identified as a terrestrial element. Nova Andromedæ (1885) to most
observers presented a continuous spectrum; but Nova Aurigæ\index{Auriga} (1892)
gave a distinctly double and singularly complex spectrum. Many pairs
of lines indicated clearly a community of origin as to substance, and
accurate measurement showed a large displacement which indicated a
relative velocity of nearly 900~kilometers, or more than 500 miles per
second; and this type of spectrum remained characteristic for more
than a month. For each bright hydrogen line\index{stars!constitution} displaced toward the
red there was a dark companion line or band, about equally displaced
toward the violet. It was as if the strange light were due to a solid
\DPPageSep{462.png}
globe moving swiftly away from us, and plunging into an irregular
nebulous mass swiftly approaching us. Tests for parallax placed Nova
Aurigæ\index{Auriga} at the distance of the Galaxy, so that this marvelous celestial
display must actually have occurred in space as remotely as the beginning
of the 19th century. Nova Normæ\index{Norma!new star in} was characterized by a spectrum
almost identical with that of Nova Aurigæ\index{Auriga}, as also Nova Persei, with
calcium, hydrogen, and helium lines.


\textbf{Irregular Variables.}---These objects are not numerous, but some of
them are very remarkable; for example, Eta Argûs\index{Argus@Argûs, Eta, nebula}, an erratic variable
in the southern hemisphere (shown in the midst of the nebulosity on
page~\pageref{p428}). Halley\index{Halley, E.@Halley, E.\ (1656--1742), Ast.\ Roy.}, who visited Saint Helena in 1677, recorded its magnitude
as the fourth. Between 1822 and 1836 it fluctuated between the
first and second magnitudes; but in 1838 the light became tripled,
rivaling all the stars except Sirius and Canopus. In 1843 it was even
brighter, but since then it has declined more or less steadily, reaching
a minimum of the $7\frac{1}{2}$~magnitude in 1886. Probably it has no
regular period, although one of a half century has been suggested.
Later the brightness of Eta Argûs exhibited a slight increase. A few
other stars vary in this irregular manner, though their fluctuations are
confined to a much narrower range.
\Restore

\textbf{Variables of the Algol Type.}\index{variable stars}\index{Algol}---Algol is the name of
the star Beta Persei, the best known object of this class.
As a rule, the periods of this
% Fig 16.12
\begin{wrapfigure}{o}{0.45\textwidth}
  \centering
  \Input[0.4\textwidth]{page_449}
  \caption{Light-Curves near Minimum of Four Algol Variables (Pickering)}
  \label{p449}\index{Pickering, E. C., Dir.\ Harv.\ Coll.\ Obs.}
  \index{variable stars}
\end{wrapfigure}
type of variables are short,
and they remain at maximum
brightness during nearly the
whole. Then almost suddenly
they drop within a few hours
to minimum light, remain there
but a fraction of an hour, and
almost as rapidly return to full
brightness again. The spectra
of all Algol variables are of
the first type.

\Smaller
Figure~\ref{p449} represents the light-curves (between maximum and
minimum) of four stars of this type, as determined by E.~C.\ Pickering\index{Pickering, E. C., Dir.\ Harv.\ Coll.\ Obs.}
at the Harvard College Observatory\index{Harvard College!obs.}. The star W~Delphini\index{Delphinus!variable in}, although
telescopic, is the most pronounced object of this type so far discovered.
\DPPageSep{463.png}
It remains at full brightness rather more than four days; then from the
9.3 magnitude (upper left-hand corner of the diagram) it drops in
seven hours to the 12.0 magnitude, becoming so faint as to be invisible
in a four-inch telescope. Algol\index{Algol}, in $4\frac{1}{4}$~hours, drops a little more than 1.0
magnitude, and returns to its full brightness in $5\frac{1}{4}$~hours, as the curve
shows. Its period, or interval from one minimum to the next, is very
accurately known; at present it is 2\,d.\:20\,h.\:48\,m.\:55.4\,s., and is very
gradually lessening. At full brightness Algol is of the 2.2 magnitude,
and is therefore a conspicuous star. It remains at minimum only about
15~minutes. Algol is best observed from early autumn to the middle of
spring. Belonging to a type regarded by some as new, though at first
classified with Algol stars, are a few such rapid variables as S Antliae
which was discovered by Paul\index{Paul, H.~M., Prof.\ U.~S.\ Navy} in 1888. These compound stars would
seem to constitute a binary system whose members swing round each
other almost in contact (page~\pageref{p469}).
\Restore

\label{p450} \textbf{Causes of Variability.}---No general explanation seems
possible covering the variety in mutations of brightness of
all classes of variables. Those
of the
Algol type are readily accounted for by
the theory of a dark eclipsing body\index{stars!dark},
smaller than the primary, and traveling
round it in an orbit lying nearly edgewise
to us. The illustration shows this: in
the upper figure the system appears as
we look at it; in the lower, as it would
seem if we could
% Fig 16.13
\begin{wrapfigure}{o}{0.48\textwidth}
  \centering
  \Input[0.3\textwidth]{page_450}
  \caption{Orbit of Algol's Dark Companion}\index{stars!constitution}
\end{wrapfigure}
look perpendicularly upon
it. Gravitation of a massive dark companion
would, by its movement round Algol, displace it
alternately toward and from the earth, when in the positions
$E$ and $F$; because the two bodies must revolve round
their common center of gravity. Just such a motion of
Algol in the line of sight has been detected with the
spectroscope, proving that the star alternately recedes
from and advances toward us at the rate of 26 miles per
second, in a period synchronous with that of its variability.

\Smaller
For variables of other types, a comprehensive explanation is found in
vast areas of spots, similar to spots on the sun, taken in connection with
\DPPageSep{464.png}
the star's rotation on its axis and a periodicity of the spots themselves.
The new stars are more likely due to tremendous outbursts of glowing
hydrogen\index{hydrogen!outbursts in stars}; perhaps in
% Fig 16.14
\begin{wrapfigure}[17]{i}{0.5\textwidth}
  \centering
  \Input[0.5\textwidth]{page_451}
  \caption{Sir Norman Lockyer's Meteoritic Theory of Variables}
  \index{Lockyer, Sir J.~N., Eng.\ ast.}\index{meteoritic theory}
\end{wrapfigure}
some cases to vaporization of dark bodies caused
by their brushing past each other, or to a faint star's actual plunging
through a gaseous region of space. Sir Norman Lockyer's\index{Lockyer, Sir J.~N., Eng.\ ast.} theory for
variables of the Omicron Ceti
class is made clear by the
illustration: variable stars are
still in the condition of meteoric
swarms; and the orbital
revolution of lesser
swarms around larger aggregations
must produce multitudes
of collisions, periodically
raising hosts of meteoric
particles to a state of incandescence.
\Restore

\label{p451} \textbf{Double Stars.}\index{double stars}\index{double stars|see{binary stars}}---Many
stars which to the unassisted
eye look simply as
one, are separated by the
telescope into more than one. According to the number,
these are called double, triple\index{stars!triple}, quadruple\index{stars!quadruple}, or multiple stars\index{stars!multiple}.
When the components of a pair appear to be associated
together in space, it is catalogued as a double star. A few
stars, however, are only apparently double, having no actual
relation to one another in space, and only seeming in
proximity because they happen to be nearly in the line of
sight from the earth. They are remote from each other,
as well as from the solar system. Such pairs of stars are
called \textit{optical doubles}\index{double stars!optical doubles}.

\Smaller
Although a few double stars were known earlier, history of the discovery
and measurement of these objects may be said to have begun
with Sir William Herschel\index{Herschel, Sir F. W. (1738--1822), Eng.\ ast.} in 1779. The Struves\index{Struve, F.~G.~W.\ (stroo´v\u uh) (1793--1864), Ger.-Russ.\ ast.}\index{Struve, O.~W.@v.\ Struve, O.~W.\ (1819--1905), Ger.\ ast.}, father and son, and
Baron Dembowski\index{Dembowski, L.\ (1815--91), Ger.\ ast.}, among others, have prosecuted these researches
vigorously. More than 10,000 double stars are now known, and discoveries
have been rapidly made in recent years, particularly by Burnham\index{Burnham, S. W., Univ.\ Chicago}
of Chicago. The next illustration shows a dozen of the easier doubles,
\DPPageSep{465.png}
within reach of small telescopes. Instruments of greater diameter
than six inches are necessary to divide the components of a double
star whose apparent distance from one another is less than $0''.8$. Bond\index{Bond, G. P. (1825--65), Am.\ ast.}
and Gould\index{Gould, B.~A.\ (1824--96), Am.\ ast.} were pioneers in the application of photography to observation
of the wider `doubles'; but here the assistance of this new method
is not as important as in other departments of astronomy. Among
other European observers of double stars are Bigourdan\index{Bigourdan, G. (be-goor-dong´), ast.\ Paris Obs.} of Paris and
Glasenapp\index{Glasenapp, S.~P.\ (gläz´näp), Dir.\ Obs.\ Saint Petersburg Univ.} of Saint Petersburg; and in America A. Hall\index{Hall, A.\ (1829--1907), Am.\ ast.}, Comstock\index{Comstock, G.~C., Dir.\ Obs.\ Univ.\ Wis.},
and Leavenworth\index{Leavenworth, F.~P., Prof.\ Univ.\ Minn.}.
\Restore

% Fig 16.15
\begin{figure}[hbt!]
  \centering
  \Input[0.8\textwidth]{page_452}
  \caption{Twelve Typical Double Stars}
  \index{Rigel ($\beta$ Orionis)}\index{Castor ($\alpha$ Geminorum)}\index{Polaris}\index{Cygni 61}\index{double stars}
\end{figure}

\textbf{Binary Stars.}\index{binary stars}---Careful and protracted observations are
necessary to determine the class to which any pair of
stars belongs. If the components of a `double' are
found to revolve in a closed or elliptic orbit, they are
called \textit{a binary star}. It is assumed, and doubtless rightly,
that this motion depends upon gravitation.

\Smaller
\index{double stars!orbits}About 200 binaries are now known, and the orbits of perhaps 50 of
them are well ascertained. In his \textit{Researches on the Evolution of the
Stellar Systems} (1896), See\index{See, T.~J.~J., Am.\ ast.} has presented a summary of present knowledge
of these bodies. According to Miss Everett's\index{Everett, Miss A., Eng.\ ast.} investigation, the
planes of their orbits sustain no definite relation to any fundamental
\DPPageSep{466.png}
plane of the heavens. The star known as $\beta$~883 (star No.~883 discovered
by Burnham\index{Burnham, S. W., Univ.\ Chicago}) is the shortest known binary, its period being
$5\frac{1}{2}$~years; the longest is Zeta Aquarii, not less than 1500 years. Several
binary stars are recognized, one component of which is dark. These
can be discovered only by the effect which the attraction of the dark
star\index{stars!constitution} produces in changing the position of the bright one. The giant
Sirius\index{Sirius} is a star of this kind, having a faint attendant only bright enough
to be detected with large telescopes, and known as the companion of
Sirius. Its orbit as determined by Burnham from observations 1862--96
is shown adjacent. Before actual discovery (by A.~G. Clark\index{Clark, A. (1804--87), A. G. (1832--97), G. B. (1827--91)} in 1862),
not only its existence but its true position had been predicted by Auwers.
The companion's period is 49
years; and its motion, and
distance both from Sirius and
from the solar system, show
that the mass of the companion
equals that of the sun,
while that of the Dog Star itself
exceeds that of the sun
$2\frac{1}{5}$~times.
\Restore

But the best known
binary system is the
one first discovered (by
Richaud\index{Richaud, M.\ (re-show´) (1650--1700), Fr.\ ast.}
% Fig 16.16
\begin{wrapfigure}{o}{0.5\textwidth}
  \centering
  \Input[0.45\textwidth]{page_453}
  \caption{Orbit of Sirius (Burnham)}
  \index{Burnham, S. W., Univ.\ Chicago}\index{Sirius}
\end{wrapfigure}
in 1689), Alpha
Centauri\index{Centauri, Alpha}, also the
nearest of all the fixed stars. Its components are of the
first and second magnitude. The period of the stars'
revolution is 81~years, the masses of the two components
are very nearly equal, and their combined mass is twice
that of the sun. The stars of a binary system are said to
be in \textit{periastron}\index{periastron} when nearest to one another in space;
and in \textit{apastron}\index{apastron} when farthest. At periastron the components
of Alpha Centauri are about as far apart as Saturn
is from the sun; in apastron their distance from each
other greatly exceeds that of Neptune from us.

\textbf{Eccentricities and Masses of Binary Stars.}\index{binary stars!eccentricities}\index{binary stars!masses}---The orbits
of binary stars are remarkable for great eccentricity; also
for the large mass-ratios of their components, always
\DPPageSep{467.png}
comparable, and in some cases nearly equal. In these
respects they differ greatly from the bodies of the planetary
system, the orbits in which are nearly circular, and
none of the planets have more than a small fraction of
the sun's mass. See\index{See, T.~J.~J., Am.\ ast.} explains the exceptionally high
eccentricity of binary orbits, according to the principles
of tidal evolution, from orbits which were nearly circular
in the beginning. Originally the system was a single
rotating nebulous mass, which became modified into a
dumb-bell figure as a result of its own contraction. The
average eccentricity of the best known binaries is 0.48,
while that of the planets and satellites in our system is
less than 0.04, or only $\frac{1}{12}$ as great; and this extraordinary
relation may be accepted as the expression of a fundamental
law of nature. Recalling the principles by which
the mass of a planet is compared with that of the sun, it
is evident that a like method will give the mass of a binary
system, also in terms of the sun. First we must measure
the major axis of the orbit, and observe the period of revolution;
also it is necessary to assume that the Newtonian
law of gravitation\index{gravitation!law of} governs their motion. Then:---
\label{p454}
\[
\frac{ \
  \left[\begin{array}{@{}c@{}}
      \text{\footnotesize Moon's distance} \\
      \text{\footnotesize from earth}
    \end{array}\right]^3 \rule[-2.8ex]{0pt}{1ex}
}{
  \left[\begin{array}{@{}c@{}}
      \text{\footnotesize Moon's sidereal} \\
      \text{\footnotesize period}
    \end{array}\right]^2 \rule{0pt}{4.2ex}
  \!\!\! ×
  \left[\begin{array}{@{}c@{}}
      \text{\footnotesize Earth's mass} \\
      \text{\footnotesize $+$ moon's}
    \end{array}\right]
}
=
\frac{ \
  \left[\begin{array}{@{}c@{}}
      \text{\footnotesize Distance between components} \\
      \text{\footnotesize of Alpha Centauri}
    \end{array}\right]^3 \rule[-2.8ex]{0pt}{1ex}
}{
  \left[\begin{array}{@{}c@{}}
      \text{\footnotesize Period of their} \\
      \text{\footnotesize revolution}
    \end{array}\right]^2 \rule{0pt}{4.2ex}
  \!\!\! ×
  \left[\begin{array}{@{}c@{}}
      \text{\footnotesize Sum of masses} \\
      \text{\footnotesize of components}
    \end{array}\right]
}
\]
Masses of the few binary systems ascertained in this manner
are about twofold or threefold that of the sun.

\textbf{Binaries discovered by the Spectroscope.}\index{binary stars!spectroscopic}---It was Bessel\index{Bessel, F. W. (1784--1846), Ger.\ ast.}
who first wrote of the `astronomy of the invisible,' and
his prediction has been marvelously fulfilled by the recent
discovery of spectroscopic binaries. They are binaries
whose components are so near each other that the telescope
cannot divide them, and whose spectra therefore
overlie. As the orbits of binary systems stand at all possible
\DPPageSep{468.png}
angles in space, a few will appear almost edge on.
Let the two components be in conjunction, as referred to
the solar system; clearly their spectra will be identical.
But when they reach quadrature, one will be receding
from the earth and the other coming toward it. A given
line in the compound spectrum, then, will appear double,
on account of displacement due to motion of the components
in opposite directions\index{Doppler's principle}. Measure the displacement,
and observe the period of its recurrence. This gives the
velocity of the components relatively to each other, the
dimensions of their orbit, and their mass in terms of the
sun, always assuming that the same law of gravitation is
regnant among the stars.

% Fig 16.17 a, b
\begin{figure}[hbt!]
  \centering
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input{page_455a}
    \caption{1889, Dec.\ 30 d.\ 17.6\,h., G.M.T.\ (single)}
  \end{minipage}
  \hfill
  \begin{minipage}{0.45\textwidth}
    \centering
    \Input{page_455b}
    \caption{1889, Dec.\ 31 d.\ 11.5\,h., G.M.T.\ (double)}
  \end{minipage}
  \caption{Spectra of $\beta$ Aurigæ (Pickering)}
  \index{Aurigæ, Beta}
\end{figure}

\Smaller
The binaries so far discovered by this method have relatively short
periods; the shortest known is $\mu^{1}$~Scorpii, only 35~hours. Beta Aurigæ
is a remarkable star of this
class, the doubling of its
lines taking place on alternate
nights, giving a period
of four days; and the combined
mass of both stars
is more than twice that
of the sun. The region of
its spectrum is here shown,
with lines both double and
single. New stars of this
type are continually coming
to light; but if the orbits
lie perpendicular to the
line of sight, the duplicity is not discoverable in this manner. Nearly one
tenth of all the stars so far examined reveal orbital motion. Possibly the
star unattended by dark companions may, Campbell\index{Campbell, W. W., Dir.\ Lick Obs.} thinks, prove to be
the rare exception. Relative velocities of the components are in some
cases as large as 300 or even 400 miles per second. Among pronounced
spectroscopic binaries are Capella\index{Capella}, Castor\index{Castor ($\alpha$ Geminorum)}, Mizar\index{Mizar, star in Ursa Major}, Polaris\index{Polaris}, and Spica\index{Spica ($\alpha$ Virginis)}.
Campbell's first catalogue of these bodies (1905) contains nearly 150, distributed
all over the sky, and there are numerous new discoveries each year.
Other discoverers in this field are Bélopolsky\index{Belopolsky@{Bélopolsky, A., ast.\ Pulkowa Obs.}}, Frost\index{Frost, E. B., Prof.\ Univ.\ Chicago}, Vogel\index{Vogel, H.~C. (1841--1907), Ger.\ ast.}, and Wright\index{Wright, W.~H.\ (1711--86), Am.\ ast.}.
\Restore

\textbf{Multiple Stars.}\index{stars!multiple}---Numerous stars have more than two
\DPPageSep{469.png}
components in the same field of view. These are generally
called \textit{multiple stars}, though the terms \textit{triple star}\index{stars!triple} for
three components, \textit{quadruple}\index{stars!quadruple} for four, and so on, are often
used. In isolated instances a star may be optically multiple;
that is, the components appear to be associated
together, from the fact that they are in or near the line of
sight, while in reality they are at vastly different distances
from the sun, and are in no sense related to each other.
Nearly all multiple stars are physically multiple; that is,
connected together in a real system. Such a system is the
star Epsilon Lyræ\index{Lyræ!epsilon (ep-si´lon)}, the well-known fourth-magnitude star,
near Vega. A keen eye, even without optical assistance,
will split it into a double. A small telescope will divide
each of the two components into a pair, forming a beautiful
quadruple system; while large telescopes show at
least three other faint stars, one of them very difficult,
between the pairs. Not only do the two stars of each pair
revolve round each other, in periods of several hundred
years, but the pairs themselves have a grander orbital motion
round each other in a vast period not yet determined.
A multiple star having more than seven or eight components
would be classed as a \textit{star cluster}.

\textbf{Stellar Clusters.}\index{clusters!stellar}\index{stars!grouping}---Seeming aggregations of stars in the
sky are called \textit{stellar clusters}, or simply \textit{clusters}. Broadly
speaking, they are embraced in two classes: The loose
clusters, so called because the stars are not very thickly
scattered, of which the Pleiades\index{Pleiades (ple´ya-deez)} are a very conspicuous
type; and the close clusters, in which the stars appear to
be thickly aggregated. The Pleiades contain six stars visible
to the ordinary naked eye, though seven, nine, and even
as many as thirteen stars have in rare instances been seen
in this group without a telescope. A medium glass shows
about 100 stars, and a photographic plate exposed an
hour displays more than 2000 stars in and close to the
\DPPageSep{470.png}
Pleiades. An exposure of six hours shows 4000 stars.
The longer the exposure, the more stars appear on the
plate. By an exposure of 17\,h.\:30\,m., continued on nine
nights, and covering a region of four square degrees,
nearly 7000 stars are counted in the Pleiades. Recent
counts make them fewer in the immediate regions of the
bright stars than in adjacent portions of the sky of equal
area; and very much fewer than in many parts of the
Milky Way. Also by photography Barnard\index{Barnard, E. E., Prof.\ Univ.\ Chicago} has discovered
extensive nebulosities surrounding the Pleiades\index{photography!discoveries by}, which
the glare of the larger stars makes difficult to see with a
telescope. They have crudely the shape of a horseshoe.

\Smaller
One type of close clusters is known as the \textit{globular cluster}\index{clusters!globular}, in which
the stars are compacted together as if in a seemingly circular area,
or in space a
% Fig 16.18
\begin{wrapfigure}{o}{0.4\textwidth}
  \centering
  \Input[0.4\textwidth]{page_457}
  \caption{Globular Cluster 15 Pegasi (Roberts)}
  \index{Roberts, I. (1829--1904), Eng.\ ast.}\index{clusters!globular}
\end{wrapfigure}
nearly globular
mass. The adjacent picture
is an excellent illustration of
this type. The more nearly
spherical a cluster is, the older
it is thought to be; for the individual
components of clusters
are no doubt subject to the
laws of central attraction, and
the more perfect approach to
a spherical figure would indicate
that the action of central
forces had been longer continued.
Thus it is possible
to infer the maturity of a
cluster from the relative disposition
of its component
numbers. One of the finest
objects in the sky is the double cluster, excellently reproduced in the
photograph \vpageref{p458}. It forms part of the Milky Way in Perseus\index{Perseus (per´suce)}, and each
component approaches the globular form. The clusters are made up of
stars of all sizes, and are without doubt at stellar distances from us,
though no parallax of a cluster has yet been measured. In all, about
200 clusters and nebulæ have been photographed, so that a half century
hence it may be possible to ascertain what changes are taking place.
\Restore
\DPPageSep{471.png}

\textbf{The Galaxy, or Milky Way.}\index{Milky Way}\index{stars!grouping}---Lying diagonally across
the dome of the sky, at varying angles and elevations in
different seasons of the year, may be seen on clear, moonless
nights an irregular belt or zone of hazy light of uneven
% Fig 16.19
\begin{figure}[hbt!]
  \centering
  \Input{page_458}
  \caption{The Double Cluster in Perseus (photographed by Roberts)}
  \label{p458}\index{Perseus (per´suce)}\index{photography!of moon}\index{Roberts, I. (1829--1904), Eng.\ ast.}
\end{figure}
brightness, about three times the breadth of the moon,
and stretching from horizon to horizon. This is part of
the Galaxy, or Milky Way. It is really a ring of light,
reaching entirely round the celestial sphere, roughly in a
great circle; and usually about half of it will be above the
horizon and half below. It intersects the ecliptic near the
solstices, at an angle of about 60°. Early in September
\DPPageSep{472.png}
evenings it nearly coincides with a vertical circle lying
northeast and southwest. The Galaxy is fixed in relation
to the stars, and part of it lies so near the south pole of
the heavens that it can never be seen in our northern
latitudes. From Cygnus to Scorpio it is a divided belt, or
double stream. Even a small telescope shows at once
that the Milky Way is composed of millions of faint stars,
nearly every one of them individually too faint for naked-eye
vision, but whose vast numbers give us collectively
the gauzy impression of the Galaxy. On page~\pageref{p13} is an
excellent reproduction from one of the finest of Barnard's\index{Barnard, E. E., Prof.\ Univ.\ Chicago}
photographs of the Milky Way, and equally striking photographs
have been obtained by Wolf\index{Wolf, M., Prof.\ Univ.\ Heidelberg}, and of the Southern
Milky Way by Russell\index{Russell, H.~C.\ (1836--1907), Eng.\ ast.}. All these stars are suns, and
probably comparable in size and constitution with the
sun himself.

\Smaller
They are not evenly scattered, but in many regions are aggregated
into close clusters of stars; for example, the double cluster in the sword
hilt of Perseus, shown opposite. It is readily visible to the naked eye
on clear, moonless nights in the position shown in diagram on page~\pageref{p66}.
According to Easton\index{Easton, C., Dutch ast.}, the galactic system accessible to our observation
has but little depth in proportion to its diameter. Study of the photographs
has led Maunder\index{Maunder, E.~W., ast.\ Obs.\ Greenwich} to direct attention to `dark lanes' in the Milky
Way\index{Milky Way!lanes}, marking regions of real barrenness of stellar material, and perhaps
indicant of galactic condensation progressing toward an ultimate
globular cluster.
\Restore

\textbf{Distribution of the Stars.}\index{stars!distribution}---As to their apparent distribution
over the face of the sky, lack of uniformity is
evident. The fact of their recognized division into constellations,
even from the earliest ages, is proof of this.
Clusters and starless vacuities are well known. Frequently
there are found streams of stars\index{stars!streams}, especially by exploration
with the telescope. One general law is known to govern
the apparent distribution in the heavens: at both poles of
the Milky Way, the stars are scattered most sparsely;
\DPPageSep{473.png}
and the number in a unit of surface of the stellar sphere
increases on all sides uniformly toward the plane of the
Milky Way itself. This important discovery was made by Sir
William Herschel\index{Herschel, Sir F. W. (1738--1822), Eng.\ ast.}, through a laborious process of actually
counting the stars, technically called `star gauges\index{stars!Herschel's gauges}.' In
Coma Berenices, for example, near the north pole of the
Milky Way, are perhaps five stars in a given area; half
way to the Galaxy the number has doubled; and in the
Milky Way itself the average number is found to exceed
120, thus increasing more rapidly as this basal plane of
the sidereal universe is approached. Kapteyn\index{Kapteyn, J.~C., Univ.\ Groningen}, a recent
investigator of this supreme problem, likens the general
shape of the stellar universe to that of the great nebula in
Andromeda (opposite); the disk-shaped nucleus representing
the cluster to which the sun belongs, and its exterior
rings the flattened layers of stars surrounded by the zone
of the Galaxy.

\textbf{The Nebulæ.}---A nebula is a celestial object, often of
irregular form and brightness, appearing like a mass of
luminous fog. In all,
over 10,000
are now
known, and their positions
among the stars
determined. They differ
% Fig 16.20
\begin{wrapfigure}{o}{0.6\textwidth}
  \centering
  \Input[0.55\textwidth]{page_460}
  \caption{Ring Nebula in Lyra (Roberts)}
  \index{Roberts, I. (1829--1904), Eng.\ ast.}\index{Lyra!ring nebula in}
  \label{p460}\index{photography!of nebulae}
\end{wrapfigure}
greatly in brightness,
form, and apparent size.
Many of them are shown
by the spectroscope to
be glowing, incandescent
gases, in large part hydrogen.
These are greenish
in tint; but a few
whitish ones are resolvable;
that is, composed of masses of separate stars too
\DPPageSep{474.png}
faint to be seen individually. The nebulæ appear like the
residue of the materials of original chaos out of which the
sun, his planets, and the stars have through many millions
of years come into being. A few of them are variable in
brightness.

\textbf{Classification of the Nebulæ.}\index{nebulae!classified}---It is usual to divide the
nebulæ into five classes, based on their various forms:
(1)~annular nebulæ\index{nebulae!annular}, (2)~spiral nebulæ\index{nebulae!spiral}, (3)~planetary nebulæ\index{nebulae!planetary},
(4)~nebulous stars, (5)~irregular nebulæ\index{nebulae!irregular}, for the most part
large. Perrine\index{Perrine, C.~D., Dir.\ Argentine Nat.\ Obs.} estimates that the entire sky contains more
than 500,000 very faint nebulæ, within photographic reach
of the great reflecting telescopes, which are better suited
to this work than refractors. Especially fine photographs
of nebulæ have been made by Ritchey\index{Ritchey, G.~W., Am.\ ast.}, Wolf\index{Wolf, M., Prof.\ Univ.\ Heidelberg}, and Keeler\index{Keeler, J.~E.\ (1857--1900), Am.\ ast.},
and Keeler concludes that spiral filaments seem to be the
prevailing type of nebular structure. A very extensive
catalogue of nebulæ is by Dreyer\index{Dreyer, J.~L.~E., Dir.\ Obs.\ Armagh}.

\Smaller
By prolonged exposures
fine photographs of the fainter
nebulæ have been obtained
by von Gothard\index{Gothard@v.\ Gothard, E.\ (go´tar) (1857--1909), Hungarian ast.} and others.
A famous nebula of the irregular
order surrounds the star
Eta Argûs (page~\pageref{p428})\index{Argus@Argûs, Eta, nebula}. In
recent years it has been frequently
photographed by Gill\index{Gill, Sir D., Scotch ast.}
and Russell\index{Russell, H.~C.\ (1836--1907), Eng.\ ast.} with exposures of
many hours' duration, and
changes in its brightness are
plainly indicated.

% Fig 16.21
\begin{figure}[hbt!]
  \centering
  \Input[\textwidth]{page_461}
  \caption{The Great Nebula in Andromeda (Roberts)}
  \label{p461}\index{Roberts, I. (1829--1904), Eng.\ ast.}\index{photography!of nebulae}
\end{figure}

\textbf{Remarkable Annular and
Elliptic Nebulæ.}\index{nebulae!annular}\index{nebulae!elliptic}---A fine object
of this class was discovered
by Gale\index{Gale, W.~F., Australian ast.} in 1894 in
the southern constellation
Grus; but the best-known
annular nebula is in the constellation
Lyra\index{Lyra!ring nebula in}. A very faint object in small telescopes, the great ones
\DPPageSep{475.png}
reveal many stars within its interior spaces. The illustration on p.~\pageref{p460}
is from a photograph of the nebula, but it does not show the complexity
and irregularity of structure which some of the large telescopes indicate.
The star near its center is thought to be variable. Among elliptic nebulæ,
the signal object is the `great nebula in Andromeda\index{Andromeda!nebula in}.' So bright is
it that the unaided eye will recognize it, near Eta Andromedæ. Its vast
size, too, as seen in the telescope, is remarkable---about seven times
the breadth of the moon, and its width more than half as great. The
illustration shows its striking structure, first clearly revealed by Roberts's\index{Roberts, I. (1829--1904), Eng.\ ast.}
splendid photographs in 1888. Apparently it is composed of a
number of partially distinct rings, with knots of condensing nebulosity,
as if companion stars in the making. Its spectrum shows that it is not
gaseous, still no telescope has yet proved competent to resolve it.
\Restore

\textbf{Spiral and Planetary Nebulæ.}\index{nebulae!spiral}\index{nebulae!planetary}---The great reflecting telescope
of Lord Rosse\index{Rosse, Lord (1800--67), Brit.\ ast.} first brought to light the wonderful
spiral nebulæ, the most
% Fig 16.22
\begin{wrapfigure}{o}{0.65\textwidth}
  \centering
  \Input[0.6\textwidth]{page_462}
  \caption{Spiral Nebula in Canes Venatici (Roberts)}
  \index{Roberts, I. (1829--1904), Eng.\ ast.}\index{Canes Venatici!nebula in}
  \label{p462}\index{photography!of nebulae}
\end{wrapfigure}
conspicuous example of
which is found in Canes
Venatici\index{Canes Venatici!nebula in}. Its structure
is such that photography
has a vast advantage in
depicting it, as the adjacent
illustration reveals.
The convolutions
of the spiral are filled
with many star-like condensations,
themselves
surrounded by nebulosity.
The spectroscope
indicates its stellar character, though, like the Andromeda
nebula, it is yet unresolved, except in parts. Planetary
nebulæ have this name because they exhibit a disk with
pretty definite outlines, round or nearly so, like the large
planets, though very much fainter. They are nearly all
gaseous in composition. Nebulous stars are stars completely
enveloped as if in hazy, nebulous fog. They are
\DPPageSep{476.png}
mostly telescopic objects, and very regular in form, some
with nebulosity well defined, others less so. One has
luminous rings surrounding it.

\Smaller
\textbf{Spectra of the Nebulæ.}\index{nebulae!spectra}---Sir William Huggins\index{Huggins, W.\ (1824--1910), Eng.\ ast.}, who in 1864 first
applied the spectroscope to nebulæ, discovered bright lines in their
spectra, indicating a community of chemical composition, due to
glowing gas, in large part hydrogen\index{hydrogen!in nebulæ}. Helium\index{helium!in nebulæ} has recently been
added; but other lines are due to substances not yet recognized as terrestrial
elements. The annular, planetary, and mostly the irregular nebulæ
give the gaseous spectrum; and exceedingly high temperatures are
indicated, or else a state of strong electric excitement. Both temperature
and pressure appear to increase toward the nucleus of the nebula.
Many nebulæ fail to yield bright lines; showing rather a continuous
spectrum, prominently the great nebula of Andromeda. Lack of lines
may be interpreted as due to gases under extreme pressure, or to aggregations
of stellar bodies. Another object of this character is the
great spiral nebula in Canes Venatici, well depicted in the photograph
by Roberts (opposite); but no telescope has yet been able to resolve
either of these objects into discrete stars. The application of photography
has revealed about 40 lines in the spectra of nebulæ; and Keeler\index{Keeler, J.~E.\ (1857--1900), Am.\ ast.}
and Campbell\index{Campbell, W. W., Dir.\ Lick Obs.} have shown, in the case of the Orion nebula, that nearly
every line in its spectrum is the counterpart of a prominent dark line in
the spectra of the brighter stars of the same constellation.
\Restore

\textbf{The Great Nebula in
Orion.}\index{nebulae!Orion}---Just below the
eastern end of Orion's
belt is this greatest of all
nebulæ. So characteristically
bright is this well-known
object that it is
readily distinguished
without a telescope. It
was the
% Fig 16.23
\begin{wrapfigure}[20]{o}{0.6\textwidth}
  \centering
  \Input[0.6\textwidth]{page_463}
  \caption{The Great Nebula in Orion (Bond)}
  \index{Bond, G. P. (1825--65), Am.\ ast.}\index{photography!of nebulae}
\end{wrapfigure}
first nebula
ever photo\-graphed---by
Henry Draper\index{Draper, H. (1837--82), Am.\ ast.} in 1880.
The spreading expanse
of its nebulosity completely envelops the multiple star
\DPPageSep{477.png}
Theta Orionis, often called the `trapezium' (not well shown
in the photograph because the blur of the nebula overlaps
it). In small instruments a very obvious feature is the
wide opening at one side, or break in the general light,
sometimes called the `Fish's mouth.' A curdling or flocculent
structure is excellently shown in the best photographs,
and a greenish tinge has been recognized in its
light. Extensive wisps of nebulosity reach out in many
directions, involving other stars. W.~H. Pickering's\index{Pickering, W.~H., Prof.\ Harv.\ Univ.} plates
indicate an approach to the spiral figure in these outlying
filaments, and Roberts's\index{Roberts, I. (1829--1904), Eng.\ ast.} photographs show vortical areas
within the nebula. Its spectrum reveals incandescent
hydrogen and helium; also other substances not yet recognized
among terrestrial elements. The nebula is as remote
as the stars are; and, according to Keeler's\index{Keeler, J.~E.\ (1857--1900), Am.\ ast.} observations,
its distance from the sun is increasing at the rate of 11
miles every second. Also they prove an intimacy of relation
between the nebula and neighboring stars. There is
no conclusive evidence of change of form in any part of
the nebula, although Holden\index{Holden, E.~S., Am.\ ast.} has investigated this question
\DPPageSep{478.png}
fully. The light of the nebula is far from homogeneous, being
different in its spectral composition in different regions.

% Fig 16.24
\begin{figure}[hbt!]
  \centering
  \Input{page_464}
  \caption{Path of Milky Way and Distribution of Nebulæ (according to Proctor)}
  \index{Proctor, R.~A.\ (1837--88), Am.\ ast.}
\end{figure}

\textbf{Distribution of the Nebulæ.}---It may be said that the
nebulæ are distributed over the sky in just the opposite
manner from the stars; for their number has a definite
relation to the Milky Way. Reference to the preceding
figure will show this at a glance. The small dots represent
nebulæ, not stars; and it is at once evident that
they are more strongly clustered the greater their angular
distance from the Milky Way. The physical reason underlying
this fact is not known. Neither is the distance of
any nebula known\index{nebulae!distance}. So that the distribution of the nebulæ
throughout space can only be surmised. Measurement
of the distance of a few nebulæ has been attempted, with
the disappointing outcome that their parallax is exceedingly
small, and probably beyond our power ever to ascertain.
They are, therefore, at distances from our solar system
estimable in light years, like those of the stars. Keeler's\index{Keeler, J.~E.\ (1857--1900), Am.\ ast.}
spectroscopic observations prove that the nebulæ are moving
in space at velocities comparable with those of the
stars; the bright nebula in Draco, for example, is coming
toward the earth at the rate of 40~miles every second.
None of the nebulæ, however, have yet been discovered to
partake of proper motion.

\textbf{The Cosmogony.}\index{cosmogony}---Cosmogony is the science of the
development of the material universe. It has nothing to
do with the origins of matter, and is concerned only with
its laws and properties, and the transformations resulting
from them. The ancient philosophers avoided the question
of the origin of matter by asserting that the universe
always had its present form from eternity; many minds
are still satisfied with a literal interpretation of the Old
Testament account of the creation, that the Almighty
Power, out of nothing, built the universe in six days, substantially
\DPPageSep{479.png}
as observed in our own age; according to the
accepted cosmogony, the universe was in the beginning
a widely diffused chaos, `without form and void,' according
to the Scriptures. Out of it has been evolved, by the
long-continued action of fixed natural laws, the present
orderly system of the universe.

\textbf{The Universe is exceedingly Old.}\index{solar system!evolution of}---In outline, the accepted
cosmogony is this: Once in the inconceivably
remote past, many hundreds of millions of years ago,
all the matter now composing earth, sun, planets, and
stars, was scattered very thinly through the untold vastness
of the celestial spaces. The universe did not then
exist, except potentially. Then, as now, every particle of
matter attracted every other particle, according to the
Newtonian law. Gradually centers of attraction formed,
and these
% Fig 16.25
\begin{wrapfigure}[15]{o}{0.6\textwidth}
  \centering
  \Input[0.525\textwidth]{page_466}
  \caption{Ideal Genesis of Planetary System (Compare with actual nebula \vpageref{p461})}
\end{wrapfigure}
centers pulled in toward themselves other particles.
As a result of the inward falling of matter toward
these centers, the collision of its particles, and their friction
upon each other, the material masses grew hotter and
hotter. Nebulæ seeming to fill the entire heavens were
formed---luminous fire
mist, like the filmy objects
still seen in the
sky, though vaster, and
exceedingly numerous.

\textbf{Stars and Suns from
Nebulous Fire Mist.}\index{planetary system, evolution of}\index{sun!evolution}---Countless
ages elapsed;
the process went on,
swifter in some regions
of space than in others.
Millions upon millions of nebular nuclei began to form;
condensation progressed; because the particles could not
fall directly toward their centers of attraction, vast nebular
\DPPageSep{480.png}
whirlpools were set in motion; axial rotation began; and
temperature rose inconceivably high at centers where
condensation was greatest. The sun was one of these
centers; earth and all the other planets had not yet a
separate existence, but the materials now composing them
were diffused through the great solar nebula. Every star,
whether lucid or telescopic, was such a center, or became
one in the gradual evolution and process of world
building.

\label{p467} \textbf{Planets from Nebulous Stars.}\index{planets!evolution}\index{planetary system, evolution of}---As contraction and condensation
went on, the whirling became swifter, because
gravitation brought the particles nearer to the axis round
which they turned, and there was no loss of
rotational
moment of momentum. Centrifugal force gave the whole
rotating mass the figure, first of an orange, then of a vast
thickened disk, shaped like a watch. Eventually the
masses composing its rim could no longer whirl round
as swiftly as the more compact central mass; so a separation
took place, the outlying nebulous regions being left
or sloughed off as a ring, while all the central portion kept
on shrinking inward from it. As shown opposite, the mass
of the ring would rarely be distributed uniformly; but being
lumpy, the more massive portions would in time draw in
the less massive ones, and the ring would thus become a
planet in embryo; and its time of revolution round the
sun would be that of the parent ring. If still nebulous,
the planet would itself go through the stages of the solar
nebula, and slough off rings to gather into moons or
satellites. Meanwhile the parent nebula went on contracting,
and leaving other rings, which in the lapse of
ages developed into inner planets, and their rings as a rule
into satellites.

\textbf{Early History of the Nebular Hypothesis.}\index{nebular hypothesis}---Such in bare
outline is the nebular hypothesis. Note that it is merely a
\DPPageSep{481.png}
highly plausible theory; it has never been absolutely demonstrated,
and probably never can be. To its development
many great minds have contributed. The Englishman
Thomas Wright, the Swede Emanuel Swedenborg\index{Swe´denborg, E.\ (1688--1772), Swed.\ phil.}, and the
German Immanuel Kant\index{Kant, I. (känt) (1724--1804), Ger.\ phil.}, all, independently and during
the 18th century, appear to have originated the hypothesis
under slightly variant forms. Of these, Kant's theory
was the most philosophic; but his greater renown as a
mental philosopher than as a physicist appears to have
hindered attention to his important speculation. When,
however, La~Place\index{La Place, P. S. de (lä-plass´) (1749--1827), Fr.\ ast.\ and math.} lent the weight of his great name to
an almost identical hypothesis, astronomers at once recognized
that it must be based on sound dynamic conceptions.
Then came the giant telescopes of the Herschels\index{Herschel, Sir F. W. (1738--1822), Eng.\ ast.}\index{Herschel, Sir J.~F.~W.\ (1792--1871), Eng.\ ast.},
father and son, and of Lord Rosse\index{Rosse, Lord (1800--67), Brit.\ ast.}, adding the evidence of
observation; for they discovered in the sky nebulæ, some
globular in figure, some disk-like, others annular, and still
others even spiral.

\textbf{Later Developments.}---But Lord Rosse's great telescope
showed, too, that some at least of the nebulæ might be resolved
into stars, thereby threatening the subversion of
the nebular hypothesis, especially if all the nebulæ could
be so resolved. Within a few years, however, and just
after the middle of the 19th century, application of the
principles of spectrum analysis\index{spectrum!analysis} to the nebulæ proved
conclusively that many of them are composed of glowing
gas, and therefore cannot be resolved into stars. About
the same time von Helmholtz\index{Helmholtz@v.\ Helmholtz, H.~L.~F.\ (1821--94), Ger.\ physicist} advanced the accepted theory
of the sun's contraction in explanation of the maintenance
of solar heat\index{sun!heat}; and Lane\index{Lane, J.~H.\ (1819--80), Am.\ physicist}, an American, proved that a
gaseous mass condensing as a result of gravitation might
actually grow hotter, in spite of its immense losses of heat.
Thus it was unnecessary to assume a high temperature of
the nebula in the beginning. Also the genius of Lord
\DPPageSep{482.png}
Kelvin, the eminent English physicist, strengthened the
hypothesis by computations on the heat of the sun, and
his probable duration\index{sun!duration} of about 20,000,000 years in the
past.

\textbf{Recent Additions.}\index{double stars!origins}---Then came Darwin\index{Darwin, G.~H., Prof.\ Univ.\ Cambridge, Eng.}, who, in the
latter part of the 19th century, demonstrated mathematically
the remarkable effects producible by tidal friction\index{evolution, tidal}\index{tidal, friction},
which had been neglected in all previous researches. The
gathering of a ring into an embryo planet was a process
not easy to explain; and Darwin showed that probably
the moon had never been a ring round the earth, but that
she separated from her parent in a globular mass, in consequence
of its too rapid whirling. He showed, too, how
the mutual action of great tides in the two plastic masses
would operate to push the moon away to her present remote
distance: the terrestrial tidal wave being in advance
of the moon, our satellite would tend to draw it backward;
also, the wave would tend to pull the moon forward, thereby
expanding her orbit, and increasing her mean distance from
us. His researches cleared up, also, the enigma of the
inner satellite of Mars, revolving round its primary in less
time than Mars himself turns on his axis; and no less the
newly discovered
% Fig 16.26
\begin{wrapfigure}[14]{o}{0.675\textwidth}
  \centering
  \Input[0.6\textwidth]{page_469}
  \caption{Various Types of Double Nebulæ (Lord Rosse)}
  \label{p469}\index{Rosse, Lord (1800--67), Brit.\ ast.}
  \index{nebulae!double}
\end{wrapfigure}
fact
that Mercury and Venus
keep a constant face to
the sun, and satellites of
Jupiter to their primary,
just as the moon to the
parent earth. %\label{p469}
Still later,
by adapting these principles
to stellar systems,
See\index{See, T.~J.~J., Am.\ ast.} explained the fact of
the great eccentricity of
the binary orbits as a result of the long-continued or secular
\DPPageSep{483.png}
action of tidal friction. The double stars, then, were
originally double nebulæ\index{nebulae!double}, separated by a process resembling
`fission' in the case of protozoans. Poincaré\index{Poincaré, H.\ (pwang-kä-ray´), Prof.\ Univ.\ Paris} has
proved mathematically that a whirling nebula, in consequence
of contraction, is liable to distortion into a pear-shaped
or hour-glass figure, and to ultimate separation.
And there is excellent observational proof in the double
nebulæ (p.~\pageref{p469}) found in different regions of the heavens.

\textbf{Evidence supporting the Nebular Hypothesis.}---To collect
evidence from the entire universe, as at present known:---

(\textit{a}) Scanning the heavens with the telescope, we find
numerous nebulæ of forms required by the theory.

(\textit{b}) Spectrum analysis\index{spectrum!analysis}\index{stars|see{spectrum, stellar}} proves a general unity of chemical
composition throughout the universe.

(\textit{c}) Stellar evolution necessitates the supposition of birth,
growth, and decay of stars,---a requirement met by the fact
that types of stellar spectra differ greatly, possibly indicating
a wide variation in age of the stars, although this is
not yet clearly made out in all detail.

(\textit{d}) Our sun is a star, and its corona resembles such
wisps of nebulous light as theory would lead us to expect.

(\textit{e}) The maintenance of solar heat is best explained on
the basis of the sun's continual contraction.

(\textit{f}) The planets revolve round the sun, and the satellites
round the planets, in nearly the same plane (with few exceptions
not difficult to account for).

(\textit{g}) The planets all rotate on their axes (so far as
known), also revolve in their orbits round the sun, in the
same direction.

(\textit{h}) The zone of small planets circling about the sun,
and the triple ring surrounding the planet Saturn, are
eminently suggestive and seemingly permanent illustrations
of a single stage of the interrupted process of world
building in accordance with the nebular hypothesis.
\DPPageSep{484.png}

\textbf{Spiral Nebulæ and the Nebular Hypothesis.}\index{nebulae!spiral}\index{nebular hypothesis}---Keeler\index{Keeler, J.~E.\ (1857--1900), Am.\ ast.} in
1900 by means of photography made the highly important
discovery, not only that the number of nebulæ is greatly in
excess of 100,000, but that fully half of them conform in
figure to the spiral type. As these objects are flat and their
planes lie in all directions in space, the number that are
actually spiral must largely exceed those that appear unmistakably
so. So we find that, next to the star itself, the
spiral nebula is the type of object most abundant in the
heavens. Had La~Place\index{La Place, P. S. de (lä-plass´) (1749--1827), Fr.\ ast.\ and math.} known of the existence of such
nebulæ, he would unquestionably have modified his statement
of the nebular hypothesis to accord with this very
significant fact. In full accord with the principles of
dynamics is the existence of such vast numbers of spiral
nebulæ: the progressive development from a formless
nebula tends toward the flat, circular, revolving disk, and
contraction makes the inner regions revolve more and more
rapidly; thus producing the spiral, or whirlpool, structure.
Therefore the spiral nebula is a fundamental and pronounced
natural form. Thousands of stellar systems, then
(probably also our planetary system), came into being, not
from rings left behind as the nebular disk contracted, but
by condensation into knots of nebulosity, here and there
detached from the whirling nebulous mass, each knot subsequently
contracting into a separate star (or planet). The
figure on page~\pageref{p462} shows this, and numerous other spiral
nebulæ indicate the same process equally clearly. This
simple modification of the nebular hypothesis obviates the
most serious objection to it, viz., the great difficulty in explaining
how rings could condense into planets. So Keeler's
discovery has greatly strengthened the evidence in general
favor of the nebular hypothesis.
\DPPageSep{485.png}

\textbf{Other Universes than Ours.}\index{universe!other universes}---When considering known
stellar distances, we found stars immensely remote from
the solar system in all directions; and everywhere scattered
among myriads remoter still, whose distances we can
see no prospect of ever ascertaining. What is beyond?
Outside the realm of fact, imagination alone can answer.
We cannot think of space except as unlimited. The concept
of infinite space\index{space, infinite} precludes all possibility of a boundary.
But the number of stars visible with our largest
telescopes is far from infinite; for we should greatly overestimate
their number in allowing but ten stars to every
human being alive this moment upon our little planet.
Are, then, the inconceivable vastnesses of space tenanted
with other universes than the one our telescopes unfold?
We are driven to conclude that in all probability they are.
Just as our planetary system is everywhere surrounded by
a roomy, starless void, so doubtless our huge sidereal cluster
rests deep in an outer space everywhere enveloping
illimitably. So remote must be these external galaxies
that unextinguished light from them, although it speeds
eight times round the earth in a single second, cannot
reach us in millions of years. Verily, infinite space transcends
apprehension by finite intelligence. Let us end
with Newton\index{Newton, Sir I. (1642--1727), Eng.\ ast.}, as we began. `Since his day,' wrote one
of England's greatest astronomers in his Cardiff address
(1891), `our knowledge of the phenomena of Nature has
wonderfully increased; but man asks, perhaps more
earnestly now than then, what is the ultimate reality
behind the reality of the perceptions? Are they only the
pebbles of the beach with which we have been playing?
Does not the ocean of ultimate reality and truth lie
beyond?'
\DPPageSep{486.png}
\backmatter
\SetRunningHeads{Index}{Index}
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\cleardoublepage

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\pagenumbering{Alph}

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usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmsy6.pfb&gt;&lt;/usr/share/texmf-texl
ive/fonts/type1/bluesky/cm/cmsy7.pfb&gt;&lt;/usr/share/texmf-texlive/fonts/type1/blue
sky/cm/cmsy8.pfb&gt;&lt;/usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmti10.pfb&gt;&lt;/
usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmti12.pfb&gt;&lt;/usr/share/texmf-tex
live/fonts/type1/bluesky/cm/cmti9.pfb&gt;&lt;/usr/share/texmf-texlive/fonts/type1/blu
esky/cm/cmtt9.pfb&gt;&lt;/usr/share/texmf-texlive/fonts/type1/bluesky/ams/msam10.pfb&gt;
&lt;/usr/share/texmf-texlive/fonts/type1/public/wasy/wasy10.pfb&gt;&lt;/usr/share/texmf-
texlive/fonts/type1/public/gothic/ygoth.pfb&gt;
Output written on 35261-t.pdf (437 pages, 22108683 bytes).
PDF statistics:
 5338 PDF objects out of 6186 (max. 8388607)
 852 named destinations out of 1000 (max. 131072)
 1902 words of extra memory for PDF output out of 10000 (max. 10000000)

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