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Comstock + +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.org + + +Title: A Text-Book of Astronomy + +Author: George C. Comstock + +Release Date: January 3, 2011 [EBook #34834] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK A TEXT-BOOK OF ASTRONOMY *** + + + + +Produced by Chris Curnow, Iris Schimandle, Lindy Walsh and +the Online Distributed Proofreading Team at +http://www.pgdp.net + + + + + + +</pre> + + + + + +<p class="center">TWENTIETH CENTURY TEXT-BOOKS</p> + + +<p class="center">EDITED BY<br /> +A. F. NIGHTINGALE, <span class="smcap">Ph.D.</span>, LL.D.<br /> +FORMERLY SUPERINTENDENT OF HIGH SCHOOLS, CHICAGO +</p> + + +<hr style="width: 65%;" /> + + +<div class="figcenter" style="width: 500px;"><a name="Frontispiece" id="Frontispiece"></a> +<a href="images/i005-full.jpg"><img src="images/i005.jpg" width="500" height="329" alt="A TOTAL SOLAR ECLIPSE. + +After Burckhalter's photographs of the eclipse of May 28, 1900." title="A TOTAL SOLAR ECLIPSE. + +After Burckhalter's photographs of the eclipse of May 28, 1900." /></a> +<span class="caption">A TOTAL SOLAR ECLIPSE.<br /> + +After Burckhalter's photographs of the eclipse of May 28, 1900.</span> +</div> + + + +<hr style="width: 65%;" /> + +<p class="center">TWENTIETH CENTURY TEXT-BOOKS</p> + + + + + +<h1>A TEXT-BOOK OF +ASTRONOMY</h1> + + +<h3>BY</h3> +<h2>GEORGE C. COMSTOCK</h2> + +<p class="center">DIRECTOR OF THE WASHBURN OBSERVATORY AND<br /> +PROFESSOR OF ASTRONOMY IN THE<br /> +UNIVERSITY OF WISCONSIN</p> + + +<div class="figcenter" style="width: 110px;"> +<img src="images/i006.jpg" width="110" height="110" alt="" title="" /> +</div> + + +<p class="center">NEW YORK<br /> +D. APPLETON AND COMPANY<br /> +1903 +</p> + + +<hr style="width: 65%;" /> +<p class="center"><span class="smcap">Copyright</span>, 1901</p> + +<p class="center"><span class="smcap">By</span> D. APPLETON AND COMPANY</p> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum">[Pg v]</span></p> +<h2>PREFACE</h2> + + +<p>The present work is not a compendium of astronomy +or an outline course of popular reading in that science. It +has been prepared as a text-book, and the author has purposely +omitted from it much matter interesting as well as +important to a complete view of the science, and has endeavored +to concentrate attention upon those parts of the +subject that possess special educational value. From this +point of view matter which permits of experimental treatment +with simple apparatus is of peculiar value and is +given a prominence in the text beyond its just due in a +well-balanced exposition of the elements of astronomy, +while topics, such as the results of spectrum analysis, +which depend upon elaborate apparatus, are in the experimental +part of the work accorded much less space than +their intrinsic importance would justify.</p> + +<p>Teacher and student are alike urged to magnify the +observational side of the subject and to strive to obtain in +their work the maximum degree of precision of which their +apparatus is capable. The instruments required are few +and easily obtained. With exception of a watch and a protractor, +all of the apparatus needed may be built by any +one of fair mechanical talent who will follow the illustrations +and descriptions of the text. In order that proper +opportunity for observations may be had, the study should +be pursued during the milder portion of the year, between +April and November in northern latitudes, using clear +<span class="pagenum">[Pg vi]</span> +weather for a direct study of the sky and cloudy days for +book work.</p> + +<p>The illustrations contained in the present work are +worthy of as careful study as is the text, and many of +them are intended as an aid to experimental work and +accurate measurement, e. g., the star maps, the diagrams +of the planetary orbits, pictures of the moon, sun, etc. If +the school possesses a projection lantern, a set of astronomical +slides to be used in connection with it may be +made of great advantage, if the pictures are studied as an +auxiliary to Nature. Mere display and scenic effect are of +little value.</p> + +<p>A brief bibliography of popular literature upon astronomy +may be found at the end of this book, and it will be +well if at least a part of these works can be placed in the +school library and systematically used for supplementary +reading. An added interest may be given to the study if +one or more of the popular periodicals which deal with +astronomy are taken regularly by the school and kept +within easy reach of the students. From time to time +the teacher may well assign topics treated in these periodicals +to be read by individual students and presented +to the class in the form of an essay.</p> + +<p>The author is under obligations to many of his professional +friends who have contributed illustrative matter for +his text, and his thanks are in an especial manner due to +the editors of the Astrophysical Journal, Astronomy and +Astrophysics, and Popular Astronomy for permission to +reproduce here plates which have appeared in those periodicals, +and to Dr. Charles Boynton, who has kindly read +and criticised the proofs.</p> + +<div style="margin-left: 75%;"><p><span class="smcap">George C. Comstock.</span><br /></p></div> + +<div style="margin-left: 2em;"><p><span class="smcap">University of Wisconsin</span>, <i>February, 1901</i>.<span class="pagenum">[Pg vii]</span><br /></p></div> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum">[Pg viii]</span></p> +<h2>CONTENTS</h2> + + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left">CHAPTER</td><td align="right">PAGE</td></tr> +<tr><td align="left"><a href="#CHAPTER_I">I.—<span class="smcap">Different kinds of measurement</span></a></td><td align="right"><a href="#Page_1">1</a></td></tr> +<tr><td align="left"><div class="indent">The measurement of angles and time.</div></td><td></td></tr> +<tr><td align="left"><a href="#CHAPTER_II">II.—<span class="smcap">The stars and their diurnal motion</span></a></td><td align="right"><a href="#Page_10">10</a></td></tr> +<tr><td align="left"><div class="indent">Finding the stars—Their apparent motion—Latitude—Direction of the meridian—Sidereal time—Definitions.</div></td><td></td></tr> +<tr><td align="left"><a href="#CHAPTER_III">III.—<span class="smcap">Fixed and wandering stars</span></a></td><td align="right"><a href="#Page_29">29</a></td></tr> +<tr><td align="left"><div class="indent">Apparent motion of the sun, moon, and planets—Orbits of the planets—How to find the planets.</div></td><td></td></tr> +<tr><td align="left"><a href="#CHAPTER_IV">IV.—<span class="smcap">Celestial mechanics</span></a></td><td align="right"><a href="#Page_46">46</a></td></tr> +<tr><td align="left"><div class="indent">Kepler's laws—Newton's laws of motion—The law of gravitation—Orbital motion—Perturbations—Masses of the planets—Discovery of Neptune—The tides.</div></td><td></td></tr> +<tr><td align="left"><a href="#CHAPTER_V">V.—<span class="smcap">The earth as a planet</span></a></td><td align="right"><a href="#Page_70">70</a></td></tr> +<tr><td align="left"><div class="indent">Size—Mass—Precession—The warming of the earth—The atmosphere—Twilight.</div></td><td></td></tr> +<tr><td align="left"><a href="#CHAPTER_VI">VI.—<span class="smcap">The measurement of time</span></a></td><td align="right"><a href="#Page_86">86</a></td></tr> +<tr><td align="left"><div class="indent">Solar and sidereal time—Longitude—The calendar—Chronology.</div></td><td></td></tr> +<tr><td align="left"><a href="#CHAPTER_VII">VII.—<span class="smcap">Eclipses</span></a></td><td align="right"><a href="#Page_101">101</a></td></tr> +<tr><td align="left"><div class="indent">Their cause and nature—Eclipse limits—Eclipse maps—Recurrence and prediction of eclipses.</div></td><td></td></tr> +<tr><td align="left"><a href="#CHAPTER_VIII">VIII.—<span class="smcap">Instruments and the principles involved in their use</span></a></td><td align="right"><a href="#Page_121">121</a></td></tr> +<tr><td align="left"><div class="indent">The clock—Radiant energy—Mirrors and lenses—The telescope—Camera—Spectroscope—Principles of spectrum analysis.</div></td><td></td></tr> +<tr><td align="left"><a href="#CHAPTER_IX">IX.—<span class="smcap">The moon</span></a></td><td align="right"><a href="#Page_150">150</a></td></tr> +<tr><td align="left"><div class="indent">Numerical data—Phases—Motion—Librations—Lunar topography—Physical condition.</div></td><td></td></tr> +<tr><td align="left"><a href="#CHAPTER_X">X.—<span class="smcap">The sun</span></a></td><td align="right"><a href="#Page_178">178</a></td></tr> +<tr><td align="left"><div class="indent">Numerical data—Chemical nature—Temperature—Visible and invisible parts—Photosphere—Spots—Faculę—Chromosphere—Prominences—Corona—The sun-spot period—The sun's rotation—Mechanical theory of the sun.</div></td><td></td></tr> +<tr><td align="left"><a href="#CHAPTER_XI">XI.—<span class="smcap">The planets</span></a></td><td align="right"><a href="#Page_212">212</a></td></tr> +<tr><td align="left"><div class="indent">Arrangement of the solar system—Bode's law—Physical condition of the planets—Jupiter—Saturn—Uranus and Neptune—Venus—Mercury—Mars—The asteroids.</div></td><td></td></tr> +<tr><td align="left"><a href="#CHAPTER_XII">XII.—<span class="smcap">Comets and meteors</span></a></td><td align="right"><a href="#Page_251">251</a></td></tr> +<tr><td align="left"><div class="indent">Motion, size, and mass of comets—Meteors—Their number and distribution—Meteor showers—Relation of comets and meteors—Periodic comets—Comet families and groups—Comet tails—Physical nature of comets—Collisions.</div></td><td></td></tr> +<tr><td align="left"><a href="#CHAPTER_XIII">XIII.—<span class="smcap">The fixed stars</span></a></td><td align="right"><a href="#Page_291">291</a></td></tr> +<tr><td align="left"><div class="indent">Number of the stars—Brightness—Distance—Proper motion—Motion in line of sight—Double stars—Variable stars—New stars.</div></td><td></td></tr> +<tr><td align="left"><a href="#CHAPTER_XIV">XIV.—<span class="smcap">Stars and nebulę</span></a></td><td align="right"><a href="#Page_330">330</a></td></tr> +<tr><td align="left"><div class="indent">Stellar colors and spectra—Classes of stars—Clusters—Nebulę—Their spectra and physical condition—The Milky Way—Construction of the heavens—Extent of the stellar system.</div></td><td></td></tr> +<tr><td align="left"><a href="#CHAPTER_XV">XV.—<span class="smcap">Growth and decay</span></a></td><td align="right"><a href="#Page_358">358</a></td></tr> +<tr><td align="left"><div class="indent">Logical bases and limitations—Development of the sun—The nebular hypothesis—Tidal friction—Roche's limit—Development of the moon—Development of stars and nebulę—The future.</div></td><td></td></tr> +<tr><td align="left"><a href="#APPENDIX"><span class="smcap">Appendix</span></a></td><td align="right"><a href="#Page_383">383</a></td></tr> +<tr><td align="left"><a href="#INDEX"><span class="smcap">Index</span></a></td><td align="right"><a href="#Page_387">387</a></td></tr> +</table></div> + + +<hr style="width: 65%;" /> +<p><span class="pagenum">[Pg ix]</span></p> +<h2>LIST OF LITHOGRAPHIC PLATES</h2> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left"></td><td align="right">FACING PAGE</td></tr> +<tr><td align="left"><a href="#PLATE_I">I.—Northern Constellations</a></td><td align="right"><a href="#Page_124">124</a></td></tr> +<tr><td align="left"><a href="#PLATE_II">II.—Equatorial Constellations</a></td><td align="right"><a href="#Page_190">190</a></td></tr> +<tr><td align="left"><a href="#PLATE_III">III.—Map of Mars</a></td><td align="right"><a href="#Page_246">246</a></td></tr> +<tr><td align="left"><a href="#PLATE_IV">IV.—The Pleiades</a></td><td align="right"><a href="#Page_344">344</a></td></tr> +<tr><td align="left"><a href="#PROTRACTOR">Protractor</a></td><td align="right"><a href="#PROTRACTOR"><i>In pocket at back of book</i></a></td></tr> +</table></div> + + + +<hr style="width: 65%;" /> +<h2>LIST OF FULL-PAGE ILLUSTRATIONS</h2> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left"></td><td align="right">FACING PAGE</td></tr> +<tr><td align="left"><a href="#Frontispiece">A Total Solar Eclipse</a></td><td align="right"><a href="#Frontispiece"><i>Frontispiece</i></a></td></tr> +<tr><td align="left"><a href="#THE_HARVARD_COLLEGE_OBSERVATORY">The Harvard College Observatory, Cambridge, Mass.</a></td><td align="right"><a href="#Page_24">24</a></td></tr> +<tr><td align="left"><a href="#ISAAC_NEWTON">Isaac Newton</a></td><td align="right"><a href="#Page_46">46</a></td></tr> +<tr><td align="left"><a href="#GALILEO_GALILEI">Galileo Galilei</a></td><td align="right"><a href="#Page_52">52</a></td></tr> +<tr><td align="left"><a href="#LICK_OBSERVATORY">The Lick Observatory, Mount Hamilton, Cal.</a></td><td align="right"><a href="#Page_60">60</a></td></tr> +<tr><td align="left"><a href="#YERKES_OBSERVATORY">The Yerkes Observatory, Williams Bay, Wis.</a></td><td align="right"><a href="#Page_100">100</a></td></tr> +<tr><td align="left"><a href="#THE_MOON">The Moon, one day after First Quarter</a></td><td align="right"><a href="#Page_150">150</a></td></tr> +<tr><td align="left"><a href="#WILLIAM_HERSCHEL">William Herschel</a></td><td align="right"><a href="#Page_234">234</a></td></tr> +<tr><td align="left"><a href="#LAPLACE">Pierre Simon Laplace</a></td><td align="right"><a href="#Page_364">364</a></td></tr> +</table></div> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_1" id="Page_1">[Pg 1]</a></span></p> +<h1>ASTRONOMY</h1> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_I" id="CHAPTER_I"></a>CHAPTER I</h2> + +<h3>DIFFERENT KINDS OF MEASUREMENT</h3> + + +<p><a name="S_1" id="S_1"></a>1. <b>Accurate measurement.</b>—Accurate measurement is the +foundation of exact science, and at the very beginning of +his study in astronomy the student should learn something +of the astronomer's kind of measurement. He should practice +measuring the stars with all possible care, and should +seek to attain the most accurate results of which his instruments +and apparatus are capable. The ordinary affairs of +life furnish abundant illustration of some of these measurements, +such as finding the length of a board in inches or +the weight of a load of coal in pounds and measurements +of both length and weight are of importance in astronomy, +but of far greater astronomical importance than these are +the measurement of angles and the measurement of time. +A kitchen clock or a cheap watch is usually thought of as +a machine to tell the "time of day," but it may be used to +time a horse or a bicycler upon a race course, and then it +becomes an instrument to measure the amount of time +required for covering the length of the course. Astronomers +use a clock in both of these ways—to tell the time at +which something happens or is done, and to measure the +amount of time required for something; and in using a +clock for either purpose the student should learn to take +the time from it to the nearest second or better, if it has a<span class="pagenum"><a name="Page_2" id="Page_2">[Pg 2]</a></span> +seconds hand, or to a small fraction of a minute, by estimating +the position of the minute hand between the minute +marks on the dial. Estimate the fraction in tenths of +a minute, not in halves or quarters.</p> + +<p><span class="smcap">Exercise 1.</span>—If several watches are available, let one +person tap sharply upon a desk with a pencil and let each +of the others note the time by the minute hand to the +nearest tenth of a minute and record the observations as +follows:</p> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left">2h. 44.5m.</td><td align="left">First tap.</td><td align="left">2h. 46.4m.</td><td align="left">1.9m.</td></tr> +<tr><td align="left">2h. 44.9m.</td><td align="left">Second tap.</td><td align="left">2h. 46.7m.</td><td align="left">1.8m.</td></tr> +<tr><td align="left">2h. 46.6m.</td><td align="left">Third tap.</td><td align="left">2h. 48.6m.</td><td align="left">2.0m.</td></tr> +</table></div> + +<p>The letters h and m are used as abbreviations for hour and +minute. The first and second columns of the table are the +record made by one student, and second and third the record +made by another. After all the observations have been +made and recorded they should be brought together and +compared by taking the differences between the times recorded +for each tap, as is shown in the last column. This +difference shows how much faster one watch is than the +other, and the agreement or disagreement of these differences +shows the degree of accuracy of the observations. +Keep up this practice until tenths of a minute can be estimated +with fair precision.</p> + +<p><a name="S_2" id="S_2"></a>2. <b>Angles and their use.</b>—An angle is the amount of +opening or difference of direction between two lines that +cross each other. At twelve o'clock the hour and minute +hand of a watch point in the same direction and the angle +between them is zero. At one o'clock the minute hand is +again at XII, but the hour hand has moved to I, one +twelfth part of the circumference of the dial, and the angle +between the hands is one twelfth of a circumference. It is +customary to imagine the circumference of a dial to be cut +up into 360 equal parts—i. e., each minute space of an ordinary +dial to be subdivided into six equal parts, each of<span class="pagenum"><a name="Page_3" id="Page_3">[Pg 3]</a></span> +which is called a degree, and the measurement of an angle +consists in finding how many of these degrees are included +in the opening between its sides. At one o'clock the angle +between the hands of a watch is thirty degrees, which is +usually written 30°, at three o'clock it is 90°, at six o'clock +180°, etc.</p> + +<p>A watch may be used to measure angles. How? But +a more convenient instrument is the protractor, which is +shown in <a href="#Fig_1">Fig. 1</a>, applied to the angle <i>A B C</i> and showing +that <i>A B C</i> = 85° as nearly +as the protractor scale +can be read.</p> + +<p>The student should +have and use a protractor, +such as is furnished +with this book, +for the numerous exercises +which are to follow.</p> + +<div class="figright" style="width: 300px;"><a name="Fig_1" id="Fig_1"></a> +<img src="images/i016.png" width="300" height="223" alt="Fig. 1.—A protractor." title="Fig. 1.—A protractor." /> +<span class="caption"><span class="smcap">Fig. 1.</span>—A protractor.</span> +</div> + +<p><a name="Exercise_2" id="Exercise_2"></a><span class="smcap">Exercise 2.</span>—Draw +neatly a triangle with +sides about 100 millimeters long, measure each of its angles +and take their sum. No matter what may be the +shape of the triangle, this sum should be very nearly 180°—exactly +180° if the work were perfect—but perfection +can seldom be attained and one of the first lessons to +be learned in any science which deals with measurement +is, that however careful we may be in our work some +minute error will cling to it and our results can be only +approximately correct. This, however, should not be +taken as an excuse for careless work, but rather as a stimulus +to extra effort in order that the unavoidable errors +may be made as small as possible. In the present case +the measured angles may be improved a little by adding +(algebraically) to each of them one third of the amount by +which their sum falls short of 180°, as in the following +example:<span class="pagenum"><a name="Page_4" id="Page_4">[Pg 4]</a></span></p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><th align="left"></th><th align="center">Measured angles.</th><th align="center">Correction</th><th align="center">Corrected angles.</th></tr> +<tr><td align="left"></td><td align="right">° </td><td align="right">° </td><td align="right">° </td></tr> +<tr><td align="left">A</td><td align="right">73.4</td><td align="right">+ 0.1</td><td align="right">73.5</td></tr> +<tr><td align="left">B</td><td align="right">49.3</td><td align="right">+ 0.1</td><td align="right">49.4</td></tr> +<tr><td align="left">C</td><td align="right">57.0</td><td align="right">+ 0.1</td><td align="right">57.1</td></tr> +<tr><td align="left">Sum</td><td align="right"><span class="bt">179.7</span></td><td> </td><td align="right"><span class="bt">180.0</span></td></tr> +<tr><td align="left">Defect</td><td align="right">+ 0.3</td><td></td><td></td></tr> +</table></div> + +<p>This process is in very common use among astronomers, +and is called "adjusting" the observations.</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_2" id="Fig_2"></a> +<img src="images/i017.png" width="350" height="208" alt="Fig. 2.—Triangulation." title="Fig. 2.—Triangulation." /> +<span class="caption"><span class="smcap">Fig. 2.</span>—Triangulation.</span> +</div> + +<p><a name="S_3" id="S_3"></a>3. <b>Triangles.</b>—The instruments used by astronomers for +the measurement of angles are usually provided with a +telescope, which may be pointed at different objects, and +with a scale, like that of the protractor, to measure the +angle through which the telescope is turned in passing +from one object to another. In this way it is possible to +measure the angle between lines drawn from the instrument +to two distant objects, +such as two church +steeples or the sun and +moon, and this is usually +called the angle between +the objects. By measuring +angles in this way +it is possible to determine +the distance to an +inaccessible point, as shown in <a href="#Fig_2">Fig. 2</a>. A surveyor at <i>A</i> +desires to know the distance to <i>C</i>, on the opposite side of a +river which he can not cross. He measures with a tape line +along his own side of the stream the distance <i>A B</i> = 100 +yards and then, with a suitable instrument, measures the +angle at <i>A</i> between the points <i>C</i> and <i>B</i>, and the angle at +<i>B</i> between <i>C</i> and <i>A</i>, finding <i>B A C</i> = 73.4°, <i>A B C</i> = 49.3°. +To determine the distance <i>A C</i> he draws upon paper a line +100 millimeters long, and marks the ends <i>a</i> and <i>b</i>; with a +protractor he constructs at <i>a</i> the angle <i>b a c</i> = 73.4°, and at +<i>b</i> the angle <i>a b c</i> = 49.3°, and marks by <i>c</i> the point where<span class="pagenum"><a name="Page_5" id="Page_5">[Pg 5]</a></span> +the two lines thus drawn meet. With the millimeter scale +he now measures the distance <i>a c</i> = 90.2 millimeters, which +determines the distance <i>A C</i> across the river to be 90.2 +yards, since the triangle on paper has been made similar +to the one across the river, and millimeters on the one +correspond to yards on the other. What is the proposition +of geometry upon which this depends? The measured +distance <i>A B</i> in the surveyor's problem is called a base line.</p> + +<p><a name="Exercise_3" id="Exercise_3"></a><span class="smcap">Exercise 3.</span>—With a foot rule and a protractor measure +a base line and the angles necessary to determine the +length of the schoolroom. After the length has been thus +found, measure it directly with the foot rule and compare +the measured length with the one found from the angles. +If any part of the work has been carelessly done, the student +need not expect the results to agree.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_3" id="Fig_3"></a> +<img src="images/i018.png" width="500" height="230" alt="Fig. 3.—Finding the moon's distance from the earth." title="Fig. 3.—Finding the moon's distance from the earth." /> +<span class="caption"><span class="smcap">Fig. 3.</span>—Finding the moon's distance from the earth.</span> +</div> + +<p>In the same manner, by sighting at the moon from +widely different parts of the earth, as in <a href="#Fig_3">Fig. 3</a>, the moon's +distance from us is found to be about a quarter of a million +miles. What is the base line in this case?</p> + +<p><a name="S_4" id="S_4"></a>4. <b>The horizon</b>—<b>altitudes.</b>—In their observations astronomers +and sailors make much use of the <i>plane of the horizon</i>, +and practically any flat and level surface, such as that +of a smooth pond, may be regarded as a part of this plane +and used as such. A very common observation relating to<span class="pagenum"><a name="Page_6" id="Page_6">[Pg 6]</a></span> +the plane of the horizon is called "taking the sun's altitude," +and consists in measuring the angle between the +sun's rays and the plane of the horizon upon which they +fall. This angle between a line and a plane appears slightly +different from the angle between two lines, but is really the +same thing, since it means the angle between the sun's rays +and a line drawn in the plane of the horizon toward the +point directly under the sun. Compare this with the definition +given in the geographies, "The latitude of a point +on the earth's surface is its angular distance north or south +of the equator," and note that the latitude is the angle +between the plane of the equator and a line drawn from +the earth's center to the given point on its surface.</p> + +<p>A convenient method of obtaining a part of the plane +of the horizon for use in observation is as follows: Place +a slate or a pane of glass upon a table in the sunshine. +Slightly moisten its whole surface and then pour a little +more water upon it near the center. If the water runs +toward one side, thrust the edge of a thin wooden wedge +under this side and block it up until the water shows no +tendency to run one way rather than another; it is then +level and a part of the plane of the horizon. Get several +wedges ready before commencing the experiment. After +they have been properly placed, drive a pin or tack behind +each one so that it may not slip.</p> + +<p><a name="S_5" id="S_5"></a>5. <b>Taking the sun's altitude.</b> <a name="Exercise_4" id="Exercise_4"></a><span class="smcap">Exercise 4.</span>—Prepare a +piece of board 20 centimeters, or more, square, planed +smooth on one face and one edge. Drive a pin perpendicularly +into the face of the board, near the middle of the +planed edge. Set the board on edge on the horizon plane +and turn it edgewise toward the sun so that a shadow of +the pin is cast on the plane. Stick another pin into the +board, near its upper edge, so that its shadow shall fall +exactly upon the shadow of the first pin, and with a watch +or clock observe the time at which the two shadows coincide. +Without lifting the board from the plane, turn it<span class="pagenum"><a name="Page_7" id="Page_7">[Pg 7]</a></span> +around so that the opposite edge is directed toward the sun +and set a third pin just as the second one was placed, and +again take the time. Remove the pins and draw fine pencil +lines, connecting the holes, as shown in <a href="#Fig_4">Fig. 4</a>, and with +the protractor measure the angle +thus marked. The student +who has studied elementary geometry +should be able to demonstrate +that at the mean of the +two recorded times the sun's altitude +was equal to one half of the +angle measured in the figure.</p> + +<div class="figright" style="width: 300px;"><a name="Fig_4" id="Fig_4"></a> +<img src="images/i020.png" width="300" height="203" alt="Fig. 4.—Taking the sun's +altitude." title="Fig. 4.—Taking the sun's +altitude." /> +<span class="caption"><span class="smcap">Fig. 4.</span>—Taking the sun's +altitude.</span> +</div> + +<p>When the board is turned +edgewise toward the sun so that its shadow is as thin as +possible, rule a pencil line alongside it on the horizon plane. +The angle which this line makes with a line pointing due +south is called the sun's <i>azimuth</i>. When the sun is south, +its azimuth is zero; when west, it is 90°; when east, +270°, etc.</p> + +<p><span class="smcap">Exercise 5.</span>—Let a number of different students take +the sun's altitude during both the morning and afternoon +session and note the time of each observation, to the nearest +minute. Verify the setting of the plane of the horizon +from time to time, to make sure that no change has occurred +in it.</p> + +<p><a name="S_6" id="S_6"></a>6. <b>Graphical representations.</b>—Make a graph (drawing) +of all the observations, similar to <a href="#Fig_5">Fig. 5</a>, and find by bisecting +a set of chords <i>g</i> to <i>g</i>, <i>e</i> to <i>e</i>, <i>d</i> to <i>d</i>, drawn parallel to +<i>B B</i>, the time at which the sun's altitude was greatest. In +<a href="#Fig_5">Fig. 5</a> we see from the intersection of <i>M M</i> with <i>B B</i> that +this time was 11h. 50m.</p> + +<p>The method of graphs which is here introduced is of +great importance in physical science, and the student +should carefully observe in <a href="#Fig_5">Fig. 5</a> that the line <i>B B</i> is a +scale of times, which may be made long or short, provided +only the intervals between consecutive hours 9 to 10, 10 to<span class="pagenum"><a name="Page_8" id="Page_8">[Pg 8]</a></span> +11, 11 to 12, etc., are equal. The distance of each little +circle from <i>B B</i> is taken proportional to the sun's altitude, +and may be upon any desired scale—e. g., a millimeter to +a degree—provided the same scale is used for all observations. +Each circle is placed accurately over that part of +the base line which corresponds to the time at which the +altitude was taken. Square ruled paper is very convenient, +although not necessary, for such diagrams. It is especially +to be noted that from the few observations which are represented +in the figure a smooth curve has been drawn +through the circles which represent the sun's altitude, and +this curve shows the altitude of the sun at every moment +between 9 <span class="smcap">A. M.</span> and 3 <span class="smcap">P. M.</span> In <a href="#Fig_5">Fig. 5</a> the sun's altitude at +noon was 57°. What was it at half past two?</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_5" id="Fig_5"></a> +<img src="images/i021.png" width="500" height="211" alt="Fig. 5.—A graph of the sun's altitude." title="Fig. 5.—A graph of the sun's altitude." /> +<span class="caption"><span class="smcap">Fig. 5.</span>—A graph of the sun's altitude.</span> +</div> + +<p><a name="S_7" id="S_7"></a>7. <b>Diameter of a distant object.</b>—By sighting over a protractor, +measure the angle between imaginary lines drawn +from it to the opposite sides of a window. Carry the protractor +farther away from the window and repeat the experiment, +to see how much the angle changes. The angle +thus measured is called "the angle subtended" by the window +at the place where the measurement was made. If +this place was squarely in front of the window we may +draw upon paper an angle equal to the measured one and +lay off from the vertex along its sides a distance proportional +to the distance of the window—e. g., a millimeter for<span class="pagenum"><a name="Page_9" id="Page_9">[Pg 9]</a></span> +each centimeter of real distance. If a cross line be now +drawn connecting the points thus found, its length will be +proportional to the width of the window, and the width +may be read off to scale, a centimeter for every millimeter +in the length of the cross line.</p> + +<p>The astronomer who measures with an appropriate instrument +the angle subtended by the moon may in an +entirely similar manner find the moon's diameter and has, +in fact, found it to be 2,163 miles. Can the same method +be used to find the diameter of the sun? A planet? The +earth?</p> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_10" id="Page_10">[Pg 10]</a></span></p> +<h2><a name="CHAPTER_II" id="CHAPTER_II"></a>CHAPTER II</h2> + +<h3>THE STARS AND THEIR DIURNAL MOTION</h3> + + +<p><a name="S_8" id="S_8"></a>8. <b>The stars.</b>—From the very beginning of his study in +astronomy, and as frequently as possible, the student should +practice watching the stars by night, to become acquainted +with the constellations and their movements. As an introduction +to this study he may face toward the north, and +compare the stars which he sees in that part of the sky with +the map of the northern heavens, given on <a href="#PLATE_I">Plate I</a>, opposite +<a href="#Page_124">page 124</a>. Turn the map around, upside down if +necessary, until the stars upon it match the brighter ones +in the sky. Note how the stars are grouped in such conspicuous +constellations as the Big Dipper (Ursa Major), the +Little Dipper (Ursa Minor), and Cassiopeia. These three +constellations should be learned so that they can be recognized +at any time.</p> + +<p><i>The names of the stars.</i>—Facing the star map is a key +which contains the names of the more important constellations +and the names of the brighter stars in their constellations. +These names are for the most part a Greek letter +prefixed to the genitive case of the Latin name of the constellation. +(See the Greek alphabet printed at the end of +the book.)</p> + +<p><a name="S_9" id="S_9"></a>9. <b>Magnitudes of the stars.</b>—Nearly nineteen centuries +ago St. Paul noted that "one star differeth from another +star in glory," and no more apt words can be found to mark +the difference of brightness which the stars present. Even +prior to St. Paul's day the ancient Greek astronomers had +divided the stars in respect of brightness into six groups,<span class="pagenum"><a name="Page_11" id="Page_11">[Pg 11]</a></span> +which the modern astronomers still use, calling each group +a <i>magnitude</i>. Thus a few of the brightest stars are said to +be of the first magnitude, the great mass of faint ones +which are just visible to the unaided eye are said to be of +the sixth magnitude, and intermediate degrees of brilliancy +are represented by the intermediate magnitudes, second, +third, fourth, and fifth. The student must not be misled +by the word magnitude. It has no reference to the size of +the stars, but only to their brightness, and on the star maps +of this book the larger and smaller circles by which the +stars are represented indicate only the brightness of the +stars according to the system of magnitudes. Following +the indications of these maps, the student should, in learning +the principal stars and constellations, learn also to +recognize how bright is a star of the second, fourth, or +other magnitude.</p> + +<p><a name="S_10" id="S_10"></a>10. <b>Observing the stars.</b>—Find on the map and in the +sky the stars α Ursę Minoris, α Ursę Majoris, β Ursę Majoris. +What geometrical figure will fit on to these stars? +In addition to its regular name, α Ursę Minoris is frequently +called by the special name Polaris, or the pole star. +Why are the other two stars called "the Pointers"? What +letter of the alphabet do the five bright stars in Cassiopeia +suggest?</p> + +<p><a name="Exercise_6" id="Exercise_6"></a><span class="smcap">Exercise 6.</span>—Stand in such a position that Polaris is +just hidden behind the corner of a building or some other +vertical line, and mark upon the key map as accurately as +possible the position of this line with respect to the other +stars, showing which stars are to the right and which are +to the left of it. Record the time (date, hour, and minute) +at which this observation was made. An hour or two later +repeat the observation at the same place, draw the line and +note the time, and you will find that the line last drawn +upon the map does not agree with the first one. The stars +have changed their positions, and with respect to the vertical +line the Pointers are now in a different direction from<span class="pagenum"><a name="Page_12" id="Page_12">[Pg 12]</a></span> +Polaris. Measure with a protractor the angle between the +two lines drawn in the map, and use this angle and the +recorded times of the observation to find how many degrees +per hour this direction is changing. It should be about 15° +per hour. If the observation were repeated 12 hours after +the first recorded time, what would be the position of the +vertical line among the stars? What would it be 24 hours +later? A week later? Repeat the observation on the next +clear night, and allowing for the number of whole revolutions +made by the stars between the two dates, again determine +from the time interval a more accurate value of the +rate at which the stars move.</p> + +<p>The motion of the stars which the student has here detected +is called their "diurnal" motion. What is the significance +of the word diurnal?</p> + +<p>In the preceding paragraph there is introduced a method +of great importance in astronomical practice—i. e., determining +something—in this case the rate per hour, from observations +separated by a long interval of time, in order to get +a more accurate value than could be found from a short +interval. Why is it more accurate? To determine the +rate at which the planet Mars rotates about its axis, astronomers +use observations separated by an interval of more +than 200 years, during which the planet made more than +75,000 revolutions upon its axis. If we were to write out +in algebraic form an equation for determining the length +of one revolution of Mars about its axis, the large number, +75,000, would appear in the equation as a divisor, and in +the final result would greatly reduce whatever errors existed +in the observations employed.</p> + +<p>Repeat <a href="#Exercise_6">Exercise 6</a> night after night, and note whether +the stars come back to the same position at the same hour +and minute every night.</p> + + +<div class="figcenter" style="width: 650px"> + +<div class="figleft" style="width: 300px;"><a name="Fig_6" id="Fig_6"></a> +<img src="images/i026a.jpg" width="300" height="580" alt="Fig. 6. +The plumb-line apparatus." title="Fig. 6. +The plumb-line apparatus." /> +<span class="caption"><span class="smcap">Fig. 6.</span></span> +</div> + +<div class="figright" style="width: 300px;"><a name="Fig_7" id="Fig_7"></a> +<img src="images/i026b.jpg" width="300" height="578" alt="Fig. 7. +The plumb-line apparatus." title="Fig. 7. +The plumb-line apparatus." /> +<span class="caption"><span class="smcap">Fig. 7.</span></span> +</div> +<div style="clear: both;"></div> +<span class="caption">The plumb-line apparatus.</span> +</div> + +<p><a name="S_11" id="S_11"></a>11. <b>The plumb-line apparatus.</b>—This experiment, and +many others, may be conveniently and accurately made +with no other apparatus than a plumb line, and a device<span class="pagenum"><a name="Page_13" id="Page_13">[Pg 13]</a></span> +for sighting past it. In Figs. <a href="#Fig_6">6</a> and <a href="#Fig_7">7</a> there is shown a +simple form of such apparatus, consisting essentially of a +board which rests in a horizontal position upon the points +of three screws that pass through it. This board carries +a small box, to one side of which is nailed in vertical position +another board 5 or 6 feet long to carry the plumb line. +This consists of a wire or fish line with any heavy weight—e. g., +a brick or flatiron—tied to its lower end and immersed +in a vessel of water placed inside the box, so as to check +any swinging motion of the weight. In the cover of the +box is a small hole through which the wire passes, and by +turning the screws in the baseboard the apparatus may be +readily leveled, so that the wire shall swing freely in the +center of the hole without touching the cover of the box.<span class="pagenum"><a name="Page_14" id="Page_14">[Pg 14]</a></span> +Guy wires, shown in the figure, are applied so as to stiffen +the whole apparatus. A board with a screw eye at each +end may be pivoted to the upright, as in <a href="#Fig_6">Fig. 6</a>, for measuring +altitudes; or to the box, as in <a href="#Fig_7">Fig. 7</a>, for observing the +time at which a star in its diurnal motion passes through +the plane determined by the plumb line and the center of +the screw eye through which the observer looks.</p> + +<p>The whole apparatus may be constructed by any person +of ordinary mechanical skill at a very small cost, and it or +something equivalent should be provided for every class beginning +observational astronomy. To use the apparatus for +the experiment of <a href="#S_10">§ 10</a>, it should be leveled, and the board +with the screw eyes, attached as in <a href="#Fig_7">Fig. 7</a>, should be turned +until the observer, looking through the screw eye, sees +Polaris exactly behind the wire. Use a bicycle lamp to +illumine the wire by night. The apparatus is now adjusted, +and the observer has only to wait for the stars which he +desires to observe, and to note by his watch the time at +which they pass behind the wire. It will be seen that the +wire takes the place of the vertical edge of the building, +and that the board with the screw eyes is introduced solely +to keep the observer in the right place relative to the +wire.</p> + +<p><a name="S_12" id="S_12"></a>12. <b>A sidereal clock.</b>—Clocks are sometimes so made and +regulated that they show always the same hour and minute +when the stars come back to the same place, and such a +timepiece is called a sidereal clock—i. e., a star-time clock. +Would such a clock gain or lose in comparison with an ordinary +watch? Could an ordinary watch be turned into a +sidereal watch by moving the regulator?</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_8" id="Fig_8"></a> +<a href="images/i028-full.jpg"><img src="images/i028.jpg" width="500" height="502" alt="Fig. 8.—Photographing the circumpolar stars.—Barnard." title="Fig. 8.—Photographing the circumpolar stars.—Barnard." /></a> +<span class="caption"><span class="smcap">Fig. 8.</span>—Photographing the circumpolar stars.—<span class="smcap">Barnard.</span></span> +</div> + +<p><a name="S_13" id="S_13"></a>13. <b>Photographing the stars.</b>—<a name="Exercise_7" id="Exercise_7"></a><span class="smcap">Exercise 7.</span>—For any student +who uses a camera. Upon some clear and moonless +night point the camera, properly focused, at Polaris, and +expose a plate for three or four hours. Upon developing +the plate you should find a series of circular trails such as +are shown in <a href="#Fig_8">Fig. 8</a>, only longer. Each one of these is produced<span class="pagenum"><a name="Page_15" id="Page_15">[Pg 15]</a></span> +by a star moving slowly over the plate, in consequence +of its changing position in the sky. The center +indicated by these curved trails is called the pole of the +heavens. It is that part of the sky toward which is pointed +the axis about which the earth rotates, and the motion of +the stars around the center is only an apparent motion due +to the rotation of the earth which daily carries the observer +and his camera around this axis while the stars stand still, +just as trees and fences and telegraph poles stand still, +although to the passenger upon a railway train they appear +to be in rapid motion. So far as simple observations are +concerned, there is no method by which the pupil can tell +for himself that the motion of the stars is an apparent +rather than a real one, and, following the custom of astronomers, +we shall habitually speak as if it were a real movement +of the stars. How long was the plate exposed in +photographing <a href="#Fig_8">Fig. 8</a>?<span class="pagenum"><a name="Page_16" id="Page_16">[Pg 16]</a></span></p> + +<p><a name="S_14" id="S_14"></a>14. <b>Finding the stars.</b>—On <a href="#PLATE_I">Plate I</a>, opposite <a href="#Page_124">page 124</a>, +the pole of the heavens is at the center of the map, near +Polaris, and the heavy trail near the center of <a href="#Fig_8">Fig. 8</a> is +made by Polaris. See if you can identify from the map +any of the stars whose trails show in the photograph. The +brighter the star the bolder and heavier its trail.</p> + +<p>Find from the map and locate in the sky the two bright +stars Capella and Vega, which are on opposite sides of +Polaris and nearly equidistant from it. Do these stars +share in the motion around the pole? Are they visible on +every clear night, and all night?</p> + +<p>Observe other bright stars farther from Polaris than +are Vega and Capella and note their movement. Do they +move like the sun and moon? Do they rise and set?</p> + +<p>In what part of the sky do the stars move most rapidly, +near the pole or far from it?</p> + +<p>How long does it take the fastest moving stars to make +the circuit of the sky and come back to the same place? +How long does it take the slow stars?</p> + +<p><a name="S_15" id="S_15"></a>15. <b>Rising and setting of the stars.</b>—A study of the sky +along the lines indicated in these questions will show that +there is a considerable part of it surrounding the pole +whose stars are visible on every clear night. The same +star is sometimes high in the sky, sometimes low, sometimes +to the east of the pole and at other times west of it, +but is always above the horizon. Such stars are said to +be circumpolar. A little farther from the pole each star, +when at the lowest point of its circular path, dips for a +time below the horizon and is lost to view, and the farther +it is away from the pole the longer does it remain invisible, +until, in the case of stars 90° away from the pole, we find +them hidden below the horizon for twelve hours out of +every twenty-four (see <a href="#Fig_9">Fig. 9</a>). The sun is such a star, +and in its rising and setting acts precisely as does every +other star at a similar distance from the pole—only, as we +shall find later, each star keeps always at (nearly) the same<span class="pagenum"><a name="Page_17" id="Page_17">[Pg 17]</a></span> +distance from the pole, while the sun in the course of a +year changes its distance from the pole very greatly, and +thus changes the amount of time it spends above and below +the horizon, producing in this way the long days of +summer and the short ones of winter.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_9" id="Fig_9"></a> +<a href="images/i030-full.jpg"><img src="images/i030.jpg" width="500" height="472" alt="Fig. 9.—Diurnal motion of the northern constellations." title="Fig. 9.—Diurnal motion of the northern constellations." /></a> +<span class="caption"><span class="smcap">Fig. 9.</span>—Diurnal motion of the northern constellations.</span> +</div> + +<p>How much time do stars which are more than 90° from +the pole spend above the horizon?</p> + +<p>We say in common speech that the sun rises in the +east, but this is strictly true only at the time when it is 90° +distant from the pole—i. e., in March and September. At +other seasons it rises north or south of east according as +its distance from the pole is less or greater than 90°, and +the same is true for the stars.<span class="pagenum"><a name="Page_18" id="Page_18">[Pg 18]</a></span></p> + +<p><a name="S_16" id="S_16"></a>16. <b>The geography of the sky.</b>—Find from a map the +latitude and longitude of your schoolhouse. Find on the +map the place whose latitude is 39° and longitude 77° west +of the meridian of Greenwich. Is there any other place in +the world which has the same latitude and longitude as +your schoolhouse?</p> + +<p>The places of the stars in the sky are located in exactly +the manner which is illustrated by these geographical +questions, only different names are used. Instead of latitude +the astronomer says <i>declination</i>, in place of longitude +he says <i>right ascension</i>, in place of meridian he says <i>hour +circle</i>, but he means by these new names the same ideas +that the geographer expresses by the old ones.</p> + +<p>Imagine the earth swollen up until it fills the whole +sky; the earth's equator would meet the sky along a line +(a great circle) everywhere 90° distant from the pole, and +this line is called the <i>celestial equator</i>. Trace its position +along the middle of the map opposite <a href="#Page_190">page 190</a> and +notice near what stars it runs. Every meridian of the +swollen earth would touch the sky along an hour circle—i. e., +a great circle passing through the pole and therefore +perpendicular to the equator. Note that in the map one of +these hour circles is marked 0. It plays the same part in +measuring right ascensions as does the meridian of Greenwich +in measuring longitudes; it is the beginning, from +which they are reckoned. Note also, at the extreme left +end of the map, the four bright stars in the form of a +square, one side of which is parallel and close to the hour +circle, which is marked 0. This is familiarly called the +Great Square in Pegasus, and may be found high up in the +southern sky whenever the Big Dipper lies below the pole. +Why can it not be seen when Ursa Major is above the +pole?</p> + +<p>Astronomers use the right ascensions of the stars not +only to tell in what part of the sky the star is placed, but +also in time reckonings, to regulate their sidereal clocks, and<span class="pagenum"><a name="Page_19" id="Page_19">[Pg 19]</a></span> +with regard to this use they find it convenient to express +right ascension not in degrees but in hours, 24 of which +fill up the circuit of the sky and each of which is equal to +15° of arc, 24 × 15 = 360. The right ascension of Capella +is 5h. 9m. = 77.2°, but the student should accustom himself +to using it in hours and minutes as given and not to +change it into degrees. He should also note that some +stars lie on the side of the celestial equator toward Polaris, +and others are on the opposite side, so that the astronomer +has to distinguish between north declinations and south +declinations, just as the geographer distinguishes between +north latitudes and south latitudes. This is done by the +use of the + and - signs, a + denoting that the star lies +north of the celestial equator, i. e., toward Polaris.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_10" id="Fig_10"></a> +<a href="images/i032-full.jpg"><img src="images/i032.jpg" width="500" height="432" alt="Fig. 10.—From a photograph of the Pleiades." title="Fig. 10.—From a photograph of the Pleiades." /></a> +<span class="caption"><span class="smcap">Fig. 10.</span>—From a photograph of the Pleiades.</span> +</div> + +<p>Find on <a href="#PLATE_II">Plate II</a>, opposite <a href="#Page_190">page 190</a>, the Pleiades<span class="pagenum"><a name="Page_20" id="Page_20">[Pg 20]</a></span> +(Plēadēs), R. A. = 3h. 42m., Dec. = +23.8°. Why do +they not show on <a href="#PLATE_I">Plate I</a>, opposite <a href="#Page_124">page 124</a>? In what +direction are they from Polaris? This is one of the +finest star clusters in the sky, but it needs a telescope to +bring out its richness. See how many stars you can count +in it with the naked eye, and afterward examine it with +an opera glass. Compare what you see with <a href="#Fig_10">Fig. 10</a>. Find +Antares, R. A. = 16h. 23m. Dec. = -26.2°. How far is +it, in degrees, from the pole? Is it visible in your sky? +If so, what is its color?</p> + +<p>Find the R. A. and Dec. of α Ursę Majoris; of β Ursę +Majoris; of Polaris. Find the Northern Crown, <i>Corona +Borealis</i>, R. A. = 15h. 30m., Dec. = +27.0°; the Beehive, +<i>Pręsepe</i>, R. A. = 8h. 33m., Dec. = +20.4°.</p> + +<p>These should be looked up, not only on the map, but +also in the sky.</p> + +<p><a name="S_17" id="S_17"></a>17. <b>Reference lines and circles.</b>—As the stars move across +the sky in their diurnal motion, they carry the framework +of hour circles and equator with them, so that the right +ascension and declination of each star remain unchanged +by this motion, just as longitudes and latitudes remain unchanged +by the earth's rotation. They are the same when +a star is rising and when it is setting; when it is above the +pole and when it is below it. During each day the hour +circle of every star in the heavens passes overhead, and at +the moment when any particular hour circle is exactly +overhead all the stars which lie upon it are said to be "on +the meridian"—i. e., at that particular moment they stand +directly over the observer's geographical meridian and upon +the corresponding celestial meridian.</p> + +<p>An eye placed at the center of the earth and capable of +looking through its solid substance would see your geographical +meridian against the background of the sky exactly covering +your celestial meridian and passing from one pole +through your zenith to the other pole. In <a href="#Fig_11">Fig. 11</a> the inner +circle represents the terrestrial meridian of a certain place,<span class="pagenum"><a name="Page_21" id="Page_21">[Pg 21]</a></span> +<i>O</i>, as seen from the center of the earth, <i>C</i>, and the outer +circle represents the celestial meridian of <i>O</i> as seen from +<i>C</i>, only we must imagine, what can not be shown on the +figure, that the outer circle is so large that the inner one +shrinks to a mere point in +comparison with it. If <i>C P</i> +represents the direction in +which the earth's axis passes +through the center, then <i>C E</i> +at right angles to it must +be the direction of the equator +which we suppose to be +turned edgewise toward us; +and if <i>C O</i> is the direction of +some particular point on the +earth's surface, then <i>Z</i> directly +overhead is called the +<i>zenith</i> of that point, upon +the celestial sphere. The line <i>C H</i> represents a direction +parallel to the horizon plane at <i>O</i>, and <i>H C P</i> is the angle +which the axis of the earth makes with this horizon plane. +The arc <i>O E</i> measures the latitude of <i>O</i>, and the arc <i>Z E</i> +measures the declination of <i>Z</i>, and since by elementary +geometry each of these arcs contains the same number of +degrees as the angle <i>E C Z</i>, we have the</p> + +<div class="figright" style="width: 300px;"><a name="Fig_11" id="Fig_11"></a> +<img src="images/i034.png" width="300" height="303" alt="Fig. 11.—Reference lines and circles." title="Fig. 11.—Reference lines and circles." /> +<span class="caption"><span class="smcap">Fig. 11.</span>—Reference lines and circles.</span> +</div> + +<p><i>Theorem.</i>—The latitude of any place is equal to the +declination of its zenith.</p> + +<p><i>Corollary.</i>—Any star whose declination is equal to your +latitude will once in each day pass through your zenith.</p> + +<p><a name="S_18" id="S_18"></a>18. <b>Latitude.</b>—From the construction of the figure</p> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="right">∠ <i>E C Z</i> + ∠ <i>Z C P</i></td><td align="center">=</td><td align="left">90°</td></tr> +<tr><td align="right">∠ <i>H C P</i> + ∠ <i>Z C P</i></td><td align="center">=</td><td align="left">90°</td></tr> +</table></div> + +<p>from which we find by subtraction and transposition</p> + +<p class="center">∠ <i>E C Z</i> = ∠ <i>H C P</i></p> + +<p>and this gives the further<span class="pagenum"><a name="Page_22" id="Page_22">[Pg 22]</a></span></p> + +<p><i>Theorem.</i>—The latitude of any place is equal to the +elevation of the pole above its horizon plane.</p> + +<p>An observer who travels north or south over the earth +changes his latitude, and therefore changes the angle between +his horizon plane and the axis of the earth. What +effect will this have upon the position of stars in his sky? +If you were to go to the earth's equator, in what part of +the sky would you look for Polaris? Can Polaris be seen +from Australia? From South America? If you were to +go from Minnesota to Texas, in what +respect would the appearance of +stars in the northern sky be changed? +How would the appearance of stars +in the southern sky be changed?</p> + +<div class="figleft" style="width: 300px;"><a name="Fig_12" id="Fig_12"></a> +<img src="images/i035.png" width="300" height="305" alt="Fig. 12.—Diurnal path of +Polaris." title="Fig. 12.—Diurnal path of +Polaris." /> +<span class="caption"><span class="smcap">Fig. 12.</span>—Diurnal path of +Polaris.</span> +</div> + +<p><a name="Exercise_8" id="Exercise_8"></a><span class="smcap">Exercise 8.</span>—Determine your +latitude by taking the altitude of +Polaris when it is at some one of the +four points of its diurnal path, shown +in <a href="#Fig_12">Fig. 12</a>. When it is at <i>1</i> it is +said to be at upper culmination, and +the star ζ Ursę Majoris in the handle of the Big Dipper +will be directly below it. When at <i>2</i> it is at western elongation, +and the star Castor is near the meridian. When it +is at <i>3</i> it is at lower culmination, and the star Spica is on +the meridian. When it is at <i>4</i> it is at eastern elongation, +and Altair is near the meridian. All of these stars are +conspicuous ones, which the student should find upon the +map and learn to recognize in the sky. The altitude observed +at either <i>2</i> or <i>4</i> may be considered equal to the latitude +of the place, but the altitude observed when Polaris +is at the positions marked <i>1</i> and <i>3</i> must be corrected for +the star's distance from the pole, which may be assumed +equal to 1.3°.</p> + +<p>The plumb-line apparatus described at <a href="#Page_12">page 12</a> is shown +in <a href="#Fig_6">Fig. 6</a> slightly modified, so as to adapt it to measuring +the altitudes of stars. Note that the board with the screw<span class="pagenum"><a name="Page_23" id="Page_23">[Pg 23]</a></span> +eye at one end has been transferred from the box to the +vertical standard, and has a screw eye at each end. When +the apparatus has been properly leveled, so that the plumb +line hangs at the middle of the hole in the box cover, the +board is to be pointed at the star by sighting through the +centers of the two screw eyes, and a pencil line is to be +ruled along its edge upon the face of the vertical standard. +After this has been done turn the apparatus halfway around +so that what was the north side now points south, level it +again and revolve the board about the screw which holds it +to the vertical standard, until the screw eyes again point to +the star. Rule another line along the same edge of the +board as before and with a protractor measure the angle +between these lines. Use a bicycle lamp if you need artificial +light for your work. The student who has studied +plane geometry should be able to prove that one half of the +angle between these lines is equal to the altitude of the +star.</p> + +<p>After you have determined your latitude from Polaris, +compare the result with your position as shown upon the +best map available. With a little practice and considerable +care the latitude may be thus determined within one tenth +of a degree, which is equivalent to about 7 miles. If +you go 10 miles north or south from your first station you +should find the pole higher up or lower down in the sky by +an amount which can be measured with your apparatus.</p> + +<p><a name="S_19" id="S_19"></a>19. <b>The meridian line.</b>—To establish a true north and +south line upon the ground, use the apparatus as described +at <a href="#Page_13">page 13</a>, and when Polaris is at upper or lower culmination +drive into the ground two stakes in line with the star +and the plumb line. Such a meridian line is of great convenience +in observing the stars and should be laid out and +permanently marked in some convenient open space from +which, if possible, all parts of the sky are visible. June and +November are convenient months for this exercise, since +Polaris then comes to culmination early in the evening.<span class="pagenum"><a name="Page_24" id="Page_24">[Pg 24]</a></span></p> + +<p><a name="S_20" id="S_20"></a>20. <b>Time.</b>—What is <i>the time</i> at which school begins in +the morning? What do you mean by "<i>the time</i>"?</p> + +<p>The sidereal time at any moment is the right ascension +of the hour circle which at that moment coincides with the +meridian. When the hour circle passing through Sirius +coincides with the meridian, the sidereal time is 6h. 40m., +since that is the right ascension of Sirius, and in astronomical +language Sirius is "<i>on the meridian</i>" at 6h. 40m. +sidereal time. As may be seen from the map, this 6h. 40m. +is the right ascension of Sirius, and if a clock be set to indicate +6h. 40m. when Sirius crosses the meridian, it will +show sidereal time. If the clock is properly regulated, +every other star in the heavens will come to the meridian +at the moment when the time shown by the clock is equal +to the right ascension of the star. A clock properly regulated +for this purpose will gain about four minutes per +day in comparison with ordinary clocks, and when so regulated +it is called a sidereal clock. The student should +be provided with such a clock for his future work, but +one such clock will serve for several persons, and a nutmeg +clock or a watch of the cheapest kind is quite sufficient.</p> + +<div class="figcenter" style="width: 600px;"><a name="THE_HARVARD_COLLEGE_OBSERVATORY" id="THE_HARVARD_COLLEGE_OBSERVATORY"></a> +<a href="images/i038-full.jpg"><img src="images/i038.jpg" width="600" height="341" alt="THE HARVARD COLLEGE OBSERVATORY, CAMBRIDGE, MASS." title="THE HARVARD COLLEGE OBSERVATORY, CAMBRIDGE, MASS." /></a> +<span class="caption">THE HARVARD COLLEGE OBSERVATORY, CAMBRIDGE, MASS.</span> +</div> + +<p><a name="Exercise_9" id="Exercise_9"></a><span class="smcap">Exercise 9.</span>—Set such a clock to sidereal time by +means of the transit of a star over your meridian. For this +experiment it is presupposed that a meridian line has been +marked out on the ground as in <a href="#S_19">§ 19</a>, and the simplest +mode of performing the experiment required is for the +observer, having chosen a suitable star in the southern part +of the sky, to place his eye accurately over the northern end +of the meridian line and to estimate as nearly as possible +the beginning and end of the period during which the star +appears to stand exactly above the southern end of the +line. The middle of this period may be taken as the time +at which the star crossed the meridian and at this moment +the sidereal time is equal to the right ascension of the star. +The difference between this right ascension and the observed<span class="pagenum"><a name="Page_25" id="Page_25">[Pg 25]</a></span> +middle instant is the error of the clock or the +amount by which its hands must be set back or forward in +order to indicate true sidereal time.</p> + +<p>A more accurate mode of performing the experiment +consists in using the plumb-line apparatus carefully adjusted, +as in <a href="#Fig_7">Fig. 7</a>, so that the line joining the wire to +the center of the screw eye shall be parallel to the meridian +line. Observe the time by the clock at which the star disappears +behind the wire as seen through the center of the +screw eye. If the star is too high up in the sky for convenient +observation, place a mirror, face up, just north of +the screw eye and observe star, wire and screw eye by reflection +in it.</p> + +<p>The numerical right ascension of the observed star is +needed for this experiment, and it may be measured from +the star map, but it will usually be best to observe one of +the stars of the table at the end of the book, and to obtain +its right ascension as follows: The table gives the right +ascension and declination of each star as they were at the +beginning of the year 1900, but on account of the precession +(see <a href="#CHAPTER_V">Chapter V</a>), these numbers all change slowly with +the lapse of time, and on the average the right ascension +of each star of the table must be increased by one twentieth +of a minute for each year after 1900—i. e., in 1910 +the right ascension of the first star of the table will be +0h. 38.6m. + (10/20)m. = 0h. 39.1m. The declinations also +change slightly, but as they are only intended to help in +finding the star on the star maps, their change may be +ignored.</p> + +<p>Having set the clock approximately to sidereal time, +observe one or two more stars in the same way as above. +The difference between the observed time and the right +ascension, if any is found, is the "correction" of the +clock. This correction ought not to exceed a minute if due +care has been taken in the several operations prescribed. +The relation of the clock to the right ascension of the stars<span class="pagenum"><a name="Page_26" id="Page_26">[Pg 26]</a></span> +is expressed in the following equation, with which the +student should become thoroughly familiar:</p> + +<p class="center"><i>A</i> = <i>T</i> ± <i>U</i></p> + +<p><i>T</i> stands for the time by the clock at which the star crossed +the meridian. <i>A</i> is the right ascension of the star, and <i>U</i> +is the correction of the clock. Use the + sign in the equation +whenever the clock is too slow, and the - sign when +it is too fast. <i>U</i> may be found from this equation when <i>A</i> +and <i>T</i> are given, or <i>A</i> may be found when <i>T</i> and <i>U</i> are +given. It is in this way that astronomers measure the right +ascensions of the stars and planets.</p> + +<p>Determine <i>U</i> from each star you have observed, and +note how the several results agree one with another.</p> + +<p><a name="S_21" id="S_21"></a>21. <b>Definitions.</b>—To define a thing or an idea is to give +a description sufficient to identify it and distinguish it +from every other possible thing or idea. If a definition +does not come up to this standard it is insufficient. Anything +beyond this requirement is certainly useless and +probably mischievous.</p> + +<p>Let the student define the following geographical terms, +and let him also criticise the definitions offered by his fellow-students: +Equator, poles, meridian, latitude, longitude, +north, south, east, west.</p> + +<p>Compare the following astronomical definitions with +your geographical definitions, and criticise them in the +same way. If you are not able to improve upon them, commit +them to memory:</p> + +<p><i>The Poles</i> of the heavens are those points in the sky +toward which the earth's axis points. How many are +there? The one near Polaris is called the north pole.</p> + +<p><i>The Celestial Equator</i> is a great circle of the sky distant +90° from the poles.</p> + +<p><i>The Zenith</i> is that point of the sky, overhead, toward +which a plumb line points. Why is the word overhead +placed in the definition? Is there more than one zenith?<span class="pagenum"><a name="Page_27" id="Page_27">[Pg 27]</a></span></p> + +<p><i>The Horizon</i> is a great circle of the sky 90° distant +from the zenith.</p> + +<p><i>An Hour Circle</i> is any great circle of the sky which +passes through the poles. Every star has its own hour +circle.</p> + +<p><i>The Meridian</i> is that hour circle which passes through +the zenith.</p> + +<p><i>A Vertical Circle</i> is any great circle that passes through +the zenith. Is the meridian a vertical circle?</p> + +<p><i>The Declination</i> of a star is its angular distance north +or south of the celestial equator.</p> + +<p><i>The Right Ascension</i> of a star is the angle included between +its hour circle and the hour circle of a certain point +on the equator which is called the <i>Vernal Equinox</i>. From +spherical geometry we learn that this angle is to be measured +either at the pole where the two hour circles intersect, +as is done in the star map opposite <a href="#Page_124">page 124</a>, or +along the equator, as is done in the map opposite page +190. Right ascension is always measured from the vernal +equinox in the direction opposite to that in which the +stars appear to travel in their diurnal motion—i. e., from +west toward east.</p> + +<p><i>The Altitude</i> of a star is its angular distance above the +horizon.</p> + +<p><i>The Azimuth</i> of a star is the angle between the meridian +and the vertical circle passing through the star. A star +due south has an azimuth of 0°. Due west, 90°. Due +north, 180°. Due east, 270°.</p> + +<p>What is the azimuth of Polaris in degrees?</p> + +<p>What is the azimuth of the sun at sunrise? At sunset? +At noon? Are these azimuths the same on different days?</p> + +<p><i>The Hour Angle</i> of a star is the angle between its hour +circle and the meridian. It is measured from the meridian +in the direction in which the stars appear to travel in their +diurnal motion—i. e., from east toward west.</p> + +<p>What is the hour angle of the sun at noon? What is<span class="pagenum"><a name="Page_28" id="Page_28">[Pg 28]</a></span> +the hour angle of Polaris when it is at the lowest point in +its daily motion?</p> + +<p><a name="S_22" id="S_22"></a>22. <b>Exercises.</b>—The student must not be satisfied with +merely learning these definitions. He must learn to see +these points and lines in his mind as if they were visibly +painted upon the sky. To this end it will help him to note +that the poles, the zenith, the meridian, the horizon, and +the equator seem to stand still in the sky, always in the +same place with respect to the observer, while the hour +circles and the vernal equinox move with the stars and +keep the same place among them. Does the apparent motion +of a star change its declination or right ascension? +What is the hour angle of the sun when it has the greatest +altitude? Will your answer to the preceding question be +true for a star? What is the altitude of the sun after sunset? +In what direction is the north pole from the zenith? +From the vernal equinox? Where are the points in which +the meridian and equator respectively intersect the horizon?</p> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_29" id="Page_29">[Pg 29]</a></span></p> +<h2><a name="CHAPTER_III" id="CHAPTER_III"></a>CHAPTER III</h2> + +<h3>FIXED AND WANDERING STARS</h3> + + +<p><a name="S_23" id="S_23"></a>23. <b>Star maps.</b>—Select from the map some conspicuous +constellation that will be conveniently placed for observation +in the evening, and make on a large scale a copy of all +the stars of the constellation that are shown upon the map. +At night compare this copy with the sky, and mark in upon +your paper all the stars of the constellation which are not +already there. Both the original drawing and the additions +made to it by night should be carefully done, and for +the latter purpose what is called the method of allineations +may be used with advantage—i. e., the new star is in line +with two already on the drawing and is midway between +them, or it makes an equilateral triangle with two others, +or a square with three others, etc.</p> + +<p>A series of maps of the more prominent constellations, +such as Ursa Major, Cassiopea, Pegasus, Taurus, Orion, +Gemini, Canis Major, Leo, Corvus, Bootes, Virgo, Hercules, +Lyra, Aquila, Scorpius, should be constructed in this manner +upon a uniform scale and preserved as a part of the +student's work. Let the magnitude of the stars be represented +on the maps as accurately as may be, and note the +peculiarity of color which some stars present. For the +most part their color is a very pale yellow, but occasionally +one may be found of a decidedly ruddy hue—e. g., Aldebaran +or Antares. Such a star map, not quite complete, is +shown in <a href="#Fig_13">Fig. 13</a>.</p> + +<p>So, too, a sharp eye may detect that some stars do not +remain always of the same magnitude, but change their<span class="pagenum"><a name="Page_30" id="Page_30">[Pg 30]</a></span> +brightness from night to night, and this not on account of +cloud or mist in the atmosphere, but from something in the +star itself. Algol is one of the most conspicuous of these +<i>variable stars</i>, as they are called.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_13" id="Fig_13"></a> +<img src="images/i045.png" width="500" height="514" alt="Fig. 13.—Star map of the region about Orion." title="" /> +<span class="caption"><span class="smcap">Fig. 13.</span>—Star map of the region about Orion.</span> +</div> + +<p><a name="S_24" id="S_24"></a>24. <b>The moon's motion among the stars.</b>—Whenever the +moon is visible note its position among the stars by allineations, +and plot it on the key map opposite <a href="#Page_190">page 190</a>. Keep +a record of the day and hour corresponding to each such +observation. You will find, if the work is correctly done, +that the positions of the moon all fall near the curved line +shown on the map. This line is called the ecliptic.<span class="pagenum"><a name="Page_31" id="Page_31">[Pg 31]</a></span></p> + +<p>After several such observations have been made and +plotted, find by measurement from the map how many +degrees per day the moon moves. How long would it require +to make the circuit of the heavens and come back to +the starting point?</p> + +<p>On each night when you observe the moon, make on a +separate piece of paper a drawing of it about 10 centimeters +in diameter and show in the drawing every feature of +the moon's face which you can see—e. g., the shape of the +illuminated surface (phase); the direction among the stars +of the line joining the horns; any spots which you can see +upon the moon's face, etc. An opera glass will prove of +great assistance in this work.</p> + +<p>Use your drawings and the positions of the moon plotted +upon the map to answer the following questions: Does +the direction of the line joining the horns have any special +relation to the ecliptic? Does the amount of illuminated +surface of the moon have any relation to the moon's angular +distance from the sun? Does it have any relation to the +time at which the moon sets? Do the spots on the moon +when visible remain always in the same place? Do they +come and go? Do they change their position with relation +to each other? Can you determine from these spots that +the moon rotates about an axis, as the earth does? In +what direction does its axis point? How long does it take +to make one revolution about the axis? Is there any day +and night upon the moon?</p> + +<p>Each of these questions can be correctly answered from +the student's own observations without recourse to any +book.</p> + +<p><a name="S_25" id="S_25"></a>25. <b>The sun and its motion.</b>—Examine the face of the +sun through a smoked glass to see if there is anything +there that you can sketch.</p> + +<p>By day as well as by night the sky is studded with stars, +only they can not be seen by day on account of the overwhelming +glare of sunlight, but the position of the sun<span class="pagenum"><a name="Page_32" id="Page_32">[Pg 32]</a></span> +among the stars may be found quite as accurately as was +that of the moon, by observing from day to day its right +ascension and declination, and this should be practiced at +noon on clear days by different members of the class.</p> + +<p><span class="smcap">Exercise 10.</span>—The right ascension of the sun may be +found by observing with the sidereal clock the time of its +transit over the meridian. Use the equation in <a href="#S_20">§ 20</a>, and +substitute in place of <i>U</i> the value of the clock correction +found from observations of stars on a preceding or following +night. If the clock gains or loses <i>with respect to +sidereal time</i>, take this into account in the value of <i>U</i>.</p> + +<p><a name="Exercise_11" id="Exercise_11"></a><span class="smcap">Exercise 11.</span>—To determine the sun's declination, +measure its altitude at the time it crosses the meridian. +Use either the method of <a href="#Exercise_4">Exercise 4</a>, or that used with +Polaris in <a href="#Exercise_8">Exercise 8</a>. The student should be able to show +from <a href="#Fig_11">Fig. 11</a> that the declination is equal to the sum of +the altitude and the latitude of the place diminished by +90°, or in an equation</p> + +<p class="center">Declination = Altitude + Latitude - 90°.</p> + +<p>If the declination as found from this equation is a negative +number it indicates that the sun is on the south side of the +equator.</p> + +<p>The right ascension and declination of the sun as observed +on each day should be plotted on the map and the +date, written opposite it. If the work has been correctly +done, the plotted points should fall upon the curved line +(ecliptic) which runs lengthwise of the map. This line, in +fact, represents the sun's path among the stars.</p> + +<p>Note that the hours of right ascension increase from 0 +up to 24, while the numbers on the clock dial go only from +0 to 12, and then repeat 0 to 12 again during the same +day. When the sidereal time is 13 hours, 14 hours, etc., +the clock will indicate 1 hour, 2 hours, etc., and 12 hours +must then be added to the time shown on the dial.</p> + +<p>If observations of the sun's right ascension and declination<span class="pagenum"><a name="Page_33" id="Page_33">[Pg 33]</a></span> +are made in the latter part of either March or September +the student will find that the sun crosses the equator +at these times, and he should determine from his observations, +as accurately as possible, the date and hour of this +crossing and the point on the equator at which the sun +crosses it. These points are called the equinoxes, Vernal +Equinox and Autumnal Equinox for the spring and autumn +crossings respectively, and the student will recall that the +vernal equinox is the point from which right ascensions +are measured. Its position among the stars is found by +astronomers from observations like those above described, +only made with much more elaborate apparatus.</p> + +<p>Similar observations made in June and December show +that the sun's midday altitude is about 47° greater in summer +than in winter. They show also that the sun is as far +north of the equator in June as he is south of it in December, +from which it is easily inferred that his path, the +ecliptic, is inclined to the equator at an angle of 23°.5, one +half of 47°. This angle is called the obliquity of the ecliptic. +The student may recall that in the geographies the +torrid zone is said to extend 23°.5 on either side of the +earth's equator. Is there any connection between these +limits and the obliquity of the ecliptic? Would it be correct +to define the torrid zone as that part of the earth's +surface within which the sun may at some season of the +year pass through the zenith?</p> + +<p><a name="Exercise_12" id="Exercise_12"></a><span class="smcap">Exercise 12.</span>—After a half dozen observations of the +sun have been plotted upon the map, find by measurement +the rate, in degrees per day, at which the sun moves along +the ecliptic. How many days will be required for it to +move completely around the ecliptic from vernal equinox +back to vernal equinox again? Accurate observations with +the elaborate apparatus used by professional astronomers +show that this period, which is called a <i>tropical year</i>, is 365 +days 5 hours 48 minutes 46 seconds. Is this the same as +the ordinary year of our calendars?<span class="pagenum"><a name="Page_34" id="Page_34">[Pg 34]</a></span></p> + +<p><a name="S_26" id="S_26"></a>26. <b>The planets.</b>—Any one who has watched the sky and +who has made the drawings prescribed in this chapter can +hardly fail to have found in the course of his observations +some bright stars not set down on the printed star maps, +and to have found also that these stars do not remain fixed +in position among their fellows, but wander about from +one constellation to another. Observe the motion of one +of these planets from night to night and plot its positions +on the star map, precisely as was done for the moon. +What kind of path does it follow?</p> + +<p>Both the ancient Greeks and the modern Germans have +called these bodies wandering stars, and in English we name +them planets, which is simply the Greek word for wanderer, +bent to our use. Besides the sun and moon there are in +the heavens five planets easily visible to the naked eye and, +as we shall see later, a great number of smaller ones visible +only in the telescope. More than 2,000 years ago astronomers +began observing the motion of sun, moon, and +planets among the stars, and endeavored to account for +these motions by the theory that each wandering star +moved in an orbit about the earth. Classical and medięval +literature are permeated with this idea, which was displaced +only after a long struggle begun by Copernicus (1543 <span class="smcap">A. D.</span>), +who taught that the moon alone of these bodies revolves +about the earth, while the earth and the other planets revolve +around the sun. The ecliptic is the intersection of +the plane of the earth's orbit with the sky, and the sun appears +to move along the ecliptic because, as the earth moves +around its orbit, the sun is always seen projected against +the opposite side of it. The moon and planets all appear +to move near the ecliptic because the planes of their orbits +nearly coincide with the plane of the earth's orbit, and a +narrow strip on either side of the ecliptic, following its +course completely around the sky, is called the <i>zodiac</i>, a +word which may be regarded as the name of a narrow street +(16° wide) within which all the wanderings of the visible<span class="pagenum"><a name="Page_35" id="Page_35">[Pg 35]</a></span> +planets are confined and outside of which they never venture. +Indeed, Mars is the only planet which ever approaches +the edge of the street, the others traveling near the middle +of the road.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_14" id="Fig_14"></a> +<img src="images/i050.png" width="500" height="487" alt="Fig. 14.—The apparent motion of a planet." title="Fig. 14.—The apparent motion of a planet." /> +<span class="caption"><span class="smcap">Fig. 14.</span>—The apparent motion of a planet.</span> +</div> + +<p><a name="S_27" id="S_27"></a>27. <b>A typical case of planetary motion.</b>—The Copernican +theory, enormously extended and developed through the +Newtonian law of gravitation (see <a href="#CHAPTER_IV">Chapter IV</a>), has completely +supplanted the older Ptolemaic doctrine, and an +illustration of the simple manner in which it accounts for +the apparently complicated motions of a planet among the +stars is found in Figs. <a href="#Fig_14">14</a> and <a href="#Fig_15">15</a>, the first of which represents +the apparent motion of the planet Mars through the +constellations Aries and Pisces during the latter part of the<span class="pagenum"><a name="Page_36" id="Page_36">[Pg 36]</a></span> +year 1894, while the second shows the true motions of Mars +and the earth in their orbits about the sun during the same +period. The straight line in <a href="#Fig_14">Fig. 14</a>, with cross ruling upon +it, is a part of the ecliptic, and the numbers placed opposite +it represent the distance, in degrees, from the vernal equinox. +In <a href="#Fig_15">Fig. 15</a> the straight line represents the direction +from the sun toward the vernal equinox, and the angle +which this line makes with the line joining earth and sun is +called the earth's longitude. The imaginary line joining +the earth and sun is called the earth's radius vector, and +the pupil should note that the longitude and length of the +radius vector taken together show the direction and distance +of the earth from the sun—i. e., they fix the relative +positions of the two bodies. The same is nearly true for +Mars and would be wholly true if the orbit of Mars lay in +the same plane with that of the earth. How does <a href="#Fig_14">Fig. 14</a> +show that the orbit of Mars does not lie exactly in the same +plane with the orbit of the earth?</p> + +<p><a name="Exercise_13" id="Exercise_13"></a><span class="smcap">Exercise 13.</span>—Find from <a href="#Fig_15">Fig. 15</a> what ought to have +been the apparent course of Mars among the stars during +the period shown in the two figures, and compare what you +find with <a href="#Fig_14">Fig. 14</a>. The apparent position of Mars among +the stars is merely its direction from the earth, and this +direction is represented in <a href="#Fig_14">Fig. 14</a> by the distance of the +planet from the ecliptic and by its longitude.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_15" id="Fig_15"></a> +<img src="images/i052.png" width="500" height="605" alt="Fig. 15.—The real motion of a planet." title="Fig. 15.—The real motion of a planet." /> +<span class="caption"><span class="smcap">Fig. 15.</span>—The real motion of a planet.</span> +</div> + +<p>The longitude of Mars for each date can be found from +<a href="#Fig_15">Fig. 15</a> by measuring the angle between the straight line +<i>S V</i> and the line drawn from the earth to Mars. Thus for +October 12th we may find with the protractor that the angle +between the line <i>S V</i> and the line joining the earth to Mars +is a little more than 30°, and in <a href="#Fig_14">Fig. 14</a> the position of +Mars for this date is shown nearly opposite the cross line +corresponding to 30° on the ecliptic. Just how far below +the ecliptic this position of Mars should fall can not be +told from <a href="#Fig_15">Fig. 15</a>, which from necessity is constructed as if +the orbits of Mars and the earth lay in the same plane, and<span class="pagenum"><a name="Page_37" id="Page_37">[Pg 37]</a></span> +Mars in this case would always appear to stand exactly on +the ecliptic and to oscillate back and forth as shown in <a href="#Fig_14">Fig. 14</a>, +but without the up-and-down motion there shown. In +this way plot in <a href="#Fig_14">Fig. 14</a> the longitudes of Mars as seen from +the earth for other dates and observe how the forward motion +of the two planets in their orbits accounts for the apparently +capricious motion of Mars to and fro among the stars.<span class="pagenum"><a name="Page_38" id="Page_38">[Pg 38]</a></span></p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_16" id="Fig_16"></a> +<img src="images/i053.png" width="500" height="491" alt="Fig. 16.—The orbits of Jupiter and Saturn." title="Fig. 16.—The orbits of Jupiter and Saturn." /> +<span class="caption"><span class="smcap">Fig. 16.</span>—The orbits of Jupiter and Saturn.</span> +</div> + +<p><a name="S_28" id="S_28"></a>28. <b>The orbits of the planets.</b>—Each planet, great or +small, moves in its own appropriate orbit about the sun, +and the exact determination of these orbits, their sizes, +shapes, positions, etc., has been one of the great problems +of astronomy for more than 2,000 years, in which successive +generations of astronomers have striven to push to a +still higher degree of accuracy the knowledge attained by +their predecessors. Without attempting to enter into the +details of this problem we may say, generally, that every<span class="pagenum"><a name="Page_39" id="Page_39">[Pg 39]</a></span> +planet moves in a plane passing through the sun, and for +the six planets visible to the naked eye these planes nearly +coincide, so that the six orbits may all be shown without +much error as lying in the flat surface of one map. It is, +however, more convenient to use two maps, such as Figs. <a href="#Fig_16">16</a> +and <a href="#Fig_17">17</a>, one of which shows the group of planets, Mercury, +Venus, the earth, and Mars, which are near the sun, and +on this account are sometimes called the inner planets, +while the other shows the more distant planets, Jupiter and +Saturn, together with the earth, whose orbit is thus made +to serve as a connecting link between the two diagrams. +These diagrams are accurately drawn to scale, and are intended +to be used by the student for accurate measurement +in connection with the exercises and problems which +follow.</p> + +<p>In addition to the six planets shown in the figures the +solar system contains two large planets and several hundred +small ones, for the most part invisible to the naked eye, +which are omitted in order to avoid confusing the diagrams.</p> + +<p><a name="S_29" id="S_29"></a>29. <b>Jupiter and Saturn.</b>—In <a href="#Fig_16">Fig. 16</a> the sun at the center +is encircled by the orbits of the three planets, and inclosing +all of these is a circular border showing the directions from +the sun of the constellations which lie along the zodiac. +The student must note carefully that it is only the directions +of these constellations that are correctly shown, and +that in order to show them at all they have been placed +very much too close to the sun. The cross lines extending +from the orbit of the earth toward the sun with Roman +numerals opposite them show the positions of the earth in +its orbit on the first day of January (<i>I</i>), first day of February +(<i>II</i>), etc., and the similar lines attached to the orbits +of Jupiter and Saturn with Arabic numerals show the positions +of those planets on the first day of January of each +year indicated, so that the figure serves to show not only +the orbits of the planets, but their actual positions in their<span class="pagenum"><a name="Page_40" id="Page_40">[Pg 40]</a></span> +orbits for something more than the first decade of the twentieth +century.</p> + +<p>The line drawn from the sun toward the right of the +figure shows the direction to the vernal equinox. It forms +one side of the angle which measures a planet's longitude.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_17" id="Fig_17"></a> +<img src="images/i055.png" width="500" height="489" alt="Fig. 17.—The orbits of the inner planets." title="Fig. 17.—The orbits of the inner planets." /> +<span class="caption"><span class="smcap">Fig. 17.</span>—The orbits of the inner planets.</span> +</div> + +<p><a name="Exercise_14" id="Exercise_14"></a><span class="smcap">Exercise 14.</span>—Measure with your protractor the longitude +of the earth on January 1st. Is this longitude the +same in all years? Measure the longitude of Jupiter on +January 1, 1900; on July 1, 1900; on September 25, 1906.<span class="pagenum"><a name="Page_41" id="Page_41">[Pg 41]</a></span></p> + +<p>Draw neatly on the map a pencil line connecting the +position of the earth for January 1, 1900, with the position +of Jupiter for the same date, and produce the line beyond +Jupiter until it meets the circle of the constellations. This +line represents the direction of Jupiter from the earth, and +points toward the constellation in which the planet appears +at that date. But this representation of the place of Jupiter +in the sky is not a very accurate one, since on the scale +of the diagram the stars are in fact more than 100,000 times +as far off as they are shown in the figure, and the pencil +mark does not meet the line of constellations at the same +intersection it would have if this line were pushed back +to its true position. To remedy this defect we must draw +another line from the sun parallel to the one first drawn, +and its intersection with the constellations will give very +approximately the true position of Jupiter in the sky.</p> + +<p><a name="Exercise_15" id="Exercise_15"></a><span class="smcap">Exercise 15.</span>—Find the present positions of Jupiter +and Saturn, and look them up in the sky by means of your +star maps. The planets will appear in the indicated constellations +as very bright stars not shown on the map.</p> + +<p>Which of the planets, Jupiter and Saturn, changes its +direction from the sun more rapidly? Which travels the +greater number of miles per day? When will Jupiter and +Saturn be in the same constellation? Does the earth move +faster or slower than Jupiter?</p> + +<p>The distance of Jupiter or Saturn from the earth at any +time may be readily obtained from the figure. Thus, by +direct measurement with the millimeter scale we find for +January 1, 1900, the distance of Jupiter from the earth is 6.1 +times the distance of the sun from the earth, and this may +be turned into miles by multiplying it by 93,000,000, which +is approximately the distance of the sun from the earth. +For most purposes it is quite as well to dispense with this +multiplication and call the distance 6.1 astronomical units, +remembering that the astronomical unit is the distance of +the sun from the earth.<span class="pagenum"><a name="Page_42" id="Page_42">[Pg 42]</a></span></p> + +<p><a name="Exercise_16" id="Exercise_16"></a><span class="smcap">Exercise 16.</span>—What is Jupiter's distance from the earth +at its nearest approach? What is the greatest distance it +ever attains? Is Jupiter's least distance from the earth +greater or less than its least distance from Saturn?</p> + +<p>On what day in the year 1906 will the earth be on +line between Jupiter and the sun? On this day Jupiter +is said to be in <i>opposition</i>—i. e., the planet and the sun +are on opposite sides of the earth, and Jupiter then comes +to the meridian of any and every place at midnight. When +the sun is between the earth and Jupiter (at what date in +1906?) the planet is said to be in <i>conjunction</i> with the +sun, and of course passes the meridian with the sun at +noon. Can you determine from the figure the time at +which Jupiter comes to the meridian at other dates than +opposition and conjunction? Can you determine when it +is visible in the evening hours? Tell from the figure what +constellation is on the meridian at midnight on January +1st. Will it be the same constellation in every year?</p> + +<p><a name="S_30" id="S_30"></a>30. <b>Mercury, Venus, and Mars.</b>—<a href="#Fig_17">Fig. 17</a>, which represents +the orbits of the inner planets, differs from <a href="#Fig_16">Fig. 16</a> +only in the method of fixing the positions of the planets +in their orbits at any given date. The motion of these planets +is so rapid, on account of their proximity to the sun, that +it would not do to mark their positions as was done for +Jupiter and Saturn, and with the exception of the earth they +do not always return to the same place on the same day in +each year. It is therefore necessary to adopt a slightly different +method, as follows: The straight line extending from +the sun toward the vernal equinox, <i>V</i>, is called the prime +radius, and we know from past observations that the earth +in its motion around the sun crosses this line on September +23d in each year, and to fix the earth's position for September +23d in the diagram we have only to take the point at +which the prime radius intersects the earth's orbit. A +month later, on October 23d, the earth will no longer be at +this point, but will have moved on along its orbit to the<span class="pagenum"><a name="Page_43" id="Page_43">[Pg 43]</a></span> +point marked 30 (thirty days after September 23d). Sixty +days after September 23d it will be at the point marked 60, +etc., and for any date we have only to find the number of +days intervening between it and the preceding September +23d, and this number will show at once the position of the +earth in its orbit. Thus for the date July 4, 1900, we find</p> + +<p class="center">1900, July 4 - 1899, September 23 = 284 days,</p> + +<p>and the little circle marked upon the earth's orbit between +the numbers 270 and 300 shows the position of the earth on +that date.</p> + +<p>In what constellation was the sun on July 4, 1900? +What zodiacal constellation came to the meridian at midnight +on that date? What other constellations came to +the meridian at the same time?</p> + +<p>The positions of the other planets in their orbits are +found in the same manner, save that they do not cross the +prime radius on the same date in each year, and the times +at which they do cross it must be taken from the following +table:</p> + +<h3><span class="smcap">Table of Epochs</span></h3> + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" rules="groups" frame="hsides"> +<colgroup></colgroup><colgroup></colgroup><colgroup></colgroup><colgroup></colgroup><colgroup></colgroup> +<thead> +<tr><th align="center">A. D.</th><th align="center">Mercury.</th><th align="center">Venus.</th><th align="center">Earth.</th><th align="center">Mars.</th></tr> +</thead> +<tbody> +<tr><td align="left">Period</td><td align="left">88.0 days.</td><td align="left">224.7 days.</td><td align="left">365.25 days.</td><td align="left">687.1 days.</td></tr> +<tr><td align="left">1900</td><td align="left">Feb. 18th.</td><td align="left">Jan. 11th.</td><td align="left">Sept. 23d.</td><td align="left">April 28th.</td></tr> +<tr><td align="left">1901</td><td align="left">Feb. 5th.</td><td align="left">April 5th.</td><td align="left">Sept. 23d.</td><td align="center">...</td></tr> +<tr><td align="left">1902</td><td align="left">Jan. 23d.</td><td align="left">June 29th.</td><td align="left">Sept. 23d.</td><td align="left">March 16th.</td></tr> +<tr><td align="left">1903</td><td align="left">April 8th.</td><td align="left">Feb. 8th.</td><td align="left">Sept. 23d.</td><td align="center">...</td></tr> +<tr><td align="left">1904</td><td align="left">March 25th.</td><td align="left">May 3d. </td><td align="left">Sept. 23d.</td><td align="left">Feb. 1st.</td></tr> +<tr><td align="left">1905</td><td align="left">March 12th.</td><td align="left">July 26th.</td><td align="left">Sept. 23d.</td><td align="left">Dec. 19th.</td></tr> +<tr><td align="left">1906</td><td align="left">Feb. 27th.</td><td align="left">March 8th.</td><td align="left">Sept. 23d.</td><td align="center">...</td></tr> +<tr><td align="left">1907</td><td align="left">Feb. 14th.</td><td align="left">May 31st.</td><td align="left">Sept. 23d.</td><td align="left">Nov. 6th.</td></tr> +<tr><td align="left">1908</td><td align="left">Feb. 1st.</td><td align="left">Jan. 11th.</td><td align="left">Sept. 23d.</td><td align="center">...</td></tr> +<tr><td align="left">1909</td><td align="left">Jan. 18th.</td><td align="left">April 4th.</td><td align="left">Sept. 23d.</td><td align="left">Sept. 23d.</td></tr> +<tr><td align="left">1910</td><td align="left">Jan. 5th.</td><td align="left">June 28th.</td><td align="left">Sept. 23d.</td><td align="center">...</td></tr> +</tbody> +</table></div> + +<p>The first line of figures in this table shows the number +of days that each of these planets requires to make +a complete revolution about the sun, and it appears from +these numbers that Mercury makes about four revolutions<span class="pagenum"><a name="Page_44" id="Page_44">[Pg 44]</a></span> +in its orbit per year, and therefore crosses the prime radius +four times in each year, while the other planets are decidedly +slower in their movements. The following lines of +the table show for each year the date at which each planet +first crossed the prime radius in that year; the dates of +subsequent crossings in any year can be found by adding +once, twice, or three times the period to the given date, +and the table may be extended to later years, if need be, by +continuously adding multiples of the period. In the case +of Mars it appears that there is only about one year out of +two in which this planet crosses the prime radius.</p> + +<p>After the date at which the planet crosses the prime +radius has been determined its position for any required +date is found exactly as in the case of the earth, and the +constellation in which the planet will appear from the +earth is found as explained above in connection with Jupiter +and Saturn.</p> + +<p>The broken lines in the figure represent the construction +for finding the places in the sky occupied by Mercury, +Venus, and Mars on July 4, 1900. Let the student make a +similar construction and find the positions of these planets +at the present time. Look them up in the sky and see if +they are where your work puts them.</p> + +<p><a name="S_31" id="S_31"></a>31. <b>Exercises.</b>—The "evening star" is a term loosely +applied to any planet which is visible in the western sky +soon after sunset. It is easy to see that such a planet must +be farther toward the east in the sky than is the sun, and +in either <a href="#Fig_16">Fig. 16</a> or <a href="#Fig_17">Fig. 17</a> any planet which viewed from +the position of the earth lies to the left of the sun and +not more than 50° away from it will be an evening star. +If to the right of the sun it is a morning star, and may be +seen in the eastern sky shortly before sunrise.</p> + +<p>What planet is the evening star <i>now</i>? Is there more +than one evening star at a time? What is the morning +star now?</p> + +<p>Do Mercury, Venus, or Mars ever appear in opposition?<span class="pagenum"><a name="Page_45" id="Page_45">[Pg 45]</a></span> +What is the maximum angular distance from the sun at +which Venus can ever be seen? Why is Mercury a more +difficult planet to see than Venus? In what month of the +year does Mars come nearest to the earth? Will it always +be brighter in this month than in any other? Which of +all the planets comes nearest to the earth?</p> + +<p>The earth always comes to the same longitude on the +same day of each year. Why is not this true of the other +planets?</p> + +<p>The student should remember that in one respect Figs. <a href="#Fig_16">16</a> +and <a href="#Fig_17">17</a> are not altogether correct representations, since +they show the orbits as all lying in the same plane. If this +were strictly true, every planet would move, like the sun, +always along the ecliptic; but in fact all of the orbits are +tilted a little out of the plane of the ecliptic and every +planet in its motion deviates a little from the ecliptic, first +to one side then to the other; but not even Mars, which is +the most erratic in this respect, ever gets more than eight +degrees away from the ecliptic, and for the most part all +of them are much closer to the ecliptic than this limit.</p> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_46" id="Page_46">[Pg 46]</a></span></p> +<h2><a name="CHAPTER_IV" id="CHAPTER_IV"></a>CHAPTER IV</h2> + +<h3>CELESTIAL MECHANICS</h3> + + +<p><a name="S_32" id="S_32"></a>32. <b>The beginnings of celestial mechanics.</b>—From the earliest +dawn of civilization, long before the beginnings of +written history, the motions of sun and moon and planets +among the stars from constellation to constellation had +commanded the attention of thinking men, particularly of +the class of priests. The religions of which they were the +guardians and teachers stood in closest relations with the +movements of the stars, and their own power and influence +were increased by a knowledge of them.</p> + +<div class="figcenter" style="width: 500px;"><a name="ISAAC_NEWTON" id="ISAAC_NEWTON"></a> +<img src="images/i062.jpg" width="500" height="619" alt="ISAAC NEWTON (1643-1727)." title="ISAAC NEWTON (1643-1727)." /> +<span class="caption">ISAAC NEWTON (1643-1727).</span> +</div> + +<p>Out of these professional needs, as well as from a spirit +of scientific research, there grew up and flourished for +many centuries a study of the motions of the planets, simple +and crude at first, because the observations that could +then be made were at best but rough ones, but growing +more accurate and more complex as the development of the +mechanic arts put better and more precise instruments into +the hands of astronomers and enabled them to observe with +increasing accuracy the movements of these bodies. It was +early seen that while for the most part the planets, including +the sun and moon, traveled through the constellations +from west to east, some of them sometimes reversed their +motion and for a time traveled in the opposite way. This +clearly can not be explained by the simple theory which +had early been adopted that a planet moves always in the +same direction around a circular orbit having the earth at +its center, and so it was said to move around in a small +circular orbit, called an epicycle, whose center was situated<span class="pagenum"><a name="Page_47" id="Page_47">[Pg 47]</a></span> +upon and moved along a circular orbit, called the deferent, +within which the earth was placed, as is shown in <a href="#Fig_18">Fig. 18</a>, +where the small circle is the epicycle, the large circle is the +deferent, <i>P</i> is the planet, and <i>E</i> the earth. When this +proved inadequate to account for the really complicated +movements of the planets, another epicycle was put on top +of the first one, and then another and another, until the +supposed system became so complicated that Copernicus, a +Polish astronomer, repudiated +its fundamental theorem and +taught that the motions of +the planets take place in circles +around the sun instead +of about the earth, and that +the earth itself is only one of +the planets moving around +the sun in its own appropriate +orbit and itself largely responsible +for the seemingly +erratic movements of the +other planets, since from day to day we see them and observe +their positions from different points of view.</p> + +<div class="figright" style="width: 350px;"><a name="Fig_18" id="Fig_18"></a> +<img src="images/i064.png" width="350" height="333" alt="Fig. 18.—Epicycle and deferent." title="Fig. 18.—Epicycle and deferent." /> +<span class="caption"><span class="smcap">Fig. 18.</span>—Epicycle and deferent.</span> +</div> + +<p><a name="S_33" id="S_33"></a>33. <b>Kepler's laws.</b>—Two generations later came Kepler +with his three famous laws of planetary motion:</p> + +<p>I. Every planet moves in an ellipse which has the sun +at one of its foci.</p> + +<p>II. The radius vector of each planet moves over equal +areas in equal times.</p> + +<p>III. The squares of the periodic times of the planets +are proportional to the cubes of their mean distances from +the sun.</p> + +<p>These laws are the crowning glory, not only of Kepler's +career, but of all astronomical discovery from the beginning +up to his time, and they well deserve careful study +and explanation, although more modern progress has shown +that they are only approximately true.<span class="pagenum"><a name="Page_48" id="Page_48">[Pg 48]</a></span></p> + +<p><a name="Exercise_17" id="Exercise_17"></a><span class="smcap">Exercise 17.</span>—Drive two pins into a smooth board an +inch apart and fasten to them the ends of a string a foot +long. Take up the slack of the string with the point of a +lead pencil and, keeping the string drawn taut, move the +pencil point over the board into every possible position. +The curve thus traced will be an ellipse having the pins at +the two points which are called its foci.</p> + +<p>In the case of the planetary orbits one focus of the +ellipse is vacant, and, in accordance with the first law, the +center of the sun is at the other focus. In <a href="#Fig_17">Fig. 17</a> the dot, +inside the orbit of Mercury, which is marked <i>a</i>, shows the +position of the vacant focus of the orbit of Mars, and the +dot <i>b</i> is the vacant focus of Mercury's orbit. The orbits of +Venus and the earth are so nearly circular that their vacant +foci lie very close to the sun and are not marked in the +figure. The line drawn from the sun to any point of the +orbit (the string from pin to pencil point) is a <i>radius vector</i>. +The point midway between the pins is the <i>center</i> of the +ellipse, and the distance of either pin from the center measures +the <i>eccentricity</i> of the ellipse.</p> + +<p>Draw several ellipses with the same length of string, +but with the pins at different distances apart, and note that +the greater the eccentricity the flatter is the ellipse, but +that all of them have the same length.</p> + +<p>If both pins were driven into the same hole, what kind +of an ellipse would you get?</p> + +<p>The Second Law was worked out by Kepler as his answer +to a problem suggested by the first law. In <a href="#Fig_17">Fig. 17</a> it is +apparent from a mere inspection of the orbit of Mercury +that this planet travels much faster on one side of its orbit +than on the other, the distance covered in ten days between +the numbers 10 and 20 being more than fifty per cent greater +than that between 50 and 60. The same difference is found, +though usually in less degree, for every other planet, and +Kepler's problem was to discover a means by which to +mark upon the orbit the figures showing the positions of<span class="pagenum"><a name="Page_49" id="Page_49">[Pg 49]</a></span> +the planet at the end of equal intervals of time. His solution +of this problem, contained in the second law, asserts +that if we draw radii vectors from the sun to each of the +marked points taken at equal time intervals around the +orbit, then the area of the sector formed by two adjacent +radii vectores and the arc included between them is equal +to the area of each and every other such sector, the short +radii vectores being spread apart so as to include a long +arc between them while the long radii vectores have a short +arc. In Kepler's form of stating the law the radius vector +is supposed to travel with the planet and in each day to +sweep over the same fractional part of the total area of the +orbit. The spacing of the numbers in <a href="#Fig_17">Fig. 17</a> was done by +means of this law.</p> + +<p>For the proper understanding of Kepler's Third Law we +must note that the "mean distance" which appears in it is +one half of the long diameter of the orbit and that the +"periodic time" means the number of days or years required +by the planet to make a complete circuit in its orbit. +Representing the first of these by <i>a</i> and the second by <i>T</i>, +we have, as the mathematical equivalent of the law,</p> + +<p class="center"><i>a</i><sup>3</sup> ÷ <i>T</i><sup>2</sup> = <i>C</i></p> + +<p>where the quotient, <i>C</i>, is a number which, as Kepler found, +is the same for every planet of the solar system. If we take +the mean distance of the earth from the sun as the unit of +distance, and the year as the unit of time, we shall find by +applying the equation to the earth's motion, <i>C</i> = 1. Applying +this value to any other planet we shall find in the +same units, <i>a</i> = <i>T</i><sup>2/3</sup>, by means of which we may determine +the distance of any planet from the sun when its periodic +time, <i>T</i>, has been learned from observation.</p> + +<p><a name="Exercise_18" id="Exercise_18"></a><span class="smcap">Exercise 18.</span>—Uranus requires 84 years to make a +revolution in its orbit. What is its mean distance from the +sun? What are the mean distances of Mercury, Venus, and +Mars? (See <a href="#CHAPTER_III">Chapter III</a> for their periodic times.) Would<span class="pagenum"><a name="Page_50" id="Page_50">[Pg 50]</a></span> +it be possible for two planets at different distances from +the sun to move around their orbits in the same time?</p> + +<p>A circle is an ellipse in which the two foci have been +brought together. Would Kepler's laws hold true for such +an orbit?</p> + +<p><a name="S_34" id="S_34"></a>34. <b>Newton's laws of motion.</b>—Kepler studied and described +the motion of the planets. Newton, three generations +later (1727 <span class="smcap">A. D.</span>), studied and described the mechanism +which controls that motion. To Kepler and his age the +heavens were supernatural, while to Newton and his successors +they are a part of Nature, governed by the same +laws which obtain upon the earth, and we turn to the ordinary +things of everyday life as the foundation of celestial +mechanics.</p> + +<p>Every one who has ridden a bicycle knows that he can +coast farther upon a level road if it is smooth than if it is +rough; but however smooth and hard the road may be and +however fast the wheel may have been started, it is sooner +or later stopped by the resistance which the road and the +air offer to its motion, and when once stopped or checked +it can be started again only by applying fresh power. We +have here a familiar illustration of what is called</p> + +<p><b>The first law of motion.</b>—"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." A gust of wind, a stone, a careless movement of +the rider may turn the bicycle to the right or the left, but +unless some disturbing force is applied it will go straight +ahead, and if all resistance to its motion could be removed +it would go always at the speed given it by the last power +applied, swerving neither to the one hand nor the other.</p> + +<p>When a slow rider increases his speed we recognize at +once that he has applied additional power to the wheel, and +when this speed is slackened it equally shows that force has +been applied against the motion. It is force alone which +can produce a change in either velocity or direction of<span class="pagenum"><a name="Page_51" id="Page_51">[Pg 51]</a></span> +motion; but simple as this law now appears it required the +genius of Galileo to discover it and of Newton to give it the +form in which it is stated above.</p> + +<p><a name="S_35" id="S_35"></a>35. <b>The second law of motion</b>, which is also due to Galileo +and Newton, is:</p> + +<p>"Change of motion is proportional to force applied and +takes place in the direction of the straight line in which +the force acts." Suppose a man to fall from a balloon at +some great elevation in the air; his own weight is the force +which pulls him down, and that force operating at every +instant is sufficient to give him at the end of the first second +of his fall a downward velocity of 32 feet per second—i. e., +it has changed his state from rest, to motion at this +rate, and the motion is toward the earth because the force +acts in that direction. During the next second the ceaseless +operation of this force will have the same effect as in +the first second and will add another 32 feet to his velocity, +so that two seconds from the time he commenced to +fall he will be moving at the rate of 64 feet per second, etc. +The column of figures marked <i>v</i> in the table below shows +what his velocity will be at the end of subsequent seconds. +The changing velocity here shown is the change of motion +to which the law refers, and the velocity is proportional to +the time shown in the first column of the table, because the +amount of force exerted in this case is proportional to the +time during which it operated. The distance through +which the man will fall in each second is shown in the column +marked <i>d</i>, and is found by taking the average of his +velocity at the beginning and end of this second, and the +total distance through which he has fallen at the end of +each second, marked <i>s</i> in the table, is found by taking the +sum of all the preceding values of <i>d</i>. The velocity, 32 feet +per second, which measures the change of motion in each +second, also measures the <i>accelerating force</i> which produces +this motion, and it is usually represented in formulę by +the letter <i>g</i>. Let the student show from the numbers in<span class="pagenum"><a name="Page_52" id="Page_52">[Pg 52]</a></span> +the table that the accelerating force, the time, <i>t</i>, during +which it operates, and the space, <i>s</i>, fallen through, satisfy +the relation</p> + +<p class="center"><i>s</i> = 1/2 <i>gt</i><sup>2</sup>,</p> + +<p>which is usually called the law of falling bodies. How does +the table show that <i>g</i> is equal to 32?</p> + +<h3><span class="smcap">Table</span></h3> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><th align="center"><i>t</i></th><th align="center"><i>v</i></th><th align="center"><i>d</i></th><th align="center"><i>s</i></th></tr> +<tr><td align="center">0</td><td align="right">0</td><td align="right">0</td><td align="right">0</td></tr> +<tr><td align="center">1</td><td align="right">32</td><td align="right">16</td><td align="right">16</td></tr> +<tr><td align="center">2</td><td align="right">64</td><td align="right">48</td><td align="right">64</td></tr> +<tr><td align="center">3</td><td align="right">96</td><td align="right">80</td><td align="right">144</td></tr> +<tr><td align="center">4</td><td align="right">128</td><td align="right">112</td><td align="right">256</td></tr> +<tr><td align="center">5</td><td align="right">160</td><td align="right">144</td><td align="right">400</td></tr> +<tr><td align="center">etc.</td><td align="center">etc.</td><td align="center">etc.</td><td align="center">etc.</td></tr> +</table></div> + +<p>If the balloon were half a mile high how long would it +take to fall to the ground? What would be the velocity +just before reaching the ground?</p> + +<div class="figcenter" style="width: 500px;"><a name="GALILEO_GALILEI" id="GALILEO_GALILEI"></a> +<a href="images/i070-full.jpg"><img src="images/i070.jpg" width="500" height="674" alt="GALILEO GALILEI (1564-1642)." title="GALILEO GALILEI (1564-1642)." /></a> +<span class="caption">GALILEO GALILEI (1564-1642).</span> +</div> + +<p><a href="#Fig_19">Fig. 19</a> shows the path through the air of a ball which +has been struck by a bat at the point <i>A</i>, and started off in +the direction <i>A B</i> with a velocity of 200 feet per second. +In accordance with the first law of motion, if it were acted +upon by no other force than the impulse given by the bat, +it should travel along the straight line <i>A B</i> at the uniform +rate of 200 feet per second, and at the end of the fourth +second it should be 800 feet from <i>A</i>, at the point marked 4, +but during these four seconds its weight has caused it to +fall 256 feet, and its actual position, 4', is 256 feet below +the point 4. In this way we find its position at the end of +each second, 1', 2', 3', 4', etc., and drawing a line through +these points we shall find the actual path of the ball under +the influence of the two forces to be the curved line <i>A C</i>. +No matter how far the ball may go before striking the +ground, it can not get back to the point <i>A</i>, and the curve<span class="pagenum"><a name="Page_53" id="Page_53">[Pg 53]</a></span> +<i>A C</i> therefore can not be a part of a circle, since that curve +returns into itself. It is, in fact, a part of a <i>parabola</i>, +which, as we shall see later, is a kind of orbit in which +comets and some other heavenly bodies move. A skyrocket +moves in the same kind of a path, and so does a stone, a +bullet, or any other object hurled through the air.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_19" id="Fig_19"></a> +<img src="images/i072.png" width="500" height="449" alt="Fig. 19.—The path of a ball." title="Fig. 19.—The path of a ball." /> +<span class="caption"><span class="smcap">Fig. 19.</span>—The path of a ball.</span> +</div> + +<p><a name="S_36" id="S_36"></a>36. <b>The third law of motion.</b>—"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 is well illustrated in the case of a man +climbing a rope hand over hand. The direct force or action +which he exerts is a downward pull upon the rope, and it is +the reaction of the rope to this pull which lifts him along +it. We shall find in a later chapter a curious application +of this law to the history of the earth and moon.<span class="pagenum"><a name="Page_54" id="Page_54">[Pg 54]</a></span></p> + +<p>It is the great glory of Sir Isaac Newton that he first of +all men recognized that these simple laws of motion hold +true in the heavens as well as upon the earth; that the +complicated motion of a planet, a comet, or a star is determined +in accordance with these laws by the forces +which act upon the bodies, and that these forces are +essentially the same as that which we call weight. The +formal statement of the principle last named is included +in—</p> + +<p><a name="S_37" id="S_37"></a>37. <b>Newton's law of gravitation.</b>—"Every particle of +matter in the universe attracts every other particle with a +force whose direction is that of a line joining the two, and +whose magnitude is directly as the product of their masses, +and inversely as the square of their distance from each +other." We know that we ourselves and the things about +us are pulled toward the earth by a force (weight) which is +called, in the Latin that Newton wrote, <i>gravitas</i>, and the +word marks well the true significance of the law of gravitation. +Newton did not discover a new force in the heavens, +but he extended an old and familiar one from a limited +terrestrial sphere of action to an unlimited and celestial +one, and furnished a precise statement of the way in which +the force operates. Whether a body be hot or cold, wet or +dry, solid, liquid, or gaseous, is of no account in determining +the force which it exerts, since this depends solely +upon mass and distance.</p> + +<p>The student should perhaps be warned against straining +too far the language which it is customary to employ in +this connection. The law of gravitation is certainly a far-reaching +one, and it may operate in every remotest corner +of the universe precisely as stated above, but additional +information about those corners would be welcome to supplement +our rather scanty stock of knowledge concerning +what happens there. We may not controvert the words of +a popular preacher who says, "When I lift my hand I move +the stars in Ursa Major," but we should not wish to stand<span class="pagenum"><a name="Page_55" id="Page_55">[Pg 55]</a></span> +sponsor for them, even though they are justified by a rigorous +interpretation of the Newtonian law.</p> + +<p>The word <i>mass</i>, in the statement of the law of gravitation, +means the quantity of matter contained in the body, +and if we represent by the letters <i>m'</i> and <i>m''</i> the respective +quantities of matter contained in the two bodies whose distance +from each other is <i>r</i>, we shall have, in accordance +with the law of gravitation, the following mathematical +expression for the force, <i>F</i>, which acts between them:</p> + +<p class="center"><i>F</i> = <i>k</i> (<i>m'm''</i>)/<i>r</i><sup>2</sup>.</p> + +<p>This equation, which is the general mathematical expression +for the law of gravitation, may be made to yield +some curious results. Thus, if we select two bullets, each +having a mass of 1 gram, and place them so that their centers +are 1 centimeter apart, the above expression for the +force exerted between them becomes</p> + +<p class="center"><i>F</i> = <i>k</i> {(1 × 1)/1<sup>2</sup>} = <i>k</i>,</p> + +<p>from which it appears that the coefficient <i>k</i> is the force +exerted between these bodies. This is called the gravitation +constant, and it evidently furnishes a measure of the +specific intensity with which one particle of matter attracts +another. Elaborate experiments which have been made to +determine the amount of this force show that it is surprisingly +small, for in the case of the two bullets whose +mass of 1 gram each is supposed to be concentrated into +an indefinitely small space, gravity would have to operate +between them continuously for more than forty minutes in +order to pull them together, although they were separated +by only 1 centimeter to start with, and nothing save their +own inertia opposed their movements. It is only when one +or both of the masses <i>m'</i>, <i>m''</i> are very great that the force +of gravity becomes large, and the weight of bodies at the<span class="pagenum"><a name="Page_56" id="Page_56">[Pg 56]</a></span> +surface of the earth is considerable because of the great +quantity of matter which goes to make up the earth. +Many of the heavenly bodies are much more massive than +the earth, as the mathematical astronomers have found by +applying the law of gravitation to determine numerically +their masses, or, in more popular language, to "weigh" +them.</p> + +<p>The student should observe that the two terms mass +and weight are not synonymous; mass is defined above as +the quantity of matter contained in a body, while weight +is the force with which the earth attracts that body, and +in accordance with the law of gravitation its weight depends +upon its distance from the center of the earth, while +its mass is quite independent of its position with respect +to the earth.</p> + +<p>By the third law of motion the earth is pulled toward a +falling body just as strongly as the body is pulled toward +the earth—i. e., by a force equal to the weight of the body. +How much does the earth rise toward the body?</p> + +<p><a name="S_38" id="S_38"></a>38. <b>The motion of a planet.</b>—In <a href="#Fig_20">Fig. 20</a> <i>S</i> represents the +sun and <i>P</i> a planet or other celestial body, which for the +moment is moving along the straight line <i>P 1</i>. In accordance +with the first law of motion it would continue to move +along this line with uniform velocity if no external force +acted upon it; but such a force, the sun's attraction, is +acting, and by virtue of this attraction the body is pulled +aside from the line <i>P 1</i>.</p> + +<p>Knowing the velocity and direction of the body's motion +and the force with which the sun attracts it, the mathematician +is able to apply Newton's laws of motion so as to +determine the path of the body, and a few of the possible +orbits are shown in the figure where the short cross stroke +marks the point of each orbit which is nearest to the sun. +This point is called the <i>perihelion</i>.</p> + +<p>Without any formal application of mathematics we may +readily see that the swifter the motion of the body at <i>P</i><span class="pagenum"><a name="Page_57" id="Page_57">[Pg 57]</a></span> +the shorter will be the time during which it is subjected to +the sun's attraction at close range, and therefore the force +exerted by the sun, and the resulting change of motion, will +be small, as in the orbits <i>P 1</i> and <i>P 2</i>.</p> + +<p>On the other hand, <i>P 5</i> and <i>P 6</i> represent orbits in which +the velocity at <i>P</i> was comparatively small, and the resulting +change of motion greater +than would be possible for +a more swiftly moving body.</p> + +<p>What would be the orbit +if the velocity at <i>P</i> were +reduced to nothing at all?</p> + +<p>What would be the effect +if the body starting at <i>P</i> +moved directly away from <i>1</i>?</p> + +<div class="figright" style="width: 350px;"><a name="Fig_20" id="Fig_20"></a> +<img src="images/i076.png" width="350" height="411" alt="Fig. 20.—Different kinds of orbits." title="Fig. 20.—Different kinds of orbits." /> +<span class="caption"><span class="smcap">Fig. 20.</span>—Different kinds of orbits.</span> +</div> + +<p>The student should not +fail to observe that the sun's +attraction tends to pull the +body at <i>P</i> forward along its +path, and therefore increases +its velocity, and that this +influence continues until +the planet reaches perihelion, at which point it attains its +greatest velocity, and the force of the sun's attraction is +wholly expended in changing the direction of its motion. +After the planet has passed perihelion the sun begins to +pull backward and to retard the motion in just the same +measure that before perihelion passage it increased it, so +that the two halves of the orbit on opposite sides of a line +drawn from the perihelion through the sun are exactly +alike. We may here note the explanation of Kepler's second +law: when the planet is near the sun it moves faster, +and the radius vector changes its direction more rapidly +than when the planet is remote from the sun on account +of the greater force with which it is attracted, and the exact +relation between the rates at which the radius vector<span class="pagenum"><a name="Page_58" id="Page_58">[Pg 58]</a></span> +turns in different parts of the orbit, as given by the second +law, depends upon the changes in this force.</p> + +<p>When the velocity is not too great, the sun's backward +pull, after a planet has passed perihelion, finally overcomes +it and turns the planet toward the sun again, in such a way +that it comes back to the point <i>P</i>, moving in the same direction +and with the same speed as before—i. e., it has gone +around the sun in an orbit like <i>P 6</i> or <i>P 4</i>, an ellipse, along +which it will continue to move ever after. But we must +not fail to note that this return into the same orbit is a +consequence of the last line in the statement of the law of +gravitation (p. 54), and that, if the magnitude of this force +were inversely as the cube of the distance or any other proportion +than the square, the orbit would be something very +different. If the velocity is too great for the sun's attraction +to overcome, the orbit will be a hyperbola, like <i>P 2</i>, +along which the body will move away never to return, while +a velocity just at the limit of what the sun can control gives +an orbit like <i>P 3</i>, a parabola, along which the body moves +with <i>parabolic velocity</i>, which is ever diminishing as the +body gets farther from the sun, but is always just sufficient +to keep it from returning. If the earth's velocity could be +increased 41 per cent, from 19 up to 27 miles per second, it +would have parabolic velocity, and would quit the sun's +company.</p> + +<p>The summation of the whole matter is that the orbit in +which a body moves around the sun, or past the sun, depends +upon its velocity and if this velocity and the direction +of the motion at any one point in the orbit are known +the whole orbit is determined by them, and the position of +the planet in its orbit for past as well as future times can +be determined through the application of Newton's laws; +and the same is true for any other heavenly body—moon, +comet, meteor, etc. It is in this way that astronomers are +able to predict, years in advance, in what particular part of +the sky a given planet will appear at a given time.<span class="pagenum"><a name="Page_59" id="Page_59">[Pg 59]</a></span></p> + +<p>It is sometimes a source of wonder that the planets +move in ellipses instead of circles, but it is easily seen from +<a href="#Fig_20">Fig. 20</a> that the planet, <i>P</i>, could not by any possibility +move in a circle, since the direction of its motion at <i>P</i> is +not at right angles with the line joining it to the sun as it +must be in a circular orbit, and even if it were perpendicular +to the radius vector the planet must needs have +exactly the right velocity given to it at this point, since +either more or less speed would change the circle into an +ellipse. In order to produce circular motion there must be +a balancing of conditions as nice as is required to make a +pin stand upon its point, and the really surprising thing is +that the orbits of the planets should be so nearly circular +as they are. If the orbit of the earth were drawn accurately +to scale, the untrained eye would not detect the +slightest deviation from a true circle, and even the orbit of +Mercury (<a href="#Fig_17">Fig. 17</a>), which is much more +eccentric than that of the earth, might almost +pass for a circle.</p> + +<div class="figright" style="width: 200px;"><a name="Fig_21" id="Fig_21"></a> +<img src="images/i078.png" width="200" height="331" alt="Fig. 21. +An impossible orbit." title="Fig. 21. +An impossible orbit." /> +<span class="caption"><span class="smcap">Fig. 21.</span> +An impossible orbit.</span> +</div> + +<p>The orbit <i>P 2</i>, which lies between the +parabola and the straight line, is called in +geometry a hyperbola, and Newton succeeded +in proving from the law of gravitation +that a body might move under the +sun's attraction in a hyperbola as well as +in a parabola or ellipse; but it must move +in some one of these curves; no other orbit +is possible.<a name="FNanchor_A_1" id="FNanchor_A_1"></a><a href="#Footnote_A_1" class="fnanchor">[A]</a> Thus it would not be +possible for a body moving under the law +of gravitation to describe about the sun any such orbit +as is shown in <a href="#Fig_21">Fig. 21</a>. If the body passes a second time +through any point of its orbit, such as <i>P</i> in the figure, then +it must retrace, time after time, the whole path that it first<span class="pagenum"><a name="Page_60" id="Page_60">[Pg 60]</a></span> +traversed in getting from <i>P</i> around to <i>P</i> again—i. e., the +orbit must be an ellipse.</p> + +<p>Newton also proved that Kepler's three laws are mere +corollaries from the law of gravitation, and that to be +strictly correct the third law must be slightly altered so as +to take into account the masses of the planets. These are, +however, so small in comparison with that of the sun, that +the correction is of comparatively little moment.</p> + +<p><a name="S_39" id="S_39"></a>39. <b>Perturbations.</b>—In what precedes we have considered +the motion of a planet under the influence of no other +force than the sun's attraction, while in fact, as the law of +gravitation asserts, every other body in the universe is in +some measure attracting it and changing its motion. The +resulting disturbances in the motion of the attracted body +are called <i>perturbations</i>, but for the most part these are +insignificant, because the bodies by whose disturbing attractions +they are caused are either very small or very remote, +and it is only when our moving planet, <i>P</i>, comes under the +influence of some great disturbing power like Jupiter or +one of the other planets that the perturbations caused by +their influence need to be taken into account.</p> + +<p>The problem of the motion of three bodies—sun, Jupiter, +planet—which must then be dealt with is vastly more complicated +than that which we have considered, and the ablest +mathematicians and astronomers have not been able to furnish +a complete solution for it, although they have worked +upon the problem for two centuries, and have developed an +immense amount of detailed information concerning it.</p> + +<div class="figcenter" style="width: 600px;"><a name="LICK_OBSERVATORY" id="LICK_OBSERVATORY"></a> +<a href="images/i080-full.jpg"><img src="images/i080.jpg" width="600" height="338" alt="THE LICK OBSERVATORY, MOUNT HAMILTON, CAL." title="" /></a> +<span class="caption">THE LICK OBSERVATORY, MOUNT HAMILTON, CAL.</span> +</div> + +<p>In general each planet works ceaselessly upon the orbit +of every other, changing its size and shape and position, +backward and forward in accordance with the law of gravitation, +and it is a question of serious moment how far this +process may extend. If the diameter of the earth's orbit +were very much increased or diminished by the perturbing +action of the other planets, the amount of heat received +from the sun would be correspondingly changed, and the<span class="pagenum"><a name="Page_61" id="Page_61">[Pg 61]</a></span> +earth, perhaps, be rendered unfit for the support of life. +The tipping of the plane of the earth's orbit into a new +position might also produce serious consequences; but the +great French mathematician of a century ago, Laplace, +succeeded in proving from the law of gravitation that although +both of these changes are actually in progress they +can not, at least for millions of years, go far enough to +prove of serious consequence, and the same is true for all +the other planets, unless here and there an asteroid may +prove an exception to the rule.</p> + +<p>The precession (<a href="#CHAPTER_V">Chapter V</a>) is a striking illustration +of a perturbation of slightly different character from the +above, and another is found in connection with the plane +of the moon's orbit. It will be remembered that the moon +in its motion among the stars never goes far from the +ecliptic, but in a complete circuit of the heavens crosses it +twice, once in going from south to north and once in the +opposite direction. The points at which it crosses the +ecliptic are called the <i>nodes</i>, and under the perturbing influence +of the sun these nodes move westward along the +ecliptic about twenty degrees per year, an extraordinarily +rapid perturbation, and one of great consequence in the +theory of eclipses.</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_22" id="Fig_22"></a> +<img src="images/i083.png" width="350" height="335" alt="Fig. 22.—A planet subject to great perturbations +by Jupiter." title="Fig. 22.—A planet subject to great perturbations +by Jupiter." /> +<span class="caption"><span class="smcap">Fig. 22.</span>—A planet subject to great perturbations +by Jupiter.</span> +</div> + +<p><a name="S_40" id="S_40"></a>40. <b>Weighing the planets.</b>—Although these perturbations +can not be considered dangerous, they are interesting since +they furnish a method for weighing the planets which produce +them. From the law of gravitation we learn that the +ability of a planet to produce perturbations depends directly +upon its mass, since the force <i>F</i> which it exerts contains +this mass, <i>m'</i>, as a factor. So, too, the divisor <i>r</i><sup>2</sup> in +the expression for the force shows that the distance between +the disturbing and disturbed bodies is a matter of +great consequence, for the smaller the distance the greater +the force. When, therefore, the mass of a planet such as +Jupiter is to be determined from the perturbations it produces, +it is customary to select some such opportunity as<span class="pagenum"><a name="Page_62" id="Page_62">[Pg 62]</a></span> +is presented in <a href="#Fig_22">Fig. 22</a>, where one of the small planets, +called asteroids, is represented as moving in a very eccentric +orbit, which at one point approaches close to the orbit +of Jupiter, and at another place comes near to the orbit of +the earth. For the most part +Jupiter will not exert any +very great disturbing influence +upon a planet moving in +such an orbit as this, since it +is only at rare intervals that +the asteroid and Jupiter approach +so close to each other, +as is shown in the figure. +The time during which the +asteroid is little affected by +the attraction of Jupiter is +used to study the motion given +to it by the sun's attraction—that +is, to determine carefully the undisturbed orbit +in which it moves; but there comes a time at which the +asteroid passes close to Jupiter, as shown in the figure, and +the orbital motion which the sun imparts to it will then be +greatly disturbed, and when the planet next comes round +to the part of its orbit near the earth the effect of these +disturbances upon its apparent position in the sky will be +exaggerated by its close proximity to the earth. If now +the astronomer observes the actual position of the asteroid +in the sky, its right ascension and declination, and compares +these with the position assigned to the planet by the +law of gravitation when the attraction of Jupiter is ignored, +the differences between the observed right ascensions and +declinations and those computed upon the theory of undisturbed +motion will measure the influence that Jupiter has +had upon the asteroid, and the amount by which Jupiter has +shifted it, compared with the amount by which the sun has +moved it—that is, with the motion in its orbit—furnishes<span class="pagenum"><a name="Page_63" id="Page_63">[Pg 63]</a></span> +the mass of Jupiter expressed as a fractional part of the +mass of the sun.</p> + +<p>There has been determined in this manner the mass of +every planet in the solar system which is large enough to +produce any appreciable perturbation, and all these masses +prove to be exceedingly small fractions of the mass of the +sun, as may be seen from the following table, in which is +given opposite the name of each planet the number by +which the mass of the sun must be divided in order to +get the mass of the planet:</p> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left">Mercury</td><td align="right">7,000,000 (?)</td></tr> +<tr><td align="left">Venus</td><td align="right">408,000</td></tr> +<tr><td align="left">Earth</td><td align="right">329,000</td></tr> +<tr><td align="left">Mars</td><td align="right">3,093,500</td></tr> +<tr><td align="left">Jupiter</td><td align="right">1,047.4</td></tr> +<tr><td align="left">Saturn</td><td align="right">3,502</td></tr> +<tr><td align="left">Uranus</td><td align="right">22,800</td></tr> +<tr><td align="left">Neptune</td><td align="right">19,700</td></tr> +</table></div> + +<p>It is to be especially noted that the mass given for each +planet includes the mass of all the satellites which attend +it, since their influence was felt in the perturbations from +which the mass was derived. Thus the mass assigned to +the earth is the combined mass of earth and moon.</p> + +<p><a name="S_41" id="S_41"></a>41. <b>Discovery of Neptune.</b>—The most famous example of +perturbations is found in connection with the discovery, +in the year 1846, of Neptune, the outermost planet of the +solar system. For many years the motion of Uranus, his +next neighbor, had proved a puzzle to astronomers. In +accordance with Kepler's first law this planet should move +in an ellipse having the sun at one of its foci, but no ellipse +could be found which exactly fitted its observed path among +the stars, although, to be sure, the misfit was not very pronounced. +Astronomers surmised that the small deviations +of Uranus from the best path which theory combined with +observation could assign, were due to perturbations in its<span class="pagenum"><a name="Page_64" id="Page_64">[Pg 64]</a></span> +motion caused by an unknown planet more remote from +the sun—a thing easy to conjecture but hard to prove, and +harder still to find the unknown disturber. But almost +simultaneously two young men, Adams in England and +Le Verrier in France, attacked the problem quite independently +of each other, and carried it to a successful solution, +showing that if the irregularities in the motion of +Uranus were indeed caused by an unknown planet, then +that planet must, in September, 1846, be in the direction +of the constellation Aquarius; and there it was found on +September 23d by the astronomers of the Berlin Observatory +whom Le Verrier had invited to search for it, and found +within a degree of the exact point which the law of gravitation +in his hands had assigned to it.</p> + +<p>This working backward from the perturbations experienced +by Uranus to the cause which produced them is justly +regarded as one of the greatest scientific achievements of +the human intellect, and it is worthy of note that we are +approaching the time at which it may be repeated, for Neptune +now behaves much as did Uranus three quarters of a +century ago, and the most plausible explanation which can +be offered for these anomalies in its path is that the bounds +of the solar system must be again enlarged to include another +disturbing planet.</p> + +<p><a name="S_42" id="S_42"></a>42. <b>The shape of a planet.</b>—There is an effect of gravitation +not yet touched upon, which is of considerable interest +and wide application in astronomy—viz., its influence in determining +the shape of the heavenly bodies. The earth is +a globe because every part of it is drawn toward the center +by the attraction of the other parts, and if this attraction +on its surface were everywhere of equal force the material +of the earth would be crushed by it into a truly spherical +form, no matter what may have been the shape in which it +was originally made. But such is not the real condition of +the earth, for its diurnal rotation develops in every particle +of its body a force which is sometimes called <i>centrifugal</i>,<span class="pagenum"><a name="Page_65" id="Page_65">[Pg 65]</a></span> +but which is really nothing more than the inertia of its +particles, which tend at every moment to keep unchanged +the direction of their motion and which thus resist the attraction +that pulls them into a circular path marked out +by the earth's rotation, just as a stone tied at the end of +a string and swung swiftly in a circle pulls upon the +string and opposes the constraint which keeps it moving +in a circle. A few experiments with such a stone will +show that the faster it goes the harder does it pull upon +the string, and the same is true of each particle of the +earth, the swiftly moving ones near the equator having +a greater centrifugal force than the slow ones near the +poles. At the equator the centrifugal force is directly +opposed to the force of gravity, and in effect diminishes it, +so that, comparatively, there is an excess of gravity at the +poles which compresses the earth along its axis and causes +it to bulge out at the equator until a balance is thus restored. +As we have learned from the study of geography, +in the case of the earth, this compression amounts to about +27 miles, but in the larger planets, Jupiter and Saturn, it +is much greater, amounting to several thousand miles.</p> + +<p>But rotation is not the only influence that tends to +pull a planet out of shape. The attraction which the earth +exerts upon the moon is stronger on the near side and +weaker on the far side of our satellite than at its center, +and this difference of attraction tends to warp the moon, as +is illustrated in <a href="#Fig_23">Fig. 23</a> where <i>1</i>, <i>2</i>, and <i>3</i> represent pieces +of iron of equal mass placed in line on a table near a horseshoe +magnet, <i>H</i>. Each piece of iron is attracted by the +magnet and is held back by a weight to which it is +fastened by means of a cord running over a pulley, <i>P</i>, +at the edge of the table. These weights are all to be +supposed equally heavy and each of them pulls upon its +piece of iron with a force just sufficient to balance the +attraction of the magnet for the middle piece, No. <i>2</i>. +It is clear that under this arrangement No. <i>2</i> will move<span class="pagenum"><a name="Page_66" id="Page_66">[Pg 66]</a></span> +neither to the right nor to the left, since the forces exerted +upon it by the magnet and the weight just balance each +other. Upon No. <i>1</i>, however, the magnet pulls harder +than upon No. <i>2</i>, because it is nearer and its pull therefore +more than balances the force exerted by the weight, +so that No. <i>1</i> will be pulled away from No. <i>2</i> and will +stretch the elastic cords, which are represented by the +lines joining <i>1</i> and <i>2</i>, until their tension, together with the +force exerted by the weight, just balances the attraction +of the magnet. For No. <i>3</i>, the force exerted by the magnet +is less than that of the weight, and it will also be pulled +away from No. <i>2</i> until its elastic cords are stretched to the +proper tension. The net result is that the three blocks +which, without the magnet's influence, would be held close +together by the elastic cords, are pulled apart by this outside +force as far as the resistance of the cords will permit.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_23" id="Fig_23"></a> +<img src="images/i087.png" width="500" height="258" alt="Fig. 23.—Tide-raising forces." title="Fig. 23.—Tide-raising forces." /> +<span class="caption"><span class="smcap">Fig. 23.</span>—Tide-raising forces.</span> +</div> + +<p>An entirely analogous set of forces produces a similar +effect upon the shape of the moon. The elastic cords of +<a href="#Fig_23">Fig. 23</a> stand for the attraction of gravitation by which all +the parts of the moon are bound together. The magnet +represents the earth pulling with unequal force upon different +parts of the moon. The weights are the inertia of the +moon in its orbital motion which, as we have seen in a<span class="pagenum"><a name="Page_67" id="Page_67">[Pg 67]</a></span> +previous section, upon the whole just balances the earth's +attraction and keeps the moon from falling into it. The +effect of these forces is to stretch out the moon along a line +pointing toward the earth, just as the blocks were stretched +out along the line of the magnet, and to make this diameter +of the moon slightly but permanently longer than +the others.</p> + +<div class="figright" style="width: 200px;"><a name="Fig_24" id="Fig_24"></a> +<img src="images/i088.png" width="200" height="581" alt="Fig. 24.—The tides." title="Fig. 24.—The tides." /> +<span class="caption"><span class="smcap">Fig. 24.</span>—The tides.</span> +</div> + +<p><b>The tides.</b>—Similarly the moon and the sun attract opposite +sides of the earth with different forces and feebly +tend to pull it out of shape. But here +a new element comes into play: the +earth turns so rapidly upon its axis +that its solid parts have no time in +which to yield sensibly to the strains, +which shift rapidly from one diameter +to another as different parts of the +earth are turned toward the moon, and +it is chiefly the waters of the sea which +respond to the distorting effect of the +sun's and moon's attraction. These are +heaped up on opposite sides of the +earth so as to produce a slight elongation +of its diameter, and <a href="#Fig_24">Fig. 24</a> shows +how by the earth's rotation this swelling +of the waters is swept out from +under the moon and is pulled back by +the moon until it finally takes up some +such position as that shown in the figure +where the effect of the earth's rotation +in carrying it one way is just balanced +by the moon's attraction urging +it back on line with the moon. This heaping up of the +waters is called a <i>tide</i>. If <i>I</i> in the figure represents a little +island in the sea the waters which surround it will of +course accompany it in its diurnal rotation about the +earth's axis, but whenever the island comes back to the<span class="pagenum"><a name="Page_68" id="Page_68">[Pg 68]</a></span> +position <i>I</i>, the waters will swell up as a part of the tidal +wave and will encroach upon the land in what is called +high tide or flood tide. So too when they reach <i>I''</i>, half a +day later, they will again rise in flood tide, and midway +between these points, at <i>I'</i>, the waters must subside, giving +low or ebb tide.</p> + +<p>The height of the tide raised by the moon in the open +sea is only a very few feet, and the tide raised by the sun is +even less, but along the coast of a continent, in bays and +angles of the shore, it often happens that a broad but low +tidal wave is forced into a narrow corner, and then the rise +of the water may be many feet, especially when the solar +tide and the lunar tide come in together, as they do twice +in every month, at new and full moon. Why do they come +together at these times instead of some other?</p> + +<p>Small as are these tidal effects, it is worth noting that +they may in certain cases be very much greater—e. g., if +the moon were as massive as is the sun its tidal effect +would be some millions of times greater than it now is and +would suffice to grind the earth into fragments. Although +the earth escapes this fate, some other bodies are not so +fortunate, and we shall see in later chapters some evidence +of their disintegration.</p> + +<p><a name="S_43" id="S_43"></a>43. <b>The scope of the law of gravitation.</b>—In all the domain +of physical science there is no other law so famous as +the Newtonian law of gravitation; none other that has been +so dwelt upon, studied, and elaborated by astronomers and +mathematicians, and perhaps none that can be considered +so indisputably proved. Over and over again mathematical +analysis, based upon this law, has pointed out conclusions +which, though hitherto unsuspected, have afterward +been found true, as when Newton himself derived as a corollary +from this law that the earth ought to be flattened at +the poles—a thing not known at that time, and not proved +by actual measurement until long afterward. It is, in fact, +this capacity for predicting the unknown and for explaining<span class="pagenum"><a name="Page_69" id="Page_69">[Pg 69]</a></span> +in minutest detail the complicated phenomena of the +heavens and the earth that constitutes the real proof of the +law of gravitation, and it is therefore worth while to note +that at the present time there are a very few points at +which the law fails to furnish a satisfactory account of +things observed. Chief among these is the case of the planet +Mercury, the long diameter of whose orbit is slowly turning +around in a way for which the law of gravitation as yet furnishes +no explanation. Whether this is because the law itself +is inaccurate or incomplete, or whether it only marks a case +in which astronomers have not yet properly applied the +law and traced out its consequences, we do not know; but +whether it be the one or the other, this and other similar +cases show that even here, in its most perfect chapter, +astronomy still remains an incomplete science.</p> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_70" id="Page_70">[Pg 70]</a></span></p> +<h2><a name="CHAPTER_V" id="CHAPTER_V"></a>CHAPTER V</h2> + +<h3>THE EARTH AS A PLANET</h3> + + +<p><a name="S_44" id="S_44"></a>44. <b>The size of the earth.</b>—The student is presumed to +have learned, in his study of geography, that the earth is a +globe about 8,000 miles in diameter and, without dwelling +upon the "proofs" which are commonly given for these +statements, we proceed to consider the principles upon +which the measurement of +the earth's size and shape +are based.</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_25" id="Fig_25"></a> +<img src="images/i091.png" width="350" height="367" alt="Fig. 25.—Measuring the size of the earth." title="Fig. 25.—Measuring the size of the earth." /> +<span class="caption"><span class="smcap">Fig. 25.</span>—Measuring the size of the earth.</span> +</div> + +<p>In <a href="#Fig_25">Fig. 25</a> the circle represents +a meridian section +of the earth; <i>P P'</i> is the +axis about which it rotates, +and the dotted lines represent +a beam of light coming +from a star in the plane +of the meridian, and so distant +that the dotted lines +are all practically parallel +to each other. The several +radii drawn through the points <i>1</i>, <i>2</i>, <i>3</i>, represent the direction +of the vertical at these points, and the angles which +these radii produced, make with the rays of starlight are +each equal to the angular distance of the star from the +zenith of the place at the moment the star crosses the meridian. +We have already seen, in <a href="#CHAPTER_II">Chapter II</a>, how these +angles may be measured, and it is apparent from the figure +that the difference between any two of these angles—e. g.,<span class="pagenum"><a name="Page_71" id="Page_71">[Pg 71]</a></span> +the angles at <i>1</i> and <i>2</i>—is equal to the angle at the center, +<i>O</i>, between the points <i>1</i> and <i>2</i>. By measuring these angular +distances of the star from the zenith, the astronomer +finds the angles at the center of the earth between the stations +<i>1</i>, <i>2</i>, <i>3</i>, etc., at which his observations are made. If +the meridian were a perfect circle the change of zenith distance +of the star, as one traveled along a meridian from the +equator to the pole, would be perfectly uniform—the same +number of degrees for each hundred miles traveled—and +observations made in many parts of the earth show that +this is very nearly true, but that, on the whole, as we approach +the pole it is necessary to travel a little greater distance +than is required for a given change in the angle at +the equator. The earth is, in fact, flattened at the poles to +the amount of about 27 miles in the length of its diameter, +and by this amount, as well as by smaller variations due to +mountains and valleys, the shape of the earth differs from +a perfect sphere. These astronomical measurements of the +curvature of the earth's surface furnish by far the most satisfactory +proof that it is very approximately a sphere, and +furnish as its equatorial diameter 7,926 miles.</p> + +<p>Neglecting the <i>compression</i>, as it is called, i. e., the 27 +miles by which the equatorial diameter exceeds the polar, +the size of the earth may easily be found by measuring the +distance <i>1</i> - <i>2</i> along the surface and by combining with this +the angle <i>1 O 2</i> obtained through measuring the meridian +altitudes of any star as seen from <i>1</i> and <i>2</i>. Draw on paper +an angle equal to the measured difference of altitude and +find how far you must go from its vertex in order to have +the distance between the sides, measured along an arc of +a circle, equal to the measured distance between <i>1</i> and <i>2</i>. +This distance from the vertex will be the earth's radius.</p> + +<p><a name="Exercise_19" id="Exercise_19"></a><span class="smcap">Exercise 19.</span>—Measure the diameter of the earth by +the method given above. In order that this may be done +satisfactorily, the two stations at which observations are +made must be separated by a considerable distance—i. e.,<span class="pagenum"><a name="Page_72" id="Page_72">[Pg 72]</a></span> +200 miles. They need not be on the same meridian, but if +they are on different meridians in place of the actual distance +between them, there must be used the projection of +that distance upon the meridian—i. e., the north and south +part of the distance.</p> + +<p>By co-operation between schools in the Northern and +Southern States, using a good map to obtain the required +distances, the diameter of the earth +may be measured with the plumb-line +apparatus described in <a href="#CHAPTER_II">Chapter II</a> +and determined within a small +percentage of its true value.</p> + +<p><a name="S_45" id="S_45"></a>45. <b>The mass of the earth.</b>—We +have seen in <a href="#CHAPTER_IV">Chapter IV</a> the possibility +of determining the masses of +the planets as fractional parts of +the sun's mass, but nothing was +there shown, or could be shown, +about measuring these masses after +the common fashion in kilogrammes +or tons. To do this we must first +get the mass of the earth in tons or +kilogrammes, and while the principles +involved in this determination +are simple enough, their actual application +is delicate and difficult.</p> + +<div class="figleft" style="width: 225px;"><a name="Fig_26" id="Fig_26"></a> +<img src="images/i093.png" width="225" height="458" alt="Fig. 26.—Illustrating the principles +involved in weighing +the earth." title="Fig. 26.—Illustrating the principles +involved in weighing +the earth." /> +<span class="caption"><span class="smcap">Fig. 26.</span>—Illustrating the principles +involved in weighing +the earth.</span> +</div> + +<p>In <a href="#Fig_26">Fig. 26</a> we suppose a long +plumb line to be suspended above +the surface of the earth and to be attracted toward the +center of the earth, <i>C</i>, by a force whose intensity is (<a href="#CHAPTER_IV">Chapter IV</a>)</p> + +<p class="center"><i>F</i> = <i>k</i> <i>mE</i>/<i>R</i><sup>2</sup>,</p> + +<p>where <i>E</i> denotes the mass of the earth, which is to be determined +by experiment, and <i>R</i> is the radius of the earth, +3,963 miles. If there is no disturbing influence present,<span class="pagenum"><a name="Page_73" id="Page_73">[Pg 73]</a></span> +the plumb line will point directly downward, but if a massive +ball of lead or other heavy substance is placed at one +side, <i>1</i>, it will attract the plumb line with a force equal to</p> + +<p class="center"><i>f</i> = <i>k</i> <i>mB</i>/<i>r</i><sup>2</sup>,</p> + +<p>where <i>r</i> is the distance of its center from the plumb bob +and <i>B</i> is its mass which we may suppose, for illustration, +to be a ton. In consequence of this attraction the plumb +line will be pulled a little to one side, as shown by the dotted +line, and if we represent by <i>l</i> the length of the plumb +line and by <i>d</i> the distance between the original and the +disturbed positions of the plumb bob we may write the proportion</p> + +<p class="center"><i>F</i> : <i>f</i> :: <i>l</i> : <i>d</i>;</p> + +<p>and introducing the values of <i>F</i> and <i>f</i> given above, and +solving for <i>E</i> the proportion thus transformed, we find</p> + +<p class="center"><i>E</i> = <i>B</i> · <i>l</i>/<i>d</i> · (<i>R</i>/<i>r</i>)<sup>2</sup>.</p> + +<p>In this equation the mass of the ball, <i>B</i>, the length of the +plumb line, <i>l</i>, the distance between the center of the ball +and the center of the plumb bob, <i>r</i>, and the radius of the +earth, <i>R</i>, can all be measured directly, and <i>d</i>, the amount +by which the plumb bob is pulled to one side by the ball, is +readily found by shifting the ball over to the other side, at +<i>2</i>, and measuring with a microscope how far the plumb +bob moves. This distance will, of course, be equal to <i>2 d</i>.</p> + +<p>By methods involving these principles, but applied in a +manner more complicated as well as more precise, the mass +of the earth is found to be, in tons, 6,642 × 10<sup>18</sup>—i. e., 6,642 +followed by 18 ciphers, or in kilogrammes 60,258 × 10<sup>20</sup>. +The earth's atmosphere makes up about a millionth part +of this mass.</p> + +<p>If the length of the plumb line were 100 feet, the +weight of the ball a ton, and the distance between the two<span class="pagenum"><a name="Page_74" id="Page_74">[Pg 74]</a></span> +positions of the ball, <i>1</i> and <i>2</i>, six feet, how many inches, <i>d</i>, +would the plumb bob be pulled out of place?</p> + +<p>Find from the mass of the earth and the data of <a href="#S_40">§ 40</a> +the mass of the sun in tons. Find also the mass of Mars. +The computation can be very greatly abridged by the use +of logarithms.</p> + +<p><a name="S_46" id="S_46"></a>46. <b>Precession.</b>—That the earth is isolated in space and +has no support upon which to rest, is sufficiently shown by +the fact that the stars are visible upon every side of it, and +no support can be seen stretching out toward them. We +must then consider the earth to be a globe traveling freely +about the sun in a circuit which it completes once every +year, and rotating once in every twenty-four hours about +an axis which remains at all seasons directed very nearly +toward the star Polaris. The student should be able to +show from his own observations of the sun that, with reference +to the stars, the direction of the sun from the earth +changes about a degree a day. Does this prove that the +earth revolves about the sun?</p> + +<p>But it is only in appearance that the pole maintains its +fixed position among the stars. If photographs are taken +year after year, after the manner of <a href="#Exercise_7">Exercise 7</a>, it will be +found that slowly the pole is moving (nearly) toward Polaris, +and making this star describe a smaller and smaller +circle in its diurnal path, while stars on the other side of +the pole (in right ascension 12h.) become more distant +from it and describe larger circles in their diurnal motion; +but the process takes place so slowly that the space of a +lifetime is required for the motion of the pole to equal the +angular diameter of the full moon.</p> + +<p>Spin a top and note how its rapid whirl about its axis +corresponds to the earth's diurnal rotation. When the axis +about which the top spins is truly vertical the top "sleeps"; +but if the axis is tipped ever so little away from the vertical +it begins to wobble, so that if we imagine the axis prolonged +out to the sky and provided with a pencil point as<span class="pagenum"><a name="Page_75" id="Page_75">[Pg 75]</a></span> +a marker, this would trace a circle around the zenith, along +which the pole of the top would move, and a little observation +will show that the more the top is tipped from the +vertical the larger does this circle become and the more +rapidly does the wobbling take place. Were it not for the +spinning of the top about its axis, it would promptly fall +over when tipped from the vertical position, but the spin +combines with the force which pulls the top over and produces +the wobbling motion. Spin the top in opposite +directions, with the hands of a watch and contrary to the +hands of a watch, and note the effect which is produced +upon the wobbling.</p> + +<p>The earth presents many points of resemblance to the +top. Its diurnal rotation is the spin about the axis. This +axis is tipped 23.5° away from the perpendicular to its +orbit (obliquity of the ecliptic) just as the axis of the top +is tipped away from the vertical line. In consequence of +its rapid spin, the body of the earth bulges out at the equator +(27 miles), and the sun and moon, by virtue of their attraction +(see <a href="#CHAPTER_IV">Chapter IV</a>), lay hold of this protuberance and +pull it down toward the plane of the earth's orbit, so that if +it were not for the spin this force would straighten the axis +up and set it perpendicular to the orbit plane. But here, as +in the case of the top, the spin and the tipping force combine +to produce a wobble which is called precession, and +whose effect we recognize in the shifting position of the +pole among the stars. The motion of precession is very +much slower than the wobbling of the top, since the tipping +force for the earth is relatively very small, and a period +of nearly 26,000 years is required for a complete circuit +of the pole about its center of motion. Friction ultimately +stops both the spin and the wobble of the top, but +this influence seems wholly absent in the case of the earth, +and both rotation and precession go on unchanged from +century to century, save for certain minor forces which for +a time change the direction or rate of the precessional<span class="pagenum"><a name="Page_76" id="Page_76">[Pg 76]</a></span> +motion, first in one way and then in another, without in +the long run producing any results of consequence.</p> + +<p>The center of motion, about which the pole travels in a +small circle having an angular radius of 23.5°, is at that +point of the heavens toward which a perpendicular to the +plane of the earth's orbit points, and may be found on the +star map in right ascension 18h. 0m. and declination 66.5°.</p> + +<p><a name="Exercise_20" id="Exercise_20"></a><span class="smcap">Exercise 20.</span>—Find this point on the map, and draw +as well as you can the path of the pole about it. The motion +of the pole along its path is toward the constellation +Cepheus. Mark the position of the pole along this path +at intervals of 1,000 years, and refer to these positions in +dealing with some of the following questions:</p> + +<p>Does the wobbling of the top occur in the same direction +as the motion of precession? Do the tipping forces +applied to the earth and top act in the same direction? +What will be the polar star 12,000 years hence? The +Great Pyramid of Egypt is thought to have been used +as an observatory when Alpha Draconis was the bright star +nearest the pole. How long ago was that?</p> + +<p>The motion of the pole of course carries the equator +and the equinoxes with it, and thus slowly changes the +right ascensions and declinations of all the stars. On this +account it is frequently called the precession of the equinoxes, +and this motion of the equinox, slow though it is, +is a matter of some consequence in connection with chronology +and the length of the year.</p> + +<p>Will the precession ever bring back the right ascensions +and declinations to be again what they now are?</p> + +<p>In what direction is the pole moving with respect to +the Big Dipper? Will its motion ever bring it exactly to +Polaris? How far away from Polaris will the precession +carry the pole? What other bright stars will be brought +near the pole by the precession?</p> + +<p><a name="S_47" id="S_47"></a>47. <b>The warming of the earth.</b>—Winter and summer alike +the day is on the average warmer than the night, and it is<span class="pagenum"><a name="Page_77" id="Page_77">[Pg 77]</a></span> +easy to see that this surplus of heat comes from the sun by +day and is lost by night through radiation into the void +which surrounds the earth; just as the heat contained in a +mass of molten iron is radiated away and the iron cooled +when it is taken out from the furnace and placed amid +colder surroundings. The earth's loss of heat by radiation +goes on ceaselessly day and night, and were it not for the +influx of solar heat this radiation would steadily diminish +the temperature toward what is called the "absolute zero"—i. e., +a state in which all heat has been taken away and +beyond which there can be no greater degree of cold. This +must not be confounded with the zero temperatures shown +by our thermometers, since it lies nearly 500° below the zero +of the Fahrenheit scale (-273° Centigrade), a temperature +which by comparison makes the coldest winter weather +seem warm, although the ordinary thermometer may register +many degrees below its zero. The heat radiated by the +sun into the surrounding space on every side of it is another +example of the same cooling process, a hot body giving up +its heat to the colder space about it, and it is the minute +fraction of this heat poured out by the sun, and in small +part intercepted by the earth, which warms the latter and +produces what we call weather, climate, the seasons, etc.</p> + +<p>Observe the fluctuations, the ebb and flow, which are +inherent in this process. From sunset to sunrise there is +nothing to compensate the steady outflow of heat, and +air and ground grow steadily colder, but with the sunrise +there comes an influx of solar heat, feeble at first because +it strikes the earth's surface very obliquely, but becoming +more and more efficient as the sun rises higher in the sky. +But as the air and the ground grow warm during the morning +hours they part more and more readily and rapidly with +their store of heat, just as a steam pipe or a cup of coffee +radiates heat more rapidly when very hot. The warmest +hour of the day is reached when these opposing tendencies +of income and expenditure of heat are just balanced; and<span class="pagenum"><a name="Page_78" id="Page_78">[Pg 78]</a></span> +barring such disturbing factors as wind and clouds, the gain +in temperature usually extends to the time—an hour or two +beyond noon—at which the diminishing altitude of the sun +renders his rays less efficient, when radiation gains the +upper hand and the temperature becomes for a short time +stationary, and then commences to fall steadily until the +next sunrise.</p> + +<p>We have here an example of what is called a periodic +change—i. e., one which, within a definite and uniform +period (24 hours), oscillates from a minimum up to a +maximum temperature and then back again to a minimum, +repeating substantially the same variation day after day. +But it must be understood that minor causes not taken +into account above, such as winds, water, etc., produce +other fluctuations from day to day which sometimes obscure +or even obliterate the diurnal variation of temperature +caused by the sun.</p> + +<p>Expose the back of your hand to the sun, holding the +hand in such a position that the sunlight strikes perpendicularly +upon it; then turn the hand so that the light +falls quite obliquely upon it and note how much more vigorous +is the warming effect of the sun in the first position +than in the second. It is chiefly this difference of angle +that makes the sun's warmth more effective when he is +high up in the sky than when he is near the horizon, and +more effective in summer than in winter.</p> + +<p>We have seen in <a href="#CHAPTER_III">Chapter III</a> that the sun's motion +among the stars takes place along a path which carries it +alternately north and south of the equator to a distance +of 23.5°, and the stars show by their earlier risings and +later settings, as we pass from the equator toward the +north pole of the heavens, that as the sun moves northward +from the equator, each day in the northern hemisphere +will become a little longer, each night a little shorter, +and every day the sun will rise higher toward the zenith +until this process culminates toward the end of June, when<span class="pagenum"><a name="Page_79" id="Page_79">[Pg 79]</a></span> +the sun begins to move southward, bringing shorter days +and smaller altitudes until the Christmas season, when +again it is reversed and the sun moves northward. We +have here another periodic variation, which runs its complete +course in a period of a year, and it is easy to see that +this variation must have a marked effect on the warming +of the earth, the long days and great altitudes of summer +producing the greater warmth of that season, while the +shorter days and lower altitudes of December, by diminishing +the daily supply of solar heat, bring on the winter's +cold. The succession of the seasons, winter following summer +and summer winter, is caused by the varying altitude +of the sun, and this in turn is due to the obliquity of the +ecliptic, or, what is the same thing, the amount by which +the axis of the earth is tipped from being perpendicular to +the plane of its orbit, and the seasons are simply a periodic +change in the warming of the earth, quite comparable with +the diurnal change but of longer period.</p> + +<p>It is evident that the period within which the succession +of winter and summer is completed, the year, as we commonly +call it, must equal the time required by the sun to +go from the vernal equinox around to the vernal equinox +again, since this furnishes a complete cycle of the sun's +motions north and south from the equator. On account +of the westward motion of the equinox (precession) this +is not quite the same as the time required for a complete +revolution of the earth in its orbit, but is a little +shorter (20m. 23s.), since the equinox moves back to meet +the sun.</p> + +<p><a name="S_48" id="S_48"></a>48. <b>Relation of the sun to climate.</b>—It is clear that both +the northern and southern hemispheres of the earth must +have substantially the same kind of seasons, since the motion +of the sun north and south affects both alike; but +when the sun is north of the equator and warming our +hemisphere most effectively, his light falls more obliquely +upon the other hemisphere, the days there are short and<span class="pagenum"><a name="Page_80" id="Page_80">[Pg 80]</a></span> +winter reigns at the time we are enjoying summer, while +six months later the conditions are reversed.</p> + +<p>In those parts of the earth near the equator—the torrid +zone—there is no such marked change from cold to warm +as we experience, because, as the sun never gets more than +23.5° away from the celestial equator, on every day of the +year he mounts high in the tropic skies, always coming +within 23.5° of the zenith, and usually closer than this, so +that there is no such periodic change in the heat supply as +is experienced in higher latitudes, and within the tropics +the temperature is therefore both higher and more uniform +than in our latitude.</p> + +<p>In the frigid zones, on the contrary, the sun never rises +high in the sky; at the poles his greatest altitude is only +23.5°, and during the winter season he does not rise at all, +so that the temperature is here low the whole year round, +and during the winter season, when for weeks or months at +a time the supply of solar light is entirely cut off, the temperature +falls to a degree unknown in more favored climes.</p> + +<p>If the obliquity of the ecliptic were made 10° greater, +what would be the effect upon the seasons in the temperate +zones? What if it were made 10° less?</p> + +<p>Does the precession of the equinoxes have any effect +upon the seasons or upon the climate of different parts of +the earth?</p> + +<p>If the axis of the earth pointed toward Arcturus instead +of Polaris, would the seasons be any different from what +they are now?</p> + +<p><a name="S_49" id="S_49"></a>49. <b>The atmosphere.</b>—Although we live upon its surface, +we are not outside the earth, but at the bottom of a sea of +air which forms the earth's outermost layer and extends +above our heads to a height of many miles. The study of +most of the phenomena of the atmosphere belongs to that +branch of physics called meteorology, but there are a few +matters which fairly come within our consideration of the +earth as a planet.<span class="pagenum"><a name="Page_81" id="Page_81">[Pg 81]</a></span> We can not see the stars save as we look through this +atmosphere, and the light which comes through it is bent +and oftentimes distorted so as to present serious obstacles +to any accurate telescopic study of the heavenly bodies. +Frequently this disturbance is visible to the naked eye, and +the stars are said to twinkle—i. e., to quiver and change +color many times per second, solely in consequence of a disturbed +condition of the air and not from anything which +goes on in the star. This effect is more marked low down +in the sky than near the zenith, and it is worth noting that +the planets show very little of it because the light they +send to the earth comes from a disk of sensible area, while +a star, being much smaller and farther from the earth, has +its disk reduced practically to a mere point whose light is +more easily affected by local disturbances in the atmosphere +than is the broader beam which comes from the planets' +disk.</p> + +<p><a name="S_50" id="S_50"></a>50. <b>Refraction.</b>—At all times, whether the stars twinkle +or not, their light is bent in its passage through the atmosphere, +so that the stars appear to stand higher up in the +sky than their true positions. This effect, which the astronomer +calls refraction, must be allowed for in observations +of the more precise class, although save at low altitudes +its amount is a very small fraction of a degree, but +near the horizon it is much exaggerated in amount and +becomes easily visible to the naked eye by distorting the +disks of the sun and moon from circles into ovals with +their long diameters horizontal. The refraction lifts both +upper and lower edge of the sun, but lifts the lower edge +more than the upper, thus shortening the vertical diameter. +See <a href="#Fig_27">Fig. 27</a>, which shows not only this effect, but also the +reflection of the sun from the curved surface of the sea, +still further flattening the image. If the surface of the +water were flat, the reflected image would have the same +shape as the sun's disk, and its altered appearance is sometimes +cited as a proof that the earth's surface is curved.<span class="pagenum"><a name="Page_82" id="Page_82">[Pg 82]</a></span></p> + +<p>The total amount of the refraction at the horizon is a +little more than half a degree, and since the diameters of +the sun and moon subtend an angle of about half a degree, +we have the remarkable result that in reality the whole +disk of either sun or moon is below the horizon at the +instant that the lower edge appears to touch the horizon +and sunset or moonset begins. The same effect exists at +sunrise, and as a consequence the duration of sunshine or +of moonshine is on the average about six minutes longer +each day than it would be if there were no atmosphere and +no refraction. A partial offset to this benefit is found in +the fact that the atmosphere absorbs the light of the heavenly +bodies, so that stars appear much less bright when +near the horizon than when they are higher up in the sky, +and by reason of this absorption the setting sun can be +looked at with the naked eye without the discomfort which +its dazzling luster causes at noon.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_27" id="Fig_27"></a> +<a href="images/i103-full.jpg"><img src="images/i103.jpg" width="500" height="317" alt="Fig. 27.—Flattening of the sun's disk by refraction and by reflection from the +surface of the sea." title="Fig. 27.—Flattening of the sun's disk by refraction and by reflection from the +surface of the sea." /></a> +<span class="caption"><span class="smcap">Fig. 27.</span>—Flattening of the sun's disk by refraction and by reflection from the +surface of the sea.</span> +</div> + +<p><a name="S_51" id="S_51"></a>51. <b>The twilight.</b>—Another effect of the atmosphere, +even more marked than the preceding, is the twilight. As<span class="pagenum"><a name="Page_83" id="Page_83">[Pg 83]</a></span> +at sunrise the mountain top catches the rays of the coming +sun before they reach the lowland, and at sunset it keeps +them after they have faded from the regions below, so the +particles of dust and vapor, which always float in the atmosphere, +catch the sunlight and reflect it to the surface of the +earth while the sun is still below the horizon, giving at the +beginning and end of day that vague and diffuse light which +we call twilight.</p> + +<div class="figright" style="width: 350px;"><a name="Fig_28" id="Fig_28"></a> +<img src="images/i104.png" width="350" height="170" alt="Fig. 28.—Twilight phenomena." title="Fig. 28.—Twilight phenomena." /> +<span class="caption"><span class="smcap">Fig. 28.</span>—Twilight phenomena.</span> +</div> + +<p><a href="#Fig_28">Fig. 28</a> shows a part of the earth surrounded by such a +dust-laden atmosphere, which is illuminated on the left by +the rays of the sun, but which, on the right of the figure, +lies in the shadow cast +by the earth. To an +observer placed at <i>1</i> the +sun is just setting, and +all the atmosphere +above him is illumined +with its rays, which +furnish a bright twilight. +When, by the earth's rotation, this observer has been +carried to <i>2</i>, all the region to the east of his zenith lies in +the shadow, while to the west there is a part of the atmosphere +from which there still comes a twilight, but now comparatively +faint, because the lower part of the atmosphere +about our observer lies in the shadow, and it is mainly +its upper regions from which the light comes, and here the +dust and moisture are much less abundant than in the lower +strata. Still later, when the observer has been carried by the +earth's rotation to the point <i>3</i>, every vestige of twilight will +have vanished from his sky, because all of the illuminated +part of the atmosphere is now below his horizon, which is +represented by the line <i>3 L</i>. In the figure the sun is represented +to be 78° below this horizon line at the end of twilight, +but this is a gross exaggeration, made for the sake of +clearness in the drawing—in fact, twilight is usually said +to end when the sun is 18° below the horizon.<span class="pagenum"><a name="Page_84" id="Page_84">[Pg 84]</a></span></p> + +<p>Let the student redraw <a href="#Fig_28">Fig. 28</a> on a large scale, so that +the points <i>1</i> and <i>3</i> shall be only 18° apart, as seen from the +earth's center. He will find that the point <i>L</i> is brought +down much closer to the surface of the earth, and measuring +the length of the line <i>2 L</i>, he should find for the "height +of the atmosphere" about one-eightieth part of the radius +of the earth—i. e., a little less than 50 miles. This, however, +is not the true height of the atmosphere. The air +extends far beyond this, but the particles of dust and vapor +which are capable of sending sunlight down to the earth +seem all to lie below this limit.</p> + +<p>The student should not fail to watch the eastern sky +after sunset, and see the shadow of the earth rise up and +fill it while the twilight arch retreats steadily toward the +west.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_29" id="Fig_29"></a> +<img src="images/i105.png" width="500" height="191" alt="Fig. 29.—The cause of long and short twilights." title="Fig. 29.—The cause of long and short twilights." /> +<span class="caption"><span class="smcap">Fig. 29.</span>—The cause of long and short twilights.</span> +</div> + +<p><i>Duration of twilight.</i>—Since twilight ends when the sun +is 18° below the horizon, any circumstance which makes +the sun go down rapidly will shorten the duration of twilight, +and anything which retards the downward motion +of the sun will correspondingly prolong it. Chief among +influences of this kind is the angle which the sun's course +makes with the horizon. If it goes straight down, as at +<i>a</i>, <a href="#Fig_29">Fig. 29</a>, a much shorter time will suffice to carry it to +a depression of 18° than is needed in the case shown at +<i>b</i> in the same figure, where the motion is very oblique to +the horizon. If we consider different latitudes and different +seasons of the year, we shall find every possible variety +<span class="pagenum"><a name="Page_85" id="Page_85">[Pg 85]</a></span> +of circumstance from <i>a</i> to <i>b</i>, and corresponding to these, +the duration of twilight varies from an all-night duration +in the summers of Scotland and more northern lands to an +hour or less in the mountains of Peru. For the sake of +graphical effect, the shortness of tropical twilight is somewhat +exaggerated by Coleridge in the lines,</p> + +<div class="poem"><div class="stanza"> +<span class="i0">"The sun's rim dips; the stars rush out:<br /></span> +<span class="i0">At one stride comes the dark."<br /></span> +<span class="i24"><i>The Ancient Mariner.</i><br /></span> +</div></div> + +<p>In the United States the longest twilights come at the +end of June, and last for a little more than two hours, +while the shortest ones are in March and September, +amounting to a little more than an hour and a half; but +at all times the last half hour of twilight is hardly to be +distinguished from night, so small is the quantity of reflecting +matter in the upper regions of the atmosphere. +For practical convenience it is customary to assume in +the courts of law that twilight ends an hour after sunset.</p> + +<p>How long does twilight last at the north pole?</p> + +<p><i>The Aurora.</i>—One other phenomenon of the atmosphere +may be mentioned, only to point out that it is not +of an astronomical character. The Aurora, or northern +lights, is as purely an affair of the earth as is a thunderstorm, +and its explanation belongs to the subject of terrestrial +magnetism.</p> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_86" id="Page_86">[Pg 86]</a></span></p> +<h2><a name="CHAPTER_VI" id="CHAPTER_VI"></a>CHAPTER VI</h2> + +<h3>THE MEASUREMENT OF TIME</h3> + + +<p><a name="S_52" id="S_52"></a>52. <b>Solar time.</b>—To measure any quantity we need a unit +in terms of which it must be expressed. Angles are measured +in degrees, and the degree is the unit for angular measurement. +For most scientific purposes the centimeter is +adopted as the unit with which to measure distances, and +similarly a day is the fundamental unit for the measurement +of time. Hours, minutes, and seconds are aliquot +parts of this unit convenient for use in dealing with shorter +periods than a day, and the week, month, and year which +we use in our calendars are multiples of the day.</p> + +<p>Strictly speaking, a day is not the time required by the +earth to make one revolution upon its axis, but it is best +defined as the amount of time required for a particular part +of the sky to make the complete circuit from the meridian +of a particular place through west and east back to the +meridian again. The day begins at the moment when this +specified part of the sky is on the meridian, and "the time" +at any moment is the hour angle of this particular part of +the sky—i. e., the number of hours, minutes, etc., that have +elapsed since it was on the meridian.</p> + +<p>The student has already become familiar with the kind +of day which is based upon the motion of the vernal equinox, +and which furnishes sidereal time, and he has seen +that sidereal time, while very convenient in dealing with +the motions of the stars, is decidedly inconvenient for the +ordinary affairs of life since in the reckoning of the hours +it takes no account of daylight and darkness. One can not<span class="pagenum"><a name="Page_87" id="Page_87">[Pg 87]</a></span> +tell off-hand whether 10 hours, sidereal time, falls in the day +or in the night. We must in some way obtain a day and a +system of time reckoning based upon the apparent diurnal +motion of the sun, and we may, if we choose, take the sun +itself as the point in the heavens whose transit over the +meridian shall mark the beginning and the end of the day. +In this system "the time" is the number of hours, minutes, +etc., which have elapsed since the sun was on the meridian, +and this is the kind of time which is shown by a sun dial, +and which was in general use, years ago, before clocks and +watches became common. Since the sun moves among the +stars about a degree per day, it is easily seen that the rotating +earth will have to turn farther in order to carry any +particular meridian from the sun around to the sun again, +than to carry it from a star around to the same star, or +from the vernal equinox around to the vernal equinox +again; just as the minute hand of a clock turns farther +in going from the hour hand round to the hour hand again +than it turns in going from XII to XII. These solar days +and hours and minutes are therefore a little longer than +the corresponding sidereal ones, and this furnishes the explanation +why the stars come to the meridian a little earlier, +by solar time, every night than on the night before, and +why sidereal time gains steadily upon solar time, this gain +amounting to approximately 3m. 56.5s. per day, or exactly +one day per year, since the sun makes the complete circuit +of the constellations once in a year.</p> + +<p>With the general introduction of clocks and watches +into use about a century ago this kind of solar time went +out of common use, since no well-regulated clock could +keep the time correctly. The earth in its orbital motion +around the sun goes faster in some parts of its orbit than +in others, and in consequence the sun appears to move +more rapidly among the stars in winter than in summer; +moreover, on account of the convergence of hour circles +as we go away from the equator, the same amount of motion<span class="pagenum"><a name="Page_88" id="Page_88">[Pg 88]</a></span> +along the ecliptic produces more effect in winter and +summer when the sun is north or south, than it does in the +spring and autumn when the sun is near the equator, and +as a combined result of these causes and other minor ones +true solar time, as it is called, is itself not uniform, but +falls behind the uniform lapse of sidereal time at a variable +rate, sometimes quicker, sometimes slower. A true solar +day, from noon to noon, is 51 seconds shorter in September +than in December.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_30" id="Fig_30"></a> +<img src="images/i109.png" width="500" height="242" alt="Fig. 30.—The equation of time." title="" /> +<span class="caption"><span class="smcap">Fig. 30.</span>—The equation of time.</span> +</div> + +<p><a name="S_53" id="S_53"></a>53. <b>Mean solar time.</b>—To remedy these inconveniences +there has been invented and brought into common use +what is called <i>mean solar time</i>, which is perfectly uniform +in its lapse and which, by comparison with sidereal time, +loses exactly one day per year. "The time" in this system +never differs much from true solar time, and the difference +between the two for any particular day may be found in +any good almanac, or may be read from the curve in <a href="#Fig_30">Fig. 30</a>, +in which the part of the curve above the line marked +<i>0m</i> shows how many minutes mean solar time is faster than +true solar time. The correct name for this difference between +the two kinds of solar time is the <i>equation of time</i>, but +in the almanacs it is frequently marked "sun fast" or "sun +slow." In sidereal time and true solar time the distinction<span class="pagenum"><a name="Page_89" id="Page_89">[Pg 89]</a></span> +between <span class="smcap">A. M.</span> hours (<i>ante meridiem</i> = before the sun reaches +the meridian) and <span class="smcap">P. M.</span> hours (<i>post meridiem</i> = after the +sun has passed the meridian) is not observed, "the time" +being counted from 0 hours to 24 hours, commencing when +the sun or vernal equinox is on the meridian. Occasionally +the attempt is made to introduce into common use +this mode of reckoning the hours, beginning the day +(date) at midnight and counting the hours consecutively +up to 24, when the next date is reached and a new start +made. Such a system would simplify railway time tables +and similar publications; but the American public is slow +to adopt it, although the system has come into practical +use in Canada and Spain.</p> + +<p><a name="S_54" id="S_54"></a>54. <b>To find (approximately) the sidereal time at any moment.</b>—<span class="smcap">Rule +I.</span> When the mean solar time is known. Let +<i>W</i> represent the time shown by an ordinary watch, and +represent by <i>S</i> the corresponding sidereal time and by <i>D</i> +the number of days that have elapsed from March 23d to +the date in question. Then</p> + +<p class="center"><i>S</i> = <i>W</i> + 69/70 × <i>D</i> × 4.</p> + +<p>The last term is expressed in minutes, and should be reduced +to hours and minutes. Thus at 4 <span class="smcap">P. M.</span> on July 4th—</p> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="right"><i>D</i></td><td align="center">=</td><td align="left">103 days.</td></tr> +<tr><td align="right">69/70 × <i>D</i> × 4</td><td align="center">=</td><td align="left">406m.</td></tr> +<tr><td align="right"></td><td align="center">=</td><td align="left">6h. 46m.</td></tr> +<tr><td align="right"><i>W</i></td><td align="center">=</td><td align="left">4h. 0m.</td></tr> +<tr><td align="right"><i>S</i></td><td align="center">=</td><td align="left">10h. 46m.</td></tr> +</table></div> + +<p>The daily gain of sidereal upon mean solar time is 69/70 of 4 +minutes, and March 23d is the date on which sidereal and +mean solar time are together, taking the average of one year +with another, but it varies a little from year to year on +account of the extra day introduced in leap years.</p> + +<p><span class="smcap">Rule II.</span> When the stars in the northern sky can be +seen. Find β Cassiopeię, and imagine a line drawn from it<span class="pagenum"><a name="Page_90" id="Page_90">[Pg 90]</a></span> +to Polaris, and another line from Polaris to the zenith. +The sidereal time is equal to the angle between these lines, +provided that that angle must be measured from the zenith +toward the west. Turn the angle from degrees into hours +by dividing by 15.</p> + +<p><a name="S_55" id="S_55"></a>55. <b>The earth's rotation.</b>—We are familiar with the fact +that a watch may run faster at one time than at another, +and it is worth while to inquire if the same is not true of +our chief timepiece—the earth. It is assumed in the sections +upon the measurement of time that the earth turns +about its axis with absolute uniformity, so that mean solar +time never gains or loses even the smallest fraction of a +second. Whether this be absolutely true or not, no one has +ever succeeded in finding convincing proof of a variation +large enough to be measured, although it has recently been +shown that the axis about which it rotates is not perfectly +fixed within the body of the earth. The solid body of the +earth wriggles about this axis like a fish upon a hook, so +that the position of the north pole upon the earth's surface +changes within a year to the extent of 40 or 50 feet +(15 meters) without ever getting more than this distance +away from its average position. This is probably caused +by the periodical shifting of masses of air and water from +one part of the earth to another as the seasons change, +and it seems probable that these changes will produce +some small effect upon the rotation of the earth. But in +spite of these, for any such moderate interval of time as a +year or a century, so far as present knowledge goes, we may +regard the earth's rotation as uniform and undisturbed. +For longer intervals—e. g., 1,000,000 or 10,000,000 years—the +question is a very different one, and we shall have to +meet it again in another connection.</p> + +<div class="figright" style="width: 350px;"><a name="Fig_31" id="Fig_31"></a> +<img src="images/i112.png" width="350" height="252" alt="Fig. 31.—Longitude and time" title="Fig. 31.—Longitude and time" /> +<span class="caption"><span class="smcap">Fig. 31.</span>—Longitude and time</span> +</div> + +<p><a name="S_56" id="S_56"></a>56. <b>Longitude and time.</b>—In what precedes there has +been constant reference to the meridian. The day begins +when the sun is on the meridian. Solar time is the angular +distance of the sun past the meridian. Sidereal time<span class="pagenum"><a name="Page_91" id="Page_91">[Pg 91]</a></span> +was determined by observing transits of stars over a meridian +line actually laid out upon the ground, etc. But +every place upon the earth has its own meridian from +which "the time" may be reckoned, and in <a href="#Fig_31">Fig. 31</a>, where +the rays of sunlight +are represented as +falling upon a part +of the earth's equator +through which +the meridians of +New York, Chicago, +and San Francisco +pass, it is evident +that these rays make +different angles with +the meridians, and +that the sun is farther from the meridian of New York +than from that of San Francisco by an amount just equal +to the angle at <i>O</i> between these meridians. This angle is +called by geographers the difference of longitude between +the two places, and the student should note that the word +longitude is here used in a different sense from that on +<a href="#Page_36">page 36</a>. From <a href="#Fig_31">Fig. 31</a> we obtain the</p> + +<p><i>Theorem.</i>—The difference between "the times" at any +two meridians is equal to their difference of longitude, and +the time at the eastern meridian is greater than at the +western meridian. Astronomers usually express differences +of longitude in hours instead of degrees. 1h. = 15°.</p> + +<p>The name given to any kind of time should distinguish +all the elements which enter into it—e. g., New York +sidereal time means the hour angle of the vernal equinox +measured from the meridian of New York, Chicago true +solar time is the hour angle of the sun reckoned from the +meridian of Chicago, etc.</p> + +<div class="figcenter" style="width: 600px;"><a name="Fig_32" id="Fig_32"></a> +<a href="images/i113-full.png"><img src="images/i113.png" width="600" height="422" alt="Fig. 32.—Standard time." title="Fig. 32.—Standard time." /></a> +<span class="caption"><span class="smcap">Fig. 32.</span>—Standard time.</span> +</div> + +<p><a name="S_57" id="S_57"></a>57. <b>Standard time.</b>—The requirements of railroad traffic +have led to the use throughout the United States and<span class="pagenum"><a name="Page_93" id="Page_93">[Pg 93]</a></span> +Canada of four "standard times," each of which is a mean +solar time some integral number of hours slower than the +time of the meridian passing through the Royal Observatory +at Greenwich, England.</p> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left">Eastern</td><td align="center">time is</td><td align="center">5</td><td align="center">hours</td><td align="center">slower</td><td align="center">than</td><td align="center">that</td><td align="center">of Greenwich.</td></tr> +<tr><td align="left">Central</td><td align="center">"</td><td align="center">6</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td></tr> +<tr><td align="left">Mountain</td><td align="center">"</td><td align="center">7</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td></tr> +<tr><td align="left">Pacific</td><td align="center">"</td><td align="center">8</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td></tr> +</table></div> + +<p>In <a href="#Fig_32">Fig. 32</a> the broken lines indicate roughly the parts of +the United States and Canada in which these several kinds +of time are used, and illustrate how irregular are the boundaries +of these parts.</p> + +<p>Standard time is sent daily into all of the more important +telegraph offices of the United States, and serves to +regulate watches and clocks, to the almost complete exclusion +of local time.</p> + +<p><a name="S_58" id="S_58"></a>58. <b>To determine the longitude.</b>—With an ordinary watch +observe the time of the sun's transit over your local meridian, +and correct the observed time for the equation of +time by means of the curve in <a href="#Fig_30">Fig. 30</a>. The difference +between the corrected time and 12 o'clock will be the correction +of your watch referred to local mean solar time. +Compare your watch with the time signals in the nearest +telegraph office and find its correction referred to standard +time. The difference between the two corrections is the +difference between your longitude and that of the standard +meridian.</p> + +<p>N. B.—Don't tamper with the watch by trying to "set it +right." No harm will be done if it is wrong, provided you +take due account of the correction as indicated above.</p> + +<p>If the correction of the watch changed between your +observation and the comparison in the telegraph office, +what effect would it have upon the longitude determination? +How can you avoid this effect?</p> + +<p><a name="S_59" id="S_59"></a>59. <b>Chronology.</b>—The Century Dictionary defines chronology +as "the science of time"—that is, "the method of<span class="pagenum"><a name="Page_94" id="Page_94">[Pg 94]</a></span> +measuring or computing time by regular divisions or periods +according to the revolutions of the sun or moon."</p> + +<p>We have already seen that for the measurement of short +intervals of time the day and its subdivisions—hours, +minutes, seconds—furnish a very complete and convenient +system. But for longer periods, extending to hundreds and +thousands of days, a larger unit of time is required, and for +the most part these longer units have in all ages and among +all peoples been based upon astronomical considerations. +But to this there is one marked exception. The week is a +simple multiple of the day, as the dime is a multiple of the +cent, and while it may have had its origin in the changing +phases of the moon this is at best doubtful, since it does +not follow these with any considerable accuracy. If the +still longer units of time—the month and the year—had +equally been made to consist of an integral number of days +much confusion and misunderstanding might have been +avoided, and the annals of ancient times would have presented +fewer pitfalls to the historian than is now the case. +The month is plainly connected with the motion of the +moon among the stars. The year is, of course, based upon +the motion of the sun through the heavens and the change +of seasons which is thus produced; although, as commonly +employed, it is not quite the same as the time required by +the earth to make one complete revolution in its orbit. +This time of one revolution is called a sidereal year, while, +as we have already seen in <a href="#CHAPTER_V">Chapter V</a>, the year which +measures the course of the seasons is shorter than this on +account of the precession of the equinoxes. It is called a +tropical year with reference to the circuit which the sun +makes from one tropic to the other and back again.</p> + +<p>We can readily understand why primitive peoples should +adopt as units of time these natural periods, but in so +doing they incurred much the same kind of difficulty that +we should experience in trying to use both English and +American money in the ordinary transactions of life. How<span class="pagenum"><a name="Page_95" id="Page_95">[Pg 95]</a></span> +many dollars make a pound sterling? How shall we make +change with English shillings and American dimes, etc.? +How much is one unit worth in terms of the other?</p> + +<p>One of the Greek poets<a name="FNanchor_B_2" id="FNanchor_B_2"></a><a href="#Footnote_B_2" class="fnanchor">[B]</a> has left us a quaint account of +the confusion which existed in his time with regard to the +place of months and moons in the calendar:</p> + +<div class="poem"><div class="stanza"> +<span class="i0">"The moon by us to you her greeting sends,<br /></span> +<span class="i0">But bids us say that she's an ill-used moon<br /></span> +<span class="i0">And takes it much amiss that you will still<br /></span> +<span class="i0">Shuffle her days and turn them topsy-turvy,<br /></span> +<span class="i0">So that when gods, who know their feast days well,<br /></span> +<span class="i0">By your false count are sent home supperless,<br /></span> +<span class="i0">They scold and storm at her for your neglect."<br /></span> +</div></div> + + +<p><a name="S_60" id="S_60"></a>60. <b>Day, month, and year.</b>—If the day, the month, and +the year are to be used concurrently, it is necessary to +determine how many days are contained in the month and +year, and when this has been done by the astronomer the +numbers are found to be very awkward and inconvenient +for daily use; and much of the history of chronology +consists in an account of the various devices by which ingenious +men have sought to use integral numbers to replace +the cumbrous decimal fractions which follow.</p> + +<p>According to Professor Harkness, for the epoch 1900 +<span class="smcap">A. D.</span>—</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="center">One</td><td align="center">tropical</td><td align="center">year</td><td align="center">=</td><td align="left">365.242197 mean solar days.</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">=</td><td align="left">365d. 5h. 48m. 45.8s.</td></tr> +</table></div> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="center">One</td><td align="center">lunation</td><td align="center">=</td><td align="left">29.530588 mean solar days.</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td align="center">=</td><td align="left">29d. 12h. 44m. 2.8s.</td></tr> +</table></div> + +<p>The word <i>lunation</i> means the average interval from one +new moon to the next one—i. e., the time required by the +moon to go from conjunction with the sun round to conjunction +again.</p> + +<p>A very ancient device was to call a year equal to 365<span class="pagenum"><a name="Page_96" id="Page_96">[Pg 96]</a></span> +days, and to have months alternately of 29 and 30 days in +length, but this was unsatisfactory in more than one way. +At the end of four years this artificial calendar would be +about one day ahead of the true one, at the end of forty +years ten days in error, and within a single lifetime the +seasons would have appreciably changed their position in +the year, April weather being due in March, according to +the calendar. So, too, the year under this arrangement +did not consist of any integral number of months, 12 +months of the average length of 29.5 days being 354 days, +and 13 months 383.5 days, thus making any particular +month change its position from the beginning to the middle +and the end of the year within a comparatively short +time. Some peoples gave up the astronomical year as an +independent unit and adopted a conventional year of 12 +lunar months, 354 days, which is now in use in certain +Mohammedan countries, where it is known as the wandering +year, with reference to the changing positions of the +seasons in such a year. Others held to the astronomical +year and adopted a system of conventional months, such +that twelve of them would just make up a year, as is done +to this day in our own calendar, whose months of arbitrary +length we are compelled to remember by some such jingle +as the following:</p> + +<div class="poem"><div class="stanza"> +<span class="i0">"Thirty days hath September,<br /></span> +<span class="i0">April, June, and November;<br /></span> +<span class="i0">All the rest have thirty-one<br /></span> +<span class="i0">Save February,<br /></span> +<span class="i0">Which alone hath twenty-eight,<br /></span> +<span class="i0">Till leap year gives it twenty-nine."<br /></span> +</div></div> + + +<p><a name="S_61" id="S_61"></a>61. <b>The calendar.</b>—The foundations of our calendar may +fairly be ascribed to Julius Cęsar, who, under the advice +of the Egyptian astronomer Sosigines, adopted the old +Egyptian device of a leap year, whereby every fourth year +was to consist of 366 days, while ordinary years were only +365 days long. He also placed the beginning of the year<span class="pagenum"><a name="Page_97" id="Page_97">[Pg 97]</a></span> +at the first of January, instead of in March, where it had +formerly been, and gave his own name, Julius, to the month +which we now call July. August was afterward named in +honor of his successor, Augustus. The names of the earlier +months of the year are drawn from Roman mythology; +those of the later months, September, October, etc., meaning +seventh month, eighth month, represent the places of +these months in the year, before Cęsar's reformation, and +also their places in some of the subsequent calendars, for +the widest diversity of practice existed during medięval +times with regard to the day on which the new year should +begin, Christmas, Easter, March 25th, and others having been +employed at different times and places.</p> + +<p>The system of leap years introduced by Cęsar makes +the average length of a year 365.25 days, which differs by +about eleven minutes from the true length of the tropical +year, a difference so small that for ordinary purposes no +better approximation to the true length of the year need +be desired. But <i>any</i> deviation from the true length, however +small, must in the course of time shift the seasons, the +vernal and autumnal equinox, to another part of the year, +and the ecclesiastical authorities of medięval Europe found +here ground for objection to Cęsar's calendar, since the +great Church festival of Easter has its date determined +with reference to the vernal equinox, and with the lapse of +centuries Easter became more and more displaced in the +calendar, until Pope Gregory XIII, late in the sixteenth +century, decreed another reformation, whereby ten days +were dropped from the calendar, the day after March 11th +being called March 21st, to bring back the vernal equinox +to the date on which it fell in <span class="smcap">A. D.</span> 325, the time of the +Council of Nicęa, which Gregory adopted as the fundamental +epoch of his calendar.</p> + +<p>The calendar having thus been brought back into agreement +with that of old time, Gregory purposed to keep it in +such agreement for the future by modifying Cęsar's leap-year<span class="pagenum"><a name="Page_98" id="Page_98">[Pg 98]</a></span> +rule so that it should run: Every year whose number +is divisible by 4 shall be a leap year except those years +whose numbers are divisible by 100 but not divisible by +400. These latter years—e. g., 1900—are counted as common +years. The calendar thus altered is called Gregorian +to distinguish it from the older, Julian calendar, and it +found speedy acceptance in those civilized countries whose +Church adhered to Rome; but the Protestant powers were +slow to adopt it, and it was introduced into England and +her American colonies by act of Parliament in the year +1752, nearly two centuries after Gregory's time. In Russia +the Julian calendar has remained in common use to +our own day, but in commercial affairs it is there customary +to write the date according to both calendars—e. g., +July 4/16, and at the present time strenuous exertions +are making in that country for the adoption of the Gregorian +calendar to the complete exclusion of the Julian +one.</p> + +<p>The Julian and Gregorian calendars are frequently represented +by the abbreviations O. S. and N. S., old style, +new style, and as the older historical dates are usually expressed +in O. S., it is sometimes convenient to transform a +date from the one calendar to the other. This is readily +done by the formula</p> + +<p class="center"><i>G</i> = <i>J</i> + (<i>N</i> - 2) - <i>N</i>/4,</p> + +<p>where <i>G</i> and <i>J</i> are the respective dates, <i>N</i> is the number +of the century, and the remainder is to be neglected in the +division by 4. For September 3, 1752, O. S., we have</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary="" rules="groups" frame="void"> +<tfoot> +<tr><td align="right"><i>G</i></td><td align="center">=</td><td align="left">Sept. 14</td></tr> +</tfoot> +<tbody> +<tr><td align="right"><i>J</i></td><td align="center">=</td><td align="left">Sept. 3</td></tr> +<tr><td align="right"><i>N</i> - 2</td><td align="center">=</td><td align="left">+ 15</td></tr> +<tr><td align="right">- <i>N</i>/4</td><td align="center">=</td><td align="left">- 4</td></tr> +</tbody> +</table> +</div> + +<p><span class="pagenum"><a name="Page_99" id="Page_99">[Pg 99]</a></span></p> + +<p>and September 14 is the date fixed by act of Parliament to +correspond to September 3, 1752, O. S. Columbus discovered +America on October 12, 1492, O. S. What is the corresponding +date in the Gregorian calendar?</p> + +<p><a name="S_62" id="S_62"></a>62. <b>The day of the week.</b>—A problem similar to the +above but more complicated consists in finding the day of +the week on which any given date of the Gregorian calendar +falls—e. g., October 21, 1492.</p> + +<p>The formula for this case is</p> + +<p class="center">7<i>q</i> + <i>r</i> = <i>Y</i> + <i>D</i> + (<i>Y</i> - 1)/4 - (<i>Y</i> - 1)/100 + (<i>Y</i> - 1)/400</p> + +<p>where <i>Y</i> denotes the given year, <i>D</i> the number of the day +(date) in that year, and <i>q</i> and <i>r</i> are respectively the quotient +and the remainder obtained by dividing the second +member of the equation by 7. If <i>r</i> = 1 the date falls on +Sunday, etc., and if <i>r</i> = 0 the day is Saturday. For the +example suggested above we have</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary="" rules="groups" frame="void"> +<tfoot> +<tr><td align="right">D =</td><td align="right">295</td></tr> +</tfoot> +<tbody> +<tr><td align="left">Jan.</td><td align="right">31</td></tr> +<tr><td align="left">Feb.</td><td align="right">29</td></tr> +<tr><td align="left">Mch.</td><td align="right">31</td></tr> +<tr><td align="left">April</td><td align="right">30</td></tr> +<tr><td align="left">May</td><td align="right">31</td></tr> +<tr><td align="left">June</td><td align="right">30</td></tr> +<tr><td align="left">July</td><td align="right">31</td></tr> +<tr><td align="left">Aug.</td><td align="right">31</td></tr> +<tr><td align="left">Sept.</td><td align="right">30</td></tr> +<tr><td align="left">Oct.</td><td align="right">21</td></tr> +</tbody> +</table></div> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary="" rules="groups" frame="void"> +<tfoot> +<tr><td align="center"></td><td align="right"><i>q</i></td><td align="center">=</td><td align="right">306</td></tr> +<tr><td align="center"></td><td align="right"><i>r</i></td><td align="center">=</td><td align="right">6</td><td align="left">= Friday.</td></tr> +</tfoot> +<tbody> +<tr><td align="center"><i>Y</i></td><td align="right"></td><td align="center">=</td><td align="right">1492</td></tr> +<tr><td align="center">+ <i>D</i></td><td align="right"></td><td align="center">=</td><td align="right">+ 295</td></tr> +<tr><td align="center">+ (<i>Y</i> - 1) ÷</td><td align="right">4</td><td align="center">=</td><td align="right">+ 372</td></tr> +<tr><td align="center">- (<i>Y</i> - 1) ÷</td><td align="right">100</td><td align="center">=</td><td align="right">- 14</td></tr> +<tr><td align="center">+ (<i>Y</i> - 1) ÷</td><td align="right">400</td><td align="center">=</td><td align="right">+ 3</td></tr> +</tbody> +<tbody> +<tr><td align="center"></td><td align="right"></td><td align="center"> </td><td align="right">7 )<span class="overline"> 2148</span></td></tr> +</tbody> +</table></div> + +<p>Find from some history the day of the week on which +Columbus first saw America, and compare this with the +above.</p> + +<p>On what day of the week did last Christmas fall? On +what day of the week were you born? In the formula for +the day of the week why does <i>q</i> have the coefficient 7?<span class="pagenum"><a name="Page_100" id="Page_100">[Pg 100]</a></span> +What principles in the calendar give rise to the divisors 4, +100, 400?</p> + +<p>For much curious and interesting information about +methods of reckoning the lapse of time the student may +consult the articles Calendar and Chronology in any good +encyclopędia.</p> + +<div class="figcenter" style="width: 600px;"><a name="YERKES_OBSERVATORY" id="YERKES_OBSERVATORY"></a> +<a href="images/i122-full.jpg"><img src="images/i122.jpg" width="600" height="321" alt="THE YERKES OBSERVATORY, WILLIAMS BAY, WIS." title="THE YERKES OBSERVATORY, WILLIAMS BAY, WIS." /></a> +<span class="caption">THE YERKES OBSERVATORY, WILLIAMS BAY, WIS.</span> +</div> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_101" id="Page_101">[Pg 101]</a></span></p> +<h2><a name="CHAPTER_VII" id="CHAPTER_VII"></a>CHAPTER VII</h2> + +<h3>ECLIPSES</h3> + + +<p><a name="S_63" id="S_63"></a>63. <b>The nature of eclipses.</b>—Every planet has a shadow +which travels with the planet along its orbit, always pointing +directly away from the sun, and cutting off from a certain +region of space the sunlight which otherwise would fill +it. For the most part these shadows are invisible, but occasionally +one of them falls upon a planet or some other body +which shines by reflected sunlight, and, cutting off its supply +of light, produces the striking phenomenon which we +call an eclipse. The satellites of Jupiter, Saturn, and Mars +are eclipsed whenever they plunge into the shadows cast by +their respective planets, and Jupiter himself is partially +eclipsed when one of his own satellites passes between him +and the sun, and casts upon his broad surface a shadow too +small to cover more than a fraction of it.</p> + +<p>But the eclipses of most interest to us are those of the +sun and moon, called respectively solar and lunar eclipses. +In <a href="#Fig_33">Fig. 33</a> the full moon, <i>M'</i>, is shown immersed in the +shadow cast by the earth, and therefore eclipsed, and in the +same figure the new moon, <i>M</i>, is shown as casting its shadow +upon the earth and producing an eclipse of the sun. From +a mere inspection of the figure we may learn that an eclipse +of the sun can occur only at new moon—i. e., when the +moon is on line between the earth and sun—and an eclipse +of the moon can occur only at full moon. Why? Also, the +eclipsed moon, <i>M'</i>, will present substantially the same appearance +from every part of the earth where it is at all visible—the +same from North America as from South America—but<span class="pagenum"><a name="Page_102" id="Page_102">[Pg 102]</a></span> +the eclipsed sun will present very +different aspects from different parts of +the earth. Thus, at <i>L</i>, within the moon's +shadow, the sunlight will be entirely cut +off, producing what is called a total eclipse. +At points of the earth's surface near <i>J</i> and +<i>K</i> there will be no interference whatever +with the sunlight, and no eclipse, since the +moon is quite off the line joining these regions +to any part of the sun. At places between +<i>J</i> and <i>L</i> or <i>K</i> and <i>L</i> the moon will +cut off a part of the sun's light, but not all +of it, and will produce what is called a partial +eclipse, which, as seen from the northern +parts of the earth, will be an eclipse of +the lower (southern) part of the sun, and +as seen from the southern hemisphere will +be an eclipse of the northern part of the +sun.</p> + +<div class="figcenter" style="width: 600px;"><a name="Fig_33" id="Fig_33"></a> +<img src="images/i125.png" width="600" height="91" alt="Fig. 33.—Different kinds of eclipse." title="Fig. 33.—Different kinds of eclipse." /> +<span class="caption"><span class="smcap">Fig. 33.</span>—Different kinds of eclipse.</span> +</div> + +<p>The moon revolves around the earth in +a plane, which, in the figure, we suppose to +be perpendicular to the surface of the paper, +and to pass through the sun along the +line <i>M' M</i> produced. But it frequently +happens that this plane is turned to one +side of the sun, along some such line as +<i>P Q</i>, and in this case the full moon would +cut through the edge of the earth's shadow +without being at any time wholly immersed +in it, giving a partial eclipse of the moon, +as is shown in the figure.</p> + +<p>In what parts of the earth would this +eclipse be visible? What kinds of solar +eclipse would be produced by the new moon +at <i>Q</i>? In what parts of the earth would +they be visible?<span class="pagenum"><a name="Page_103" id="Page_103">[Pg 103]</a></span></p> + +<p><a name="S_64" id="S_64"></a>64. <b>The shadow cone.</b>—The shape and position of the +earth's shadow are indicated in <a href="#Fig_33">Fig. 33</a> by the lines drawn +tangent to the circles which represent the sun and earth, +since it is only between these lines that the earth interferes +with the free radiation of sunlight, and since both sun and +earth are spheres, and the earth is much the smaller of the +two, it is evident that the earth's shadow must be, in geometrical +language, a cone whose base is at the earth, and +whose vertex lies far to the right of the figure—in other +words, the earth's shadow, although very long, tapers off +finally to a point and ends. So, too, the shadow of the +moon is a cone, having its base at the moon and its vertex +turned away from the sun, and, as shown in the figure, just +about long enough to reach the earth.</p> + +<p>It is easily shown, by the theorem of similar triangles in +connection with the known size of the earth and sun, that +the distance from the center of the earth to the vertex of +its shadow is always equal to the distance of the earth from +the sun divided by 108, and, similarly, that the length of +the moon's shadow is equal to the distance of the moon +from the sun divided by 400, the moon's shadow being the +smaller and shorter of the two, because the moon is smaller +than the earth. The radius of the moon's orbit is just about +1/400th part of the radius of the earth's orbit—i. e., the distance +of the moon from the earth is 1/400th part of the distance +of the earth from the sun, and it is this "chance" +agreement between the length of the moon's shadow and +the distance of the moon from the earth which makes the +tip of the moon's shadow fall very near the earth at the +time of solar eclipses. Indeed, the elliptical shape of the +moon's orbit produces considerable variations in the distance +of the moon from the earth, and in consequence of +these variations the vertex of the shadow sometimes falls +short of reaching the earth, and sometimes even projects +considerably beyond its farther side. When the moon's +distance is too great for the shadow to bridge the space between<span class="pagenum"><a name="Page_104" id="Page_104">[Pg 104]</a></span> +earth and moon there can be no total eclipse of the +sun, for there is no shadow which can fall upon the earth, +even though the moon does come directly between earth +and sun. But there is then produced a peculiar kind of +partial eclipse called <i>annular</i>, or ring-shaped, because the +moon, although eclipsing the central parts of the sun, is +not large enough to cover the whole of it, but leaves the +sun's edge visible as a ring of light, which completely surrounds +the moon. Although, strictly speaking, this is only +a partial eclipse, it is customary to put total and annular +eclipses together in one class, which is called central eclipses, +since in these eclipses the line of centers of sun and moon +strikes the earth, while in ordinary partial eclipses it passes +to one side of the earth without striking it. In this latter +case we have to consider another cone called the <i>penumbra</i>—i. e., +partial shadow—which is shown in <a href="#Fig_33">Fig. 33</a> by the +broken lines tangent to the sun and moon, and crossing at +the point <i>V</i>, which is the vertex of this cone. This penumbral +cone includes within its surface all that region of space +within which the moon cuts off any of the sunlight, and +of course it includes the shadow cone which produces total +eclipses. Wherever the penumbra falls there will be a solar +eclipse of some kind, and the nearer the place is to the axis +of the penumbra, the more nearly total will be the eclipse. +Since the moon stands about midway between the earth and +the vertex of the penumbra, the diameter of the penumbra +where it strikes the earth will be about twice as great as +the diameter of the moon, and the student should be able +to show from this that the region of the earth's surface +within which a partial solar eclipse is visible extends in a +straight line about 2,100 miles on either side of the region +where the eclipse is total. Measured along the curved +surface of the earth, this distance is frequently much +greater.</p> + +<p>Is it true that if at any time the axis of the shadow cone +comes within 2,100 miles of the earth's surface a partial<span class="pagenum"><a name="Page_105" id="Page_105">[Pg 105]</a></span> eclipse will be visible in those parts of the earth nearest the +axis of the shadow?</p> + +<p><a name="S_65" id="S_65"></a>65. <b>Different characteristics of lunar and solar eclipses.</b>—One +marked difference between lunar and solar eclipses +which has been already suggested, may be learned from <a href="#Fig_33">Fig. 33</a>. +The full moon, <i>M'</i>, will be seen eclipsed from every +part of the earth where it is visible at all at the time of the +eclipse—that is, from the whole night side of the earth; +while the eclipsed sun will be seen eclipsed only from those +parts of the day side of the earth upon which the moon's +shadow or penumbra falls. Since the point of the shadow +at best but little more than reaches to the earth, the +amount of space upon the earth which it can cover at any +one moment is very small, seldom more than 100 to 200 +miles in length, and it is only within the space thus actually +covered by the shadow that the sun is at any given +moment totally eclipsed, but within this region the sun +disappears, absolutely, behind the solid body of the moon, +leaving to view only such outlying parts and appendages as +are too large for the moon to cover. At a lunar eclipse, on +the other hand, the earth coming between sun and moon +cuts off the light from the latter, but, curiously enough, +does not cut it off so completely that the moon disappears +altogether from sight even in mid-eclipse. The explanation +of this continued visibility is furnished by the broken +lines extending, in <a href="#Fig_33">Fig. 33</a>, from the earth through the +moon. These represent sunlight, which, entering the +earth's atmosphere near the edge of the earth (edge as seen +from sun and moon), passes through it and emerges in a +changed direction, refracted, into the shadow cone and +feebly illumines the moon's surface with a ruddy light like +that often shown in our red sunsets. Eclipse and sunset +alike show that when the sun's light shines through dense +layers of air it is the red rays which come through most +freely, and the attentive observer may often see at a clear +sunset something which corresponds exactly to the bending<span class="pagenum"><a name="Page_106" id="Page_106">[Pg 106]</a></span> +of the sunlight into the shadow cone; just before the sun +reaches the horizon its disk is distorted from a circle into +an oval whose horizontal diameter is longer than the vertical +one (see <a href="#S_50">§ 50</a>).</p> + +<p><span class="smcap">Query.</span>—At a total lunar eclipse what would be the +effect upon the appearance of the moon if the atmosphere +around the edge of the earth were heavily laden with +clouds?</p> + +<p><a name="S_66" id="S_66"></a>66. <b>The track of the shadow.</b>—We may regard the moon's +shadow cone as a huge pencil attached to the moon, moving +with it along its orbit in the direction of the arrowhead +(<a href="#Fig_34">Fig. 34</a>), and as it moves drawing a black line across +the face of the earth at the time of total eclipse. This black +line is the path of the shadow and marks out those regions +within which the eclipse will be total at some stage of its +progress. If the point of the shadow just reaches the +earth its trace will have no sensible width, while, if the +moon is nearer, the point of the cone will be broken off, +and, like a blunt pencil, it will draw a broad streak across +the earth, and this under the most favorable circumstances +may have a breadth of a little more than 160 miles and a +length of 10,000 or 12,000 miles. The student should +be able to show from the known distance of the moon +(240,000 miles) and the known interval between consecutive +new moons (29.5 days) that on the average the moon's +shadow sweeps past the earth at the rate of 2,100 miles per +hour, and that in a general way this motion is from west +to east, since that is the direction of the moon's motion in +its orbit. The actual velocity with which the moon's shadow +moves past a given station may, however, be considerably +greater or less than this, since on the one hand when the +shadow falls very obliquely, as when the eclipse occurs near +sunrise or sunset, the shifting of the shadow will be very +much greater than the actual motion of the moon which +produces it, and on the other hand the earth in revolving +upon its axis carries the spectator and the ground upon<span class="pagenum"><a name="Page_107" id="Page_107">[Pg 107]</a></span> +which he stands along the same direction in which the +shadow is moving. At the equator, with the sun and moon +overhead, this motion of the earth subtracts about 1,000 +miles per hour from the velocity with which the shadow +passes by. It is chiefly on this account, the diminished +velocity with which the shadow passes by, that total solar +eclipses last longer in the tropics than in higher latitudes, +but even under the most favorable circumstances the duration +of totality does not reach eight minutes at any one +place, although it may take the shadow several hours to +sweep the entire length of its path across the earth.</p> + +<p>According to Whitmell the greatest possible duration of +a total solar eclipse is 7m. 40s., and it can attain this limit +only when the eclipse occurs near the beginning of July +and is visible at a place 5° north of the equator.</p> + +<p>The duration of a lunar eclipse depends mainly upon +the position of the moon with respect to the earth's shadow. +If it strikes the shadow centrally, as at <i>M'</i>, <a href="#Fig_33">Fig. 33</a>, a total +eclipse may last for about two hours, with an additional +hour at the beginning and end, during which the moon is +entering and leaving the earth's shadow. If the moon +meets the shadow at one side of the axis, as at <i>P</i>, the total +phase of the eclipse may fail altogether, and between these +extremes the duration of totality may be anything from +two hours downward.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_34" id="Fig_34"></a> +<img src="images/i131.png" width="500" height="248" alt="Fig. 34.—Relation of the lunar nodes to eclipses." title="Fig. 34.—Relation of the lunar nodes to eclipses." /> +<span class="caption"><span class="smcap">Fig. 34.</span>—Relation of the lunar nodes to eclipses.</span> +</div> + +<p><a name="S_67" id="S_67"></a>67. <b>Relation of the lunar nodes to eclipses.</b>—To show why +the moon sometimes encounters the earth's shadow centrally +and more frequently at full moon passes by without +touching it at all, we resort to <a href="#Fig_34">Fig. 34</a>, which represents a +part of the orbit of the earth about the sun, with dates +showing the time in each year at which the earth passes +the part of its orbit thus marked. The orbit of the moon +about the earth, <i>M M'</i>, is also shown, with the new moon, +<i>M</i>, casting its shadow toward the earth and the full moon, +<i>M'</i>, apparently immersed in the earth's shadow. But here +appearances are deceptive, and the student who has made<span class="pagenum"><a name="Page_108" id="Page_108">[Pg 108]</a></span> +the observations set forth in <a href="#CHAPTER_III">Chapter III</a> has learned for +himself a fact of which careful account must now be taken. +The apparent paths of the moon and sun among the stars +are great circles which lie near each other, but are not +exactly the same; and since these great circles are only the +intersections of the sky with the planes of the earth's orbit +and the moon's orbit, we see that these planes are slightly +inclined to each other and must therefore intersect along +some line passing through the center of the earth. This +line, <i>N' N''</i>, is shown in the figure, and if we suppose the +surface of the paper to represent the plane of the earth's +orbit, we shall have to suppose the moon's orbit to be tipped +around this line, so that the left side of the orbit lies above +and the right side below the surface of the paper. But +since the earth's shadow lies in the plane of its orbit—i. e., +in the surface of the paper—the full moon of March, <i>M'</i>, +must have passed below the shadow, and the new moon, <i>M</i>, +must have cast its shadow above the earth, so that neither +a lunar nor a solar eclipse could occur in that month. But +toward the end of May the earth and moon have reached +a position where the line <i>N' N''</i> points almost directly +toward the sun, in line with the shadow cones which hide +it. Note that the line <i>N' N''</i> remains very nearly parallel +to its original position, while the earth is moving along<span class="pagenum"><a name="Page_109" id="Page_109">[Pg 109]</a></span> +its orbit. The full moon will now be very near this line +and therefore very close to the plane of the earth's orbit, if +not actually in it, and must pass through the shadow of the +earth and be eclipsed. So also the new moon will cast its +shadow in the plane of the ecliptic, and this shadow, falling +upon the earth, produced the total solar eclipse of May 28, +1900.</p> + +<p><i>N' N''</i> is called the line of nodes of the moon's orbit (<a href="#S_39">§ 39</a>), +and the two positions of the earth in its orbit, diametrically +opposite each other, at which <i>N' N''</i> points exactly toward +the sun, we shall call the <i>nodes</i> of the lunar orbit. Strictly +speaking, the nodes are those points of the sky against +which the moon's center is projected at the moment when +in its orbital motion it cuts through the plane of the earth's +orbit. Bearing in mind these definitions, we may condense +much of what precedes into the proposition: Eclipses of +either sun or moon can occur only when the earth is at or +near one of the nodes of the moon's orbit. Corresponding +to these positions of the earth there are in each year two +seasons, about six months apart, at which times, and at +these only, eclipses can occur. Thus in the year 1900 the +earth passed these two points on June 2d and November +24th respectively, and the following list of eclipses which +occurred in that year shows that all of them were within a +few days of one or the other of these dates:</p> + +<h4><i>Eclipses of the Year 1900</i></h4> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left">Total solar eclipse</td><td align="left">May 28th.</td></tr> +<tr><td align="left">Partial lunar eclipse</td><td align="left">June 12th.</td></tr> +<tr><td align="left">Annular (solar) eclipse</td><td align="left">November 21st.</td></tr> +</table></div> + +<p><a name="S_68" id="S_68"></a>68. <b>Eclipse limits.</b>—If the earth is exactly at the node at +the time of new moon, the moon's shadow will fall centrally +upon it and will produce an eclipse visible within the +torrid zone, since this is that part of the earth's surface +nearest the plane of its orbit. If the earth is near but not +at the node, the new moon will stand a little north or south<span class="pagenum"><a name="Page_110" id="Page_110">[Pg 110]</a></span> +of the plane of the earth's orbit, and its shadow will strike +the earth farther north or south than before, producing an +eclipse in the temperate or frigid zones; or the shadow may +even pass entirely above or below the earth, producing no +eclipse whatever, or at most a partial eclipse visible near +the north or south pole. Just how many days' motion the +earth may be away from the node and still permit an eclipse +is shown in the following brief table of eclipse limits, as +they are called:</p> + +<h4><i>Solar Eclipse Limits</i></h4> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left" colspan="5">If at any new moon the earth is</td></tr> +<tr><td align="left">Less than 10 days away</td><td align="center">from</td><td align="center">a</td><td align="center">node,</td><td align="left">a central eclipse is certain.</td></tr> +<tr><td align="left">Between 10 and 16 days</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="left">some kind of eclipse is certain.</td></tr> +<tr><td align="left">Between 16 and 19 days</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="left">a partial eclipse is possible.</td></tr> +<tr><td align="left">More than 19 days</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="left">no eclipse is possible.</td></tr> +</table></div> + +<h4><i>Lunar Eclipse Limits</i></h4> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left" colspan="5">If at any full moon the earth is</td></tr> +<tr><td align="left">Less than 4 days away</td><td align="center">from</td><td align="center">a</td><td align="center">node,</td><td align="left">a total eclipse is certain.</td></tr> +<tr><td align="left">Between 4 and 10 days</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="left">some kind of eclipse is certain.</td></tr> +<tr><td align="left">Between 10 and 14 days</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="left">a partial eclipse is possible.</td></tr> +<tr><td align="left">More than 14 days</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="left">no eclipse is possible.</td></tr> +</table></div> + +<p>From this table of eclipse limits we may draw some +interesting conclusions about the frequency with which +eclipses occur.</p> + +<p><a name="S_69" id="S_69"></a>69. <b>Number of eclipses in a year.</b>—Whenever the earth +passes a node of the moon's orbit a new moon must occur at +some time during the 2 × 16 days that the earth remains +inside the limits where some kind of eclipse is certain, and +there must therefore be an eclipse of the sun every time the +earth passes a node of the moon's orbit. But, since there +are two nodes past which the earth moves at least once in +each year, there must be at least two solar eclipses every +year. Can there be more than two? On the average, will +central or partial eclipses be the more numerous?</p> + +<p>A similar line of reasoning will not hold true for +eclipses of the moon, since it is quite possible that no full<span class="pagenum"><a name="Page_111" id="Page_111">[Pg 111]</a></span> +moon should occur during the 20 days required by the +earth to move past the node from the western to the eastern +limit. This omission of a full moon while the earth is +within the eclipse limits sometimes happens at both nodes +in the same year, and then we have a year with no eclipse +of the moon. The student may note in the list of eclipses +for 1900 that the partial lunar eclipse of June 12th occurred +10 days after the earth passed the node, and was +therefore within the doubtful zone where eclipses may +occur and may fail, and corresponding to this position the +eclipse was a very small one, only a thousandth part of the +moon's diameter dipping into the shadow of the earth. +By so much the year 1900 escaped being an illustration of +a year in which no lunar eclipse occurred.</p> + +<p>A partial eclipse of the moon will usually occur about a +fortnight before or after a total eclipse of the sun, since +the full moon will then be within the eclipse limit at the +opposite node. A partial eclipse of the sun will always +occur about a fortnight before or after a total eclipse of the +moon.</p> + +<div class="figcenter" style="width: 600px;"><a name="Fig_35" id="Fig_35"></a> +<a href="images/i135-full.png"><img src="images/i135.png" width="600" height="404" alt="Fig. 35.—The eclipse of May 28, 1900." title="Fig. 35.—The eclipse of May 28, 1900." /></a> +<span class="caption"><span class="smcap">Fig. 35.</span>—The eclipse of May 28, 1900.</span> +</div> + +<p><a name="S_70" id="S_70"></a>70. <b>Eclipse maps.</b>—It is the custom of astronomers to +prepare, in advance of the more important eclipses, maps +showing the trace of the moon's shadow across the earth, +and indicating the times of beginning and ending of the +eclipses, as is shown in <a href="#Fig_35">Fig. 35</a>. While the actual construction +of such a map requires much technical knowledge, the +principles involved are simple enough: the straight line +passed through the center of sun and moon is the axis of +the shadow cone, and the map contains little more than a +graphical representation of when and where this cone meets +the surface of the earth. Thus in the map, the "Path of +Total Eclipse" is the trace of the shadow cone across the +face of the earth, and the width of this path shows that the +earth encountered the shadow considerably inside the vertex +of the cone. The general direction of the path is from +west to east, and the slight sinuousities which it present<span class="pagenum"><a name="Page_113" id="Page_113">[Pg 113]</a></span><span class="pagenum"><a name="Page_112" id="Page_112">[Pg 112]</a></span>s +are for the most part due to unavoidable distortion of the +map caused by the attempt to represent the curved surface +of the earth upon the flat surface of the paper. On either +side of the Path of Total Eclipse is the region within which +the eclipse was only partial, and the broken lines marked Begins +at 3h., Ends at 3h., show the intersection of the penumbral +cone with the surface of the earth at 3 <span class="smcap">P. M.</span>, Greenwich +time. These two lines inclose every part of the earth's +surface from which at that time any eclipse whatever could +be seen, and at this moment the partial eclipse was just beginning +at every point on the eastern edge of the penumbra +and just ending at every point on the western edge, while +at the center of the penumbra, on the Path of Total Eclipse, +lay the shadow of the moon, an oval patch whose greatest +diameter was but little more than 60 miles in length, and +within which lay every part of the earth where the eclipse +was total at that moment.</p> + +<p>The position of the penumbra at other hours is also +shown on the map, although with more distortion, because +it then meets the surface of the earth more obliquely, and +from these lines it is easy to obtain the time of beginning +and end of the eclipse at any desired place, and to estimate +by the distance of the place from the Path of Total Eclipse +how much of the sun's face was obscured.</p> + +<p>Let the student make these "predictions" for Washington, +Chicago, London, and Algiers.</p> + +<p>The points in the map marked First Contact, Last Contact, +show the places at which the penumbral cone first +touched the earth and finally left it. According to computations +made as a basis for the construction of the map the +Greenwich time of First Contact was 0h. 12.5m. and of Last +Contact 5h. 35.6m., and the difference between these two +times gives the total duration of the eclipse upon the earth—i. e., +5 hours 23.1 minutes.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_36" id="Fig_36"></a> +<a href="images/i137-full.jpg"><img src="images/i137.jpg" width="500" height="500" alt="Fig. 36.—Central eclipses for the first two decades of the twentieth century. +Oppolzer." title="Fig. 36.—Central eclipses for the first two decades of the twentieth century. +Oppolzer." /></a> +<span class="caption"><span class="smcap">Fig. 36.</span>—Central eclipses for the first two decades of the twentieth century. +<span class="smcap">Oppolzer.</span></span> +</div> + +<p><a name="S_71" id="S_71"></a>71. <b>Future eclipses.</b>—An eclipse map of a different kind +is shown in <a href="#Fig_36">Fig. 36</a>, which represents the shadow paths of<span class="pagenum"><a name="Page_114" id="Page_114">[Pg 114]</a></span> +all the central eclipses of the sun, visible during the period +1900-1918 <span class="smcap">A. D.</span>, in those parts of the earth north of the +south temperate zone. Each continuous black line shows +the path of the shadow in a total eclipse, from its beginning, +at sunrise, at the western end of the line to its end, +sunset, at the eastern end, the little circle near the middle +of the line showing the place at which the eclipse +was total at noon. The broken lines represent similar +data for the annular eclipses. This map is one of a series +prepared by the Austrian astronomer, Oppolzer, showing +the path of every such eclipse from the year 1200<span class="pagenum"><a name="Page_115" id="Page_115">[Pg 115]</a></span> +<span class="smcap">B. C.</span> to 2160 <span class="smcap">A. D.</span>, a period of more than three thousand +years.</p> + +<p>If we examine the dates of the eclipses shown in this +map we shall find that they are not limited to the particular +seasons, May and November, in which those of the year +1900 occurred, but are scattered through all the months of +the year, from January to December. This shows at once +that the line of nodes, <i>N' N''</i>, of <a href="#Fig_34">Fig. 34</a>, does not remain +in a fixed position, but turns round in the plane of the +earth's orbit so that in different years the earth reaches the +node in different months. The precession has already furnished +us an illustration of a similar change, the slow rotation +of the earth's axis, producing a corresponding shifting +of the line in which the planes of the equator and ecliptic +intersect; and in much the same way, through the disturbing +influence of the sun's attraction, the line <i>N' N''</i> is made +to revolve westward, opposite to the arrowheads in <a href="#Fig_34">Fig. 34</a>, +at the rate of nearly 20° per year, so that the earth +comes to each node about 19 days earlier in each year than +in the year preceding, and the eclipse season in each year +comes on the average about 19 days earlier than in the year +before, although there is a good deal of irregularity in the +amount of change in particular years.</p> + +<p><a name="S_72" id="S_72"></a>72. <b>Recurrence of eclipses.</b>—Before the beginning of the +Christian era astronomers had found out a rough-and-ready +method of predicting eclipses, which is still of interest and +value. The substance of the method is that if we start +with any eclipse whatever—e. g., the eclipse of May 28, 1900—and +reckon forward or backward from that date a period of +18 years and 10 or 11 days, we shall find another eclipse quite +similar in its general characteristics to the one with which +we started. Thus, from the map of eclipses (<a href="#Fig_36">Fig. 36</a>), we +find that a total solar eclipse will occur on June 8, 1918, +18 years and 11 days after the one illustrated in <a href="#Fig_35">Fig. 35</a>. +This period of 18 years and 11 days is called <i>saros</i>, an +ancient word which means cycle or repetition, and since<span class="pagenum"><a name="Page_116" id="Page_116">[Pg 116]</a></span> +every eclipse is repeated after the lapse of a saros, we may +find the dates of all the eclipses of 1918 by adding 11 +days to the dates given in the table of eclipses for 1900 +(<a href="#S_67">§ 67</a>), and it is to be especially noted that each eclipse of +1918 will be like its predecessor of 1900 in character—lunar, +solar, partial, total, etc. The eclipses of any year +may be predicted by a similar reference to those which +occurred eighteen years earlier. Consult a file of old +almanacs.</p> + +<p>The exact length of a saros is 223 lunar months, each of +which is a little more than 29.5 days long, and if we multiply +the exact value of this last number (see <a href="#S_60">§ 60</a>) by 223, +we shall find for the product 6,585.32 days, which is equal +to 18 years 11.32 days when there are four leap years included +in the 18, or 18 years 10.32 days when the number +of leap years is five; and in applying the saros to the +prediction of eclipses, due heed must be paid to the number +of intervening leap years. To explain why eclipses are +repeated at the end of the saros, we note that the occurrence +of an eclipse depends solely upon the relative positions of +the earth, moon, and node of the moon's orbit, and the +eclipse will be repeated as often as these three come back +to the position which first produced it. This happens at +the end of every saros, since the saros is, approximately, the +least common multiple of the length of the year, the length +of the lunar month, and the length of time required by the +line of nodes to make a complete revolution around the +ecliptic. If the saros were exactly a multiple of these +three periods, every eclipse would be repeated over and +over again for thousands of years; but such is not the +case, the saros is not an exact multiple of a year, nor +is it an exact multiple of the time required for a revolution +of the line of nodes, and in consequence the +restitution which comes at the end of the saros is not a +perfect one. The earth at the 223d new moon is in fact +about half a day's motion farther west, relative to the node,<span class="pagenum"><a name="Page_117" id="Page_117">[Pg 117]</a></span> +than it was at the beginning, and the resulting +eclipse, while very similar, is not +precisely the same as before. After another +18 years, at the second repetition, the earth +is a day farther from the node than at first, +and the eclipse differs still more in character, +etc. This is shown in <a href="#Fig_37">Fig. 37</a>, which +represents the apparent positions of the +disks of the sun and moon as seen from the +center of the earth at the end of each sixth +saros, 108 years, where the upper row of +figures represents the number of repetitions +of the eclipse from the beginning, marked +<i>0</i>, to the end, <i>72</i>. The solar eclipse limits, +10, 16, 19 days, are also shown, and all those +eclipses which fall between the 10-day limits +will be central as seen from some part of +the earth, those between 16 and 19 partial +wherever seen, while between 10 and 16 +they may be either total or partial. Compare +the figure with the following description +given by Professor Newcomb: "A series +of such eclipses commences with a very +small eclipse near one pole of the earth. +Gradually increasing for about eleven recurrences, +it will become central near the same +pole. Forty or more central eclipses will +then recur, the central line moving slowly +toward the other pole. The series will then +become partial, and finally cease. The entire +duration of the series will be more than +a thousand years. A new series commences, +on the average, at intervals of thirty years."</p> + +<div class="figcenter" style="width: 600px;"><a name="Fig_37" id="Fig_37"></a> +<img src="images/i140.png" width="600" height="77" alt="Fig. 37.—Graphical illustration of the saros." title="Fig. 37.—Graphical illustration of the saros." /> +<span class="caption"><span class="smcap">Fig. 37.</span>—Graphical illustration of the saros.</span> +</div> + +<p>A similar figure may be constructed to +represent the recurrence of lunar eclipses; +but here, in consequence of the smaller<span class="pagenum"><a name="Page_118" id="Page_118">[Pg 118]</a></span> +eclipse limits, we shall find that a series is of shorter duration, +a little over eight centuries as compared with twelve +centuries, which is the average duration of a series of solar +eclipses.</p> + +<p>One further matter connected with the saros deserves +attention. During the period of 6,585.32 days the earth +has 6,585 times turned toward the sun the same face upon +which the moon's shadow fell at the beginning of the saros, +but at the end of the saros the odd 0.32 of a day gives the +earth time to make about a third of a revolution more +before the eclipse is repeated, and in consequence the +eclipse is seen in a different region of the earth, on the +average about 116° farther west in longitude. Compare in +<a href="#Fig_36">Fig. 36</a> the regions in which the eclipses of 1900 and 1918 +are visible.</p> + +<p>Is this change in the region where the repeated eclipse +is visible, true of lunar eclipses as well as solar?</p> + +<p><a name="S_73" id="S_73"></a>73. <b>Use of eclipses.</b>—At all times and among all peoples +eclipses, and particularly total eclipses of the sun, have +been reckoned among the most impressive phenomena of +Nature. In early times and among uncultivated people +they were usually regarded with apprehension, often amounting +to a terror and frenzy, which civilized travelers have +not scrupled to use for their own purposes with the aid of +the eclipse predictions contained in their almanacs, threatening +at the proper time to destroy the sun or moon, and +pointing to the advancing eclipse as proof that their +threats were not vain. In our own day and our own land +these feelings of awe have not quite disappeared, but for +the most part eclipses are now awaited with an interest and +pleasure which, contrasted with the former feelings of mankind, +furnish one of the most striking illustrations of the +effect of scientific knowledge in transforming human fear +and misery into a sense of security and enjoyment.</p> + +<p>But to the astronomer an eclipse is more than a beautiful +illustration of the working of natural laws; it is in<span class="pagenum"><a name="Page_119" id="Page_119">[Pg 119]</a></span> +varying degree an opportunity of adding to his store of +knowledge respecting the heavenly bodies. The region +immediately surrounding the sun is at most times closed to +research by the blinding glare of the sun's own light, so +that a planet as large as the moon might exist here unseen +were it not for the occasional opportunity presented by a +total eclipse which shuts off the excessive light and permits +not only a search for unknown planets but for anything +and everything which may exist around the sun. More +than one astronomer has reported the discovery of such +planets, and at least one of these has found a name and a +description in some of the books, but at the present time +most astronomers are very skeptical about the existence of +any such object of considerable size, although there is +some reason to believe that an enormous number of little +bodies, ranging in size from grains of sand upward, do +move in this region, as yet unseen and offering to the +future problems for investigation.</p> + +<p>But in other directions the study of this region at the +times of total eclipse has yielded far larger returns, and in +the chapter on the sun we shall have to consider the marvelous +appearances presented by the solar prominences and +by the corona, an appendage of the sun which reaches out +from his surface for millions of miles but is never seen +save at an eclipse. Photographs of the corona are taken +by astronomers at every opportunity, and reproductions of +some of these may be found in <a href="#CHAPTER_X">Chapter X</a>.</p> + +<p>Annular eclipses and lunar eclipses are of comparatively +little consequence, but any recorded eclipse may become of +value in connection with chronology. We date our letters +in a particular year of the twentieth century, and commonly +suppose that the years are reckoned from the birth of +Christ; but this is an error, for the eclipses which were observed +of old and by the chroniclers have been associated +with events of his life, when examined by the astronomers +are found quite inconsistent with astronomic theory.<span class="pagenum"><a name="Page_120" id="Page_120">[Pg 120]</a></span> +They are, however, reconciled with it if we assume that our +system of dates has its origin four years after the birth of +Christ, or, in other words, that Christ was born in the +year 4 <span class="smcap">B. C.</span> A mistake was doubtless made at the time +the Christian era was introduced into chronology. At +many other points the chance record of an eclipse in +the early annals of civilization furnishes a similar means of +controlling and correcting the dates assigned by the historian +to events long past.</p> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_121" id="Page_121">[Pg 121]</a></span></p> +<h2><a name="CHAPTER_VIII" id="CHAPTER_VIII"></a>CHAPTER VIII</h2> + +<h3>INSTRUMENTS AND THE PRINCIPLES INVOLVED +IN THEIR USE</h3> + + +<p><a name="S_74" id="S_74"></a>74. <b>Two familiar instruments.</b>—In previous chapters we +have seen that a clock and a divided circle (protractor) are +needed for the observations which an astronomer makes, +and it is worth while to note here that the geography of +the sky and the science of celestial motions depend fundamentally +upon these two instruments. The protractor is a +simple instrument, a humble member of the family of +divided circles, but untold labor and ingenuity have been +expended on this family to make possible the construction +of a circle so accurately divided that with it angles may be +measured to the tenth of a second instead of to the tenth +of a degree—i. e., 3,600 times as accurate as the protractor +furnishes.</p> + +<p>The building of a good clock is equally important and +has cost a like amount of labor and pains, so that it is a far +cry from Galileo and his discovery that a pendulum "keeps +time" to the modern clock with its accurate construction +and elaborate provision against disturbing influences of +every kind. Every such timepiece, whether it be of the +nutmeg variety which sells for a dollar, or whether it be the +standard clock of a great national observatory, is made up +of the same essential parts that fall naturally into four +classes, which we may compare with the departments of a +well-ordered factory: I. A timekeeping department, the +pendulum or balance spring, whose oscillations must all be +of equal duration. II. A power department, the weights or<span class="pagenum"><a name="Page_122" id="Page_122">[Pg 122]</a></span> +mainspring, which, when wound, store up the power applied +from outside and give it out piecemeal as required to keep +the first department running. III. A publication department, +the dial and hands, which give out the time furnished +by Department I. IV. A transportation department, +the wheels, which connect the other three and serve as a +means of transmitting power and time from one to the +other. The case of either clock or watch is merely the +roof which shelters it and forms no department of its industry. +Of these departments the first is by far the most +important, and its good or bad performance makes or mars +the credit of the clock. Beware of meddling with the +balance wheel of your watch.</p> + +<p><a name="S_75" id="S_75"></a>75. <b>Radiant energy.</b>—But we have now to consider other +instruments which in practice supplement or displace the +simple apparatus hitherto employed. Among the most important +of these modern instruments are the telescope, the +spectroscope, and the photographic camera; and since all +these instruments deal with the light which comes from +the stars to the earth, we must for their proper understanding +take account of the nature of that light, or, more strictly +speaking, we must take account of the radiant energy emitted +by the sun and stars, which energy, coming from the +sun, is translated by our nerves into the two different sensations +of light and heat. The radiant energy which comes +from the stars is not fundamentally different from that of +the sun, but the amount of energy furnished by any star is +so small that it is unable to produce through our nerves +any sensible perception of heat, and for the same reason +the vast majority of stars are invisible to the unaided eye; +they do not furnish a sufficient amount of energy to affect +the optic nerves. A hot brick taken into the hand reveals +its presence by the two different sensations of heat and +pressure (weight); but as there is only one brick to produce +the two sensations, so there is only one energy to produce +through its action upon different nerves the two sensations<span class="pagenum"><a name="Page_123" id="Page_123">[Pg 123]</a></span> +of light and heat, and this energy is called <i>radiant</i> because +it appears to stream forth radially from everything which +has the capacity of emitting it. For the detailed study +of radiant energy the student is referred to that branch +of science called physics; but some of its elementary principles +may be learned through the following simple experiment, +which the student should not fail to perform for +himself:</p> + +<p>Drop a bullet or other similar object into a bucket +of water and observe the circular waves which spread +from the place where it enters the water. These waves +are a form of radiant energy, but differing from light or +heat in that they are visibly confined to a single plane, +the surface of the water, instead of filling the entire surrounding +space. By varying the size of the bucket, the +depth of the water, the weight of the bullet, etc., different +kinds of waves, big and little, may be produced; but +every such set of waves may be described and defined in +all its principal characteristics by means of three numbers—viz., +the vertical height of the waves from hollow +to crest; the distance of one wave from the next; and +the velocity with which the waves travel across the water. +The last of these quantities is called the velocity of propagation; +the second is called the wave length; one half +of the first is called the amplitude; and all these terms +find important applications in the theory of light and +heat.</p> + +<p>The energy of the falling bullet, the disturbance which +it produced on entering the water, was carried by the +waves from the center to the edge of the bucket but not +beyond, for the wave can go only so far as the water +extends. The transfer of energy in this way requires a +perfectly continuous medium through which the waves +may travel, and the whole visible universe is supposed to +be filled with something called <i>ether</i>, which serves everywhere +as a medium for the transmission of radiant energy<span class="pagenum"><a name="Page_124" id="Page_124">[Pg 124]</a></span> +just as the water in the experiment served as a medium +for transmitting in waves the energy furnished to it by the +falling bullet. The student may think of this energy as being +transmitted in spherical waves through the ether, every +glowing body, such as a star, a candle flame, an arc lamp, a +hot coal, etc., being the origin and center of such systems +of waves, and determining by its own physical and chemical +properties the wave length and amplitude of the wave +systems given off.</p> + +<p>The intensity of any light depends upon the amplitude +of the corresponding vibration, and its color depends upon +the wave length. By ingenious devices which need not be +here described it has been found possible to measure the +wave length corresponding to different colors—e. g., all of +the colors of the rainbow, and some of these wave lengths +expressed in tenth meters are as follows: A tenth meter is +the length obtained by dividing a meter into 10<sup>10</sup> equal +parts. 10<sup>10</sup> = 10,000,000,000.</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><th align="center" colspan="3">Color.</th><th align="center">Wave length.</th></tr> +<tr><td align="left">Extreme</td><td align="left">limit</td><td align="left">of visible violet</td><td align="center">3,900</td></tr> +<tr><td align="left">Middle</td><td align="left">of the</td><td align="left">violet</td><td align="center">4,060</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td align="left">blue</td><td align="center">4,730</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td align="left">green</td><td align="center">5,270</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td align="left">yellow</td><td align="center">5,810</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td align="left">orange</td><td align="center">5,970</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td align="left">red</td><td align="center">7,000</td></tr> +<tr><td align="left">Extreme</td><td align="left">limit</td><td align="left">of visible red</td><td align="center">7,600</td></tr> +</table></div> + +<div class="figcenter" style="width: 500px;"><a name="PLATE_I" id="PLATE_I"></a> +<a href="images/i148-full.jpg"><img src="images/i148.jpg" width="500" height="817" alt="PLATE I. +THE NORTHERN CONSTELLATIONS" title="PLATE I. +THE NORTHERN CONSTELLATIONS" /></a> +<span class="caption">PLATE I. +THE NORTHERN CONSTELLATIONS</span> +</div> + +<p>The phrase "extreme limit of visible violet" or red +used above must be understood to mean that in general the +eye is not able to detect radiant energy having a wave +length less than 3,900 or greater than 7,600 tenth meters. +Radiant energy, however, exists in waves of both greater +and shorter length than the above, and may be readily +detected by apparatus not subject to the limitations of the +human eye—e. g., a common thermometer will show a rise +of temperature when its bulb is exposed to radiant energy +of wave length much greater than 7,600 tenth meters, and<span class="pagenum"><a name="Page_125" id="Page_125">[Pg 125]</a></span> +a photographic plate will be strongly affected by energy of +shorter wave length than 3,900 tenth meters.</p> + +<p><a name="S_76" id="S_76"></a>76. <b>Reflection and condensation of waves.</b>—When the +waves produced by dropping a bullet into a bucket of +water meet the sides of the bucket, they appear to rebound +and are reflected back toward the center, and if the bullet is +dropped very near the center of the bucket the reflected +waves will meet simultaneously at this point and produce +there by their combined action a wave higher than that +which was reflected at the walls of the bucket. There has +been a condensation of energy produced by the reflection, +and this increased energy is shown by the greater amplitude +of the wave. The student should not fail to notice that +each portion of the wave has traveled out and back over +the radius of the bucket, and that they meet simultaneously +at the center because of this equality of the paths over which +they travel, and the resulting equality of time required to +go out and back. If the bullet were dropped at one side of +the center, would the reflected waves produce <i>at any point</i> +a condensation of energy?</p> + +<p>If the bucket were of elliptical instead of circular cross +section and the bullet were dropped at one focus of the +ellipse there would be produced a condensation of reflected +energy at the other focus, since the sum of the paths traversed +by each portion of the wave before and after reflection +is equal to the sum of the paths traversed by every +other portion, and all parts of the wave reach the second +focus at the same time. Upon what geometrical principle +does this depend?</p> + +<p>The condensation of wave energy in the circular and +elliptical buckets are special cases under the general principle +that such a condensation will be produced at any +point which is so placed that different parts of the wave +front reach it simultaneously, whether by reflection or by +some other means, as shown below.</p> + +<p>The student will note that for the sake of greater precision<span class="pagenum"><a name="Page_126" id="Page_126">[Pg 126]</a></span> +we here say <i>wave front</i> instead of wave. If in any +wave we imagine a line drawn along the crest, so as to touch +every drop which at that moment is exactly at the crest, we +shall have what is called a wave front, and similarly a line +drawn through the trough between two waves, or through +any set of drops similarly placed on a wave, constitutes a +wave front.</p> + +<p><a name="S_77" id="S_77"></a>77. <b>Mirrors and lenses.</b>—That form of radiant energy +which we recognize as light and heat may be reflected and +condensed precisely as are the waves of water in the exercise +considered above, but owing to the extreme shortness +of the wave length in this case the reflecting surface should +be very smooth and highly polished. A piece of glass hollowed +out in the center by grinding, and with a light film +of silver chemically deposited upon the hollow surface and +carefully polished, is often used by astronomers for this purpose, +and is called a concave mirror.</p> + +<p>The radiant energy coming from a star or other distant +object and falling upon the silvered face of such a mirror +is reflected and condensed at a point a little in front of the +mirror, and there forms an image of the star, which may be +seen with the unaided eye, if it is held in the right place, or +may be examined through a magnifying glass. Similarly, +an image of the sun, a planet, or a distant terrestrial object +is formed by the mirror, which condenses at its appropriate +place the radiant energy proceeding from each and every +point in the surface of the object, and this, in common +phrase, produces an image of the object.</p> + +<p>Another device more frequently used by astronomers +for the production of images (condensation of energy) is a +lens which in its simplest form is a round piece of glass, +thick in the center and thin at the edge, with a cross section, +such as is shown at <i>A B</i> in <a href="#Fig_38">Fig. 38</a>. If we suppose +<i>E G D</i> to represent a small part of a wave front coming from +a very distant source of radiant energy, such as a star, this +wave front will be practically a plane surface represented<span class="pagenum"><a name="Page_127" id="Page_127">[Pg 127]</a></span> +by the straight line <i>E D</i>, but in passing through the lens +this surface will become warped, since light travels slower +in glass than in air, and the central part of the beam, <i>G</i>, +in its onward motion will be retarded by the thick center +of the lens, more than <i>E</i> or <i>D</i> will be retarded by the comparatively +thin outer edges of <i>A B</i>. On the right of the +lens the wave front therefore will be transformed into a +curved surface whose exact character depends upon the +shape of the lens and the kind of glass of which it is made. +By properly choosing these the new wave front may be +made a part of a sphere having its center at the point <i>F</i> and +the whole energy of the wave front, <i>E G D</i>, will then be condensed +at <i>F</i>, because this point is equally distant from all +parts of the warped wave front, and therefore is in a position +to receive them simultaneously. The distance of <i>F</i> +from <i>A B</i> is called the focal length of the lens, and <i>F</i> itself +is called the focus. The significance of this last word +(Latin, <i>focus</i> = fireplace) will become painfully apparent to +the student if he will hold a common reading glass between +his hand and the sun in such a way that the focus falls +upon his hand.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_38" id="Fig_38"></a> +<img src="images/i152.png" width="500" height="141" alt="Fig. 38.—Illustrating the theory of lenses." title="Fig. 38.—Illustrating the theory of lenses." /> +<span class="caption"><span class="smcap">Fig. 38.</span>—Illustrating the theory of lenses.</span> +</div> + +<p>All the energy transmitted by the lens in the direction +<i>G F</i> is concentrated upon a very small area at <i>F</i>, and +an image of the object—e. g., a star, from which the light +came—is formed here. Other stars situated near the one in +question will also send beams of light along slightly different +directions to the lens, and these will be concentrated, +each in its appropriate place, in the <i>focal plane</i>, <i>F H</i>, passed +through the focus, <i>F</i>, perpendicular to the line, <i>F G</i>, and<span class="pagenum"><a name="Page_128" id="Page_128">[Pg 128]</a></span> +we shall find in this plane a picture of all the stars or other +objects within the range of the lens.</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_39" id="Fig_39"></a> +<img src="images/i153a.png" width="350" height="214" alt="Fig. 39.—Essential parts of a reflecting +telescope." title="Fig. 39.—Essential parts of a reflecting +telescope." /> +<span class="caption"><span class="smcap">Fig. 39.</span>—Essential parts of a reflecting +telescope.</span> +</div> + +<p><a name="S_78" id="S_78"></a>78. <b>Telescopes.</b>—The simplest kind of telescope consists +of a concave mirror to produce images, and a magnifying +glass, called an <i>eyepiece</i>, through which to examine them; +but for convenience' +sake, so that the observer +may not stand in his +own light, a small mirror +is frequently added +to this combination, as +at <i>H</i> in <a href="#Fig_39">Fig. 39</a>, where +the lines represent the +directions along which +the energy is propagated. +By reflection from this mirror the focal plane and the +images are shifted to <i>F</i>, where they may be examined from +one side through the magnifying glass <i>E</i>.</p> + +<p>Such a combination of parts is called a <i>reflecting</i> telescope, +while one in which the images are produced by a +lens or combination of lenses is called a <i>refracting</i> telescope, +the adjective having reference to the bending, refraction, +produced by the glass upon the direction in which +the energy is propagated. The customary arrangement of +parts in such a telescope is shown in <a href="#Fig_40">Fig. 40</a>, where the +part marked <i>O</i> is called the objective and <i>V E</i> (the magnifying +glass) is the eyepiece, or ocular, as it is sometimes +called.</p> + + +<div class="figcenter" style="width: 500px;"><a name="Fig_40" id="Fig_40"></a> +<img src="images/i153b.png" width="500" height="96" alt="Fig. 40.—A simple form of refracting telescope." title="Fig. 40.—A simple form of refracting telescope." /> +<span class="caption"><span class="smcap">Fig. 40.</span>—A simple form of refracting telescope.</span> +</div> + +<p>Most objects with which we have to deal in using a +telescope send to it not light of one color only, but a mixture +<span class="pagenum"><a name="Page_129" id="Page_129">[Pg 129]</a></span> +of light of many colors, many different wave lengths, +some of which are refracted more than others by the glass +of which the lens is composed, and in consequence of these +different amounts of refraction a single lens does not furnish +a single image of a star, but gives a confused jumble of +red and yellow and blue images much inferior in sharpness +of outline (definition) to the images made by a good concave +mirror. To remedy this defect it is customary to +make the objective of two or more pieces of glass of different +densities and ground to different shapes as is shown at <i>O</i> +in <a href="#Fig_40">Fig. 40</a>. The two pieces of glass thus mounted in one +frame constitute a compound lens having its own focal +plane, shown at <i>F</i> in the figure, and similarly the lenses +composing the eyepiece have a focal plane between the +eyepiece and the objective which must also fall at <i>F</i>, and +in the use of a telescope the eyepiece must be pushed out +or in until its focal plane coincides with that of the objective. +This process, which is called focusing, is what is +accomplished in the ordinary opera glass by turning a screw +placed between the two tubes, and it must be carefully +done with every telescope in order to obtain distinct vision.</p> + +<p><a name="S_79" id="S_79"></a>79. <b>Magnifying power.</b>—The amount by which a given +telescope magnifies depends upon the focal length of the objective +(or mirror) and the focal length of the eyepiece, and +is equal to the ratio of these two quantities. Thus in <a href="#Fig_40">Fig. 40</a> +the distance of the objective from the focal plane <i>F</i> is +about 16 times as great as the distance of the eyepiece +from the same plane, and the magnifying power of this +telescope is therefore 16 diameters. A magnifying power +of 16 diameters means that the diameter of any object seen +in the telescope looks 16 times as large as it appears without +the telescope, and is nearly equivalent to saying that +the object appears only one sixteenth as far off. Sometimes +the magnifying power is assumed to be the number +of times that the <i>area</i> of an object seems increased; and +since areas are proportional to the squares of lines, the<span class="pagenum"><a name="Page_130" id="Page_130">[Pg 130]</a></span> +magnifying power of 16 diameters might be called a power +of 256. Every large telescope is provided with several eyepieces +of different focal lengths, ranging from a quarter of +an inch to two and a half inches, which are used to furnish +different magnifying powers as may be required for +the different kinds of work undertaken with the instrument. +Higher powers can be used with large telescopes +than with small ones, but it is seldom advantageous to +use with any telescope an eyepiece giving a higher power +than 60 diameters for each inch of diameter of the objective.</p> + +<p>The part played by the eyepiece in determining magnifying +power will be readily understood from the following +experiment:</p> + +<p>Make a pin hole in a piece of cardboard. Bring a +printed page so close to one eye that you can no longer see +the letters distinctly, and then place the pin hole between +the eye and the page. The letters which were before +blurred may now be seen plainly through the pin hole, +even when the page is brought nearer to the eye than before. +As it is brought nearer, notice how the letters seem +to become larger, solely because they are nearer. A pin +hole is the simplest kind of a magnifier, and the eyepiece +in a telescope plays the same part as does the pin hole in +the experiment; it enables the eye to be brought nearer to +the image, and the shorter the focal length of the eyepiece +the nearer is the eye brought to the image and the higher +is the magnifying power.</p> + +<div class="figright" style="width: 350px;"><a name="Fig_41" id="Fig_41"></a> +<img src="images/i156.png" width="350" height="585" alt="Fig. 41.—A simple equatorial mounting." title="Fig. 41.—A simple equatorial mounting." /> +<span class="caption"><span class="smcap">Fig. 41.</span>—A simple equatorial mounting.</span> +</div> + +<p><a name="S_80" id="S_80"></a>80. <b>The equatorial mounting.</b>—Telescopes are of all sizes, +from the modest opera glass which may be carried in the +pocket and which requires no other support than the hand, +to the giant which must have a special roof to shelter it +and elaborate machinery to support and direct it toward +the sky. But for even the largest telescopes this machinery +consists of the following parts, which are illustrated, with +exception of the last one, in the small equatorial telescope<span class="pagenum"><a name="Page_131" id="Page_131">[Pg 131]</a></span> +shown in <a href="#Fig_41">Fig. 41</a>. It is not customary to place a driving +clock on so small a telescope as this:</p> + +<p>(<i>a</i>) A supporting pier or tripod.</p> + +<p>(<i>b</i>) An axis placed parallel to the axis of the earth.</p> + +<p>(<i>c</i>) Another axis at +right angles to <i>b</i> and +capable of revolving +upon <i>b</i> as an axle.</p> + +<p>(<i>d</i>) The telescope +tube attached to <i>c</i> and capable +of revolving about <i>c</i>.</p> + +<p>(<i>e</i>) Graduated circles +attached to <i>c</i> and <i>b</i> to +measure the amount by +which the telescope is +turned on these axes.</p> + +<p>(<i>f</i>) A driving clock so +connected with <i>b</i> as to +make <i>c</i> (and <i>d</i>) revolve +about <i>b</i> with an angular +velocity equal and opposite +to that with which the +earth turns upon its axis.</p> + +<p>Such a support is called +an equatorial mounting, +and the student should +note from the figure that +the circles, <i>e</i>, measure the +hour angle and declination +of any star toward which +the telescope is directed, +and conversely if the telescope be so set that these circles +indicate the hour angle and declination of any given star, +the telescope will then point toward that star. In this +way it is easy to find with the telescope any moderately +bright star, even in broad daylight, although it is then +<span class="pagenum"><a name="Page_133" id="Page_133">[Pg 133]</a></span> +absolutely invisible to the naked eye. The rotation of the +earth about its axis will speedily carry the telescope away +from the star, but if the driving clock be started, its effect +is to turn the telescope toward the west just as fast as the +earth's rotation carries it toward the east, and by these +compensating motions +to keep it directed toward +the star. In <a href="#Fig_42">Fig. 42</a>, +which represents +the largest and one of +the most perfect refracting +telescopes +ever built, let the student +pick out and identify +the several parts +of the mounting above +described. A part of +the driving clock may +be seen within the head +of the pier. In <a href="#Fig_43">Fig. 43</a> +trace out the corresponding +parts in +the mounting of a reflecting +telescope.</p> + + +<div class="figcenter" style="width: 600px;"><a name="Fig_42" id="Fig_42"></a> +<a href="images/i157-full.jpg"><img src="images/i157.jpg" width="600" height="370" alt="Fig. 42.—Equatorial mounting of the great telescope of the Yerkes Observatory." title="Fig. 42.—Equatorial mounting of the great telescope of the Yerkes Observatory." /></a> +<span class="caption"><span class="smcap">Fig. 42.</span>—Equatorial mounting of the great telescope of the Yerkes Observatory.</span> +</div> + + +<div class="figright" style="width: 350px;"><a name="Fig_43" id="Fig_43"></a> +<img src="images/i158.jpg" width="350" height="582" alt="Fig. 43.—The reflecting telescope of the +Paris Observatory." title="Fig. 43.—The reflecting telescope of the +Paris Observatory." /> +<span class="caption"><span class="smcap">Fig. 43.</span>—The reflecting telescope of the +Paris Observatory.</span> +</div> + +<p>A telescope is often +only a subordinate part +of some instrument or +apparatus, and then its +style of mounting is +determined by the requirements of the special case; but +when the telescope is the chief thing, and the remainder +of the apparatus is subordinate to it, the equatorial mounting +is almost always adopted, although sometimes the arrangement +of the parts is very different in appearance from +any of those shown above. Beware of the popular error that +an object held close in front of a telescope can be seen by an<span class="pagenum"><a name="Page_134" id="Page_134">[Pg 134]</a></span> +observer at the eyepiece. The numerous stories of astronomers +who saw spiders crawling over the objective of their +telescope, and imagined they were beholding strange objects +in the sky, are all fictitious, since nothing on or near +the objective could possibly be seen through the telescope.</p> + +<p><a name="S_81" id="S_81"></a>81. <b>Photography.</b>—A photographic camera consists of a +lens and a device for holding at its focus a specially prepared +plate or film. This +plate carries a chemical +deposit which is very +sensitive to the action +of light, and which may +be made to preserve the +imprint of any picture +which the lens forms +upon it. If such a sensitive +plate is placed at +the focus of a reflecting +telescope, the combination +becomes a camera +available for astronomical +photography, and at +the present time the +tendency is strong in +nearly every branch of +astronomical research to +substitute the sensitive +plate in place of the observer +at a telescope. A +refracting telescope may also be used for astronomical photography, +and is very much used, but some complications +occur here on account of the resolution of the light into +its constituent colors in passing through the objective. +<a href="#Fig_44">Fig. 44</a> shows such a telescope, or rather two telescopes, one +photographic, the other visual, supported side by side upon +the same equatorial mounting.</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_44" id="Fig_44"></a> +<img src="images/i159.png" width="350" height="539" alt="Fig. 44.—Photographic telescope of the Paris +Observatory." title="Fig. 44.—Photographic telescope of the Paris +Observatory." /> +<span class="caption"><span class="smcap">Fig. 44.</span>—Photographic telescope of the Paris +Observatory.</span> +</div><p><span class="pagenum"><a name="Page_135" id="Page_135">[Pg 135]</a></span></p> + +<p>One of the great advantages of photography is found in +connection with what is called—</p> + +<p><a name="S_82" id="S_82"></a>82. <b>Personal equation.</b>—It is a remarkable fact, first investigated +by the German astronomer Bessel, three quarters +of a century ago, that where extreme accuracy is required +the human senses can not be implicitly relied upon. +The most skillful observers will not agree exactly in their +measurement of an angle or in estimating the exact instant +at which a star crossed the meridian; the most skillful +artists can not draw identical pictures of the same object, +etc.</p> + +<p>These minor deceptions of the senses are included in +the term <i>personal equation</i>, which is a famous phrase in +astronomy, denoting that the observations of any given +person require to be corrected by means of some equation +involving his personality.</p> + +<p>General health, digestion, nerves, fatigue, all influence +the personal equation, and it was in reference to such matters +that one of the most eminent of living astronomers has +given this description of his habits of observing:</p> + +<p>"In order to avoid every physiological disturbance, I +have adopted the rule to abstain for one or two hours before +commencing observations from every laborious occupation; +never to go to the telescope with stomach loaded with +food; to abstain from everything which could affect the +nervous system, from narcotics and alcohol, and especially +from the abuse of coffee, which I have found to be exceedingly +prejudicial to the accuracy of observation."<a name="FNanchor_C_3" id="FNanchor_C_3"></a><a href="#Footnote_C_3" class="fnanchor">[C]</a> A +regimen suggestive of preparation for an athletic contest +rather than for the more quiet labors of an astronomer.</p> + +<p><a name="S_83" id="S_83"></a>83. <b>Visual and photographic work.</b>—The photographic +plate has no stomach and no nerves, and is thus free from +many of the sources of error which inhere in visual observations, +and in special classes of work it possesses other<span class="pagenum"><a name="Page_136" id="Page_136">[Pg 136]</a></span> +marked advantages, such as rapidity when many stars are +to be dealt with simultaneously, permanence of record, and +owing to the cumulative effect of long exposure of the plate +it is possible to photograph with a given telescope stars far +too faint to be seen through it. On the other hand, the +eye has the advantage in some respects, such as studying +the minute details of a fairly bright object—e. g., the surface +of a planet, or the sun's corona and, for the present at +least, neither method of observing can exclude the other. +For a remarkable case of discordance between the results +of photographic and visual observations compare the pictures +of the great nebula in the constellation Andromeda, +which are given in <a href="#CHAPTER_XIV">Chapter XIV</a>. A partial explanation +of these discordances and other similar ones is that the +eye is most strongly affected by greenish-yellow light, +while the photographic plate responds most strongly to +violet light; the photograph, therefore, represents things +which the eye has little capacity for seeing, and <i>vice versa</i>.</p> + +<p><a name="S_84" id="S_84"></a>84. <b>The spectroscope.</b>—In some respects the spectroscope +is the exact counterpart of the telescope. The latter condenses +radiant energy and the former disperses it. As a +measuring instrument the telescope is mainly concerned +with the direction from which light comes, and the different +colors of which that light is composed affect it only as +an obstacle to be overcome in its construction. On the +other hand, with the spectroscope the direction from which +the radiant energy comes is of minor consequence, and the +all-important consideration is the intrinsic character of +that radiation. What colors are present in the light and +in what proportions? What can these colors be made to +tell about the nature and condition of the body from which +they come, be it sun, or star, or some terrestrial source of +light, such as an arc lamp, a candle flame, or a furnace in +blast? These are some of the characteristic questions of +the spectrum analysis, and, as the name implies, they are +solved by analyzing the radiant energy into its component<span class="pagenum"><a name="Page_137" id="Page_137">[Pg 137]</a></span> +parts, setting down the blue light in one place, the yellow +in another, the red in still another, etc., and interpreting +this array of colors by means of principles which we shall +have to consider. Something of this process of color +analysis may be seen in the brilliant hues shown by a soap +bubble, or reflected from a piece of mother-of-pearl, and +still more strikingly exhibited in the rainbow, produced by +raindrops which break up the sunlight into its component +colors and arrange them each in its appropriate place. +Any of these natural methods of decomposing light might +be employed in the construction of a spectroscope, but in +spectroscopes which are used for analyzing the light from +feeble sources, such as a star, or a candle flame, a glass +prism of triangular cross section is usually employed to resolve +the light into its component colors, which it does by +refracting it as shown at the edges of the lens in <a href="#Fig_38">Fig. 38</a>.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_45" id="Fig_45"></a> +<img src="images/i162.png" width="500" height="290" alt="Fig. 45.—Resolution of light into its component colors." title="Fig. 45.—Resolution of light into its component colors." /> +<span class="caption"><span class="smcap">Fig. 45.</span>—Resolution of light into its component colors.</span> +</div> + +<p>The course of a beam of light in passing through such +a prism is shown in <a href="#Fig_45">Fig. 45</a>. Note that the bending of the +light from its original course into a new one, which is here +shown as produced by the prism, is quite similar to the +bending shown at the edges of a lens and comes from the<span class="pagenum"><a name="Page_138" id="Page_138">[Pg 138]</a></span> +same cause, the slower velocity of light in glass than in +air. It takes the light-waves as long to move over the +path <i>A B</i> in glass as over the longer path <i>1</i>, <i>2</i>, <i>3</i>, <i>4</i>, of +which only the middle section lies in the glass.</p> + +<p>Not only does the prism bend the beam of light transmitted +by it, but it bends in different degree light of different +colors, as is shown in the figure, where the beam at the +left of the prism is supposed to be made up of a mixture of +blue and red light, while at the right of the prism the +greater deviation imparted to the blue quite separates the +colors, so that they fall at different places on the screen, +<i>S S</i>. The compound light has been analyzed into its constituents, +and in the same way every other color would be +put down at its appropriate place on the screen, and a beam +of white light falling upon the prism would be resolved by +it into a sequence of colors, falling upon the screen in the +order red, orange, yellow, green, blue, indigo, violet. The +initial letters of these names make the word <i>Roygbiv</i>, and +by means of it their order is easily remembered.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_46" id="Fig_46"></a> +<img src="images/i164.png" width="500" height="230" alt="Fig. 46.—Principal parts of a spectroscope." title="Fig. 46.—Principal parts of a spectroscope." /> +<span class="caption"><span class="smcap">Fig. 46.</span>—Principal parts of a spectroscope.</span> +</div> + +<p>If the light which is to be examined comes from a star +the analysis made by the prism is complete, and when +viewed through a telescope the image of the star is seen to +be drawn out into a band of light, which is called a <i>spectrum</i>, +and is red at one end and violet or blue at the other, +with all the colors of the rainbow intervening in proper +order between these extremes. Such a prism placed in +front of the objective of a telescope is called an objective +prism, and has been used for stellar work with marked +success at the Harvard College Observatory. But if the +light to be analyzed comes from an object having an appreciable +extent of surface, such as the sun or a planet, +the objective prism can not be successfully employed, +since each point of the surface will produce its own spectrum, +and these will appear in the <i>view telescope</i> superposed +and confused one with another in a very objectionable +manner. To avoid this difficulty there is placed<span class="pagenum"><a name="Page_139" id="Page_139">[Pg 139]</a></span> +between the prism and the source of light an opaque +screen, <i>S</i>, with a very narrow slit cut in it, through which all +the light to be analyzed must pass and must also go through +a lens, <i>A</i>, placed between the slit and the prism, as shown +in <a href="#Fig_46">Fig. 46</a>. The slit and lens, together with the tube in +which they are usually supported, are called a <i>collimator</i>. +By this device a very limited amount of light is permitted +to pass from the object through the slit and lens to the +prism and is there resolved into a spectrum, which is in +effect a series of images of the slit in light of different +colors, placed side by side so close as to make practically a +continuous ribbon of light whose width is the length of +each individual picture of the slit. The length of the ribbon +(dispersion) depends mainly upon the shape of the prism +and the kind of glass of which it is made, and it may be +very greatly increased and the efficiency of the spectroscope +enhanced by putting two, three, or more prisms in +place of the single one above described. When the amount +of light is very great, as in the case of the sun or an electric +arc lamp, it is advantageous to alter slightly the arrangement +of the spectroscope and to substitute in place +of the prism a grating—i. e., a metallic mirror with a great +number of fine parallel lines ruled upon its surface at equal +intervals, one from another. It is by virtue of such a system +of fine parallel grooves that mother-of-pearl displays<span class="pagenum"><a name="Page_140" id="Page_140">[Pg 140]</a></span> +its beautiful color effects, and a brilliant spectrum of great +purity and high dispersion is furnished by a grating ruled +with from 10,000 to 20,000 lines to the inch. <a href="#Fig_47">Fig. 47</a> represents, +rather crudely, a part of the spectrum +of an arc light furnished by such a +grating, or rather it shows three different +spectra arranged side by side, and looking +something like a rude ladder. The sides +of the ladder are the spectra furnished by +the incandescent carbons of the lamp, and +the cross pieces are the spectrum of the +electric arc filling the space between the +carbons. <a href="#Fig_48">Fig. 48</a> shows a continuation of +the same spectra into a region where the +radiant energy is invisible to the eye, but +is capable of being photographed.</p> + +<div class="figcenter" style="width: 600px;"><a name="Fig_47" id="Fig_47"></a> +<a href="images/i165.jpg"><img src="images/i165.jpg" width="600" height="96" alt="Fig. 47.—Green and blue part of the spectrum of an electric arc light." title="Fig. 47.—Green and blue part of the spectrum of an electric arc light." /></a> +<span class="caption"><span class="smcap">Fig. 47.</span>—Green and blue part of the spectrum of an electric arc light.</span> +</div> + +<p>It is only when a lens is placed between +the lamp and the slit of the spectroscope +that the three spectra are shown +distinct from each other as in the figure. +The purpose of the lens is to make a picture +of the lamp upon the slit, so that +all the radiant energy from any one point +of the arc may be brought to one part of +the slit, and thus appear in the resulting +spectrum separated from the energy +which comes from every other part of +the arc. Such an instrument is called +an <i>analyzing spectroscope</i> while one without +the lens is called an <i>integrating spectroscope</i>, +since it furnishes to each point +of the slit a sample of the radiant energy +coming from every part of the source of +light, and thus produces only an average +spectrum of that source without distinction of its parts. +When a spectroscope is attached to a telescope, as is often<span class="pagenum"><a name="Page_141" id="Page_141">[Pg 141]</a></span> +done (see <a href="#Fig_49">Fig. 49</a>), the eyepiece is removed to make way +for it, and the telescope objective takes the part of the +analyzing lens. A camera is frequently combined with +such an apparatus to photograph the spectra it furnishes, +and the whole instrument is then called a <i>spectrograph</i>.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_48" id="Fig_48"></a> +<a href="images/i166.jpg"><img src="images/i166.jpg" width="500" height="93" alt="Fig. 48.—Violet and ultraviolet parts of spectrum of an arc lamp." title="Fig. 48.—Violet and ultraviolet parts of spectrum of an arc lamp." /></a> +<span class="caption"><span class="smcap">Fig. 48.</span>—Violet and ultraviolet parts of spectrum of an arc lamp.</span> +</div> + +<p><a name="S_85" id="S_85"></a>85. <b>Spectrum analysis.</b>—Having seen the mechanism of +the spectroscope by which the light incident upon it is +resolved into its constituent parts and drawn out into a +series of colors arranged in the order of their wave lengths, +we have now to consider the interpretation which is to be +placed upon the various kinds of spectra which may be +seen, and here we rely upon the experience of physicists +and chemists, from whom we learn as follows:</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_49" id="Fig_49"></a> +<a href="images/i167-full.jpg"><img src="images/i167.jpg" width="500" height="388" alt="Fig. 49.—A spectroscope attached to the Yerkes telescope." title="Fig. 49.—A spectroscope attached to the Yerkes telescope." /></a> +<span class="caption"><span class="smcap">Fig. 49.</span>—A spectroscope attached to the Yerkes telescope.</span> +</div> + +<p>The radiant energy which is analyzed by the spectroscope +has its source in the atoms and molecules which make +up the luminous body from which the energy is radiated, +and these atoms and molecules are able to impress upon +the ether their own peculiarities in the shape of waves of +different length and amplitude. We have seen that by +varying the conditions of the experiment different kinds of +waves may be produced in a bucket of water; and as a +study of these waves might furnish an index to the conditions +which produced them, so the study of the waves +peculiar to the light which comes from any source may be +made to give information about the molecules which make +up that source. Thus the molecules of iron produce a +system of waves peculiar to themselves and which can be +duplicated by nothing else, and every other substance +gives off its own peculiar type of energy, presenting a<span class="pagenum"><a name="Page_142" id="Page_142">[Pg 142]</a></span> +limited and definite number of wave lengths dependent +upon the nature and condition of its molecules. If these +molecules are free to behave in their own characteristic +fashion without disturbance or crowding, they emit light of +these wave lengths only, and we find in the spectrum a +series of bright lines, pictures of the slit produced by light +of these particular wave lengths, while between these bright +lines lie dark spaces showing the absence from the radiant +energy of light of intermediate wave lengths. Such a +spectrum is shown in the central portion of <a href="#Fig_47">Fig. 47</a>, which, +as we have already seen, is produced by the space between +the carbons of the arc lamp. On the other hand, if the +molecules are closely packed together under pressure they +so interfere with each other as to give off a jumble of +energy of all wave lengths, and this is translated by the +spectroscope into a continuous ribbon of light with no dark +spaces intervening, as in the upper and lower parts of Figs. <a href="#Fig_47">47</a><span class="pagenum"><a name="Page_143" id="Page_143">[Pg 143]</a></span> +and <a href="#Fig_48">48</a>, produced by the incandescent solid carbons of +the lamp. These two types are known as the continuous +and discontinuous spectrum, and we may lay down the following +principle regarding them:</p> + +<p>A discontinuous spectrum, or bright-line spectrum as +it is familiarly called, indicates that the molecules of the +source of light are not crowded together, and therefore the +light must come from an incandescent gas. A continuous +spectrum shows only that the molecules are crowded together, +or are so numerous that the body to which they +belong is not transparent and gives no further information. +The body may be solid, liquid, or gaseous, but in +the latter case the gas must be under considerable pressure +or of great extent.</p> + +<p>A second principle is: The lines which appear in a spectrum +are characteristic of the source from which the light +came—e. g., the double line in the yellow part of the spectrum +at the extreme left in <a href="#Fig_47">Fig. 47</a> is produced by sodium +vapor in and around the electric arc and is never produced +by anything but sodium. When by laboratory experiments +we have learned the particular set of lines +corresponding to iron, we may treat the presence of these +lines in another spectrum as proof that iron is present +in the source from which the light came, whether that +source be a white-hot poker in the next room or a star +immeasurably distant. The evidence that iron is present +lies in the nature of the light, and there is no reason +to suppose that nature to be altered on the way from +star to earth. It may, however, be altered by something +happening to the source from which it comes—e. g., changing +temperature or pressure may affect, and does affect, the +spectrum which such a substance as iron emits, and we must +be prepared to find the same substance presenting different +spectra under different conditions, only these conditions +must be greatly altered in order to produce radical changes +in the spectrum.<span class="pagenum"><a name="Page_144" id="Page_144">[Pg 144]</a></span></p> + +<div class="figcenter" style="width: 600px;"><a name="Fig_50" id="Fig_50"></a> +<img src="images/i169.png" width="600" height="137" alt="Fig. 50.—The chief lines in the spectrum of sunlight.—Herschel." title="Fig. 50.—The chief lines in the spectrum of sunlight.—Herschel." /> +<span class="caption"><span class="smcap">Fig. 50.</span>—The chief lines in the spectrum of sunlight.—<span class="smcap">Herschel.</span></span> +</div> + +<p><a name="S_86" id="S_86"></a>86. <b>Wave lengths.</b>—To identify +a line as belonging to and produced +by iron or any other substance, +its position in the spectrum—i. e., +its wave length—must +be very accurately determined, +and for the identification of a substance +by means of its spectrum it +is often necessary to determine accurately +the wave lengths of many +lines. A complicated spectrum +may consist of hundreds or thousands +of lines, due to the presence +of many different substances in +the source of light, and unless +great care is taken in assigning +the exact position of these lines +in the spectrum, confusion and +wrong identifications are sure to +result. For the measurement of +the required wave length a tenth +meter (<a href="#S_75">§ 75</a>) is the unit employed, +and a scale of wave lengths expressed +in this unit is presented +in <a href="#Fig_50">Fig. 50</a>. The accuracy with +which some of these wave lengths +are determined is truly astounding; +a ten-billionth of an inch! +These numerical wave lengths +save all necessity for referring to +the color of any part of the spectrum, +and pictures of spectra for +scientific use are not usually +printed in colors.</p> + +<p><a name="S_87" id="S_87"></a>87. <b>Absorption spectra.</b>—There +is another kind of spectrum, of<span class="pagenum"><a name="Page_145" id="Page_145">[Pg 145]</a></span> +greater importance than either of those above considered, +which is well illustrated by the spectrum of sunlight (<a href="#Fig_50">Fig. 50</a>). +This is a nearly continuous spectrum crossed by numerous +<i>dark</i> lines due to absorption of radiant energy in a +comparatively cool gas through which it passes on its way +to the spectroscope. Fraunhofer, who made the first careful +study of spectra, designated some of the more conspicuous +of these lines by letters of the alphabet which are shown +in the plate, and which are still in common use as names +for the lines, not only in the spectrum of sunlight but +wherever they occur in other spectra. Thus the double +line marked <i>D</i>, wave length 5893, falls at precisely the same +place in the spectrum as does the double (sodium) line +which we have already seen in the yellow part of the arc-light +spectrum, which line is also called <i>D</i> and bears a very +intimate relation to the dark <i>D</i> line of the solar spectrum.</p> + +<p>The student who has access to colored crayons should +color one edge of <a href="#Fig_50">Fig. 50</a> in accordance with the lettering +there given and, so far as possible, he should make the +transition from one color to the next a gradual one, as it is +in the rainbow.</p> + +<p><a href="#Fig_50">Fig. 50</a> is far from being a complete representation of +the spectrum of sunlight. Not only does this spectrum extend +both to the right and to the left into regions invisible +to the human eye, but within the limits of the figure, instead +of the seventy-five lines there shown, there are literally +thousands upon thousands of lines, of which only the +most conspicuous can be shown in such a cut as this.</p> + +<p>The dark lines which appear in the spectrum of sunlight +can, under proper conditions, be made to appear in +the spectrum of an arc light, and <a href="#Fig_51">Fig. 51</a> shows a magnified +representation of a small part of such a spectrum adjacent +to the <i>D</i> (sodium) lines. Down the middle of each of these +lines runs a black streak whose position (wave length) is +precisely that of the <i>D</i> lines in the spectrum of sunlight, +and whose presence is explained as follows:<span class="pagenum"><a name="Page_146" id="Page_146">[Pg 146]</a></span></p> + +<p>The very hot sodium vapor at the center of the arc gives +off its characteristic light, which, shining through the outer +and cooler layers of sodium vapor, is partially absorbed by +these, resulting in a fine dark line corresponding exactly in +position and wave length to the bright lines, and seen +against these as a background, since the higher temperature +at the center of the arc tends to broaden the bright +lines and make them diffuse. Similarly the dark lines in +the spectrum of the sun (<a href="#Fig_50">Fig. 50</a>) point to the existence of +a surrounding envelope of relatively cool gases, which absorb +from the sunlight precisely those kinds of radiant energy +which they would themselves emit if incandescent. The +resulting dark lines in the spectrum are to be interpreted +by the same set of principles which we have above applied +to the bright lines of a discontinuous spectrum, and they +may be used to determine the chemical composition of the +sun, just as the bright lines serve to determine the chemical +elements present in the electric arc. With reference to +the mode of their formation, bright-line and dark-line spectra +are sometimes called respectively <i>emission</i> and <i>absorption</i> +spectra.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_51" id="Fig_51"></a> +<img src="images/i171.jpg" width="500" height="266" alt="Fig. 51.—The lines reversed." title="Fig. 51.—The lines reversed." /> +<span class="caption"><span class="smcap">Fig. 51.</span>—The lines reversed.</span> +</div> + +<p><a name="S_88" id="S_88"></a>88. <b>Types of spectrum.</b>—The sun presents by far the +most complex spectrum known, and <a href="#Fig_50">Fig. 50</a> shows only a +small number of the more conspicuous lines which appear<span class="pagenum"><a name="Page_147" id="Page_147">[Pg 147]</a></span> +in it. Spectra of stars, <i>per contra</i>, appear relatively simple, +since their feeble light is insufficient to bring out faint +details. In Chapters <a href="#CHAPTER_XIII">XIII</a> and <a href="#CHAPTER_XIV">XIV</a> there are shown types +of the different kinds of spectra given by starlight, and +these are to be interpreted by the principles above established. +Thus the spectrum of the bright star β Aurigę +shows a continuous spectrum crossed by a few heavy absorption +lines which are known from laboratory experiments +to be produced only by hydrogen. There must +therefore be an atmosphere of relatively cool hydrogen +surrounding this star. The spectrum of Pollux is quite +similar to that of the sun and is to be interpreted as showing +a physical condition similar to that of the sun, while +the spectrum of α Herculis is quite different from either of +the others. In subsequent chapters we shall have occasion +to consider more fully these different types of spectrum.</p> + +<p><a name="S_89" id="S_89"></a>89. <b>The Doppler principle.</b>—This important principle of +the spectrum analysis is most readily appreciated through +the following experiment:</p> + +<p>Listen to the whistle of a locomotive rapidly approaching, +and observe how the pitch changes and the note becomes +more grave as the locomotive passes by and commences +to recede. During the approach of the whistle +each successive sound wave has a shorter distance to travel +in coming to the ear of the listener than had its predecessor, +and in consequence the waves appear to come in +quicker succession, producing a higher note with a correspondingly +shorter wave length than would be heard if the +same whistle were blown with the locomotive at rest. On +the other hand, the wave length is increased and the pitch +of the note lowered by the receding motion of the whistle. +A similar effect is produced upon the wave length of light +by a rapid change of distance between the source from +which it comes and the instrument which receives it, so +that a diminishing distance diminishes very slightly the +wave length of every line in the spectrum produced by the<span class="pagenum"><a name="Page_148" id="Page_148">[Pg 148]</a></span> +light, and an increasing distance increases these wave +lengths, and this holds true whether the change of distance +is produced by motion of the source of light or by +motion of the instrument which receives it.</p> + +<p>This change of wave length is sometimes described by +saying that when a body is rapidly approaching, the lines +of its spectrum are all displaced toward the violet end of +the spectrum, and are correspondingly displaced toward the +red end by a receding motion. The amount of this shifting, +when it can be measured, measures the velocity of the +body along the line of sight, but the observations are exceedingly +delicate, and it is only in recent years that it has +been found possible to make them with precision. For this +purpose there is made to pass through the spectroscope +light from an artificial source which contains one or more +chemical elements known to be present in the star which +is to be observed, and the corresponding lines in the +spectrum of this light and in the spectrum of the star +are examined to determine whether they exactly match +in position, or show, as they sometimes do, a slight displacement, +as if one spectrum had been slipped past +the other. The difficulty of the observations lies in the +extremely small amount of this slipping, which rarely if +ever in the case of a moving star amounts to one sixth part +of the interval between the close parallel lines marked <i>D</i> +in <a href="#Fig_50">Fig. 50</a>. The spectral lines furnished by the headlight +of a locomotive running at the rate of a hundred miles +per hour would be displaced by this motion less than one +six-thousandth part of the space between the <i>D</i> lines, +an amount absolutely imperceptible in the most powerful +spectroscope yet constructed. But many of the celestial +bodies have velocities so much greater than a hundred +miles per hour that these may be detected and measured +by means of the Doppler principle.</p> + +<p><a name="S_90" id="S_90"></a>90. <b>Other instruments.</b>—Other instruments of importance +to the astronomer, but of which only casual mention<span class="pagenum"><a name="Page_149" id="Page_149">[Pg 149]</a></span> +can here be made, are the meridian-circle; the transit, one +form of which is shown in <a href="#Fig_52">Fig. 52</a>, and the zenith telescope, +which furnish refined methods for making observations +similar in kind to those which the student has already +learned to make with plumb line and protractor; the sextant, +which is pre-eminently the sailor's instrument for +finding the latitude and longitude at sea, by measuring the +altitudes of sun and stars above the sea horizon; the heliometer, +which serves for the very accurate measurement of +small angles, such as the angular distance between two stars +not more than one or two degrees apart; and the photometer, +which is used for measuring the amount of light received +from the celestial bodies.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_52" id="Fig_52"></a> +<a href="images/i174-full.jpg"><img src="images/i174.jpg" width="500" height="375" alt="Fig. 52.—A combined transit instrument and zenith telescope." title="Fig. 52.—A combined transit instrument and zenith telescope." /></a> +<span class="caption"><span class="smcap">Fig. 52.</span>—A combined transit instrument and zenith telescope.</span> +</div> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_150" id="Page_150">[Pg 150]</a></span></p> +<h2><a name="CHAPTER_IX" id="CHAPTER_IX"></a>CHAPTER IX</h2> + +<h3>THE MOON</h3> + + +<p><a name="S_91" id="S_91"></a>91. <b>Results of observation with the unaided eye.</b>—The +student who has made the observations of the moon which +are indicated in <a href="#CHAPTER_III">Chapter III</a> has in hand data from which +much may be learned about the earth's satellite. Perhaps +the most striking feature brought out by them is the motion +of the moon among the stars, always from west toward +east, accompanied by that endless series of changes in +shape and brightness—new moon, first quarter, full moon, +etc.—whose successive stages we represent by the words, +the phase of the moon. From his own observation the +student should be able to verify, at least approximately, +the following statements, although the degree of numerical +precision contained in some of them can be reached +only by more elaborate apparatus and longer study than he +has given to the subject:</p> + +<p>A. The phase of the moon depends upon the distance +apart of sun and moon in the sky, new moon coming +when they are together, and full moon when they are as +far apart as possible.</p> + +<div class="figcenter" style="width: 500px;"><a name="THE_MOON" id="THE_MOON"></a> +<a href="images/i176-full.jpg"><img src="images/i176.jpg" width="500" height="756" alt="THE MOON, ONE DAY AFTER FIRST QUARTER. + +From a photograph made at the Paris Observatory." title="THE MOON, ONE DAY AFTER FIRST QUARTER. + +From a photograph made at the Paris Observatory." /></a> +<span class="caption">THE MOON, ONE DAY AFTER FIRST QUARTER. + +From a photograph made at the Paris Observatory.</span> +</div> + +<p>B. The moon is essentially a round, dark body, giving +off no light of its own, but shining solely by reflected sunlight. +The proof of this is that whenever we see a part of +the moon which is turned away from the sun it looks dark—e. g., +at new moon, sun and moon are in nearly the same +direction from us and we see little or nothing of the moon, +since the side upon which the sun shines is turned away +from us. At full moon the earth is in line between sun<span class="pagenum"><a name="Page_151" id="Page_151">[Pg 151]</a></span> +and moon, and we see, round and bright, the face upon +which the sun shines. At other phases, such as the quarters, +the moon turns toward the earth a part of its night +hemisphere and a part of its day hemisphere, but in general +only that part which belongs to the day side of the +moon is visible and the peculiar curved line which forms +the boundary—the "ragged edge," or <i>terminator</i>, as it is +called, is the dividing line between day and night upon +the moon.</p> + +<p>A partial exception to what precedes is found for a few +days after new moon when the moon and sun are not very +far apart in the sky, for then the whole round disk of the +moon may often be seen, a small part of it brightly illuminated +by the sun and the larger part feebly illuminated +by sunlight which fell first upon the earth and was by it +reflected back to the moon, giving the pleasing effect which +is sometimes called the old moon in the new moon's arms. +The new moon—i. e., the part illumined by the sun—usually +appears to belong to a sphere of larger radius than the +old moon, but this is purely a trick played by the eyes of +the observer, and the effect disappears altogether in a telescope. +Is there any similar effect in the few days before +new moon?</p> + +<p>C. The moon makes the circuit of the sky from a given +star around to the same star again in a little more than +27 days (27.32166), but the interval between successive new +moons—i. e., from the sun around to the sun again—is +more than 29 days (29.53059). This last interval, which is +called a lunar month or <i>synodical</i> month, indicates what +we have learned before—that the sun has changed its place +among the stars during the month, so that it takes the +moon an extra two days to overtake him after having +made the circuit of the sky, just as it takes the minute +hand of a clock an extra 5 minutes to catch up with +the hour hand after having made a complete circuit of the +dial.<span class="pagenum"><a name="Page_152" id="Page_152">[Pg 152]</a></span></p> + +<p>D. Wherever the moon may be in the sky, it turns +always the same face toward the earth, as is shown by the +fact that the dark markings which appear on its surface +stand always upon (nearly) the same part of its disk. It +does not always turn the same face toward the sun, for +the boundary line between the illumined and unillumined +parts of the moon shifts from one side to the other as the +phase changes, dividing at each moment day from night +upon the moon and illustrating by its slow progress that +upon the moon the day and the month are of equal length +(29.5 terrestrial days), instead of being time units of different +lengths as with us.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_53" id="Fig_53"></a> +<img src="images/i180.png" width="500" height="777" alt="Fig. 53.—Motion of moon and earth relative to the sun." title="Fig. 53.—Motion of moon and earth relative to the sun." /> +<span class="caption"><span class="smcap">Fig. 53.</span>—Motion of moon and earth relative to the sun.</span> +</div> + +<p><a name="S_92" id="S_92"></a>92. <b>The moon's motion.</b>—The student should compare the +results of his own observations, as well as the preceding +section, with <a href="#Fig_53">Fig. 53</a>, in which the lines with dates printed +on them are all supposed to radiate from the sun and to +represent the direction from the sun of earth and moon +upon the given dates which are arbitrarily assumed for +the sake of illustration, any other set would do equally +well. The black dots, small and large, represent the +moon revolving about the earth, but having the circular +path shown in <a href="#Fig_34">Fig. 34</a> (ellipse) transformed by the earth's +forward motion into the peculiar sinuous line here shown. +With respect to both earth and sun, the moon's orbit +deviates but little from a circle, since the sinuous curve +of <a href="#Fig_53">Fig. 53</a> follows very closely the earth's orbit around +the sun and is almost identical with it. For clearness +of representation the distance between earth and moon +in the figure has been made ten times too great, and to +get a proper idea of the moon's orbit with reference to +the sun, we must suppose the moon moved up toward the +earth until its distance from the line of the earth's orbit is +only a tenth part of what it is in the figure. When this is +done, the moon's path becomes almost indistinguishable +from that of the earth, as may be seen in the figure, where +the attempt has been made to show both lines, and it<span class="pagenum"><a name="Page_154" id="Page_154">[Pg 154]</a></span> +is to be especially noted that this real orbit of the moon is +everywhere concave toward the sun.</p> + +<p>The phase presented by the moon at different parts of +its path is indicated by the row of circles at the right, and +the student should show why a new moon is associated +with June 30th and a full moon with July 15th, etc. What +was the date of first quarter? Third quarter?</p> + +<p>We may find in <a href="#Fig_53">Fig. 53</a> another effect of the same +kind as that noted above in C. Between noon, June 30th, +and noon, July 3d, the earth makes upon its axis three complete +revolutions with respect to the sun, but the meridian +which points toward the moon at noon on June 30th will +not point toward it at noon on July 3d, since the moon has +moved into a new position and is now 37° away from the +meridian. Verify this statement by measuring, in <a href="#Fig_53">Fig. 53</a>, +with the protractor, the moon's angular distance from the +meridian at noon on July 3d. When will the meridian +overtake the moon?</p> + +<p><a name="S_93" id="S_93"></a>93. <b>Harvest moon.</b>—The interval between two successive +transits of the meridian past the moon is called a lunar +day, and the student should show from the figure that on +the average a lunar day is 51 minutes longer than a solar +day—i. e., upon the average each day the moon comes to +the meridian 51 minutes of solar time later than on the +day before. It is also true that on the average the moon +rises and sets 51 minutes later each day than on the day +before. But there is a good deal of irregularity in the +retardation of the time of moonrise and moonset, since +the time of rising depends largely upon the particular +point of the horizon at which the moon appears, and between +two days this point may change so much on account +of the moon's orbital motion as to make the retardation +considerably greater or less than its average value. In +northern latitudes this effect is particularly marked in the +month of September, when the eastern horizon is nearly +parallel with the moon's apparent path in the sky, and near<span class="pagenum"><a name="Page_155" id="Page_155">[Pg 155]</a></span> +the time of full moon in that month the moon rises on +several successive nights at nearly the same hour, and in +less degree the same is true for October. This highly +convenient arrangement of moonlight has caused the full +moons of these two months to be christened respectively +the Harvest Moon and the Hunter's Moon.</p> + +<p><a name="S_94" id="S_94"></a>94. <b>Size and mass of the moon.</b>—It has been shown in +<a href="#CHAPTER_I">Chapter I</a> how the distance of the moon from the earth +may be measured and its diameter determined by means of +angles, and without enlarging upon the details of these observations, +we note as their result that the moon is a globe +2,163 miles in diameter, and distant from the earth on the +average about 240,000 miles. But, as we have seen in +<a href="#CHAPTER_VII">Chapter VII</a>, this distance changes to the extent of a few +thousand miles, sometimes less, sometimes greater, mainly +on account of the elliptic shape of the moon's orbit about +the earth, but also in part from the disturbing influence of +other bodies, such as the sun, which pull the moon to and +fro, backward and forward, to quite an appreciable extent.</p> + +<p>From the known diameter of the moon it is a matter of +elementary geometry to derive in miles the area of its surface +and its volume or solid contents. Leaving this as an +exercise for the student, we adopt the earth as the standard +of comparison and find that the diameter of the moon is +rather more than a quarter, 4/15, that of the earth, the area +of its surface is a trifle more than 1/14 that of the earth, +and its volume a little more than 1/49 of the earth's. So +much is pure geometry, but we may combine with it some +mechanical principles which enable us to go a step farther +and to "weigh" the moon—i. e., determine its mass and +the average density of the material of which it is made.</p> + +<p>We have seen that the moon moves around the sun in a +path differing but little from the smooth curve shown in +<a href="#Fig_53">Fig. 53</a>, with arrows indicating the direction of motion, +and it would follow absolutely such a smooth path were +it not for the attraction of the earth, and in less degree<span class="pagenum"><a name="Page_156" id="Page_156">[Pg 156]</a></span> +of some of the other planets, which swing it about first +to one side then to the other. But action and reaction +are equal; the moon pulls as strongly upon the earth +as does the earth upon the moon, and if earth and moon +were of equal mass, the deviation of the earth from the +smooth curve in the figure would be just as large as that +of the moon. It is shown in the figure that the moon does +displace the earth from this curve, and we have only to +measure the amount of this displacement of the earth and +compare it with the displacement suffered by the moon to +find how much the mass of the one exceeds that of the +other. It may be seen from the figure that at first quarter, +about July 7th, the earth is thrust ahead in the direction +of its orbital motion, while at the third quarter, July 22d, it +is pulled back by the action of the moon, and at all times +it is more or less displaced by this action, so that, in order +to be strictly correct, we must amend our former statement +about the moon moving around the earth and make it read, +Both earth and moon revolve around a point on line between +their centers. This point is called their <i>center of +gravity</i>, and the earth and the moon both move in ellipses +having this center of gravity at their common focus. +Compare this with Kepler's First Law. These ellipses are +similarly shaped, but of very different size, corresponding +to Newton's third law of motion (<a href="#CHAPTER_IV">Chapter IV</a>), so that the +action of the earth in causing the small moon to move +around a large orbit is just equal to the reaction of the +moon in causing the larger earth to move in the smaller +orbit. This is equivalent to saying that the dimensions of +the two orbits are inversely proportional to the masses of +the earth and the moon.</p> + +<p>By observing throughout the month the direction from +the earth to the sun or to a near planet, such as Mars or +Venus, astronomers have determined that the diameter of +the ellipse in which the earth moves is about 5,850 miles, +so that the distance of the earth from the center of gravity<span class="pagenum"><a name="Page_157" id="Page_157">[Pg 157]</a></span> +is 2,925 miles, and the distance of the moon from it is +240,000 - 2,925 = 237,075. We may now write in the form +of a proportion—</p> + +<p class="center">Mass of earth : Mass of moon :: 237,075 : 2,925,</p> + +<p>and find from it that the mass of the earth is 81 times +as great as the mass of the moon—i. e., leaving kind and +quality out of account, there is enough material in the +earth to make 81 moons. We may note in this connection +that the diameter of the earth, 7,926 miles, is +greater than the diameter of the monthly orbit in which +the moon causes it to move, and therefore the center of +gravity of earth and moon always lies inside the body of +the earth, about 1,000 miles below the surface.</p> + +<p><a name="S_95" id="S_95"></a>95. <b>Density of the moon.</b>—It is believed that in a general +way the moon is made of much the same kind of material +which goes to make up the earth—metals, minerals, rocks, +etc.—and a part of the evidence upon which this belief is +based lies in the density of the moon. By density of a +substance we mean the amount of it which is contained in +a given volume—i. e., the weight of a bushel or a cubic +centimeter of the stuff. The density of chalk is twice as +great as the density of water, because a cubic centimeter +of chalk weighs twice as much as an equal volume of +water, and similarly in other cases the density is found by +dividing the mass or weight of the body by the mass or +weight of an equal volume of water.</p> + +<p>We know the mass of the earth (<a href="#S_45">§ 45</a>), and knowing +the mass of a cubic foot of water, it is easy, although a +trifle tedious, to compute what would be the mass of a volume +of water equal in size to the earth. The quotient +obtained by dividing one of these masses by the other (mass +of earth ÷ mass of water) is the average density of the material +composing the earth, and we find numerically that +this is 5.6—i. e., it would take 5.6 water earths to attract as +strongly as does the real one. From direct experiment we<span class="pagenum"><a name="Page_158" id="Page_158">[Pg 158]</a></span> +know that the average density of the principal rocks which +make up the crust of the earth is only about half of this, +showing that the deep-lying central parts of the earth are +denser than the surface parts, as we should expect them to +be, because they have to bear the weight of all that lies +above them and are compressed by it.</p> + +<p>Turning now to the moon, we find in the same way as +for the earth that its average density is 3.4 as great as that +of water.</p> + +<p><a name="S_96" id="S_96"></a>96. <b>Force of gravity upon the moon.</b>—This number, 3.4, +compared with the 5.6 which we found for the earth, shows +that on the whole the moon is made of lighter stuff than is +the body of the earth, and this again is much what we should +expect to find, for weight, the force which tends to compress +the substance of the moon, is less there than here. +The weight of a cubic yard of rock at the surface of either +earth or moon is the force with which the earth or moon +attracts it, and this by the law of gravitation is for the +earth—</p> + +<p class="center"><i>W</i> = <i>k</i> · (<i>m</i> <i>m'</i>)/(3963)<sup>2</sup>;</p> + +<p>and for the moon—</p> + +<p class="center"><i>w</i> = <i>k</i> · {<i>m</i> (<i>m'</i>/81)}/(1081)<sup>2</sup>;</p> + +<p>from which we find by division—</p> + +<p class="center"><i>w</i> = (<i>W</i>/81) (3963/1081)<sup>2</sup> = <i>W</i>/6 (approximately).</p> + +<p>The cubic yard of rock, which upon the earth weighs two +tons, would, if transported to the moon, weigh only one +third of a ton, and would have only one sixth as much +influence in compressing the rocks below it as it had upon +the earth. Note that this rock when transported to the +moon would be still attracted by the earth and would have +weight toward the earth, but it is not this of which we are<span class="pagenum"><a name="Page_159" id="Page_159">[Pg 159]</a></span> +speaking; by its weight in the moon we mean the force +with which the moon attracts it. Making due allowance +for the difference in compression produced by weight, we +may say that in general, so far as density goes, the moon is +very like a piece of the earth of equal mass set off by itself +alone.</p> + +<p><a name="S_97" id="S_97"></a>97. <b>Albedo.</b>—In another respect the lunar stuff is like +that of which the earth is made: it reflects the sunlight in +much the same way and to the same amount. The contrast +of light and dark areas on the moon's surface shows, +as we shall see in another section, the presence of different +substances upon the moon which reflect the sunlight in +different degrees. This capacity for reflecting a greater or +less percentage of the incident sunlight is called <i>albedo</i> +(Latin, whiteness), and the brilliancy of the full moon might +lead one to suppose that its albedo is very great, like that +of snow or those masses of summer cloud which we call +thunderheads. But this is only an effect of contrast with +the dark background of the sky. The same moon by day +looks pale, and its albedo is, in fact, not very different +from that of our common rocks—weather-beaten sandstone +according to Sir John Herschel—so that it would be possible +to build an artificial moon of rock or brick which +would shine in the sunlight much as does the real moon.</p> + +<p>The effect produced by the differences of albedo upon +the moon's face is commonly called the "man in the moon," +but, like the images presented by glowing coals, the face in +the moon is anything which we choose to make it. Among +the Chinese it is said to be a monkey pounding rice; in +India, a rabbit; in Persia, the earth reflected as in a mirror, +etc.</p> + +<p><a name="S_98" id="S_98"></a>98. <b>Librations.</b>—We have already learned that the moon +turns always the same face toward the earth, and we have +now to modify this statement and to find that here, as in +so many other cases, the thing we learn first is only approximately +true and needs to be limited or added to or<span class="pagenum"><a name="Page_160" id="Page_160">[Pg 160]</a></span> +modified in some way. In general, Nature is too complex +to be completely understood at first sight or to be perfectly +represented by a simple statement. In <a href="#Fig_55">Fig. 55</a> we +have two photographs of the moon, taken nearly three years +apart, the right-hand one a little after first quarter and the +left-hand one a little before third quarter. They therefore +represent different parts of the moon's surface, but +along the ragged edge the same region is shown on both +photographs, and features common to both pictures may +readily be found—e. g., the three rings which form a right-angled +triangle about one third of the way down from the +top of the cut, and the curved mountain chain just below +these. If the moon turned exactly the same face toward +us in the two pictures, the distance of any one of these +markings from any part of the moon's edge must be the +same in both pictures; but careful measurement will show +that this is not the case, and that in the left-hand picture +the upper edge of the moon is tipped toward us and +the lower edge away from us, as if the whole moon had +been rotated slightly about a horizontal line and must be +turned back a little (about 7°) in order to match perfectly +the other part of the picture.</p> + +<p>This turning is called a <i>libration</i>, and it should be borne +in mind that the moon librates not only in the direction +above measured, north and south, but also at right angles +to this, east and west, so that we are able to see a little +farther around every part of the moon's edge than would +be possible if it turned toward us at all times exactly the +same face. But in spite of the librations there remains on +the farther side of the moon an area of 6,000,000 square +miles which is forever hidden from us, and of whose character +we have no direct knowledge, although there is no +reason to suppose it very different from that which is visible, +despite the fact that some of the books contain quaint +speculations to the contrary. The continent of South +America is just about equal in extent to this unknown region,<span class="pagenum"><a name="Page_161" id="Page_161">[Pg 161]</a></span> +while North America is a fair equivalent for all the +rest of the moon's surface, both those central parts which +are constantly visible, and the zone around the edge whose +parts sometimes come into sight and are sometimes hidden.</p> + +<p>An interesting consequence of the peculiar rotation of +the moon is that from our side of it the earth is always +visible. Sun, stars, and planets rise and set there as well +as here, but to an observer on the moon the earth swings +always overhead, shifting its position a few degrees one +way or the other on account of the libration but running +through its succession of phases, new earth, first quarter, +etc., without ever going below the horizon, provided the +observer is anywhere near the center of the moon's disk.</p> + +<div class="figright" style="width: 350px;"><a name="Fig_54" id="Fig_54"></a> +<img src="images/i188.png" width="350" height="366" alt="Fig. 54.—Illustrating the moon's +rotation." title="Fig. 54.—Illustrating the moon's +rotation." /> +<span class="caption"><span class="smcap">Fig. 54.</span>—Illustrating the moon's +rotation.</span> +</div> + +<p><a name="S_99" id="S_99"></a>99. <b>Cause of librations.</b>—That the moon should librate +is by no means so remarkable a fact as that it should at all +times turn very nearly the +same face toward the earth. +This latter fact can have but +one meaning: the moon revolves +about an axis as does +the earth, but the time required +for this revolution is +just equal to the time required +to make a revolution +in its orbit. Place two coins +upon a table with their heads +turned toward the north, as +in <a href="#Fig_54">Fig. 54</a>, and move the +smaller one around the larger +in such a way that its face shall always look away from the +larger one. In making one revolution in its orbit the head +on this small coin will be successively directed toward every +point of the compass, and when it returns to its initial +position the small coin will have made just one revolution +about an axis perpendicular to the plane of its orbit. +In no other way can it be made to face always away<span class="pagenum"><a name="Page_162" id="Page_162">[Pg 162]</a></span> +from the figure at the center of its orbit while moving +around it.</p> + +<p>We are now in a position to understand the moon's +librations, for, if the small coin at any time moves faster or +slower in its orbit than it turns about its axis, a new side +will be turned toward the center, and the same may happen +if the central coin itself shifts into a new position. This is +what happens to the moon, for its orbital motion, like that +of Mercury (<a href="#Fig_17">Fig. 17</a>), is alternately fast and slow, and in +addition to this there are present other minor influences, +such as the fact that its rotation axis is not exactly perpendicular +to the plane of its orbit; in addition to this the +observer upon the earth is daily carried by its rotation from +one point of view to another, etc., so that it is only in a general +way that the rotation upon the axis and motion in the +orbit keep pace with each other. In a general way a cable +keeps a ship anchored in the same place, although wind and +waves may cause it to "librate" about the anchor.</p> + +<p>How the moon came to have this exact equality between +its times of revolution and rotation constitutes a +chapter of its history upon which we shall not now enter; +but the equality having once been established, the mechanism +by which it is preserved is simple enough.</p> + +<p>The attraction of the earth for the moon has very +slightly pulled the latter out of shape (<a href="#S_42">§ 42</a>), so that the +particular diameter, which points toward the earth, is a little +longer than any other, and thus serves as a handle which +the earth lays hold of and pulls down into its lowest possible +position—i. e., the position in which it points toward the +center of the earth. Just how long this handle is, remains +unknown, but it may be shown from the law of gravitation +that less than a hundred yards of elongation would suffice +for the work it has to do.</p> + +<p><a name="S_100" id="S_100"></a>100. <b>The moon as a world.</b>—Thus far we have considered +the moon as a satellite of the earth, dependent upon the +earth, and interesting chiefly because of its relation to it.<span class="pagenum"><a name="Page_163" id="Page_163">[Pg 163]</a></span> +But the moon is something more than this; it is a world in +itself, very different from the earth, although not wholly +unlike it. The most characteristic feature of the earth's +surface is its division into land and water, and nothing of +this kind can be found upon the moon. It is true that the +first generation of astronomers who studied the moon with +telescopes fancied that the large dark patches shown in +<a href="#Fig_55">Fig. 55</a> were bodies of water, and named them oceans, +seas, lakes, and ponds, and to the present day we keep +those names, although it is long since recognized that these +parts of the moon's surface are as dry as any other. Their +dark appearance indicates a different kind of material from +that composing the lighter parts of the moon, material +with a different albedo, just as upon the earth we have +light-colored and dark-colored rocks, marble and slate, +which seen from the moon must present similar contrasts +of brightness. Although these dark patches are almost +the only features distinguishable with the unaided eye, it +is far otherwise in the telescope or the photograph, especially +along the ragged edge where great numbers of rings +can be seen, which are apparently depressions in the moon +and are called craters. These we find in great number +all over the moon, but, as the figure shows, they are seen +to the best advantage near the <i>terminator</i>—i. e., the dividing +line between day and night, since the long shadows +cast here by the rising or setting sun bring out the details +of the surface better than elsewhere. Carefully examine +<a href="#Fig_55">Fig. 55</a> with reference to these features.</p> + +<div class="figcenter" style="width: 600px;"><a name="Fig_55" id="Fig_55"></a> +<a href="images/i191-full.jpg"><img src="images/i191.jpg" width="600" height="433" alt="Fig. 55.—The moon at first and last quarter. Lick Observatory photographs." title="Fig. 55.—The moon at first and last quarter. Lick Observatory photographs." /></a> +<span class="caption"><span class="smcap">Fig. 55.</span>—The moon at first and last quarter. Lick Observatory photographs.</span> +</div> + +<p>Another feature which exists upon both earth and +moon, although far less common there than here, is illustrated +in the chain of mountains visible near the terminator, +a little above the center of the moon in both parts of +<a href="#Fig_55">Fig. 55</a>. This particular range of mountains, which is +called the Lunar Apennines, is by far the most prominent +one upon the moon, although others, the Alps and Caucasus, +exist. But for the most part the lunar mountains<span class="pagenum"><a name="Page_165" id="Page_165">[Pg 165]</a></span> +stand alone, each by itself, instead of being grouped into +ranges, as on the earth. Note in the figure that some of +the lunar mountains stretch out into the night side of the +moon, their peaks projecting up into the sunlight, and +thus becoming visible, while the lowlands are buried in the +shadow.</p> + +<p>A subordinate feature of the moon's surface is the system +of <i>rays</i> which seem to radiate like spokes from some +of the larger craters, extending over hill and valley sometimes +for hundreds of miles. A suggestion of these rays +may be seen in <a href="#Fig_55">Fig. 55</a>, extending from the great crater +Copernicus a little southwest of the end of the Apennines, +but their most perfect development is to be seen at the +time of full moon around the crater Tycho, which lies near +the south pole of the moon. Look for them with an opera +glass.</p> + +<p>Another and even less conspicuous feature is furnished +by the rills, which, under favorable conditions of illumination, +appear like long cracks on the moon's surface, perhaps +analogous to the cańons of our Western country.</p> + +<p><a name="S_101" id="S_101"></a>101. <b>The map of the moon.</b>—<a href="#Fig_55">Fig. 55</a> furnishes a fairly +good map of a limited portion of the moon near the terminator, +but at the edges little or no detail can be seen. This +is always true; the whole of the moon can not be seen to +advantage at any one time, and to remedy this we need to +construct from many photographs or drawings a map which +shall represent the several parts of the moon as they appear +at their best. <a href="#Fig_56">Fig. 56</a> shows such a map photographed from +a relief model of the moon, and representing the principal +features of the lunar surface in a way they can never be +seen simultaneously. Perhaps its most striking feature is +the shape of the craters, which are shown round in the central +parts of the map and oval at the edges, with their long +diameters parallel to the moon's edge. This is, of course, +an effect of the curvature of the moon's surface, for we look +very obliquely at the edge portions, and thus see their formations<span class="pagenum"><a name="Page_166" id="Page_166">[Pg 166]</a></span> +much foreshortened in the direction of the moon's +radius.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_56" id="Fig_56"></a> +<a href="images/i193-full.jpg"><img src="images/i193.jpg" width="500" height="501" alt="Fig. 56.—Relief map of the moon's surface.—After Nasmyth and Carpenter." title="Fig. 56.—Relief map of the moon's surface.—After Nasmyth and Carpenter." /></a> +<span class="caption"><span class="smcap">Fig. 56.</span>—Relief map of the moon's surface.—After <span class="smcap">Nasmyth</span> and <span class="smcap">Carpenter</span>.</span> +</div> + +<p>The north and south poles of the moon are at the top +and bottom of the map respectively, and a mere inspection +of the regions around them will show how much more +rugged is the southern hemisphere of the moon than the +northern. It furnishes, too, some indication of how numerous +are the lunar craters, and how in crowded regions they +overlap one another.</p> + +<p>The student should pick out upon the map those features +which he has learned to know in the photograph (<a href="#Fig_55">Fig. 55</a>)—the +Apennines, Copernicus, and the continuation of the +Apennines, extending into the dark part of the moon.<span class="pagenum"><a name="Page_167" id="Page_167">[Pg 167]</a></span></p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_57" id="Fig_57"></a> +<a href="images/i194-full.jpg"><img src="images/i194.jpg" width="500" height="476" alt="Fig. 57.—Mare Imbrium. Photographed by G. W. Ritchey." title="Fig. 57.—Mare Imbrium. Photographed by G. W. Ritchey." /></a> +<span class="caption"><span class="smcap">Fig. 57.</span>—Mare Imbrium. Photographed by <span class="smcap">G. W. Ritchey.</span></span> +</div> + +<p><a name="S_102" id="S_102"></a>102. <b>Size of the lunar features.</b>—We may measure distances +here in the same way as upon a terrestrial map, remembering +that near the edges the scale of the map is very +much distorted parallel to the moon's diameter, and measurements +must not be taken in this direction, but may be +taken parallel to the edge. Measuring with a millimeter +scale, we find on the map for the diameter of the crater +Copernicus, 2.1 millimeters. To turn this into the diameter +of the real Copernicus in miles, we measure upon the +same map the diameter of the moon, 79.7 millimeters, and +then have the proportion—</p> + +<p class="center">Diameter of Copernicus in miles : 2,163 :: 2.1 : 79.7,</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_58" id="Fig_58"></a> +<a href="images/i195-full.jpg"><img src="images/i195.jpg" width="350" height="468" alt="Fig. 58.—Mare Crisium. +Lick Observatory photographs." title="Fig. 58.—Mare Crisium. +Lick Observatory photographs." /></a> +<span class="caption"><span class="smcap">Fig. 58.</span>—Mare Crisium. +Lick Observatory photographs.</span> +</div> + +<p>which when solved gives 57 miles. The real diameter of +Copernicus is a trifle over 56 miles. At the eastern edge +of the moon, opposite the Apennines, is a large oval spot +called the Mare Crisium (Latin, <i>ma-re</i> = sea). Measure its<span class="pagenum"><a name="Page_168" id="Page_168">[Pg 168]</a></span> +length. The large crater to the northwest of the Apennines +is called Archimedes. Measure its diameter both in +the map and in the photograph (<a href="#Fig_55">Fig. 55</a>), and see how the +two results agree. The true diameter of this crater, east +and west, is very approximately 50 miles. The great smooth +surface to the west of Archimedes is the Mare Imbrium. Is +it larger or smaller than +Lake Superior? <a href="#Fig_57">Fig. 57</a> +is from a photograph +of the Mare Imbrium, +and the amount +of detail here shown at +the bottom of the sea +is a sufficient indication +that, in this case +at least, the water has +been drawn off, if indeed +any was ever present.</p> + +<p><a href="#Fig_58">Fig. 58</a> is a representation +of the Mare +Crisium at a time when +night was beginning to +encroach upon its eastern +border, and it +serves well to show the +rugged character of the ring-shaped wall which incloses +this area.</p> + +<p>With these pictures of the smoother parts of the moon's +surface we may compare <a href="#Fig_59">Fig. 59</a>, which shows a region +near the north pole of the moon, and <a href="#Fig_60">Fig. 60</a>, giving an +early morning view of Archimedes and the Apennines. +Note how long and sharp are the shadows.</p> + +<div class="figright" style="width: 350px;"><a name="Fig_59" id="Fig_59"></a> +<a href="images/i196-full.jpg"><img src="images/i196.jpg" width="350" height="447" alt="Fig. 59.—Illustrating the rugged character of the +moon's surface.—Nasmyth and Carpenter." title="Fig. 59.—Illustrating the rugged character of the +moon's surface.—Nasmyth and Carpenter." /></a> +<span class="caption"><span class="smcap">Fig. 59.</span>—Illustrating the rugged character of the +moon's surface.—<span class="smcap">Nasmyth</span> and <span class="smcap">Carpenter</span>.</span> +</div> + +<p><a name="S_103" id="S_103"></a>103. <b>The moon's atmosphere.</b>—Upon the earth the sun +casts no shadows so sharp and black as those of <a href="#Fig_60">Fig. 60</a>, +because his rays are here scattered and reflected in all directions<span class="pagenum"><a name="Page_169" id="Page_169">[Pg 169]</a></span> +by the dust and vapors of the atmosphere (<a href="#S_51">§ 51</a>), +so that the place from which direct sunlight is cut off +is at least partially illumined by this reflected light. The +shadows of <a href="#Fig_60">Fig. 60</a> show that upon the moon it must be +otherwise, and suggest that if the moon has any atmosphere +whatever, its density must be utterly insignificant in comparison +with that of the earth. In its motion around the +earth the moon frequently +eclipses stars +(<i>occults</i> is the technical +word), and if the +moon had an atmosphere +such as is shown +in <a href="#Fig_61">Fig. 61</a>, the light +from the star <i>A</i> must +shine through this atmosphere +just before +the moon's advancing +body cuts it off, and it +must be refracted by +the atmosphere so that +the star would appear +in a slightly different +direction (nearer to +<i>B</i>) than before. The +earth's atmosphere refracts +the starlight +under such circumstances by more than a degree, but no +one has been able to find in the case of the moon any effect +of this kind amounting to even a fraction of a second of +arc. While this hardly justifies the statement sometimes +made that the moon has no atmosphere, we shall be entirely +safe in saying that if it has one at all its density is less +than a thousandth part of that of the earth's atmosphere. +Quite in keeping with this absence of an atmosphere is the +fact that clouds never float over the surface of the moon.<span class="pagenum"><a name="Page_170" id="Page_170">[Pg 170]</a></span> +Its features always stand out hard and clear, without any +of that haze and softness of outline which our atmosphere +introduces into all terrestrial landscapes.</p> + +<div class="figleft" style="width: 375px;"><a name="Fig_60" id="Fig_60"></a> +<a href="images/i197-full.jpg"><img src="images/i197.jpg" width="375" height="322" alt="Fig. 60.—Archimedes and Apennines. +Nasmyth and Carpenter." title="Fig. 60.—Archimedes and Apennines. +Nasmyth and Carpenter." /></a> +<span class="caption"><span class="smcap">Fig. 60.</span>—Archimedes and Apennines. +<span class="smcap">Nasmyth</span> and <span class="smcap">Carpenter</span>.</span> +</div> + +<p><a name="S_104" id="S_104"></a>104. <b>Height of the lunar mountains.</b>—Attention has already +been called to the detached mountain peaks, which +in <a href="#Fig_55">Fig. 55</a> prolong +the range of +Apennines into +the lunar night. +These are the beginnings +of the +Caucasus mountains, +and from +the photograph +we may measure +as follows the +height to which +they rise above +the surrounding +level of the moon: +<a href="#Fig_62">Fig. 62</a> represents +a part of +the lunar surface along the boundary line between night +and day, the horizontal line at the top of the figure representing +a level ray of sunlight which just touches the moon +at <i>T</i> and barely illuminates the top of the mountain, <i>M</i>, +whose height, <i>h</i>, is to be determined. If we let <i>R</i> stand for +the radius of the moon and <i>s</i> for the distance, <i>T M</i>, we shall +have in the right-angled triangle <i>M T C</i>,</p> + +<p class="center"><i>R</i><sup>2</sup> + <i>s</i><sup>2</sup> = (<i>R</i> + <i>h</i>)<sup>2</sup>,</p> + +<p>and we need only to measure <i>s</i>—that is, the distance from +the terminator to the detached mountain peak—to make +this equation determine <i>h</i>, since <i>R</i> is already known, being +half the diameter of the moon—1,081 miles. Practically it +is more convenient to use instead of this equation another<span class="pagenum"><a name="Page_171" id="Page_171">[Pg 171]</a></span> +form, which the student who is expert in algebra may show +to be very nearly equivalent to it:</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="right"><i>h</i> (miles)</td><td align="center">=</td><td align="left"><i>s</i><sup>2</sup> / 2163,</td></tr> +<tr><td align="right">or <i>h</i> (feet)</td><td align="center">=</td><td align="left">2.44 <i>s</i><sup>2</sup>.</td></tr> +</table></div> + +<div class="figright" style="width: 350px;"><a name="Fig_61" id="Fig_61"></a> +<img src="images/i198a.png" width="350" height="217" alt="Fig. 61.—Occultations and the moon's +atmosphere." title="Fig. 61.—Occultations and the moon's +atmosphere." /> +<span class="caption"><span class="smcap">Fig. 61.</span>—Occultations and the moon's +atmosphere.</span> +</div> + +<p>The distance <i>s</i> must be expressed in miles in all of these +equations. In <a href="#Fig_55">Fig. 55</a> the distance from the terminator +to the first detached peak +of the Caucasus mountains +is 1.7 millimeters = +52 miles, from which we +find the height of the +mountain to be 1.25 +miles, or 6,600 feet.</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_62" id="Fig_62"></a> +<img src="images/i198b.png" width="350" height="269" alt="Fig. 62.—Determining the height of a lunar +mountain." title="Fig. 62.—Determining the height of a lunar +mountain." /> +<span class="caption"><span class="smcap">Fig. 62.</span>—Determining the height of a lunar +mountain.</span> +</div> + +<p>Two things, however, +need to be borne in mind +in this connection. On +the earth we measure the +heights of mountains <i>above sea level</i>, while on the moon +there is no sea, and our 6,600 feet is simply the height of +the mountain top above +the level of that particular +point in the +terminator, from which +we measure its distance. +So too it is evident +from the appearance of +things, that the sunlight, +instead of just +touching the top of the +particular mountain +whose height we have +measured, really extends +some little distance down from its summit, and the 6,600 +feet is therefore the elevation of the lowest point on the +mountains to which the sunlight reaches. The peak itself<span class="pagenum"><a name="Page_172" id="Page_172">[Pg 172]</a></span> +may be several hundred feet higher, and our photograph +must be taken at the exact moment when this peak appears +in the lunar morning or disappears in the evening if we are +to measure the altitude of the mountain's summit. Measure +the height of the most northern visible mountain of +the Caucasus range. This is one of the outlying spurs of +the great mountain Calippus, whose principal peak, 19,000 +feet high, is shown in <a href="#Fig_55">Fig. 55</a> as the brightest part of the +Caucasus range.</p> + +<p>The highest peak of the lunar Apennines, Huyghens, +has an altitude of 18,000 feet, and the Leibnitz and Doerfel +Mountains, near the south pole of the moon, reach an altitude +50 per cent greater than this, and are probably the +highest peaks on the moon. This falls very little short of +the highest mountain on the earth, although the moon is +much smaller than the earth, and these mountains are considerably +higher than anything on the western continent of +the earth.</p> + +<p>The vagueness of outline of the terminator makes it +difficult to measure from it with precision, and somewhat +more accurate determinations of the heights of lunar +mountains can be obtained by measuring the length of +the shadows which they cast, and the depths of craters +may also be measured by means of the shadows which fall +into them.</p> + +<p><a name="S_105" id="S_105"></a>105. <b>Craters.</b>—<a href="#Fig_63">Fig. 63</a> shows a typical lunar crater, and +conveys a good idea of the ruggedness of the lunar landscape. +Compare the appearance of this crater with the +following generalizations, which are based upon the accurate +measurement of many such:</p> + +<p>A. A crater is a real depression in the surface of the +moon, surrounded usually by an elevated ring which rises +above the general level of the region outside, while the bottom +of the crater is about an equal distance below that +level.</p> + +<p>B. Craters are shallow, their diameters ranging from<span class="pagenum"><a name="Page_173" id="Page_173">[Pg 173]</a></span> +five times to more than fifty times their depth. Archimedes, +whose diameter we found to be 50 miles, has an +average depth of about 4,000 feet below the crest of its +surrounding wall, and is relatively a shallow crater.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_63" id="Fig_63"></a> +<a href="images/i200-full.jpg"><img src="images/i200.jpg" width="500" height="363" alt="Fig. 63.—A typical lunar crater.—Nasmyth and Carpenter." title="Fig. 63.—A typical lunar crater.—Nasmyth and Carpenter." /></a> +<span class="caption"><span class="smcap">Fig. 63.</span>—A typical lunar crater.—<span class="smcap">Nasmyth</span> and <span class="smcap">Carpenter</span>.</span> +</div> + +<p>C. Craters frequently have one or more hills rising +within them which, however, rarely, if ever, reach up to the +level of the surrounding wall.</p> + +<p>D. Whatever may have been the mode of their formation, +the craters can not have been produced by scooping +out material from the center and piling it up to make the +wall, for in three cases out of four the volume of the excavation +is greater than the volume of material contained in +the wall.</p> + +<p><a name="S_106" id="S_106"></a>106. <b>Moon and earth.</b>—We have gone far enough now +to appreciate both the likeness and the unlikeness of the +moon and earth. They may fairly enough be likened to +offspring of the same parent who have followed very different +careers, and in the fullness of time find themselves in +very different circumstances. The most serious point of +difference in these circumstances is the atmosphere, which +gives to the earth a wealth of phenomena altogether lacking<span class="pagenum"><a name="Page_174" id="Page_174">[Pg 174]</a></span> +in the moon. Clouds, wind, rain, snow, dew, frost, and +hail are all dependent upon the atmosphere and can not be +found where it is not. There can be nothing upon the +moon at all like that great group of changes which we +call weather, and the unruffled aspect of the moon's face +contrasts sharply with the succession of cloud and sunshine +which the earth would present if seen from the moon.</p> + +<p>The atmosphere is the chief agent in the propagation +of sound, and without it the moon must be wrapped in +silence more absolute than can be found upon the surface +of the earth. So, too, the absence of an atmosphere shows +that there can be no water or other liquid upon the moon, +for if so it would immediately evaporate and produce a +gaseous envelope which we have seen does not exist. With +air and water absent there can be of course no vegetation +or life of any kind upon the moon, and we are compelled +to regard it as an arid desert, utterly waste.</p> + +<p><a name="S_107" id="S_107"></a>107. <b>Temperature of the moon.</b>—A characteristic feature +of terrestrial deserts, which is possessed in exaggerated degree +by the moon, is the great extremes of temperature to +which they and it are subject. Owing to its slow rotation +about its axis, a point on the moon receives the solar radiation +uninterruptedly for more than a fortnight, and that +too unmitigated by any cloud or vaporous covering. Then +for a like period it is turned away from the sun and allowed +to cool off, radiating into interplanetary space without hindrance +its accumulated store of heat. It is easy to see that +the range of temperature between day and night must be +much greater under these circumstances than it is with us +where shorter days and clouded skies render day and night +more nearly alike, to say nothing of the ocean whose waters +serve as a great balance wheel for equalizing temperatures. +Just how hot or how cold the moon becomes is hard to +determine, and very different estimates are to be found in +the books. Perhaps the most reliable of these are furnished +by the recent researches of Professor Very, whose<span class="pagenum"><a name="Page_175" id="Page_175">[Pg 175]</a></span> +experiments lead him to conclude that "its rocky surface at +midday, in latitudes where the sun is high, is probably hotter +than boiling water and only the most terrible of earth's deserts, +where the burning sands blister the skin, and men, +beasts, and birds drop dead, can approach a noontide on +the cloudless surface of our satellite. Only the extreme +polar latitudes of the moon can have an endurable temperature +by day, to say nothing of the night, when we +should have to become troglodytes to preserve ourselves +from such intense cold."</p> + +<p>While the night temperature of the moon, even very +soon after sunset, sinks to something like 200° below zero +on the centigrade scale, or 320° below zero on the Fahrenheit +scale, the lowest known temperature upon the earth, +according to General Greely, is 90° Fahr. below zero, recorded +in Siberia in January, 1885.</p> + +<p>Winter and summer are not markedly different upon +the moon, since its rotation axis is nearly perpendicular to +the plane of the earth's orbit about the sun, and the sun +never goes far north or south of the moon's equator. The +month is the one cycle within which all seasonal changes in +its physical condition appear to run their complete course.</p> + +<p><a name="S_108" id="S_108"></a>108. <b>Changes in the moon.</b>—It is evidently idle to look +for any such changes in the condition of the moon's surface +as with us mark the progress of the seasons or +the spread of civilization over the wilderness. But minor +changes there may be, and it would seem that the violent +oscillations of temperature from day to night ought to have +some effect in breaking down and crumbling the sharp +peaks and crags which are there so common and so pronounced. +For a century past astronomers have searched +carefully for changes of this kind—the filling up of some +crater or the fall of a mountain peak; but while some +things of this kind have been reported from time to time, +the evidence in their behalf has not been altogether conclusive. +At the present time it is an open question whether<span class="pagenum"><a name="Page_176" id="Page_176">[Pg 176]</a></span> +changes of this sort large enough to be seen from the +earth are in progress. A crater much less than a mile +wide can be seen in the telescope, but it is not easy to +tell whether so minute an object has changed in size or +shape during a year or a decade, and even if changes are +seen they may be apparent rather than real. <a href="#Fig_64">Fig. 64</a> contains +two views of the crater Archimedes, taken under a +morning and an afternoon sun respectively, and shows a +very pronounced difference between the two which proceeds +solely from a difference of illumination. In the presence +of such large fictitious changes astronomers are slow +to accept smaller ones as real.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_64" id="Fig_64"></a> +<a href="images/i203.jpg"><img src="images/i203.jpg" width="500" height="347" alt="Fig. 64.—Archimedes in the lunar morning and afternoon.—Weinek." title="Fig. 64.—Archimedes in the lunar morning and afternoon.—Weinek." /></a> +<span class="caption"><span class="smcap">Fig. 64.</span>—Archimedes in the lunar morning and afternoon.—<span class="smcap">Weinek.</span></span> +</div> + +<p>It is this absence of change that is responsible for the +rugged and sharp-cut features of the moon which continue +substantially as they were made, while upon the earth rain +and frost are continually wearing down the mountains and +spreading their substance upon the lowland in an unending +process of smoothing off the roughnesses of its surface. +Upon the moon this process is almost if not wholly wanting, +and the moon abides to-day much more like its primitive +condition than is the earth.</p> + +<p><a name="S_109" id="S_109"></a>109. <b>The moon's influence upon the earth.</b>—There is a +widespread popular belief that in many ways the moon exercises<span class="pagenum"><a name="Page_177" id="Page_177">[Pg 177]</a></span> +a considerable influence upon terrestrial affairs: that +it affects the weather for good or ill, that crops must be +planted and harvested, pigs must be killed, and timber cut +at the right time of the moon, etc. Our common word +lunatic means moonstruck—i. e., one upon whom the moon +has shone while sleeping. There is not the slightest scientific +basis for any of these beliefs, and astronomers everywhere +class them with tales of witchcraft, magic, and popular +delusion. For the most part the moon's influence +upon the earth is limited to the light which it sends and +the effect of its gravitation, chiefly exhibited in the ocean +tides. We receive from the moon a very small amount of +second-hand solar heat and there is also a trifling magnetic +influence, but neither of these last effects comes within the +range of ordinary observation, and we shall not go far wrong +in saying that, save the moonlight and the tides, every supposed +lunar influence upon the earth is either fictitious or +too small to be readily detected.</p> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_178" id="Page_178">[Pg 178]</a></span></p> +<h2><a name="CHAPTER_X" id="CHAPTER_X"></a>CHAPTER X</h2> + +<h3>THE SUN</h3> + + +<p><a name="S_110" id="S_110"></a>110. <b>Dependence of the earth upon the sun.</b>—There is no +better introduction to the study of the sun than Byron's +Ode to Darkness, beginning with the lines—</p> + +<div class="poem"><div class="stanza"> +<span class="i0">"I dreamed a dream<br /></span> +<span class="i0">That was not all a dream.<br /></span> +<span class="i0">The bright sun was extinguished,"<br /></span> +</div></div> + +<p>and proceeding to depict in vivid words the consequences +of this extinction. The most matter-of-fact language of +science agrees with the words of the poet in declaring the +earth's dependence upon the sun for all those varied forms +of energy which make it a fit abode for living beings. The +winds blow and the rivers run; the crops grow, are gathered +and consumed, by virtue of the solar energy. Factory, +locomotive, beast, bird, and the human body furnish types +of machines run by energy derived from the sun; and the +student will find it an instructive exercise to search for +kinds of terrestrial energy which are not derived either +directly or indirectly from the sun. There are a few such, +but they are neither numerous nor important.</p> + +<p><a name="S_111" id="S_111"></a>111. <b>The sun's distance from the earth.</b>—To the astronomer +the sun presents problems of the highest consequence +and apparently of very diverse character, but all tending +toward the same goal: the framing of a mechanical explanation +of the sun considered as a machine; what it is, and +how it does its work. In the forefront of these problems +stand those numerical determinations of distance, size,<span class="pagenum"><a name="Page_179" id="Page_179">[Pg 179]</a></span> +mass, density, etc., which we have already encountered in +connection with the moon, but which must here be dealt +with in a different manner, because the immensely greater +distance of the sun makes impossible the resort to any such +simple method as the triangle used for determining the +moon's distance. It would be like determining the distance +of a steeple a mile away by observing its direction first +from one eye, then from the other; too short a base for the +triangle. In one respect, however, we stand upon a better +footing than in the case of the moon, for the mass of the +earth has already been found (<a href="#CHAPTER_IV">Chapter IV</a>) as a fractional +part of the sun's mass, and we have only to invert the +fraction in order to find that the sun's mass is 329,000 +times that of the earth and moon combined, or 333,000 +times that of the earth alone.</p> + +<p>If we could rely implicitly upon this number we might +make it determine for us the distance of the sun through +the law of gravitation as follows: It was suggested in <a href="#S_38">§ 38</a> +that Newton proved Kepler's three laws to be imperfect +corollaries from the law of gravitation, requiring a little +amendment to make them strictly correct, and below we +give in the form of an equation Kepler's statement of the +Third Law together with Newton's amendment of it. In +these equations—</p> + +<p><i>T</i> = Periodic time of any planet;</p> + +<p><i>a</i> = One half the major axis of its orbit;</p> + +<p><i>m</i> = Its mass;</p> + +<p><i>M</i> = The mass of the sun;</p> + +<p><i>k</i> = The gravitation constant corresponding to the particular +set of units in which <i>T</i>, <i>a</i>, <i>m</i>, and <i>M</i> are expressed.</p> + +<p class="center">(Kepler) <i>a</i><sup>3</sup>/<i>T</i><sup>2</sup> = <i>h</i>; (Newton) <i>a</i><sup>3</sup>/<i>T</i><sup>2</sup> = <i>k</i> (<i>M</i> + <i>m</i>).</p> + +<p>Kepler's idea was: For every planet which moves +around the sun, <i>a</i><sup>3</sup> divided by <i>T</i><sup>2</sup> always gives the same +quotient, <i>h</i>; and he did not concern himself with the significance<span class="pagenum"><a name="Page_180" id="Page_180">[Pg 180]</a></span> +of this quotient further than to note that if the +particular <i>a</i> and <i>T</i> which belong to any planet—e. g., the +earth—be taken as the units of length and time, then the +quotient will be 1. Newton, on the other hand, attached +a meaning to the quotient, and showed that it is equal to +the product obtained by multiplying the sum of the two +masses, planet and sun, by a number which is always the +same when we are dealing with the action of gravitation, +whether it be between the sun and planet, or between +moon and earth, or between the earth and a roast of beef +in the butcher's scales, provided only that we use always +the same units with which to measure times, distances, +and masses.</p> + +<p>Numerically, Newton's correction to Kepler's Third +Law does not amount to much in the motion of the +planets. Jupiter, which shows the greatest effect, makes +the circuit of his orbit in 4,333 days instead of 4,335, which +it would require if Kepler's law were strictly true. But in +another respect the change is of the utmost importance, +since it enables us to extend Kepler's law, which relates +solely to the sun and its planets, to other attracting bodies, +such as the earth, moon, and stars. Thus for the moon's +motion around the earth we write—</p> + +<p class="center">(240,000)<sup>3</sup>/(27.32)<sup>2</sup> = <i>k</i> (1 + 1/81),</p> + +<p>from which we may find that, with the units here employed, +the earth's mass as the unit of mass, the mean solar day as +the unit of time, and the mile as the unit of distance—</p> + +<p class="center"><i>k</i> = 1830 × 10<sup>10</sup>.</p> + +<p>If we introduce this value of <i>k</i> into the corresponding +equation, which represents the motion of the earth around +the sun, we shall have—</p> + +<p class="center"><i>a</i><sup>3</sup>/(365.25)<sup>2</sup> = 1830 × 10<sup>10</sup> (333,000 + 1),<span class="pagenum"><a name="Page_181" id="Page_181">[Pg 181]</a></span></p> + +<p>where the large number in the parenthesis represents the +number of times the mass of the sun is greater than the +mass of the earth. We shall find by solving this equation +that <i>a</i>, the mean distance of the sun from the earth, is +very approximately 93,000,000 miles.</p> + +<p><a name="S_113" id="S_113"></a>113. <b>Another method of determining the sun's distance.</b>—This +will be best appreciated by a reference to <a href="#Fig_17">Fig. 17</a>. It +appears here that the earth makes its nearest approach to the +orbit of Mars in the month of August, and if in any August +Mars happens to be in opposition, its distance from the earth +will be very much less than the distance of the sun from +the earth, and may be measured by methods not unlike +those which served for the moon. If now the orbits of +Mars and the earth were circles having their centers at the +sun this distance between them, which we may represent by +<i>D</i>, would be the difference of the radii of these orbits—</p> + +<p class="center"><i>D</i> = <i>a''</i> - <i>a'</i>,</p> + +<p>where the accents '', ' represent Mars and the earth respectively. +Kepler's Third Law furnishes the relation—</p> + +<p class="center">(<i>a''</i>)<sup>3</sup>/(<i>T''</i>)<sup>2</sup> = (<i>a'</i>)<sup>3</sup>/(<i>T'</i>)<sup>2</sup>;</p> + +<p>and since the periodic times of the earth and Mars, <i>T'</i>, <i>T''</i>, +are known to a high degree of accuracy, these two equations +are sufficient to determine the two unknown quantities, +<i>a'</i>, <i>a''</i>—i. e., the distance of the sun from Mars as well +as from the earth. The first of these equations is, of +course, not strictly true, on account of the elliptical shape +of the orbits, but this can be allowed for easily enough.</p> + +<p>In practice it is found better to apply this method of +determining the sun's distance through observations of an +asteroid rather than observations of Mars, and great interest +has been aroused among astronomers by the discovery, +in 1898, of an asteroid, or planet, Eros, which at times comes +much closer to the earth than does Mars or any other heavenly<span class="pagenum"><a name="Page_182" id="Page_182">[Pg 182]</a></span> +body except the moon, and which will at future oppositions +furnish a more accurate determination of the sun's +distance than any hitherto available. Observations for this +purpose are being made at the present time (October, 1900).</p> + +<p>Many other methods of measuring the sun's distance +have been devised by astronomers, some of them extremely +ingenious and interesting, but every one of them has its +weak point—e. g., the determination of the mass of the +earth in the first method given above and the measurement +of <i>D</i> in the second method, so that even the best results at +present are uncertain to the extent of 200,000 miles or more, +and astronomers, instead of relying upon any one method, +must use all of them, and take an average of their results. +According to Professor Harkness, this average value is 92,796,950 +miles, and it seems certain that a line of this length +drawn from the earth toward the sun would end somewhere +within the body of the sun, but whether on the nearer or +the farther side of the center, or exactly at it, no man +knows.</p> + +<p><a name="S_114" id="S_114"></a>114. <b>Parallax and distance.</b>—It is quite customary among +astronomers to speak of the sun's parallax, instead of its +distance from the earth, meaning by parallax its difference +of direction as seen from the center and surface of the +earth—i. e., the angle subtended at the sun by a radius of +the earth placed at right angles to the line of sight. The +greater the sun's distance the smaller will this angle be, +and it therefore makes a substitute for the distance which +has the advantage of being represented by a small number, +8".8, instead of a large one.</p> + +<p>The books abound with illustrations intended to help +the reader comprehend how great is a distance of 93,000,000 +miles, but a single one of these must suffice here. To ride +100 miles a day 365 days in the year would be counted a +good bicycling record, but the rider who started at the beginning +of the Christian era and rode at that rate toward +the sun from the year 1 <span class="smcap">A. D.</span> down to the present moment<span class="pagenum"><a name="Page_183" id="Page_183">[Pg 183]</a></span> +would not yet have reached his destination, although his +journey would be about three quarters done. He would +have crossed the orbit of Venus about the time of Charlemagne, +and that of +Mercury soon after +the discovery of +America.</p> + +<p><a name="S_115" id="S_115"></a>115. <b>Size and +density of the sun.</b>—Knowing +the distance +of the sun, +it is easy to find +from the angle subtended +by its diameter +(32 minutes +of arc) that the +length of that diameter +is 865,000 +miles. We recall +in this connection +that the diameter +of the moon's <i>orbit</i> +is only 480,000 +miles, but little +more than half the +diameter of the +sun, thus affording +abundant room inside +the sun, and +to spare, for the moon to perform the monthly revolution +about its orbit, as shown in <a href="#Fig_65">Fig. 65</a>.</p> + +<div class="figright" style="width: 375px;"><a name="Fig_65" id="Fig_65"></a> +<a href="images/i210-full.jpg"><img src="images/i210.jpg" width="375" height="619" alt="Fig. 65.—The sun's size.—Young." title="Fig. 65.—The sun's size.—Young." /></a> +<span class="caption"><span class="smcap">Fig. 65.</span>—The sun's size.—<span class="smcap">Young.</span></span> +</div> + +<p>In the same manner in which the density of the moon +was found from its mass and diameter, the student may +find from the mass and diameter of the sun given above +that its mean density is 1.4 times that of water. This is +about the same as the density of gravel or soft coal, and<span class="pagenum"><a name="Page_184" id="Page_184">[Pg 184]</a></span> +is just about one quarter of the average density of the +earth.</p> + +<p>We recall that the small density of the moon was accounted +for by the diminished weight of objects upon it, +but this explanation can not hold in the case of the sun, +for not only is the density less but the force of gravity +(weight) is there 28 times as great as upon the earth. The +athlete who here weighs 175 pounds, if transported to the +surface of the sun would weigh more than an elephant does +here, and would find his bones break under his own weight +if his muscles were strong enough to hold him upright. +The tremendous pressure exerted by gravity at the surface +of the sun must be surpassed below the surface, and as it +does not pack the material together and make it dense, we +are driven to one of two conclusions: Either the stuff of +which the sun is made is altogether unlike that of the +earth, not so readily compressed by pressure, or there is +some opposing influence at work which more than balances +the effect of gravity and makes the solar stuff much lighter +than the terrestrial.</p> + +<p><a name="S_116" id="S_116"></a>116. <b>Material of which the sun is made.</b>—As to the first +of these alternatives, the spectroscope comes to our aid and +shows in the sun's spectrum (<a href="#Fig_50">Fig. 50</a>) the characteristic +line marked <i>D</i>, which we know always indicates the presence +of sodium and identifies at least one terrestrial substance +as present in the sun in considerable quantity. The +lines marked <i>C</i> and <i>F</i> are produced by hydrogen, which is +one of the constituents of water, <i>E</i> shows calcium to be +present in the sun, <i>b</i> magnesium, etc. In this way it has +been shown that about one half of our terrestrial elements, +mainly the metallic ones, are present as gases on or near the +sun's surface, but it must not be inferred that elements not +found in this way are absent from the sun. They may be +there, probably are there, but the spectroscopic proof of +their presence is more difficult to obtain. Professor Rowland, +who has been prominent in the study of the solar<span class="pagenum"><a name="Page_185" id="Page_185">[Pg 185]</a></span> +spectrum, says: "Were the whole earth heated to the temperature +of the sun, its spectrum would probably resemble +that of the sun very closely."</p> + +<p>Some of the common terrestrial elements found in the +sun are:</p> + +<div class="center"> +<table border="0" cellpadding="1" cellspacing="0" summary=""> +<tr><td align="left">Aluminium.</td></tr> +<tr><td align="left">Calcium.</td></tr> +<tr><td align="left">Carbon.</td></tr> +<tr><td align="left">Copper.</td></tr> +<tr><td align="left">Hydrogen.</td></tr> +<tr><td align="left">Iron.</td></tr> +<tr><td align="left">Lead.</td></tr> +<tr><td align="left">Nickel.</td></tr> +<tr><td align="left">Potassium.</td></tr> +<tr><td align="left">Silicon.</td></tr> +<tr><td align="left">Silver.</td></tr> +<tr><td align="left">Sodium.</td></tr> +<tr><td align="left">Tin.</td></tr> +<tr><td align="left">Zinc.</td></tr> +<tr><td align="left">Oxygen (?)</td></tr> +</table></div> + +<p>Whatever differences of chemical structure may exist +between the sun and the earth, it seems that we must regard +these bodies as more like than unlike to each other in +substance, and we are brought back to the second of our +alternatives: there must be some influence opposing the +force of gravity and making the substance of the sun light +instead of heavy, and we need not seek far to find it in—</p> + +<p><a name="S_117" id="S_117"></a>117. <b>The heat of the sun.</b>—That the sun is hot is too +evident to require proof, and it is a familiar fact that heat +expands most substances and makes them less dense. The +sun's heat falling upon the earth expands it and diminishes +its density in some small degree, and we have only to imagine +this process of expansion continued until the earth's +diameter becomes 58 per cent larger than it now is, to find +the earth's density reduced to a level with that of the sun. +Just how much the temperature of the earth must be raised +to produce this amount of expansion we do not know, +neither do we know accurately the temperature of the sun, +but there can be no doubt that heat is the cause of the +sun's low density and that the corresponding temperature +is very high.</p> + +<p>Before we inquire more closely into the sun's temperature,<span class="pagenum"><a name="Page_186" id="Page_186">[Pg 186]</a></span> +it will be well to draw a sharp distinction between the +two terms heat and temperature, which are often used as if +they meant the same thing. Heat is a form of energy +which may be found in varying degree in every substance, +whether warm or cold—a block of ice contains a considerable +amount of heat—while temperature corresponds to our +sensations of warm and cold, and measures the extent to +which heat is concentrated in the body. It is the amount +of heat per molecule of the body. A barrel of warm water +contains more heat than the flame of a match, but its temperature +is not so high. Bearing in mind this distinction, +we seek to determine not the amount of heat contained in +the sun but the sun's temperature, and this involves the +same difficulty as does the question, What is the temperature +of a locomotive? It is one thing in the fire box and +another thing in the driving wheels, and still another at +the headlight; and so with the sun, its temperature is certainly +different in different parts—one thing at the center +and another at the surface. Even those parts which we +see are covered by a veil of gases which produce by absorption +the dark lines of the solar spectrum, and seriously +interfere both with the emission of energy from the sun +and with our attempts at measuring the temperature of +those parts of the surface from which that energy streams.</p> + +<p>In view of these and other difficulties we need not be +surprised that the wildest discordance has been found in +estimates of the solar temperature made by different investigators, +who have assigned to it values ranging from 1,400° C. +to more than 5,000,000° C. Quite recently, however, improved +methods and a better understanding of the problem +have brought about a better agreement of results, and it +now seems probable that the temperature of the visible +surface of the sun lies somewhere between 5,000° and +10,000° C., say 15,000° of the Fahrenheit scale.</p> + +<p><a name="S_118" id="S_118"></a>118. <b>Determining the sun's temperature.</b>—One ingenious +method which has been used for determining this temperature<span class="pagenum"><a name="Page_187" id="Page_187">[Pg 187]</a></span> +is based upon the principle stated above, that every +object, whether warm or cold, contains heat and gives it +off in the form of radiant energy. The radiation from a +body whose temperature is lower than 500° C. is made up +exclusively of energy whose wave length is greater than +7,600 tenth meters, and is therefore invisible to the eye, although +a thermometer or even the human hand can often +detect it as radiant heat. A brick wall in the summer sunshine +gives off energy which can be felt as heat but can +not be seen. When such a body is further heated it continues +to send off the same kinds (wave lengths) of energy +as before, but new and shorter waves are added to its radiation, +and when it begins to emit energy of wave length 7,500 +or 7,600 tenth meters, it also begins to shine with a dull-red +light, which presently becomes brighter and less ruddy +and changes to white as the temperature rises, and waves +of still shorter length are thereby added to the radiation. +We say, in common speech, the body becomes first red hot +and then white hot, and we thus recognize in a general +way that the kind or color of the radiation which a body +gives off is an index to its temperature. The greater the +proportion of energy of short wave lengths the higher is +the temperature of the radiating body. In sunlight the +maximum of brilliancy to the eye lies at or near the wave +length, 5,600 tenth meters, but the greatest intensity of +radiation of all kinds (light included) is estimated to fall +somewhere between green and blue in the spectrum at or +near the wave length 5,000 tenth meters, and if we can apply +to this wave length Paschen's law—temperature reckoned +in degrees centigrade from the absolute zero is always +equal to the quotient obtained by dividing the number +27,000,000 by the wave length corresponding to maximum +radiation—we shall find at once for the absolute temperature +of the sun's surface 5,400° C.</p> + +<p>Paschen's law has been shown to hold true, at least +approximately, for lower temperatures and longer wave<span class="pagenum"><a name="Page_188" id="Page_188">[Pg 188]</a></span> +lengths than are here involved, but as it is not yet certain +that it is strictly true and holds for all temperatures, too +great reliance must not be attached to the numerical result +furnished by it.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_66" id="Fig_66"></a> +<a href="images/i215-full.jpg"><img src="images/i215.jpg" width="500" height="498" alt="Fig. 66.—The sun, August 11, 1894. Photographed at the Goodsell Observatory." title="Fig. 66.—The sun, August 11, 1894. Photographed at the Goodsell Observatory." /></a> +<span class="caption"><span class="smcap">Fig. 66.</span>—The sun, August 11, 1894. Photographed at the Goodsell Observatory.</span> +</div> + +<div class="figcenter" style="width: 500px;"><a name="Fig_67" id="Fig_67"></a> +<a href="images/i216.jpg"><img src="images/i216.jpg" width="500" height="498" alt="Fig. 67.—The sun, August 14, 1894. Photographed at the Goodsell Observatory." title="Fig. 67.—The sun, August 14, 1894. Photographed at the Goodsell Observatory." /></a> +<span class="caption"><span class="smcap">Fig. 67.</span>—The sun, August 14, 1894. Photographed at the Goodsell Observatory.</span> +</div> + +<p><a name="S_119" id="S_119"></a>119. <b>The sun's surface.</b>—A marked contrast exists between +the faces of sun and moon in respect of the amount +of detail to be seen upon them, the sun showing nothing +whatever to correspond with the mountains, craters, and +seas of the moon. The unaided eye in general finds in the +sun only a blank bright circle as smooth and unmarked as +the surface of still water, and even the telescope at first +sight seems to show but little more. There may usually be +found upon the sun's face a certain number of black patches +called <i>sun spots</i>, such as are shown in Figs. <a href="#Fig_66">66</a> to <a href="#Fig_69">69</a>, and<span class="pagenum"><a name="Page_189" id="Page_189">[Pg 189]</a></span> +occasionally these are large enough to be seen through a +smoked glass without the aid of a telescope. When seen +near the edge of the sun they are quite frequently accompanied, +as in <a href="#Fig_69">Fig. 69</a>, by vague patches called <i>faculę</i> (Latin, +<i>facula</i> = a little torch), which look a little brighter than +the surrounding parts of the sun. So, too, a good photograph +of the sun usually shows that the central parts of +the disk are rather brighter than the edge, as indeed we +should expect them to be, since the absorption lines in the +sun's spectrum have already taught us that the visible surface +of the sun is enveloped by invisible vapors which in +some measure absorb the emitted light and render it feebler +at the edge where it passes through a greater thickness of +this envelope than at the center. See <a href="#Fig_70">Fig. 70</a>, where it is<span class="pagenum"><a name="Page_190" id="Page_190">[Pg 190]</a></span> +shown that the energy coming from the edge of the sun to +the earth has to traverse a much longer path inside the +vapors than does that coming from the center.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_68" id="Fig_68"></a> +<a href="images/i217.jpg"><img src="images/i217.jpg" width="500" height="499" alt="Fig. 68.—The sun, August 18, 1894. Photographed at the Goodsell Observatory." title="Fig. 68.—The sun, August 18, 1894. Photographed at the Goodsell Observatory." /></a> +<span class="caption"><span class="smcap">Fig. 68.</span>—The sun, August 18, 1894. Photographed at the Goodsell Observatory.</span> +</div> + +<p>Examine the sun spots in the four photographs, Figs. <a href="#Fig_66">66</a> +to <a href="#Fig_69">69</a>, and note that the two spots which appear at the +extreme left of the first photograph, very much distorted +and foreshortened by the curvature of the sun's surface, are +seen in a different part of the second picture, and are not +only more conspicuous but show better their true shape.</p> + +<div class="figcenter" style="width: 600px;"><a name="PLATE_II" id="PLATE_II"></a> +<a href="images/i219-full.jpg"><img src="images/i219.jpg" width="600" height="421" alt="PLATE II. + +THE EQUATORIAL CONSTELLATIONS" title="PLATE II. + +THE EQUATORIAL CONSTELLATIONS" /></a> +<span class="caption">PLATE II. + +THE EQUATORIAL CONSTELLATIONS</span> +</div> + +<p><a name="S_120" id="S_120"></a>120. <b>The sun's rotation.</b>—The changed position of these +spots shows that the sun rotates about an axis at right +angles to the direction of the spot's motion, and the position +of this axis is shown in the figure by a faint line ruled +obliquely across the face of the sun nearly north and south<span class="pagenum"><a name="Page_191" id="Page_191">[Pg 191]</a></span> +in each of the four photographs. This rotation in the +space of three days has carried the spots from the edge +halfway to the center of the disk, and the student should +note the progress of the spots in the two later photographs, +that of August 21st showing them just ready to disappear +around the farther edge of the sun.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_69" id="Fig_69"></a> +<a href="images/i221-full.jpg"><img src="images/i221.jpg" width="500" height="546" alt="Fig. 69.—The sun, August 21, 1894. Photographed at the Goodsell Observatory." title="Fig. 69.—The sun, August 21, 1894. Photographed at the Goodsell Observatory." /></a> +<span class="caption"><span class="smcap">Fig. 69.</span>—The sun, August 21, 1894. Photographed at the Goodsell Observatory.</span> +</div> + +<p>Plot accurately in one of these figures the positions of +the spots as shown in the other three, and observe whether +the path of the spots across the sun's face is a straight line. +Is there any reason why it should not be straight?</p> + +<p>These four pictures may be made to illustrate many +things about the sun. Thus the sun's axis is not parallel +to that of the earth, for the letters <i>N S</i> mark the direction +of a north and south line across the face of the sun, and<span class="pagenum"><a name="Page_192" id="Page_192">[Pg 192]</a></span> +this line, of course, is parallel to the earth's axis, while it is +evidently not parallel to the sun's axis. The group of +spots took more than +ten days to move +across the sun's face, +and as at least an +equal time must be +required to move +around the opposite +side of the sun, it is +evident that the period +of the sun's rotation +is something more than 20 days. It is, in fact, +rather more than 25 days, for this same group of spots reappeared +again on the left-hand edge of the sun on September +5th.</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_70" id="Fig_70"></a> +<img src="images/i222.png" width="350" height="198" alt="Fig. 70.—Absorption at the sun's edge." title="Fig. 70.—Absorption at the sun's edge." /> +<span class="caption"><span class="smcap">Fig. 70.</span>—Absorption at the sun's edge.</span> +</div> + +<p><a name="S_121" id="S_121"></a>121. <b>Sun spots.</b>—Another significant fact comes out +plainly from the photographs. The spots are not permanent +features of the sun's face, since they changed their +size and shape very appreciably in the few days covered by +the pictures. Compare particularly the photographs of +August 14th and August 18th, where the spots are least +distorted by the curvature of the sun's surface. By September +16th this group of spots had disappeared absolutely +from the sun's face, although when at its largest the group +extended more than 80,000 miles in length, and several of +the individual spots were large enough to contain the +earth if it had been dropped upon them. From <a href="#Fig_67">Fig. 67</a> +determine in miles the length of the group on August +14th. <a href="#Fig_71">Fig. 71</a> shows an enlarged view of these spots as +they appeared on August 17th, and in this we find some +details not so well shown in the preceding pictures. The +larger spots consist of a black part called the <i>nucleus</i> or +<i>umbra</i> (Latin, shadow), which is surrounded by an irregular +border called the <i>penumbra</i> (partial shadow), which is +intermediate in brightness between the nucleus and the<span class="pagenum"><a name="Page_193" id="Page_193">[Pg 193]</a></span> +surrounding parts of the sun. It should not be inferred +from the picture that the nucleus is really black or even +dark. It shines, in +fact, with a brilliancy +greater than that of +an electric lamp, but +the background furnished +by the sun's +surface is so much +brighter that by contrast +with it the nucleus +and penumbra +appear relatively dark.</p> + +<div class="figcenter" style="width: 350px;"><a name="Fig_71" id="Fig_71"></a> +<a href="images/i223a.jpg"><img src="images/i223a.jpg" width="350" height="350" alt="Fig. 71.—Sun spots, August 17, 1894. +Goodsell Observatory." title="Fig. 71.—Sun spots, August 17, 1894. +Goodsell Observatory." /></a> +<span class="caption"><span class="smcap">Fig. 71.</span>—Sun spots, August 17, 1894. +Goodsell Observatory.</span> +</div> + +<div class="figcenter" style="width: 500px;"><a name="Fig_72" id="Fig_72"></a> +<a href="images/i223b-full.jpg"><img src="images/i223b.jpg" width="500" height="335" alt="Fig. 72.—Sun spot of March 5, 1873.—From Langley, The New Astronomy. +By permission of the publishers." title="Fig. 72.—Sun spot of March 5, 1873.—From Langley, The New Astronomy. +By permission of the publishers." /></a> +<span class="caption"><span class="smcap">Fig. 72.</span>—Sun spot of March 5, 1873.—From <span class="smcap">Langley</span>, The New Astronomy. +By permission of the publishers.</span> +</div> + +<p>The bright shining +surface of the sun, the +background for the +spots, is called the +<i>photosphere</i> (Greek, +light sphere), and, as <a href="#Fig_71">Fig. 71</a> shows, it assumes under a +suitable magnifying power a mottled aspect quite different +from the featureless expanse shown in the earlier pictures. +The photosphere is, in fact, a layer of little clouds with<span class="pagenum"><a name="Page_194" id="Page_194">[Pg 194]</a></span> +darker spaces between them, and the fine detail of these +clouds, their complicated structure, and the way in which, +when projected against the background of a sun spot, they +produce its penumbra, are all brought out in <a href="#Fig_72">Fig. 72</a>. +Note that the little patch in one corner of this picture +represents North and South America drawn to the same +scale as the sun spots.</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_73" id="Fig_73"></a> +<a href="images/i224.jpg"><img src="images/i224.jpg" width="350" height="343" alt="Fig. 73.—Spectroheliograph, showing distribution +of faculę upon the sun.—Hale." title="Fig. 73.—Spectroheliograph, showing distribution +of faculę upon the sun.—Hale." /></a> +<span class="caption"><span class="smcap">Fig. 73.</span>—Spectroheliograph, showing distribution +of faculę upon the sun.—<span class="smcap">Hale.</span></span> +</div> + +<p><a name="S_122" id="S_122"></a>122. <b>Faculę.</b>—We have seen in <a href="#Fig_69">Fig. 69</a> a few of the +bright spots called faculę. At the telescope or in the +ordinary photograph these can be seen only at the edge of +the sun, because elsewhere +the background +furnished by the photosphere +is so bright +that they are lost in it. +It is possible, however, +by an ingenious application +of the spectroscope +to break up the +sunlight into a spectrum +in such a way as +to diminish the brightness +of this background, +much more +than the brightness of +the faculę is diminished, +and in this way to obtain a photograph of the sun's +surface which shall show them wherever they occur, and +such a photograph, showing faintly the spectral lines, is +reproduced in <a href="#Fig_73">Fig. 73</a>. The faculę are the bright patches +which stretch inconspicuously across the face of the sun, +in two rather irregular belts with a comparatively empty +lane between them. This lane lies along the sun's equator, +and it is upon either side of it between latitudes 5° +and 40° that faculę seem to be produced. It is significant +of their connection with sun spots that the spots occur<span class="pagenum"><a name="Page_196" id="Page_196">[Pg 196]</a></span> +in these particular zones and are rarely found outside +them.</p> + +<div class="figcenter" style="width: 600px;"><a name="Fig_74" id="Fig_74"></a> +<a href="images/i225-full.jpg"><img src="images/i225.jpg" width="600" height="431" alt="Fig. 74.—Eclipse of July 20, 1878.—Trouvelot." title="Fig. 74.—Eclipse of July 20, 1878.—Trouvelot." /></a> +<span class="caption"><span class="smcap">Fig. 74.</span>—Eclipse of July 20, 1878.—<span class="smcap">Trouvelot.</span></span> +</div> + +<div class="figcenter" style="width: 500px;"><a name="Fig_75" id="Fig_75"></a> +<a href="images/i226-full.jpg"><img src="images/i226.jpg" width="500" height="494" alt="Fig. 75.—Eclipse of April 16, 1893.—Schaeberle." title="Fig. 75.—Eclipse of April 16, 1893.—Schaeberle." /></a> +<span class="caption"><span class="smcap">Fig. 75.</span>—Eclipse of April 16, 1893.—<span class="smcap">Schaeberle.</span></span> +</div> + +<p><a name="S_123" id="S_123"></a>123. <b>Invisible parts of the sun. The Corona.</b>—Thus far +we have been dealing with parts of the sun that may be +seen and photographed under all ordinary conditions. +But outside of and surrounding these parts is an envelope, +or rather several envelopes, of much greater extent than +the visible sun. These envelopes are for the most part +invisible save at those times when the brighter central +portions of the sun are hidden in a total eclipse.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_76" id="Fig_76"></a> +<a href="images/i227-full.jpg"><img src="images/i227.jpg" width="500" height="498" alt="Fig. 76.—Eclipse of January 21, 1898.—Campbell." title="Fig. 76.—Eclipse of January 21, 1898.—Campbell." /></a> +<span class="caption"><span class="smcap">Fig. 76.</span>—Eclipse of January 21, 1898.—<span class="smcap">Campbell.</span></span> +</div> + +<p><a href="#Fig_74">Fig. 74</a> is from a drawing, and Figs. <a href="#Fig_75">75</a> and <a href="#Fig_76">76</a> are from +eclipse photographs showing this region, in which the most<span class="pagenum"><a name="Page_197" id="Page_197">[Pg 197]</a></span> +conspicuous object is the halo of soft light called the <i>corona</i>, +that completely surrounds the sun but is seen to be of differing +shapes and differing extent at the several eclipses +here shown, although a large part of these apparent differences +is due to technical difficulties in photographing, and +reproducing an object with outlines so vague as those of +the corona. The outline of the corona is so indefinite and +its outer portions so faint that it is impossible to assign to +it precise dimensions, but at its greatest extent it reaches +out for several millions of miles and fills a space more than +twenty times as large as the visible part of the sun. Despite +its huge bulk, it is of most unsubstantial character,<span class="pagenum"><a name="Page_198" id="Page_198">[Pg 198]</a></span> +an airy nothing through which comets have been known +to force their way around the sun from one side to the +other, literally for millions of miles, without having their +course influenced or their +velocity checked to any +appreciable extent. This +would hardly be possible +if the density even at the +bottom of the corona were +greater than that of the +best vacuum which we +are able to produce in laboratory +experiments. It +seems odd that a vacuum +should give off so bright +a light as the coronal pictures +show, and the exact character of that light and the +nature of the corona are still subjects of dispute among +astronomers, although it is generally agreed that, in part +at least, its light is ordinary sunlight faintly reflected +from the widely scattered molecules composing the substance +of the corona. It is also probable that in part the +light has its origin in the corona itself. A curious and at +present unconfirmed result announced by one of the observers +of the eclipse of May 28, 1900, is that <i>the corona is +not hot</i>, its effective temperature being lower than that of +the instrument used for the observation.</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_77" id="Fig_77"></a> +<a href="images/i228.jpg"><img src="images/i228.jpg" width="350" height="289" alt="Fig. 77.—Solar prominence of March 25, +1895.—Hale." title="Fig. 77.—Solar prominence of March 25, +1895.—Hale." /></a> +<span class="caption"><span class="smcap">Fig. 77.</span>—Solar prominence of March 25, +1895.—<span class="smcap">Hale.</span></span> +</div> + +<div class="figright" style="width: 375px;"><a name="Fig_78" id="Fig_78"></a> +<a href="images/i229-full.jpg"><img src="images/i229.jpg" width="375" height="437" alt="Fig. 78.—A solar prominence.—Hale." title="Fig. 78.—A solar prominence.—Hale." /></a> +<span class="caption"><span class="smcap">Fig. 78.</span>—A solar prominence.—<span class="smcap">Hale.</span></span> +</div> + + +<p><a name="S_124" id="S_124"></a>124. <b>The chromosphere.</b>—Between the corona and the +photosphere there is a thin separating layer called the +<i>chromosphere</i> (Greek, color sphere), because when seen at +an eclipse it shines with a brilliant red light quite unlike +anything else upon the sun save the <i>prominences</i> which are +themselves only parts of the chromosphere temporarily +thrown above its surface, as in a fountain a jet of water is +thrown up from the basin and remains for a few moments +suspended in mid-air. Not infrequently in such a fountain +<span class="pagenum"><a name="Page_199" id="Page_199">[Pg 199]</a></span> +foreign matter is swept up by the rush of the water—dirt, +twigs, small fish, etc.—and in like manner the prominences +often carry along with them parts of the underlying +layers of the sun, photosphere, faculę, etc., which +reveal their presence in the prominence by adding their +characteristic lines to the spectrum, like that of the chromosphere, +which the prominence presents when they are +absent. None of the eclipse photographs (Figs. <a href="#Fig_74">74</a> to <a href="#Fig_76">76</a>) +show the chromosphere, because the color effect is lacking +in them, but a great curving prominence may be seen near +the bottom of <a href="#Fig_75">Fig. 75</a>, and smaller ones at other parts of +the sun's edge.</p> + +<p><a name="S_125" id="S_125"></a>125. <b>Prominences.</b>—<a href="#Fig_77">Fig. 77</a> shows upon a larger scale one +of these prominences rising to a height of 160,000 miles +above the photosphere; +and another +photograph, +taken 18 minutes +later, but not reproduced +here, +showed the same +prominence grown +in this brief interval +to a stature +of 280,000 miles. +These pictures +were not taken +during an eclipse, +but in full sunlight, +using the +same spectroscopic +apparatus which +was employed in +connection with +the faculę to diminish the brightness of the background +without much enfeebling the brilliancy of the prominence<span class="pagenum"><a name="Page_200" id="Page_200">[Pg 200]</a></span> +itself. The dark base from which the prominence seems +to spring is not the sun's edge, but a part of the apparatus +used to cut off the direct sunlight.</p> + +<p><a href="#Fig_78">Fig. 78</a> contains a series of photographs of another +prominence taken within an interval of 1 hour 47 minutes +and showing changes in size and shape which are much +more nearly typical of the ordinary prominence than was +the very unusual change in the case of <a href="#Fig_77">Fig. 77</a>.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_79" id="Fig_79"></a> +<a href="images/i230-full.jpg"><img src="images/i230.jpg" width="500" height="375" alt="Fig. 79.—Contrasted forms of solar prominences.—Zoellner." title="Fig. 79.—Contrasted forms of solar prominences.—Zoellner." /></a> +<span class="caption"><span class="smcap">Fig. 79.</span>—Contrasted forms of solar prominences.—<span class="smcap">Zoellner.</span></span> +</div> + +<p>The preceding pictures are from photographs, and with +them the student may compare <a href="#Fig_79">Fig. 79</a>, which is constructed +from drawings made at the spectroscope by the +German astronomer Zoellner. The changes here shown +are most marked in the prominence at the left, which is +shaped like a broken tree trunk, and which appears to be +vibrating from one side to the other like a reed shaken +in the wind. Such a prominence is frequently called an +<i>eruptive</i> one, a name suggested by its appearance of having +been blown out from the sun by something like an +explosion, while the prominence at the right in this series +of drawings, which appears much less agitated, is called by +contrast with the other a <i>quiescent</i> prominence. These +quiescent prominences are, as a rule, much longer-lived<span class="pagenum"><a name="Page_201" id="Page_201">[Pg 201]</a></span> +than the eruptive ones. One more picture of prominences +(<a href="#Fig_80">Fig. 80</a>) is introduced to show the continuous stretch of +chromosphere out of which they spring.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_80" id="Fig_80"></a> +<a href="images/i231-full.jpg"><img src="images/i231.jpg" width="500" height="414" alt="Fig. 80.—Prominences and chromosphere.—Hale." title="Fig. 80.—Prominences and chromosphere.—Hale." /></a> +<span class="caption"><span class="smcap">Fig. 80.</span>—Prominences and chromosphere.—<span class="smcap">Hale.</span></span> +</div> + +<p>Prominences are seen only at the edge of the sun, because +it is there alone that the necessary background can +be obtained, but they must occur at the center of the sun +and elsewhere quite as well as at the edge, and it is probable +that quiescent prominences are distributed over all +parts of the sun's surface, but eruptive prominences show +a strong tendency toward the regions of sun spots and +faculę as if all three were intimately related phenomena.</p> + +<p><a name="S_126" id="S_126"></a>126. <b>The sun as a machine.</b>—Thus far we have considered +the anatomy of the sun, dissecting it into its several +parts, and our next step should be a consideration of its +physiology, the relation of the parts to each other, and +their function in carrying on the work of the solar organism, +but this step, unfortunately, must be a lame one. +The science of astronomy to-day possesses no comprehensive +and well-established theory of this kind, but looks to +the future for the solution of this the greatest pending<span class="pagenum"><a name="Page_202" id="Page_202">[Pg 202]</a></span> +problem of solar physics. Progress has been made toward +its solution, and among the steps of this progress that we +shall have to consider, the first and most important is the +conception of the sun as a kind of heat engine.</p> + +<p>In a steam engine coal is burned under the boiler, and +its chemical energy, transformed into heat, is taken up by +the water and delivered, through steam as a medium, to +the engine, which again transforms and gives it out as +mechanical work in the turning of shafts, the driving of +machinery, etc. Now, the function of the sun is exactly +opposite to that of the engine and boiler: it gives out, +instead of receiving, radiant energy; but, like the engine, +it must be fed from some source; it can not be run upon +nothing at all any more than the engine can run day after +day without fresh supplies of fuel under its boiler. We +know that for some thousands of years the sun has been +furnishing light and heat to the earth in practically unvarying +amount, and not to the earth alone, but it has +been pouring forth these forms of energy in every direction, +without apparent regard to either use or economy. +Of all the radiant energy given off by the sun, only two +parts out of every thousand million fall upon any planet +of the solar system, and of this small fraction the earth +takes about one tenth for the maintenance of its varied +forms of life and action. Astronomers and physicists have +sought on every hand for an explanation of the means by +which this tremendous output of energy is maintained +century after century without sensible diminution, and +have come with almost one mind to the conclusion that +the gravitative forces which reside in the sun's own mass +furnish the only adequate explanation for it, although +they may be in some small measure re-enforced by minor +influences, such as the fall of meteoric dust and stones +into the sun.</p> + +<p>Every boy who has inflated a bicycle tire with a hand +pump knows that the pump grows warm during the operation,<span class="pagenum"><a name="Page_203" id="Page_203">[Pg 203]</a></span> +on account of the compression of the air within the +cylinder. A part of the muscular force (energy) expended +in working the pump reappears in the heat which warms +both air and pump, and a similar process is forever going on +in the sun, only in place of muscular force we must there substitute +the tremendous attraction of gravitation, 28 times +as great as upon the earth. "The matter in the interior +of the sun must be as a shuttlecock between the stupendous +pressure and the enormously high temperature," the +one tending to compress and the other to expand it, but +with this important difference between them: the temperature +steadily tends to fall as the heat energy is wasted +away, while the gravitative force suffers no corresponding +diminution, and in the long run must gain the upper +hand, causing the sun to shrink and become more dense. +It is this progressive shrinking and compression of its +molecules into a smaller space which supplies the energy +contained in the sun's output of light and heat. According +to Lord Kelvin, each centimeter of shrinkage in the +sun's diameter furnishes the energy required to keep up +its radiation for something more than an hour, and, on +account of the sun's great distance, the shrinkage might +go on at this rate for many centuries without producing +any measurable effect in the sun's appearance.</p> + +<p><a name="S_127" id="S_127"></a>127. <b>Gaseous constitution of the sun.</b>—But Helmholtz's dynamical +theory of the maintenance of the sun's heat, which +we are here considering, includes one essential feature +that is not sufficiently stated above. In order that the +explanation may hold true, it is necessary that the sun +should be in the main a gaseous body, composed from center +to circumference of gases instead of solid or liquid +parts. Pumping air warms the bicycle pump in a way +that pumping water or oil will not.</p> + +<p>The high temperature of the sun itself furnishes sufficient +reason for supposing the solar material to be in the +gaseous state, but the gas composing those parts of the<span class="pagenum"><a name="Page_204" id="Page_204">[Pg 204]</a></span> +sun below the photosphere must be very different in some +of its characteristics from the air or other gases with which +we are familiar at the earth, since its average density is +1,000 times as great as that of air, and its consistence and +mechanical behavior must be more like that of honey or tar +than that of any gas with which we are familiar. It is +worth noting, however, that if a hole were dug into the +crust of the earth to a depth of 15 or 20 miles the air at +the bottom of the hole would be compressed by that above +it to a density comparable with that of the solar gases.</p> + +<p><a name="S_128" id="S_128"></a>128. <b>The sun's circulation.</b>—It is plain that under the +conditions which exist in the sun the outer portions, which +can radiate their heat freely into space, must be cooler than +the inner central parts, and this difference of temperature +must set up currents of hot matter drifting upward and outward +from within the sun and counter currents of cooler +matter settling down to take its place. So, too, there must +be some level at which the free radiation into outer space +chills the hot matter sufficiently to condense its less refractory +gases into clouds made up of liquid drops, just as on a +cloudy day there is a level in our own atmosphere at which +the vapor of water condenses into liquid drops which form +the thin shell of clouds that hovers above the earth's surface, +while above and below is the gaseous atmosphere. In the +case of the sun this cloud layer is always present and is that +part which we have learned to call the photosphere. Above +the photosphere lies the chromosphere, composed of gases +less easily liquefied, hydrogen is the chief one, while between +photosphere and chromosphere is a thin layer of metallic +vapors, perhaps indistinguishable from the top crust +of the photosphere itself, which by absorbing the light +given off from the liquid photosphere produces the greater +part of the Fraunhofer lines in the solar spectrum.</p> + +<p>From time to time the hot matter struggling up from +below breaks through the photosphere and, carrying with +it a certain amount of the metallic vapors, is launched into<span class="pagenum"><a name="Page_205" id="Page_205">[Pg 205]</a></span> +the upper and cooler regions of the sun, where, parting +with its heat, it falls back again upon the photosphere and +is absorbed into it. It is altogether probable that the +corona is chiefly composed of fine particles ejected from +the sun with velocities sufficient to carry them to a height +of millions of miles, or even sufficient to carry them off +never to return. The matter of the corona must certainly +be in a state of the most lively agitation, its particles being +alternately hurled up from the photosphere and falling +back again like fireworks, the particles which make up the +corona of to-day being quite a different set from those of +yesterday or last week. It seems beyond question that +the prominences and faculę too are produced in some +way by this up-and-down circulation of the sun's matter, +and that any mechanical explanation of the sun must be +worked out along these lines; but the problem is an exceedingly +difficult one, and must include and explain many other +features of the sun's activity of which only a few can be considered +here.</p> + +<p><a name="S_129" id="S_129"></a>129. <b>The sun-spot period.</b>—Sun spots come and go, and +at best any particular spot is but short-lived, rarely lasting +more than a month or two, and more often its duration is +a matter of only a few days. They are not equally numerous +at all times, but, like swarms of locusts, they seem to +come and abound for a season and then almost to disappear, +as if the forces which produced them were of a periodic +character alternately active and quiet. The effect of +this periodic activity since 1870 is shown in <a href="#Fig_81">Fig. 81</a>, where +the horizontal line is a scale of times, and the distance of +the curve above this line for any year shows the relative +number of spots which appeared upon the sun in that +year. This indicates very plainly that 1870, 1883, and +1893 were years of great sun-spot activity, while 1879 and +1889 were years in which few spots appeared. The older +records, covering a period of two centuries, show the same +fluctuations in the frequency of sun spots and from these<span class="pagenum"><a name="Page_206" id="Page_206">[Pg 206]</a></span> +records curves (which may be found in Young's, The Sun) +have been plotted, showing a succession of waves extending +back for many years.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_81" id="Fig_81"></a> +<img src="images/i236.png" width="500" height="197" alt="Fig. 81.—The curve of sun-spot frequency." title="Fig. 81.—The curve of sun-spot frequency." /> +<span class="caption"><span class="smcap">Fig. 81.</span>—The curve of sun-spot frequency.</span> +</div> + +<p>The sun-spot period is the interval of time from the +crest or hollow of one wave to the corresponding part of +the next one, and on the average this appears to be a little +more than eleven years, but is subject to considerable variation. +In accordance with this period there is drawn in +broken lines at the right of <a href="#Fig_81">Fig. 81</a> a predicted continuation +of the sun-spot curve for the first decade of the twentieth +century. The irregularity shown by the three preceding +waves is such that we must not expect the actual +course of future sun spots to correspond very closely to +the prediction here made; but in a general way 1901 and +1911 will probably be years of few sun spots, while they +will be numerous in 1905, but whether more or less numerous +than at preceding epochs of greatest frequency can not +be foretold with any approach to certainty so long as we +remain in our present ignorance of the causes which make +the sun-spot period.</p> + +<p>Determine from <a href="#Fig_81">Fig. 81</a> as accurately as possible the +length of the sun-spot period. It is hard to tell the exact +position of a crest or hollow of the curve. Would it +do to draw a horizontal line midway between top and bottom +of the curve and determine the length of the period<span class="pagenum"><a name="Page_207" id="Page_207">[Pg 207]</a></span> +from its intersections with the curve—e. g., in 1874 and +1885?</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_82" id="Fig_82"></a> +<img src="images/i237.png" width="500" height="506" alt="Fig. 82.—Illustrating change of the sun-spot zones." title="Fig. 82.—Illustrating change of the sun-spot zones." /> +<span class="caption"><span class="smcap">Fig. 82.</span>—Illustrating change of the sun-spot zones.</span> +</div> + +<p><a name="S_130" id="S_130"></a>130. <b>The sun-spot zones.</b>—It has been already noted that +sun spots are found only in certain zones of latitude upon +the sun, and that faculę and eruptive prominences abound +in these zones more than elsewhere, although not strictly +confined to them. We have now to note a peculiarity of +these zones which ought to furnish a clew to the sun's +mechanism, although up to the present time it has not +been successfully traced out. Just before a sun-spot minimum +the few spots which appear are for the most part +clustered near the sun's equator. As these spots die out<span class="pagenum"><a name="Page_208" id="Page_208">[Pg 208]</a></span> +two new groups appear, one north the other south of the +sun's equator and about 25° or 30° distant from it, and as +the period advances toward a maximum these groups shift +their positions more and more toward the equator, thus approaching +each other but leaving between them a vacant +lane, which becomes steadily narrower until at the close +of the period, when the next minimum is at hand, it +reaches its narrowest dimensions, but does not altogether +close up even then. In <a href="#Fig_82">Fig. 82</a> these relations are shown +for the period falling between 1879 and 1890, by means of +the horizontal lines; for each year one line in the northern +and one in the southern hemisphere of the sun, their +lengths being proportional to the number of spots which +appeared in the corresponding hemisphere during the year, +and their positions on the sun's disk showing the average +latitude of the spots in question. It is very apparent from +the figure that during this decade the sun's southern hemisphere +was much more active than the northern one in the +production of spots, and this appears to be generally the +case, although the difference is not usually as great as in +this particular decade.</p> + +<p><a name="S_131" id="S_131"></a>131. <b>Influence of the sun-spot period.</b>—Sun spots are certainly +less hot than the surrounding parts of the sun's surface, +and, in view of the intimate dependence of the earth +upon the solar radiation, it would be in no way surprising +if their presence or absence from the sun's face should +make itself felt in some degree upon the earth, raising and +lowering its temperature and quite possibly affecting it in +other ways. Ingenious men have suggested many such +kinds of influence, which, according to their investigations, +appear to run in cycles of eleven years. Abundant and +scanty harvests, cyclones, tornadoes, epidemics, rainfall, +etc., are among these alleged effects, and it is possible that +there may be a real connection between any or all of them +and the sun-spot period, but for the most part astronomers +are inclined to hold that there is only one case in which<span class="pagenum"><a name="Page_209" id="Page_209">[Pg 209]</a></span> +the evidence is strong enough to really establish a connection +of this kind. The magnetic condition of the earth +and its disturbances, which are called magnetic storms, do +certainly follow in a very marked manner the course of +sun-spot activity, and perhaps there should be added to +this the statement that auroras (northern lights) stand in +close relation to these magnetic disturbances and are most +frequent at the times of sun-spot maxima.</p> + +<p>Upon the sun, however, the influence of the spot period +is not limited to things in and near the photosphere, but +extends to the outermost limits of the corona. Determine +from <a href="#Fig_81">Fig. 81</a> the particular part of the sun-spot period +corresponding to the date of each picture of the corona +and note how the pictures which were taken near times of +sun-spot minima present a general agreement in the shape +and extent of the corona, while the pictures taken at a time +of maximum activity of the sun spots show a very differently +shaped and much smaller corona.</p> + +<p><a name="S_132" id="S_132"></a>132. <b>The law of the sun's rotation.</b>—We have seen in a +previous part of the chapter how the time required by the +sun to make a complete rotation upon its axis may be determined +from photographs showing the progress of a spot +or group of spots across its disk, and we have now to add +that when this is done systematically by means of many +spots situated in different solar latitudes it leads to a +very peculiar and extraordinary result. Each particular +parallel of latitude has its own period of rotation different +from that of its neighbors on either side, so that there can +be no such thing as a fixed geography of the sun's surface. +Every part of it is constantly taking up a new position +with respect to every other part, much as if the Gulf of +Mexico should be south of the United States this year, +southeast of it next year, and at the end of a decade should +have shifted around to the opposite side of the earth from +us. A meridian of longitude drawn down the Mississippi +Valley remains always a straight line, or, rather, great<span class="pagenum"><a name="Page_210" id="Page_210">[Pg 210]</a></span> +circle, upon the surface of the earth, while <a href="#Fig_83">Fig. 83</a> shows +what would become of such a meridian drawn through +the equatorial parts of the sun's disk. In the first diagram +it appears as a straight line running down the middle +of the sun's disk. Twenty-five days later, when the +same face of the sun comes back into view again, after +making a complete revolution about the axis, the equatorial +parts will have moved so much faster and farther +than those in higher latitudes that the meridian +will be warped as in the second diagram, and still more +warped after another and another revolution, as shown in +the figure.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_83" id="Fig_83"></a> +<img src="images/i240.png" width="500" height="140" alt="Fig. 83.—Effect of the sun's peculiar rotation in warping a meridian, originally +straight." title="Fig. 83.—Effect of the sun's peculiar rotation in warping a meridian, originally +straight." /> +<span class="caption"><span class="smcap">Fig. 83.</span>—Effect of the sun's peculiar rotation in warping a meridian, originally +straight.</span> +</div> + +<p>At least such is the case if the spots truly represent the +way in which the sun turns round. There is, however, a +possibility that the spots themselves drift with varying +speeds across the face of the sun, and that the differences +which we find in their rates of motion belong to them +rather than to the photosphere. Just what happens in the +regions near the poles is hard to say, for the sun spots only +extend about halfway from the equator to the poles, and +the spectroscope, which may be made to furnish a certain +amount of information bearing upon the case, is not as yet +altogether conclusive, nor are the faculę which have also +been observed for this purpose.</p> + +<p>The simple theory that the solar phenomena are caused +by an interchange of hotter and cooler matter between the +photosphere and the lower strata of the sun furnishes in<span class="pagenum"><a name="Page_211" id="Page_211">[Pg 211]</a></span> +its present shape little or no explanation of such features +as the sun-spot period, the variations in the corona, the +peculiar character of the sun's rotation, etc., and we have +still unsolved in the mechanical theory of the sun one of +the noblest problems of astronomy, and one upon which +both observers and theoretical astronomers are assiduously +working at the present time. A close watch is kept upon +sun spots and prominences, the corona is observed at every +total eclipse, and numerous are the ingenious methods +which are being suggested and tried for observing it without +an eclipse in ordinary daylight. Attempts, more or +less plausible, have been made and are now pending to +explain photosphere, spots and the reversing layer by means +of the refraction of light within the sun's outer envelope +of gases, and it seems altogether probable, in view of these +combined activities, that a considerable addition to our +store of knowledge concerning the sun may be expected in +the not distant future.</p> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_212" id="Page_212">[Pg 212]</a></span></p> +<h2><a name="CHAPTER_XI" id="CHAPTER_XI"></a>CHAPTER XI</h2> + +<h3>THE PLANETS</h3> + + +<p><a name="S_133" id="S_133"></a>133. <b>Planets.</b>—Circling about the sun, under the influence +of his attraction, is a family of planets each member +of which is, like the moon, a dark body shining by reflected +sunlight, and therefore presenting phases; although only +two of them, Mercury and Venus, run through the complete +series—new, first quarter, full, last quarter—which +the moon presents. The way in which their orbits are +grouped about the sun has been considered in <a href="#CHAPTER_III">Chapter III</a>, +and Figs. <a href="#Fig_16">16</a> and <a href="#Fig_17">17</a> of that chapter may be completed +so as to represent all of the planets by drawing in <a href="#Fig_16">Fig. 16</a> +two circles with radii of 7.9 and 12.4 centimeters respectively, +to represent the orbits of the planets Uranus and +Neptune, which are more remote from the sun than Saturn, +and by introducing a little inside the orbit of Jupiter +about 500 ellipses of different sizes, shapes, and positions to +represent a group of minor planets or asteroids as they are +often called. It is convenient to regard these asteroids as +composing by themselves a class of very small planets, while +the remaining 8 larger planets fall naturally into two other +classes, a group of medium-sized ones—Mercury, Venus, +Earth, and Mars—called inner planets by reason of their +nearness to the sun; and the outer planets—Jupiter, Saturn, +Uranus, Neptune—each of which is much larger and +more massive than any planet of the inner group. Compare +in Figs. <a href="#Fig_84">84</a> and <a href="#Fig_85">85</a> their relative sizes. The earth, <i>E</i>, is +introduced into <a href="#Fig_85">Fig. 85</a> as a connecting link between the +two figures.</p> + +<p>Some of these planets, like the earth, are attended by<span class="pagenum"><a name="Page_213" id="Page_213">[Pg 213]</a></span> +one or more moons, technically called satellites, which also +shine by reflected sunlight and which move about their +respective planets in accordance with the law of gravitation, +much as the moon moves around the earth.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_84" id="Fig_84"></a> +<img src="images/i243a.png" width="500" height="191" alt="Fig. 84.—The inner planets and the moon." title="Fig. 84.—The inner planets and the moon." /> +<span class="caption"><span class="smcap">Fig. 84.</span>—The inner planets and the moon.</span> +</div> + +<div class="figcenter" style="width: 500px;"><a name="Fig_85" id="Fig_85"></a> +<img src="images/i243b.png" width="500" height="188" alt="Fig. 85.—The outer planets." title="Fig. 85.—The outer planets." /> +<span class="caption"><span class="smcap">Fig. 85.</span>—The outer planets.</span> +</div> + +<p><a name="S_134" id="S_134"></a>134. <b>Distances of the planets from the sun.</b>—It is a comparatively +simple matter to observe these planets year after +year as they move among the stars, and to find from these +observations how long each one of them requires to make +its circuit around the sun—that is, its periodic time, <i>T</i>, +which figures in Kepler's Third Law, and when these periodic +times have been ascertained, to use them in connection +with that law to determine the mean distance of each +planet from the sun. Thus, Jupiter requires 4,333 days to +move completely around its orbit; and comparing this with +the periodic time and mean distance of the earth we find—</p> + +<p class="center"><i>a</i><sup>3</sup> / (4333)<sup>2</sup> = (93,000,000)<sup>3</sup> / (365.25)<sup>2</sup>,<span class="pagenum"><a name="Page_214" id="Page_214">[Pg 214]</a></span></p> + +<p>which when solved gives as the mean distance of Jupiter +from the sun, 483,730,000 miles, or 5.20 times as distant as +the earth. If we make a similar computation for each +planet, we shall find that their distances from the sun show +a remarkable agreement with an artificial series of numbers +called Bode's law. We write down the numbers contained +in the first line of figures below, each of which, after the +second, is obtained by doubling the preceding one, add 4 +to each number and point off one place of decimals; the +resulting number is (approximately) the distance of the +corresponding planet from the sun.</p> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary="" rules="groups" frame="void"> +<tfoot> +<tr><td align="right">0.4</td><td align="right">0.7</td><td align="right">1.0</td><td align="right">1.6</td><td align="right">2.8</td><td align="right">5.2</td><td align="right">10.0</td><td align="right">19.6</td><td align="right">38.8</td></tr> +<tr><td align="right">0.4</td><td align="right">0.7</td><td align="right">1.0</td><td align="right">1.5</td><td align="right">2.8</td><td align="right">5.2</td><td align="right">9.5</td><td align="right">19.2</td><td align="right">30.1</td></tr> +</tfoot> +<tbody> +<tr><td align="right">Mercury.</td><td align="right">Venus.</td><td align="right">Earth.</td><td align="right">Mars.</td><td align="right"></td><td align="right">Jupiter.</td><td align="right">Saturn.</td><td align="right">Uranus.</td><td align="right">Neptune.</td></tr> +<tr><td align="right">0</td><td align="right">3</td><td align="right">6</td><td align="right">12</td><td align="right">24</td><td align="right">48</td><td align="right">96</td><td align="right">192</td><td align="right">384</td></tr> +<tr><td align="right">4</td><td align="right">4</td><td align="right">4</td><td align="right">4</td><td align="right">4</td><td align="right">4</td><td align="right">4</td><td align="right">4</td><td align="right">4</td></tr> +</tbody> +</table></div> + +<p>The last line of figures shows the real distance of the +planet as determined from Kepler's law, the earth's mean +distance from the sun being taken as the unit for this purpose. +With exception of Neptune, the agreement between +Bode's law and the true distances is very striking, but most +remarkable is the presence in the series of a number, 2.8, +with no planet corresponding to it. This led astronomers +at the time Bode published the law, something more than +a century ago, to give new heed to a suggestion made long +before by Kepler, that there might be an unknown planet +moving between the orbits of Mars and Jupiter, and a number +of them agreed to search for such a planet, each in a +part of the sky assigned him for that purpose. But they +were anticipated by Piazzi, an Italian, who found the new +planet, by accident, on the first day of the nineteenth century, +moving at a distance from the sun represented by the +number 2.77.<span class="pagenum"><a name="Page_215" id="Page_215">[Pg 215]</a></span></p> + +<p>This planet was the first of the asteroids, and in the +century that has elapsed hundreds of them have been discovered, +while at the present time no year passes by without +several more being added to the number. While some +of these are nearer to the sun than is the first one discovered, +and others are farther from it, their average distance +is fairly represented by the number 2.8.</p> + +<p>Why Bode's law should hold true, or even so nearly +true as it does, is an unexplained riddle, and many astronomers +are inclined to call it no law at all, but only a chance +coincidence—an illustration of the "inherent capacity of +figures to be juggled with"; but if so, it is passing strange +that it should represent the distance of the asteroids and +of Uranus, which was also an undiscovered planet at the +time the law was published.</p> + +<p><a name="S_135" id="S_135"></a>135. <b>The planets compared with each other.</b>—When we +pass from general considerations to a study of the individual +peculiarities of the planets, we find great differences +in the extent of knowledge concerning them, and the reason +for this is not far to seek. Neptune and Uranus, at the +outskirts of the solar system, are so remote from us and so +feebly illumined by the sun that any detailed study of them +can go but little beyond determining the numbers which +represent their size, mass, density, the character of their +orbits, etc. The asteroids are so small that in the telescope +they look like mere points of light, absolutely indistinguishable +in appearance from the fainter stars. Mercury, although +closer at hand and presenting a disk of considerable +size, always stands so near the sun that its observation is +difficult on this account. Something of the same kind is +true for Venus, although in much less degree; while Mars, +Jupiter, and Saturn are comparatively easy objects for telescopic +study, and our knowledge of them, while far from +complete, is considerably greater than for the other planets.</p> + +<p>Figs. <a href="#Fig_84">84</a> and <a href="#Fig_85">85</a> show the relative sizes of the planets +composing the inner and outer groups respectively, and furnish +<span class="pagenum"><a name="Page_216" id="Page_216">[Pg 216]</a></span> +the numerical data concerning their diameters, masses, +densities, etc., which are of most importance in judging of +their physical condition. Each planet, save Saturn, is +represented by two circles, of which the outer is drawn +proportional to the size of the planet, and the inner shows +the amount of material that must be subtracted from the +interior in order that the remaining shell shall just float in +water. Note the great difference in thickness of shell +between the two groups. Saturn, having a mean density +less than that of water, must have something loaded upon +it, instead of removed, in order that it should float just +submerged.</p> + + +<h3><span class="smcap">Jupiter</span></h3> + +<p><a name="S_136" id="S_136"></a>136. <b>Appearance.</b>—Commencing our consideration of the +individual planets with Jupiter, which is by far the largest +of them, exceeding both in bulk and mass all the others +combined, we have in <a href="#Fig_86">Fig. 86</a> four representations of +Jupiter and his family of satellites as they may be seen in +a very small telescope—e. g., an opera glass—save that the +little dots which here represent the satellites are numbered +<i>1</i>, <i>2</i>, <i>3</i>, <i>4</i>, in order to preserve their identity in the successive +pictures.</p> + +<p>The chief interest of these pictures lies in the satellites, +but, reserving them for future consideration, we note that +the planet itself resembles in shape the full moon, although +in respect of brightness it sends to us less than 1/6000 part +as much light as the moon. From a consideration of the +motion of Jupiter and the earth in <a href="#Fig_16">Fig. 16</a>, show that +Jupiter can not present any such phases as does the moon, +but that its disk must be at all times nearly full. As seen +from Saturn, what kind of phases would Jupiter present?</p> + +<p><a name="S_137" id="S_137"></a>137. <b>The belts.</b>—Even upon the small scale of <a href="#Fig_86">Fig. 86</a> +we detect the most characteristic feature of Jupiter's appearance +in the telescope, the two bands extending across +his face parallel to the line of the satellites, and in <a href="#Fig_87">Fig. 87</a> +these same dark bands may be recognized amid the abundance<span class="pagenum"><a name="Page_217" id="Page_217">[Pg 217]</a></span> +of detail which is here brought out by a large telescope. +Photography does not succeed as a means of reproducing +this detail, and for it we have to rely upon the skill +of the artist astronomer. The lettering shows the Pacific +Standard time at which the sketches were made, and also +the longitude of the meridian of Jupiter passing down the +center of the planet's disk.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_86" id="Fig_86"></a> +<a href="images/i247-full.jpg"><img src="images/i247.jpg" width="500" height="353" alt="Fig. 86.—Jupiter and his satellites." title="Fig. 86.—Jupiter and his satellites." /></a> +<span class="caption"><span class="smcap">Fig. 86.</span>—Jupiter and his satellites.</span> +</div> + +<div class="figcenter" style="width: 500px;"><a name="Fig_87" id="Fig_87"></a> +<a href="images/i248.jpg"><img src="images/i248.jpg" width="500" height="826" alt="Fig. 87.—Drawings of Jupiter made at the 36-inch telescope of the Lick +Observatory.—Keeler." title="Fig. 87.—Drawings of Jupiter made at the 36-inch telescope of the Lick +Observatory.—Keeler." /></a> +<span class="caption"><span class="smcap">Fig. 87.</span>—Drawings of Jupiter made at the 36-inch telescope of the Lick +Observatory.—<span class="smcap">Keeler.</span></span> +</div> + +<p>The dark bands are called technically the belts of Jupiter; +and a comparison of these belts in the second and third +pictures of the group, in which nearly the same face of the +planet is turned toward us, will show that they are subject +to considerable changes of form and position even within +the space of a few days. So, too, by a comparison of such +markings as the round white spots in the upper parts of +the disks, and the indentations in the edges of the belts, +we may recognize that the planet is in the act of turning +round, and must therefore have an axis about which it +turns, and poles, an equator, etc. The belts are in fact +parallel to the planet's equator; and generalizing from what +appears in the pictures, we may say that there is always a +strongly marked belt on each side of the equator with a<span class="pagenum"><a name="Page_219" id="Page_219">[Pg 219]</a></span><span class="pagenum"><a name="Page_218" id="Page_218">[Pg 218]</a></span> +lighter colored streak between them, and that farther from +the equator are other belts variable in number, less conspicuous, +and less permanent than the two first seen. Compare +the position of the principal belts with the position of +the zones of sun-spot activity in the sun. A feature of +the planet's surface, which can not be here reproduced, is +the rich color effect to be found upon it. The principal +belts are a brick-red or salmon color, the intervening spaces +in general white but richly mottled, and streaked with +purples, browns, and greens.</p> + +<p>The drawings show the planet as it appeared in the +telescope, inverted, and they must be turned upside down +if we wish the points of the compass to appear as upon a +terrestrial map. Bearing this in mind, note in the last +picture the great oval spot in the southern hemisphere of +Jupiter. This is a famous marking, known from its color +as the <i>great red spot</i>, which appeared first in 1878 and has +persisted to the present day (1900), sometimes the most +conspicuous marking on the planet, at others reduced to a +mere ghost of itself, almost invisible save for the indentation +which it makes in the southern edge of the belt +near it.</p> + +<p><a name="S_138" id="S_138"></a>138. <b>Rotation and flattening at the poles.</b>—One further +significant fact with respect to Jupiter may be obtained +from a careful measurement of the drawings; the planet is +flattened at the poles, so that its polar diameter is about +one sixteenth part shorter than the equatorial diameter. +The flattening of the earth amounts to only one three-hundredth +part, and the marked difference between these +two numbers finds its explanation in the greater swiftness +of Jupiter's rotation about its axis, since in both cases it is +this rotation which makes the flattening.</p> + +<p>It is not easy to determine the precise dimensions of the +planet, since this involves a knowledge both of its distance +from us and of the angle subtended by its diameter, but +the most recent determinations of this kind assign as the<span class="pagenum"><a name="Page_220" id="Page_220">[Pg 220]</a></span> +equatorial diameter 90,200 miles, and for the polar diameter +84,400 miles. Determine from either of these numbers +the size of the great red spot.</p> + +<p>The earth turns on its axis once in 24 hours but no +such definite time can be assigned to Jupiter, which, like +the sun, seems to have different rotation periods in different +latitudes—9h. 50m. in the equatorial belt and 9h. 56m. +in the dark belts and higher latitudes. There is some indication +that the larger part of the visible surface rotates in +9h. 55.6m., while a broad stream along the equator flows +eastward some 270 miles per hour, and thus comes back to +the center of the planet, as seen from the earth, five or six +minutes earlier than the parts which do not share in this +motion. Judged by terrestrial standards, 270 miles per +hour is a great velocity, but Jupiter is constructed on a +colossal scale, and, too, we have to compare this movement, +not to a current flowing in the ocean, but to a wind blowing +in the upper regions of the earth's atmosphere. The +visible surface of Jupiter is only the top of a cloud formation, +and contains nothing solid or permanent, if indeed +there is anything solid even at the core of the planet. The +great red spot during the first dozen years of its existence, +instead of remaining fixed relative to the surrounding formations, +drifted two thirds of the way around the planet, +and having come to a standstill about 1891, it is now slowly +retracing its path.</p> + +<p><a name="S_139" id="S_139"></a>139. <b>Physical condition.</b>—For a better understanding of +the physical condition of Jupiter, we have now to consider +some independent lines of evidence which agree in pointing +to the conclusion that Jupiter, although classed with +the earth as a planet, is in its essential character much +more like the sun.</p> + +<p><i>Appearance.</i>—The formations which we see in <a href="#Fig_87">Fig. 87</a> +look like clouds. They gather and disappear, and the only +element of permanence about them is their tendency to +group themselves along zones of latitude. If we measure<span class="pagenum"><a name="Page_221" id="Page_221">[Pg 221]</a></span> +the light reflected from the planet we find that its albedo +is very high, like that of snow or our own cumulus clouds, +and it is of course greater from the light parts of the disk +than from the darker bands. The spectroscope shows that +the sunlight reflected from these darker belts is like that +reflected from the lighter parts, save that a larger portion of +the blue and violet rays has been absorbed out of it, thus +producing the ruddy tint of the belts, as sunset colors are +produced on the earth, and showing that here the light has +penetrated farther into the planet's atmosphere before +being thrown back by reflection from lower-lying cloud surfaces. +The dark bands are therefore to be regarded as rifts +in the clouds, reaching down to some considerable distance +and indicating an atmosphere of great depth. The great +red spot, 28,000 miles long, and obviously thrusting back +the white clouds on every side of it, year after year, can +hardly be a mere patch on the face of the planet, but indicates +some considerable depth of atmosphere.</p> + +<p><i>Density.</i>—So, too, the small mean density of the planet, +only 1.3 times that of water and actually less than the density +of the sun, suggests that the larger part of the planet's +bulk may be made of gases and clouds, with very little solid +matter even at the center; but here we get into a difficulty +from which there seems but one escape. The force of +gravity at the visible surface of Jupiter may be found +from its mass and dimensions to be 2.6 times as great as +at the surface of the earth, and the pressure exerted upon +its atmosphere by this force ought to compress the lower +strata into something more dense than we find in the +planet. Some idea of this compression may be obtained +from <a href="#Fig_88">Fig. 88</a>, where the line marked <i>E</i> shows approximately +how the density of the air increases as we move from its +upper strata down toward the surface of the earth through +a distance of 16 miles, the density at any level being proportional +to the distance of the curved line from the straight +one near it. The line marked <i>J</i> in the same figure shows<span class="pagenum"><a name="Page_222" id="Page_222">[Pg 222]</a></span> +how the density would increase if the force of gravity were +as great here as it is in Jupiter, and indicates a much +greater rate of increase. Starting from the upper surface +of the cloud in Jupiter's atmosphere, if we descend, +not 16 miles, but 1,600 or 16,000, what must the density +of the atmosphere become and how is this to be +reconciled with what we know to be the very small +mean density of the planet?</p> + +<p>We are here in a dilemma between density on the +one hand and the effects of gravity on the other, and +the only escape from it lies in the assumption that +the interior of Jupiter is tremendously hot, and that +this heat expands the substance of the planet in spite +of the pressure to which it is subject, making a large +planet with a low density, possibly gaseous at +the very center, but in its outer part surrounded +by a shell of clouds condensed +from the gases by +radiating their heat into +the cold of outer space.</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_88" id="Fig_88"></a> +<img src="images/i252.png" width="350" height="477" alt="Fig. 88.—Increase of density in the atmospheres +of Jupiter and the earth." title="Fig. 88.—Increase of density in the atmospheres +of Jupiter and the earth." /> +<span class="caption"><span class="smcap">Fig. 88.</span>—Increase of density in the atmospheres +of Jupiter and the earth.</span> +</div> + +<p>This is essentially the +same physical condition +that we found for the sun, and we may add, as further +points of resemblance between it and Jupiter, that there +seems to be a circulation of matter from the hot interior of +the planet to its cooler surface that is more pronounced in +the southern hemisphere than in the northern, and that has +its periods of maximum and minimum activity, which, curiously +enough, seem to coincide with periods of maximum +and minimum sun-spot development. Of this, however, we +can not be entirely sure, since it is only in recent years that +it has been studied with sufficient care, and further observations +are required to show whether the agreement is +something more than an accidental and short-lived coincidence.</p> + +<p><i>Temperature.</i>—The temperature of Jupiter must, of<span class="pagenum"><a name="Page_223" id="Page_223">[Pg 223]</a></span> +course, be much lower than that of the sun, since the surface +which we see is not luminous like the sun's; but below +the clouds it is not improbable that Jupiter may be incandescent, +white hot, and it is surmised with some show of +probability that a little of its light escapes through the +clouds from time to time, and helps to produce the striking +brilliancy with which this planet shines.</p> + +<p><a name="S_140" id="S_140"></a>140. <b>The satellites of Jupiter.</b>—The satellites bear much +the same relation to Jupiter that the moon bears to the +earth, revolving about the planet in accordance with the +law of gravitation, and conforming to Kepler's three laws, +as do the planets in their courses about the sun. Observe in +<a href="#Fig_86">Fig. 86</a> the position of satellite No. <i>1</i> on the four dates, and +note how it oscillates back and forth from left to right of +Jupiter, apparently making a complete revolution in about +two days, while No. <i>4</i> moves steadily from left to right during +the entire period, and has evidently made only a fraction +of a revolution in the time covered by the pictures. +This quicker motion, of course, means that No. <i>1</i> is nearer +to Jupiter than No. <i>4</i>, and the numbers given to the satellites +show the order of their distances from the planet. +The peculiar way in which the satellites are grouped, always +standing nearly in a straight line, shows that their orbits +must lie nearly in the same plane, and that this plane, which +is also the plane of the planets' equator, is turned edgewise +toward the earth.</p> + +<p>These satellites enjoy the distinction of being the first +objects ever discovered with the telescope, having been +found by Galileo almost immediately after its invention, +<span class="smcap">A. D.</span> 1610. It is quite possible that before this time they +may have been seen with the naked eye, for in more recent +years reports are current that they have been seen under +favorable circumstances by sharp-eyed persons, and very +little telescopic aid is required to show them. Look for +them with an opera or field glass. They bear the names +Io, Europa, Ganymede, Callisto, which, however, are rarely<span class="pagenum"><a name="Page_224" id="Page_224">[Pg 224]</a></span> +used, and, following the custom of astronomers, we shall +designate them by the Roman numerals I, II, III, IV.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_89" id="Fig_89"></a> +<img src="images/i254.png" width="500" height="392" alt="Fig. 89.—Orbits of Jupiter's satellites." title="Fig. 89.—Orbits of Jupiter's satellites." /> +<span class="caption"><span class="smcap">Fig. 89.</span>—Orbits of Jupiter's satellites.</span> +</div> + +<p>For nearly three centuries (1610 to 1892) astronomers +spoke of the four satellites of Jupiter; but in September, +1892, a fifth one was added to the number by Professor Barnard, +who, observing with the largest telescope then extant, +found very close to Jupiter a tiny object only 1/600 part as +bright as the other satellites, but, like them, revolving around +Jupiter, a permanent member of his system. This is called +the fifth satellite, and <a href="#Fig_89">Fig. 89</a> shows the orbits of these satellites +around Jupiter, which is here represented on the same +scale as the orbits themselves. The broken line just inside +the orbit of I represents the size of the moon's orbit. The +cut shows also the periodic times of the satellites expressed +in days, and furnishes in this respect a striking illustration +of the great mass of Jupiter. Satellite I is a little<span class="pagenum"><a name="Page_225" id="Page_225">[Pg 225]</a></span> +farther from Jupiter than is the moon from the earth, but +under the influence of a greater attraction it makes the circuit +of its orbit in 1.77 days, instead of taking 29.53 days, +as does the moon. Determine from the figure by the method +employed in <a href="#S_111">§ 111</a> how much more massive is Jupiter than +the earth.</p> + +<p>Small as these satellites seem in <a href="#Fig_86">Fig. 86</a>, they are really +bodies of considerable size, as appears from <a href="#Fig_90">Fig. 90</a>, where +their dimensions are compared with those of the earth +and moon, save that the fifth satellite is not included. +This one is so small as to escape all attempts at measuring +its diameter, but, judging from the amount of light it reflects, +the period printed with the legend of the figure +represents a gross exaggeration of this satellite's size.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_90" id="Fig_90"></a> +<img src="images/i255.png" width="500" height="165" alt="Fig. 90.—Jupiter's satellites compared with the earth and moon." title="Fig. 90.—Jupiter's satellites compared with the earth and moon." /> +<span class="caption"><span class="smcap">Fig. 90.</span>—Jupiter's satellites compared with the earth and moon.</span> +</div> + +<p>Like the moon, each of these satellites may fairly be +considered a world in itself, and as such a fitting object of +detailed study, but, unfortunately, their great distance from +us makes it impossible, even with the most powerful telescope, +to see more upon their surfaces than occasional vague +markings, which hardly suffice to show the rotations of the +satellites upon their axes.</p> + +<p>One striking feature, however, comes out from a study +of their influence in disturbing each other's motion about +Jupiter. Their masses and the resulting densities of the +satellites are smaller than we should have expected to find, +the density being less than that of the moon, and averaging +only a little greater than the density of Jupiter<span class="pagenum"><a name="Page_226" id="Page_226">[Pg 226]</a></span> +itself. At the surface of the third satellite the force of +gravity is but little less than on the moon, although the +moon's density is nearly twice as great as that of III, and +there can be no question here of accounting for the low +density through expansion by great heat, as in the case of +the sun and Jupiter. It has been surmised that these satellites +are not solid bodies, like the earth and moon, but only +shoals of rock and stone, loosely piled together and kept +from packing into a solid mass by the action of Jupiter in +raising tides within them. But the explanation can hardly +be regarded as an accepted article of astronomical belief, +although it is supported by some observations which tend +to show that the apparent shapes of the satellites change under +the influence of the tidal forces impressed upon them.</p> + +<p><a name="S_141" id="S_141"></a>141. <b>Eclipses of the satellites.</b>—It may be seen from <a href="#Fig_89">Fig. 89</a> +that in their motion around the planet Jupiter's satellites +must from time to time pass through his shadow and be +eclipsed, and that the shadows of the satellites will occasionally +fall upon the planet, producing to an observer upon +Jupiter an eclipse of the sun, but to an observer on the earth +presenting only the appearance of a round black spot moving +slowly across the face of the planet. Occasionally also +a satellite will pass exactly between the earth and Jupiter, +and may be seen projected against the planet as a background. +All of these phenomena are duly predicted and +observed by astronomers, but the eclipses are the only ones +we need consider here. The importance of these eclipses +was early recognized, and astronomers endeavored to construct +a theory of their recurrence which would permit +accurate predictions of them to be made. But in this they +met with no great success, for while it was easy enough +to foretell on what night an eclipse of a given satellite +would occur, and even to assign the hour of the night, it +was not possible to make the predicted minute agree with +the actual time of eclipse until after Roemer, a Danish +astronomer of the seventeenth century, found where lay the<span class="pagenum"><a name="Page_227" id="Page_227">[Pg 227]</a></span> +trouble. His discovery was, that whenever the earth was +on the side of its orbit toward Jupiter the eclipses really +occurred before the predicted time, and when the earth +was on the far side of its orbit they came a few minutes +later than the predicted time. He correctly inferred that +this was to be explained, not by any influence which the +earth exerted upon Jupiter and his satellites, but through +the fact that the light by which we see the satellite and its +eclipse requires an appreciable time to cross the intervening +space, and a longer time when the earth is far from +Jupiter than when it is near.</p> + +<p>For half a century Roemer's views found little credence, +but we know now that he was right, and that on the +average the eclipses come 8m. 18s. early when the earth is +nearest to Jupiter, and 8m. 18s. late when it is on the opposite +side of its orbit. This is equivalent to saying that +light takes 8m. 18s. to cover the distance from the sun to +the earth, so that at any moment we see the sun not as it +then is, but as it was 8 minutes earlier. It has been found +possible in recent years to measure by direct experiment +the velocity with which light travels—186,337 miles per +second—and multiplying this number by the 498s. (= 8m. +18s.) we obtain a new determination of the sun's distance +from the earth. The product of the two numbers is +92,795,826, in very fair agreement with the 93,000,000 +miles found in <a href="#CHAPTER_X">Chapter X</a>; but, as noted there, this method, +like every other, has its weak side, and the result may be a +good many thousands of miles in error.</p> + +<p>It is worthy of note in this connection that both methods +of obtaining the sun's distance which were given in +<a href="#CHAPTER_X">Chapter X</a> involve Kepler's Third Law, while the result +obtained from Jupiter's satellites is entirely independent +of this law, and the agreement of the several results is +therefore good evidence both for the truth of Kepler's laws +and for the soundness of Roemer's explanation of the +eclipses. This mode of proof, by comparing the numerical<span class="pagenum"><a name="Page_228" id="Page_228">[Pg 228]</a></span> +results furnished by two or more different principles, and +showing that they agree or disagree, is of wide application +and great importance in physical science.</p> + + +<h3><span class="smcap">Saturn</span></h3> + +<div class="figleft" style="width: 350px;"><a name="Fig_91" id="FIg_91"></a> +<a href="images/i258-full.jpg"><img src="images/i258.jpg" width="350" height="492" alt="Fig. 91.—Aspects of Saturn's rings." title="Fig. 91.—Aspects of Saturn's rings." /></a> +<span class="caption"><span class="smcap">Fig. 91.</span>—Aspects of Saturn's rings.</span> +</div> + +<p><a name="S_142" id="S_142"></a>142. <b>The ring of Saturn.</b>—In respect of size and mass +Saturn stands next to Jupiter, and although far inferior to +him in these respects, it contains more material than all +the remaining planets combined. But the unique feature +of Saturn which distinguishes it from every other known +body in the heavens is +its ring, which was long +a puzzle to the astronomers +who first studied +the planet with a telescope +(one of them called +Saturn a planet with +ears), but, was after +nearly half a century +correctly understood and +described by Huyghens, +whose Latin text we +translate into—"It is +surrounded by a ring, +thin, flat, nowhere touching +it, and making quite +an angle with the ecliptic."</p> + +<p>Compare with this +description <a href="#Fig_91">Fig. 91</a>, which shows some of the appearances +presented by the ring at different positions of Saturn in +its orbit. It was their varying aspects that led Huyghens +to insert the last words of his description, for, if the plane +of the ring coincided with the plane of the earth's orbit, +then at all times the ring must be turned edgewise toward +the earth, as shown in the middle picture of the group.<span class="pagenum"><a name="Page_229" id="Page_229">[Pg 229]</a></span> +<a href="#Fig_92">Fig. 92</a> shows the sun and the orbit of the earth placed +near the center of Saturn's orbit, across whose circumference +are ruled some oblique lines representing the plane +of the ring, the right end always tilted up, no matter where +the planet is in its orbit. It is evident that an observer +upon the earth will see the <i>N</i> side of the ring when the +planet is at <i>N</i> and the <i>S</i> side when it is at <i>S</i>, as is shown +in the first and third pictures of <a href="#Fig_91">Fig. 91</a>, while midway between +these positions the edge of the ring will be presented +to the earth.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_92" id="Fig_92"></a> +<img src="images/i259.png" width="500" height="503" alt="Fig. 92.—Aspects of the ring in their relation to Saturn's orbital motion." title="Fig. 92.—Aspects of the ring in their relation to Saturn's orbital motion." /> +<span class="caption"><span class="smcap">Fig. 92.</span>—Aspects of the ring in their relation to Saturn's orbital motion.</span> +</div> + +<p>The last occasion of this kind was in October, 1891, and +with the large telescope of the Washburn Observatory the<span class="pagenum"><a name="Page_230" id="Page_230">[Pg 230]</a></span> +writer at that time saw Saturn without a trace of a ring +surrounding it. The ring is so thin that it disappears +altogether when turned edgewise. The names of the zodiacal +constellations are inserted in <a href="#Fig_92">Fig. 92</a> in their proper +direction from the sun, and from these we learn that the +ring will disappear, or be exceedingly narrow, whenever +Saturn is in the constellation Pisces or near the boundary +line between Leo and Virgo. It will be broad and show its +northern side when Saturn is in Scorpius or Sagittarius, and +its southern face when the planet is in Gemini. What will +be its appearance in 1907 at the date marked in the figure?</p> + +<p><a name="S_143" id="S_143"></a>143. <b>Nature of the ring.</b>—It is apparent from Figs. <a href="#Fig_91">91</a> +and <a href="#Fig_93">93</a> that Saturn's ring is really made up of two or more +rings lying one inside of the other and completely separated +by a dark space which, though narrow, is as clean and +sharp as if cut with a knife. Also, the inner edge of the +ring fades off into an obscure border called the <i>dusky ring</i> +or <i>crape ring</i>. This requires a pretty good telescope to +show it, as may be inferred from the fact that it escaped +notice for more than two centuries during which the planet +was assiduously studied with telescopes, and was discovered +at the Harvard College Observatory as recently as 1850.</p> + +<p>Although the rings appear oval in all of the pictures, +this is mainly an effect of perspective, and they are in fact +nearly circular with the planet at their center. The extreme +diameter of the ring is 172,000 miles, and from this +number, by methods already explained (<a href="#CHAPTER_IX">Chapter IX</a>), the +student should obtain the width of the rings, their distance +from the ball of the planet, and the diameter of the ball. +As to thickness, it is evident, from the disappearance of the +ring when its edge is turned toward the earth, that it is +very thin in comparison with its diameter, probably not +more than 100 miles thick, although no exact measurement +of this can be made.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_93" id="Fig_93"></a> +<a href="images/i261-full.jpg"><img src="images/i261.jpg" width="500" height="619" alt="Fig. 93.—Saturn." title="Fig. 93.—Saturn." /></a> +<span class="caption"><span class="smcap">Fig. 93.</span>—Saturn.</span> +</div> + +<p>From theoretical reasons based upon the law of gravitation +astronomers have held that the rings of Saturn could<span class="pagenum"><a name="Page_232" id="Page_232">[Pg 232]</a></span> +not possibly be solid or liquid bodies. The strains impressed +upon them by the planet's attraction would tear +into fragments steel rings made after their size and shape. +Quite recently Professor Keeler has shown, by applying the +spectroscope (Doppler's principle) to determine the velocity +of the ring's rotation about Saturn, that the inner parts of +the ring move, as Kepler's Third Law requires, more rapidly +than do the outer parts, thus furnishing a direct proof that +they are not solid, and leaving no doubt that they are made +up of separate fragments, each moving about the planet in +its own orbit, like an independent satellite, but standing so +close to its neighbors that the whole space reflects the sunlight +as completely as if it were solid. With this understanding +of the rings it is easy to see why they are so thin. +Like Jupiter, Saturn is greatly flattened at the poles, and +this flattening, or rather the protuberant mass about the +equator, lays hold of every satellite near the planet and +exerts upon it a direct force tending to thrust it down +into the plane of the planet's equator and hold it there. +The ring lies in the plane of Saturn's equator because each +particle is constrained to move there.</p> + +<p>The division of the ring into two parts, an outer and an +inner ring, is usually explained as follows: Saturn is surrounded +by a numerous brood of satellites, which by their +attractions produce perturbations in the material composing +the rings, and the dividing line between the outer and +inner rings falls at the place where by the law of gravitation +the perturbations would have their greatest effect. +The dividing line between the rings is therefore a narrow +lane, 2,400 miles wide, from which the fragments have been +swept clean away by the perturbing action of the satellites. +Less conspicuous divisions are seen from time to time in +other parts of the ring, where the perturbations, though +less, are still appreciable. But it is open to some question +whether this explanation is sufficient.</p> + +<p>The curious darkness of the inner or crape ring is easily<span class="pagenum"><a name="Page_233" id="Page_233">[Pg 233]</a></span> +explained. The particles composing it are not packed together +so closely as in the outer ring, and therefore reflect +less sunlight. Indeed, so sparsely strewn are the particles +in this ring that it is in great measure transparent to the +sunlight, as is shown by a recorded observation of one of the +satellites which was distinctly although faintly seen while +moving through the shadow of the dark ring, but disappeared +in total eclipse when it entered the shadow cast by +the bright ring.</p> + +<p><a name="S_144" id="S_144"></a>144. <b>The ball of Saturn.</b>—The ball of the planet is in +most respects a smaller copy of Jupiter. With an equatorial +diameter of 76,000 miles, a polar diameter of 69,000 +miles, and a mass 95 times that of the earth, its density +is found to be the least of any planet in the solar system, +only 0.70 of the density of water, and about one half as +great as is the density of Jupiter. The force of gravity at +its surface is only a little greater (1.18) than on the earth; +and this, in connection with the low density, leads, as in the +case of Jupiter, to the conclusion that the planet must be +mainly composed of gases and vapors, very hot within, but +inclosed by a shell of clouds which cuts off their glow from +our eyes.</p> + +<p>Like Jupiter in another respect, the planet turns very +swiftly upon its axis, making a revolution in 10 hours 14 +minutes, but up to the present it remains unknown whether +different parts of the surface have different rotation times.</p> + +<p><a name="S_145" id="S_145"></a>145. <b>The satellites.</b>—Saturn is attended by a family of +nine satellites, a larger number than belongs to any other +planet, but with one exception they are exceedingly small +and difficult to observe save with a very large telescope. +Indeed, the latest one is said to have been discovered in +1898 by means of the image which it impressed upon a +photographic plate, and it has never been <i>seen</i>.</p> + +<p>Titan, the largest of them, is distant 771,000 miles from +the planet and bears much the same relation to Saturn that +Satellite III bears to Jupiter, the similarity in distance, size<span class="pagenum"><a name="Page_234" id="Page_234">[Pg 234]</a></span> +and mass being rather striking, although, of course, the +smaller mass of Saturn as compared with Jupiter makes the +periodic time of Titan—15 days 23 hours—much greater +than that of III. Can you apply Kepler's Third Law to +the motion of Titan so as to determine from the data given +above, the time required for a particle at the outer or inner +edge of the ring to revolve once around Saturn?</p> + +<p>Japetus, the second satellite in point of size, whose distance +from Saturn is about ten times as great as the moon's +distance from the earth, presents the remarkable peculiarity +of being always brighter in one part of its orbit than +in another, three or four times as bright when west of +Saturn as when east of it. This probably indicates that, +like our own moon, the satellite turns always the same face +toward its planet, and further, that one side of the satellite +reflects the sunlight much better than the other side—i. e., +has a higher albedo. With these two assumptions it +is easily seen that the satellite will always turn toward +the earth one face when west, and the other face when +east of Saturn, and thus give the observed difference of +brightness.</p> + + +<h3><span class="smcap">Uranus and Neptune</span></h3> + +<p><a name="S_146" id="S_146"></a>146. <b>Chief characteristics.</b>—The two remaining large +planets are interesting chiefly as modern additions to the +known members of the sun's family. The circumstances +leading to the discovery of Neptune have been touched +upon in <a href="#CHAPTER_IV">Chapter IV</a>, and for Uranus we need only note +that it was found by accident in the year 1781 by William +Herschel, who for some time after the discovery considered +it to be only a comet. It was the first planet ever discovered, +all of its predecessors having been known from prehistoric +times.</p> + +<div class="figcenter" style="width: 500px;"><a name="WILLIAM_HERSCHEL" id="WILLIAM_HERSCHEL"></a> +<a href="images/i265-full.jpg"><img src="images/i265.jpg" width="500" height="693" alt="WILLIAM HERSCHEL (1738-1822)." title="WILLIAM HERSCHEL (1738-1822)." /></a> +<span class="caption">WILLIAM HERSCHEL (1738-1822).</span> +</div> + +<p>Uranus has four satellites, all of them very faint, which +present only one feature of special importance. Instead of +moving in orbits which are approximately parallel to the<span class="pagenum"><a name="Page_235" id="Page_235">[Pg 235]</a></span> +plane of the ecliptic, as do the satellites of the inner planets, +their orbit planes are tipped up nearly perpendicular to the +planes of the orbits of both Uranus and the earth. The +one satellite which Neptune possesses has the same peculiarity +in even greater degree, for its motion around the +planet takes place in the direction opposite to that in +which all the planets move around the sun, much as if the +orbit of the satellite had been tipped over through an angle +of 150°. Turn a watch face down and note how the hands +go round in the direction opposite to that in which they +moved before the face was turned through 180°.</p> + +<p>Both Uranus and Neptune are too distant to allow +much detail to be seen upon their surfaces, but the presence +of broad absorption bands in their spectra shows that +they must possess dense atmospheres quite different in constitution +from the atmosphere of the earth. In respect of +density and the force of gravity at their surfaces, they are +not very unlike Saturn, although their density is greater +and gravity less than his, leading to the supposition that +they are for the most part gaseous bodies, but cooler and +probably more nearly solid than either Jupiter or Saturn.</p> + +<p>Under favorable circumstances Uranus may be seen +with the naked eye by one who knows just where to look +for it. Neptune is never visible save in a telescope.</p> + +<p><a name="S_147" id="S_147"></a>147. <b>The inner planets.</b>—In sharp contrast with the giant +planets which we have been considering stands the group +of four inner planets, or five if we count the moon as an +independent body, which resemble each other in being all +small, dense, and solid bodies, which by comparison with +the great distances separating the outer planets may fairly +be described as huddled together close to the sun. Their +relative sizes are shown in <a href="#Fig_84">Fig. 84</a>, together with the numerical +data concerning size, mass, density, etc., which we +have already found important for the understanding of a +planet's physical condition.<span class="pagenum"><a name="Page_236" id="Page_236">[Pg 236]</a></span></p> + + +<h3><span class="smcap">Venus</span></h3> + +<div class="figcenter" style="width: 500px;"><a name="Fig_94" id="Fig_94"></a> +<a href="images/i268-full.jpg"><img src="images/i268.jpg" width="500" height="345" alt="Fig. 94.—The phases of Venus.—Antoniadi." title="Fig. 94.—The phases of Venus.—Antoniadi." /></a> +<span class="caption"><span class="smcap">Fig. 94.</span>—The phases of Venus.—<span class="smcap">Antoniadi.</span></span> +</div> + +<p><a name="S_148" id="S_148"></a>148. <b>Appearance.</b>—Omitting the earth, Venus is by far +the most conspicuous member of this group, and when at its +brightest is, with exception of the sun and moon, the most +brilliant object in the sky, and may be seen with the naked +eye in broad daylight if the observer knows just where to +look for it. But its brilliancy is subject to considerable +variations on account of its changing distance from the +earth, and the apparent size of its disk varies for the same +reason, as may be seen from <a href="#Fig_94">Fig. 94</a>. These drawings bring +out well the phases of the planet, and the student should +determine from <a href="#Fig_17">Fig. 17</a> what are the relative positions in +their orbits of the earth and Venus at which the planet +would present each of these phases. As a guide to this, +observe that the dark part of Venus's earthward side is +always proportional in area to the angle at Venus between +the earth and sun. In the first picture of <a href="#Fig_94">Fig. 94</a> about<span class="pagenum"><a name="Page_237" id="Page_237">[Pg 237]</a></span> +two thirds of the surface corresponding to the full hemisphere +of the planet is dark, and the angle at Venus +between earth and sun is therefore two thirds of 180°—i. e., +120°. In <a href="#Fig_17">Fig. 17</a> find a place on the orbit of Venus from +which if lines be drawn to the sun and earth, as there +shown, the angle between them will be 120°. Make a similar +construction for the fourth picture in <a href="#Fig_94">Fig. 94</a>. Which +of these two positions is farther from the earth? How do +the distances compare with the apparent size of Venus in +the two pictures? What is the phase of Venus to-day?</p> + +<p>The irregularities in the shading of the illuminated +parts of the disk are too conspicuous in <a href="#Fig_94">Fig. 94</a>, on account +of difficulties of reproduction; these shadings are at the +best hard to see in the telescope, and distinct permanent +markings upon the planet are wholly lacking. This absence +of markings makes almost impossible a determination of +the planet's time of rotation about its axis, and astronomers +are divided in this respect into two parties, one of +which maintains that Venus, like the earth, turns upon its +axis in some period not very different from 24 hours, while +the other contends that, like the moon, it turns always the +same face toward the center of its orbit, making a rotation +upon its axis in the same period in which it makes a revolution +about the sun. The reason why no permanent markings +are to be seen on this planet is easily found. Like +Jupiter and Saturn, its atmosphere is at all times heavily +cloud-laden, so that we seldom, if ever, see down to the +level of its solid parts. There is, however, no reason here +to suppose the interior parts hot and gaseous. It is much +more probable that Venus, like the earth, possesses a solid +crust whose temperature we should expect to be considerably +higher than that of the earth, because Venus is nearer +the sun. But the cloud layer in its atmosphere must modify +the temperature in some degree, and we have practically +no knowledge of the real temperature conditions at the +surface of the planet.<span class="pagenum"><a name="Page_238" id="Page_238">[Pg 238]</a></span></p> + +<p>It is the clouds of Venus which in great measure are +responsible for its marked brilliancy, since they are an excellent +medium for reflecting the sunlight, and give to its +surface an albedo greater than that of any other planet, +although Saturn is nearly equal to it.</p> + +<p>Of course, the presence of such cloud formations indicates +that Venus is surrounded by a dense atmosphere, and +we have independent evidence of this in the shape of its +disk when the planet is very nearly between the earth and +sun. The illuminated part, from tip to tip of the horns, +then stretches more than halfway around the planet's circumference, +and shows that a certain amount of light must +have been refracted through its atmosphere, thus making +the horns of the crescent appear unduly prolonged. This +atmosphere is shown by the spectroscope to be not unlike +that of the earth, although, possibly, more dense.</p> + + +<h3><span class="smcap">Mercury</span></h3> + +<p><a name="S_149" id="S_149"></a>149. <b>Chief characteristics.</b>—Mercury, on account of its +nearness to the sun, is at all times a difficult object to observe, +and Copernicus, who spent most of his life in Poland, +is said, despite all his efforts, to have gone to his grave without +ever seeing it. In our more southern latitude it can +usually be seen for about a fortnight at the time of each +elongation—i. e., when at its greatest angular distance from +the sun—and the student should find from <a href="#Fig_16">Fig. 16</a> the time +at which the next elongation occurs and look for the planet, +shining like a star of the first magnitude, low down in the +sky just after sunset or before sunrise, according as the +elongation is to the east or west of the sun. When seen in +the morning sky the planet grows brighter day after day +until it disappears in the sun's rays, while in the evening +sky its brilliancy as steadily diminishes until the planet is +lost. It should therefore be looked for in the evening as +soon as possible after it emerges from the sun's rays.</p> + +<p>Mercury, as the smallest of the planets, is best compared<span class="pagenum"><a name="Page_239" id="Page_239">[Pg 239]</a></span> +with the moon, which it does not greatly surpass in size +and which it strongly resembles in other respects. Careful +comparisons of the amount of light reflected by the planet +in different parts of its orbit show not only that its albedo +agrees very closely with that of the moon, but also that its +light changes with the varying phase of the planet in almost +exactly the same way as the amount of moonlight +changes. We may therefore infer that its surface is like +that of the moon, a rough and solid one, with few or no +clouds hanging over it, and most probably covered with +very little or no atmosphere. Like Venus, its rotation period +is uncertain, with the balance of probability favoring +the view that it rotates upon its axis once in 88 days, and +therefore always turns the same face toward the sun.</p> + +<p>If such is the case, its climate must be very peculiar: +one side roasted in a perpetual day, where the direct heating +power of the sun's rays, when the planet is at perihelion, +is ten times as great as on the moon, and which six weeks +later, when the planet is at its farthest from the sun, has +fallen off to less than half of this. On the opposite side of +the planet there must reign perpetual night and perpetual +cold, mitigated by some slight access of warmth from the +day side, and perhaps feebly imitating the rapid change of +season which takes place on the day side of the planet. +This view, however, takes no account of a possible deviation +of the planet's axis from being perpendicular to the +plane of its orbit, or of the librations which must be produced +by the great eccentricity of the orbit, either of which +would complicate without entirely destroying the ideal +conditions outlined above.</p> + + +<h3><span class="smcap">Mars</span></h3> + +<p><a name="S_150" id="S_150"></a>150. <b>Appearance.</b>—The one remaining member of the +inner group, Mars, has in recent years received more attention +than any other planet, and the newspapers and magazines +have announced marvelous things concerning it: that<span class="pagenum"><a name="Page_240" id="Page_240">[Pg 240]</a></span> +it is inhabited by a race of beings superior in intelligence +to men; that the work of their hands may be seen upon +the face of the planet; that we should endeavor to communicate +with them, if indeed they are not already sending +messages to us, etc.—all of which is certainly important, +if true, but it rests upon a very slender foundation of evidence, +a part of which we shall have to consider.</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_95" id="Fig_95"></a> +<a href="images/i272.jpg"><img src="images/i272.jpg" width="350" height="440" alt="Fig. 95.—Mars.—Schaeberle." title="Fig. 95.—Mars.—Schaeberle." /></a> +<span class="caption"><span class="smcap">Fig. 95.</span>—Mars.—<span class="smcap">Schaeberle.</span></span> +</div> + +<p>Beginning with facts of which there is no doubt, this +ruddy-colored planet, which usually shines about as brightly +as a star of the first magnitude, +sometimes displays +more than tenfold +this brilliancy, surpassing +every other planet +save Venus and presenting +at these times especially +favorable opportunities +for the study of +its surface. The explanation +of this increase +of brilliancy is, of course, +that the planet approaches +unusually near to the +earth, and we have already +seen from a consideration +of <a href="#Fig_17">Fig. 17</a> +that this can only happen +in the months of August and September. The last +favorable epoch of this kind was in 1894. From <a href="#Fig_17">Fig. 17</a> +the student should determine when the next one will +come.</p> + +<p><a href="#Fig_95">Fig. 95</a> presents nine drawings of the planet made at +one of the epochs of close approach to the earth, and shows +that its face bears certain faint markings which, though +inconspicuous, are fixed and permanent features of the +planet. The dark triangular projection in the lower half<span class="pagenum"><a name="Page_241" id="Page_241">[Pg 241]</a></span> +of the second drawing was seen and sketched by Huyghens, +1659 <span class="smcap">A. D.</span> In <a href="#Fig_96">Fig. 96</a> some of these markings are shown +much more plainly, but <a href="#Fig_95">Fig. 95</a> gives a better idea of their +usual appearance in the telescope.</p> + +<div class="figright" style="width: 350px;"><a name="Fig_96" id="Fig_96"></a> +<a href="images/i273.jpg"><img src="images/i273.jpg" width="350" height="385" alt="Fig. 96.—Four views of Mars differing 90° in +longitude.—Barnard." title="Fig. 96.—Four views of Mars differing 90° in +longitude.—Barnard." /></a> +<span class="caption"><span class="smcap">Fig. 96.</span>—Four views of Mars differing 90° in +longitude.—<span class="smcap">Barnard.</span></span> +</div> + +<p><a name="S_151" id="S_151"></a>151. <b>Rotation.</b>—It may be seen readily enough, from a +comparison of the first two sketches of <a href="#Fig_95">Fig. 95</a>, that the +planet rotates about an +axis, and from a more +extensive study it is +found to be very like +the earth in this respect, +turning once in +24h. 37m. around an +axis tipped from being +perpendicular to the +plane of its orbit about +a degree and a half +more than is the earth's +axis. Since it is this +inclination of the axis +which is the cause of +changing seasons upon +the earth, there must +be similar changes, +winter and summer, as well as day and night, upon Mars, +only each season is longer there than here in the same proportion +that its year is longer than ours—i e., nearly two +to one. It is summer in the northern hemisphere of Mars +whenever the sun, as seen from Mars, stands in that constellation +which is nearest the point of the sky toward +which the planet's axis points. But this axis points toward +the constellation Cygnus, and Alpha Cygni is the bright +star nearest the north pole of Mars. As Pisces is the +zodiacal constellation nearest to Cygnus, it must be summer +in the northern hemisphere of Mars when the sun is in +Pisces, or, turning the proposition about, it must be summer<span class="pagenum"><a name="Page_242" id="Page_242">[Pg 242]</a></span> +in the <i>southern</i> hemisphere of Mars when the planet, as +seen from the sun, lies in the direction of Pisces.</p> + +<p><a name="S_152" id="S_152"></a>152. <b>The polar caps.</b>—One effect of the changing seasons +upon Mars is shown in <a href="#Fig_97">Fig. 97</a>, where we have a series of +drawings of the region about its south pole made in 1894, +on dates between May 21st and December 10th. Show +from <a href="#Fig_17">Fig. 17</a> that during this time it was summer in the +region here shown. Mars crossed the prime radius in 1894 +on September 5th. The striking thing in these pictures is +the white spot surrounding the pole, which shrinks in size +from the beginning to +near the end of the series, +and then disappears +altogether. The spot +came back again a year +later, and like a similar +spot at the north pole of +the planet it waxes in the +winter and wanes during +the summer of Mars in +endless succession.</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_97" id="Fig_97"></a> +<a href="images/i274-full.jpg"><img src="images/i274.jpg" width="350" height="418" alt="Fig. 97.—The south polar cap of Mars in +1894.—Barnard." title="Fig. 97.—The south polar cap of Mars in +1894.—Barnard." /></a> +<span class="caption"><span class="smcap">Fig. 97.</span>—The south polar cap of Mars in +1894.—<span class="smcap">Barnard.</span></span> +</div> + +<p>Sir W. Herschel, who +studied these appearances +a century ago, compared +them with the snow +fields which every winter +spread out from the region +around the terrestrial +pole, and in the summer melt and shrink, although +with us they do not entirely disappear. This explanation of +the polar caps of Mars has been generally accepted among +astronomers, and from it we may draw one interesting conclusion: +the temperature upon Mars between summer and +winter oscillates above and below the freezing point of +water, as it does in the temperate zones of the earth. But +this conclusion plunges us into a serious difficulty. The<span class="pagenum"><a name="Page_243" id="Page_243">[Pg 243]</a></span> +temperature of the earth is made by the sun, and at the +distance of Mars from the sun the heating effect of the +latter is reduced to less than half what it is at the earth, +so that, if Mars is to be kept at the same temperature as +the earth, there must be some peculiar means for storing +the solar heat and using it more economically than is done +here. Possibly there is some such mechanism, although +no one has yet found it, and some astronomers are very +confident that it does not exist, and assert that the comparison +of the polar caps with snow fields is misleading, +and that the temperature upon Mars must be at least 100°, +and perhaps 200° or more, below zero.</p> + +<p><a name="S_153" id="S_153"></a>153. <b>Atmosphere and climate.</b>—In this connection one +feature of Mars is of importance. The markings upon its +surface are always visible when turned toward the earth, +thus showing that the atmosphere contains no such amount +of cloud as does our own, but on the whole is decidedly +clear and sunny, and presumably much less dense than +ours. We have seen in comparing the earth and the moon +how important is the service which the earth's atmosphere +renders in storing the sun's heat and checking those great +vicissitudes of temperature to which the moon is subject; +and with this in mind we must regard the smaller density +and cloudless character of the atmosphere of Mars as unfavorable +to the maintenance there of a temperature like +that of the earth. Indeed, this cloudlessness must mean +one of two things: either the temperature is so low that +vapors can not exist in any considerable quantity, or the +surface of Mars is so dry that there is little water or other +liquid to be evaporated. The latter alternative is adopted +by those astronomers who look upon the polar caps as true +snow fields, which serve as the chief reservoir of the planet's +water supply, and who find in <a href="#Fig_98">Fig. 98</a> evidence that as the +snow melts and the water flows away over the flat, dry surface +of the planet, vegetation springs up, as shown by the +dark markings on the disk, and gradually dies out with<span class="pagenum"><a name="Page_244" id="Page_244">[Pg 244]</a></span> +the advancing season. Note that in the first of these pictures +the season upon Mars corresponds to the end of May +with us, and in the last picture to the beginning of August, +a period during which in much of our western country the +luxuriant vegetation of spring is burned out by the scorching +sun. From this point of view the permanent dark +spots are the low-lying parts of the planet's surface, in +which at all times there is a sufficient accumulation of +water to support vegetable life.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_98" id="Fig_98"></a> +<a href="images/i276.jpg"><img src="images/i276.jpg" width="500" height="253" alt="Fig. 98.—The same face of Mars at three different seasons.—Lowell." title="Fig. 98.—The same face of Mars at three different seasons.—Lowell." /></a> +<span class="caption"><span class="smcap">Fig. 98.</span>—The same face of Mars at three different seasons.—<span class="smcap">Lowell.</span></span> +</div> + +<p><a name="S_154" id="S_154"></a>154. <b>The canals.</b>—In <a href="#Fig_98">Fig. 98</a> the lower part of the disk +of Mars shows certain faint dark lines which are generally +called canals, and in <a href="#PLATE_III">Plate III</a> there is given a map of Mars +showing many of these canals running in narrow, dusky +streaks across the face of the planet according to a pattern +almost as geometrical as that of a spider's web. This must +not be taken for a picture of the planet's appearance in a +telescope. No man ever saw Mars look like this, but the +map is useful as a plain representation of things dimly +seen. Some of the regions of this map are marked Mare +(sea), in accordance with the older view which regarded +the darker parts of the planet—and of the moon—as bodies +of water, but this is now known to be an error in both +cases. The curved surface of a planet can not be accurately +reproduced upon the flat surface of paper, but is always +more or less distorted by the various methods of "projecting" +it which are in use. Compare the map of Mars in<span class="pagenum"><a name="Page_245" id="Page_245">[Pg 245]</a></span> +<a href="#PLATE_III">Plate III</a> with <a href="#Fig_99">Fig. 99</a>, in which the projection represents +very well the equatorial parts of the planet, but enormously +exaggerates the region around the poles.</p> + +<p>It is a remarkable feature of the canals that they all +begin and end in one of these dark parts of the planet's +surface; they show no loose ends lying on the bright parts +of the planet. Another even more remarkable feature is +that while the larger canals are permanent features of the +planet's surface, they at times appear "doubled"—i. e., in +place of one canal two parallel ones side by side, lasting +for a time and then giving place again to a single canal.</p> + +<p>It is exceedingly difficult to frame any reasonable explanation +of these canals and the varied appearances which +they present. The source of the wild speculations about +Mars, to which reference is made above, is to be found in +the suggestion frequently made, half in jest and half in +earnest, that the canals are artificial water courses constructed +upon a scale vastly exceeding any public works +upon the earth, and testifying to the presence in Mars of +an advanced civilization. The distinguished Italian astronomer, +Schiaparelli, who has studied these formations +longer than any one else, seems inclined to regard them as +water courses lined on either side by vegetation, which +flourishes as far back from the central channel as water +can be supplied from it—a plausible enough explanation if +the fundamental difficulty about temperature can be overcome.</p> + +<div class="figcenter" style="width: 600px;"><a name="Fig_99" id="Fig_99"></a> +<img src="images/i278.jpg" width="600" height="308" alt="Fig. 99.—A chart of Mars, 1898-'99.—Cerulli." title="Fig. 99.—A chart of Mars, 1898-'99.—Cerulli." /> +<span class="caption"><span class="smcap">Fig. 99.</span>—A chart of Mars, 1898-'99.—<span class="smcap">Cerulli.</span></span> +</div> + +<div class="figcenter" style="width: 600px;"><a name="PLATE_III" id="PLATE_III"></a> +<a href="images/i279-full.jpg"><img src="images/i279.jpg" width="600" height="328" alt="PLATE III. + +MAP OF MARS + +(AFTER SCHIAPARELLI)" title="PLATE III. + +MAP OF MARS + +(AFTER SCHIAPARELLI)" /></a> +<span class="caption">PLATE III. + +MAP OF MARS + +(AFTER SCHIAPARELLI)</span> +</div> + +<p><a name="S_155" id="S_155"></a>155. <b>Satellites.</b>—In 1877, one of the times of near approach, +Professor Hall, of Washington, discovered two tiny +satellites revolving about Mars in orbits so small that the +nearer one, Phobos, presents the remarkable anomaly of +completing the circuit of its orbit in less time than the +planet takes for a rotation about its axis. This satellite, in +fact, makes three revolutions in its orbit while the planet +turns once upon its axis, and it therefore rises in the west +and sets in the east, as seen from Mars, going from one<span class="pagenum"><a name="Page_247" id="Page_247">[Pg 247]</a><a name="Page_246" id="Page_246"></a></span> +horizon to the other in a little less than 6 hours. The +other satellite, Deimos, takes a few hours more than a day +to make the circuit of its orbit, but the difference is so +small that it remains continuously above the horizon of +any given place upon Mars for more than 60 hours at a +time, and during this period runs twice through its complete +set of phases—new, first quarter, full, etc. In ordinary +telescopes these satellites can be seen only under especially +favorable circumstances, and are far too small to +permit of any direct measurement of their size. The +amount of light which they reflect has been compared +with that of Mars and found to be as much inferior to it +as is Polaris to two full moons, and, judging from this comparison, +their diameters can not much exceed a half dozen +miles, unless their albedo is far less than that of Mars, +which does not seem probable.</p> + + +<h3><span class="smcap">The Asteroids</span></h3> + +<p><a name="S_156" id="S_156"></a>156. <b>Minor planets.</b>—These may be dismissed with few +words. There are about 500 of them known, all discovered +since the beginning of the nineteenth century, and new +ones are still found every year. No one pretends to +remember the names which have been assigned them, and +they are commonly represented by a number inclosed in a +circle, showing the order in which they were discovered—e. g., +➀ = Ceres, [circle 433] = Eros, etc. For the most part they +are little more than chips, world fragments, adrift in space, +and naturally it was the larger and brighter of them that +were first discovered. The size of the first four of them—Ceres, +Pallas, Juno, and Vesta—compared with the size of +the moon, according to Professor Barnard, is shown in <a href="#Fig_100">Fig. 100</a>. +The great majority of them must be much smaller +than the smallest of these, perhaps not more than a score +of miles in diameter.</p> + +<p>A few of the asteroids present problems of special interest, +such as Eros, on account of its close approach to the<span class="pagenum"><a name="Page_248" id="Page_248">[Pg 248]</a></span> +earth; Polyhymnia, whose very eccentric orbit makes it a +valuable means for determining the mass of Jupiter, etc.; +but these are special cases and the average asteroid now +receives scant attention, although half a century ago, when +only a few of them were known, they were regarded with +much interest, and the discovery of a new one was an event +of some consequence.</p> + +<p>It was then a favorite speculation that they were in fact +fragments of an ill-fated planet which once filled the gap +between the orbits of Mars +and Jupiter, but which, by +some mischance, had been +blown into pieces. This is +now known to be well-nigh +impossible, for every fragment +which after the explosion +moved in an elliptical +orbit, as all the asteroids do +move, would be brought +back once in every revolution +to the place of the explosion, +and all the asteroid +orbits must therefore intersect +at this place. But there is no such common point of +intersection.</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_100" id="Fig_100"></a> +<img src="images/i282.png" width="350" height="343" alt="Fig. 100.—The size of the first four +asteroids.—Barnard." title="Fig. 100.—The size of the first four +asteroids.—Barnard." /> +<span class="caption"><span class="smcap">Fig. 100.</span>—The size of the first four +asteroids.—<span class="smcap">Barnard.</span></span> +</div> + +<p><a name="S_157" id="S_157"></a>157. <b>Life on the planets.</b>—There is a belief firmly +grounded in the popular mind, and not without its advocates +among professional astronomers, that the planets +are inhabited by living and intelligent beings, and it seems +proper at the close of this chapter to inquire briefly how +far the facts and principles here developed are consistent +with this belief, and what support, if any, they lend to it.</p> + +<p>At the outset we must observe that the word life is an +elastic term, hard to define in any satisfactory way, and yet +standing for something which we know here upon the +earth. It is this idea, our familiar though crude knowledge<span class="pagenum"><a name="Page_249" id="Page_249">[Pg 249]</a></span> +of life, which lies at the root of the matter. Life, if +it exists in another planet, must be in its essential character +like life upon the earth, and must at least possess +those features which are common to all forms of terrestrial +life. It is an abuse of language to say that life in Mars +may be utterly unlike life in the earth; if it is absolutely +unlike, it is not life, whatever else it may be. Now, every +form of life found upon the earth has for its physical basis +a certain chemical compound, called protoplasm, which +can exist and perpetuate itself only within a narrow range +of temperature, roughly speaking, between 0° and 100° +centigrade, although these limits can be considerably overstepped +for short periods of time. Moreover, this protoplasm +can be active only in the presence of water, or water +vapor, and we may therefore establish as the necessary conditions +for the continued existence and reproduction of +life in any place that its temperature must not be permanently +above 100° or below 0°, C., and water must be present +in that place in some form.</p> + +<p>With these conditions before us it is plain that life can +not exist in the sun on account of its high temperature. +It is conceivable that active and intelligent beings, salamanders, +might exist there, but they could not properly be said +to live. In Jupiter and Saturn the same condition of high +temperature prevails, and probably also in Uranus and +Neptune, so that it seems highly improbable that any of +these planets should be the home of life.</p> + +<p>Of the inner planets, Mercury and the moon seem destitute +of any considerable atmospheres, and are therefore +lacking in the supply of water necessary for life, and the +same is almost certainly true of all the asteroids. There +remain Venus, Mars, and the satellites of the outer planets, +which latter, however, we must drop from consideration as +being too little known. On Venus there is an atmosphere +probably containing vapor of water, and it is well within +the range of possibility that liquid water should exist upon<span class="pagenum"><a name="Page_250" id="Page_250">[Pg 250]</a></span> +the surface of this planet and that its temperature should +fall within the prescribed limits. It would, however, be +straining our actual knowledge to affirm that such is the +case, or to insist that if such were the case, life would necessarily +exist upon the planet.</p> + +<p>On Mars we encounter the fundamental difficulty of +temperature already noted in <a href="#S_152">§ 152</a>. If in some unknown +way the temperature is maintained sufficiently high for the +polar caps to be real snow, thawing and forming again with +the progress of the seasons, the necessary conditions of life +would seem to be fulfilled here and life if once introduced +upon the planet might abide and flourish. But of positive +proof that such is the case we have none.</p> + +<p>On the whole, our survey lends little encouragement to +the belief in planetary life, for aside from the earth, of all +the hundreds of bodies in the solar system, not one is found +in which the necessary conditions of life are certainly fulfilled, +and only two exist in which there is a reasonable +probability that these conditions may be satisfied.</p> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_251" id="Page_251">[Pg 251]</a></span></p> +<h2><a name="CHAPTER_XII" id="CHAPTER_XII"></a>CHAPTER XII</h2> + +<h3>COMETS AND METEORS</h3> + + +<p><a name="S_158" id="S_158"></a>158. <b>Visitors in the solar system.</b>—All of the objects—sun, +moon, planets, stars—which we have thus far had to +consider, are permanent citizens of the sky, and we have no +reason to suppose that their present appearance differs appreciably +from what it was 1,000 years or 10,000 years ago. +But there is another class of objects—comets, meteors—which +appear unexpectedly, are visible for a time, and then +vanish and are seen no more. On account of this temporary +character the astronomers of ancient and medięval times +for the most part refused to regard them as celestial bodies +but classed them along with clouds, fogs, Jack-o'-lanterns, +and fireflies, as exhalations from the swamps or the volcano; +admitting them to be indeed important as harbingers +of evil to mankind, but having no especial significance for +the astronomer.</p> + +<p>The comet of 1618 <span class="smcap">A. D.</span> inspired the lines—</p> + +<div class="poem"><div class="stanza"> +<span class="i0">"Eight things there be a Comet brings,<br /></span> +<span class="i1">When it on high doth horrid range:<br /></span> +<span class="i0">Wind, Famine, Plague, and Death to Kings,<br /></span> +<span class="i1">War, Earthquakes, Floods, and Direful Change,"<br /></span> +</div></div> + +<p>which, according to White (History of the Doctrine of +Comets), were to be taught in all seriousness to peasants +and school children.</p> + +<p>It was by slow degrees, and only after direct measurements +of parallax had shown some of them to be more distant +than the moon, that the tide of old opinion was turned +and comets were transferred from the sublunary to the<span class="pagenum"><a name="Page_252" id="Page_252">[Pg 252]</a></span> +celestial sphere, and in more recent times meteors also +have been recognized as coming to us from outside the +earth. A meteor, or shooting star as it is often called, is +one of the commonest of phenomena, and one can hardly +watch the sky for an hour on any clear and moonless night +without seeing several of those quick flashes of light which +look as if some star had suddenly left its place, dashed +swiftly across a portion of the sky and then vanished. It +is this misleading appearance that probably is responsible +for the name shooting star.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_101" id="Fig_101"></a> +<a href="images/i286.jpg"><img src="images/i286.jpg" width="500" height="362" alt="Fig. 101.—Donati's comet.—Bond." title="Fig. 101.—Donati's comet.—Bond." /></a> +<span class="caption"><span class="smcap">Fig. 101.</span>—Donati's comet.—<span class="smcap">Bond.</span></span> +</div> + +<p><a name="S_159" id="S_159"></a>159. <b>Comets.</b>—Comets are less common and much longer-lived +than meteors, lasting usually for several weeks, and +may be visible night after night for many months, but +never for many years, at a time. During the last decade +there is no year in which less than three comets have +appeared, and 1898 is distinguished by the discovery of +ten of these bodies, the largest number ever found in +one year. On the average, we may expect a new comet to<span class="pagenum"><a name="Page_253" id="Page_253">[Pg 253]</a></span> +be found about once in every ten weeks, but for the most +part they are small affairs, visible only in the telescope, and +a fine large one, like Donati's comet of 1858 (<a href="#Fig_101">Fig. 101</a>), or +the Great Comet of September, +1882, which was visible in +broad daylight close beside the +sun, is a rare spectacle, and as +striking and impressive as it +is rare.</p> + +<div class="figright" style="width: 300px;"><a name="Fig_102" id="Fig_102"></a> +<a href="images/i287.jpg"><img src="images/i287.jpg" width="300" height="455" alt="Fig. 102.—Some famous comets." title="Fig. 102.—Some famous comets." /></a> +<span class="caption"><span class="smcap">Fig. 102.</span>—Some famous comets.</span> +</div> + +<p>Note in <a href="#Fig_102">Fig. 102</a> the great +variety of aspect presented +by some of the more famous +comets, which are here represented +upon a very small scale.</p> + +<p><a href="#Fig_103">Fig. 103</a> is from a photograph +of one of the faint +comets of the year 1893, which +appears here as a rather feeble +streak of light amid the stars +which are scattered over the +background of the picture. +An apparently detached portion of this comet is shown at +the extreme left of the picture, looking almost like another +independent comet. The clean, straight line running diagonally +across the picture is the flash of a bright meteor +that chanced to pass within the range of the camera while +the comet was being photographed.</p> + + +<div class="figleft" style="width: 350px;"><a name="Fig_103" id="Fig_103"></a> +<a href="images/i288-full.jpg"><img src="images/i288.jpg" width="350" height="397" alt="Fig. 103.—Brooks's comet, November 13, 1893. +Barnard." title="Fig. 103.—Brooks's comet, November 13, 1893. Barnard." /></a> +<span class="caption"><span class="smcap">Fig. 103.</span>—Brooks's comet, November 13, 1893. +<span class="smcap">Barnard.</span></span> +</div> + + +<p>A more striking representation of a moderately bright +telescopic comet is contained in Figs. <a href="#Fig_104">104</a> and <a href="#Fig_105">105</a>, which +present two different views of the same comet, showing a +considerable change in its appearance. A striking feature +of <a href="#Fig_105">Fig. 105</a> is the star images, which are here drawn out into +short lines all parallel with each other. During the exposure +of 2h. 20m. required to imprint this picture upon the +photographic plate, the comet was continually changing its +position among the stars on account of its orbital motion,<span class="pagenum"><a name="Page_254" id="Page_254">[Pg 254]</a></span> +and the plate was therefore moved from time to time, so as +to follow the comet and make its image always fall at the +same place. Hence the plate was continually shifted relative +to the stars whose images, drawn out into lines, show +the direction in which the plate was moved—i. e., the direction +in which the comet was moving across the sky. The +same effect is shown in the other photographs, but less +conspicuously than here on account of their shorter exposure +times.</p> + +<p>These pictures all show that one end of the comet is +brighter and apparently more dense than the other, and it +is customary to call +this bright part the +<i>head</i> of the comet, +while the brushlike +appendage that +streams away from +it is called the +comet's <i>tail</i>.</p> + +<p><a name="S_160" id="S_160"></a>160. <b>The parts +of a comet.</b>—It is +not every comet +that has a tail, +though all the +large ones do, and +in <a href="#Fig_103">Fig. 103</a> the detached +piece of +cometary matter at +the left of the +picture represents +very well the appearance of a tailless comet, a rather large +but not very bright star of a fuzzy or hairy appearance. +The word comet means long-haired or hairy star. Something +of this vagueness of outline is found in all comets, +whose exact boundaries are hard to define, instead of being +sharp and clean-cut like those of a planet or satellite. +<span class="pagenum"><a name="Page_255" id="Page_255">[Pg 255]</a></span> +Often, however, there is found in the head of a comet a +much more solid appearing part, like the round white ball +at the center of <a href="#Fig_106">Fig. 106</a>, which is called the nucleus of +the comet, and appears to be in some sort the center from +which its activities radiate. As shown in Figs. <a href="#Fig_106">106</a> and <a href="#Fig_107">107</a>, +the nucleus is sometimes surrounded by what are +called envelopes, which have the appearance of successive +wrappings or halos placed about it, and odd, spurlike projections, +called jets, are sometimes found in connection +with the envelopes or in place of them. These figures also +show what is quite a common characteristic of large +comets, a dark streak running down the axis of the tail, +showing that the tail is hollow, a mere shell surrounding +empty space.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_104" id="Fig_104"></a> +<a href="images/i289-full.jpg"><img src="images/i289.jpg" width="500" height="520" alt="Fig. 104.—Swift's comet, April 17, 1892.—Barnard." title="Fig. 104.—Swift's comet, April 17, 1892.—Barnard." /></a> +<span class="caption"><span class="smcap">Fig. 104.</span>—Swift's comet, April 17, 1892.—<span class="smcap">Barnard.</span></span> +</div> + +<p>The amount of detail shown in Figs. <a href="#Fig_106">106</a> and <a href="#Fig_107">107</a> is, +however, quite exceptional, and the ordinary comet is much +more like Fig. <a href="#Fig_103">103</a> or <a href="#Fig_104">104</a>. Even a great comet when it<span class="pagenum"><a name="Page_256" id="Page_256">[Pg 256]</a></span> +first appears is not unlike the detached fragment in <a href="#Fig_103">Fig. 103</a>, +a faint and roundish patch of foggy light which grows +through successive stages to its maximum estate, developing +a tail, nucleus, envelopes, etc., only to lose them again +as it shrinks and finally disappears.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_105" id="Fig_105"></a> +<a href="images/i290-full.jpg"><img src="images/i290.jpg" width="500" height="445" alt="Fig. 105.—Swift's comet, April 24, 1892.—Barnard." title="Fig. 105.—Swift's comet, April 24, 1892.—Barnard." /></a> +<span class="caption"><span class="smcap">Fig. 105.</span>—Swift's comet, April 24, 1892.—<span class="smcap">Barnard.</span></span> +</div> + +<p><a name="S_161" id="S_161"></a>161. <b>The orbits of comets.</b>—It will be remembered that +Newton found, as a theoretical consequence of the law of +gravitation, that a body moving under the influence of the +sun's attraction might have as its orbit any one of the +conic sections, ellipse, parabola, or hyperbola, and among +the 400 and more comet orbits which have been determined +every one of these orbit forms appears, but curiously +enough there is not a hyperbola among them which, if +drawn upon paper, could be distinguished by the unaided +eye from a parabola, and the ellipses are all so long and +narrow, not one of them being so nearly round as is the +most eccentric planet orbit, that astronomers are accustomed +to look upon the parabola as being the normal type<span class="pagenum"><a name="Page_257" id="Page_257">[Pg 257]</a></span> +of comet orbit, and to regard a comet whose motion differs +much from a parabola as being abnormal and calling for +some special explanation.</p> + +<div class="figright" style="width: 350px;"><a name="Fig_106" id="Fig_106"></a> +<a href="images/i291-full.jpg"><img src="images/i291.jpg" width="350" height="504" alt="Fig. 106.—Head of Coggia's comet, +July 13, 1874.—Trouvelot." title="Fig. 106.—Head of Coggia's comet, +July 13, 1874.—Trouvelot." /></a> +<span class="caption"><span class="smcap">Fig. 106.</span>—Head of Coggia's comet, +July 13, 1874.—<span class="smcap">Trouvelot.</span></span> +</div> + +<p>The fact that comet orbits are parabolas, or differ but +little from them, explains at once the temporary character +and speedy disappearance +of these bodies. They +are visitors to the solar +system and visible for +only a short time, because +the parabola in which +they travel is not a closed +curve, and the comet, having +passed once along +that portion of it near the +earth and the sun, moves +off along a path which +ever thereafter takes it +farther and farther away, +beyond the limit of visibility. +The development +of the comet during the +time it is visible, the +growth and disappearance +of tail, nucleus, etc., depend upon its changing distance +from the sun, the highest development and most complex +structure being presented when it is nearest to the sun.</p> + +<p><a href="#Fig_108">Fig. 108</a> shows the path of the Great Comet of 1882 +during the period in which it was seen, from September 3, +1882, to May 26, 1883. These dates—IX, 3, and V, 26—are +marked in the figure opposite the parts of the orbit in +which the comet stood at those times. Similarly, the positions +of the earth in its orbit at the beginning of September, +October, November, etc., are marked by the Roman +numerals IX, X, XI, etc. The line <i>S V</i> shows the direction +from the sun to the vernal equinox, and <i>S</i> Ω is the line<span class="pagenum"><a name="Page_258" id="Page_258">[Pg 258]</a></span> +along which the plane of the comet's orbit intersects the +plane of the earth's orbit—i. e., it is the line of nodes of the +comet orbit. Since the comet approached the sun from +the south side of the ecliptic, all of its orbit, save the little +segment which falls to the left of <i>S</i> Ω, lies below (south) of +the plane of the earth's orbit, and the part which would +be hidden if this plane were opaque is represented by a +broken line.</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_107" id="Fig_107"></a> +<a href="images/i292-full.jpg"><img src="images/i292.jpg" width="350" height="496" alt="Fig. 107.—Head of Donati's comet, September +30, October 2, 1858.—Bond." title="Fig. 107.—Head of Donati's comet, September +30, October 2, 1858.—Bond." /></a> +<span class="caption"><span class="smcap">Fig. 107.</span>—Head of Donati's comet, September +30, October 2, 1858.—<span class="smcap">Bond.</span></span> +</div> + +<p><a name="S_162" id="S_162"></a>162. <b>Elements of a comet's orbit.</b>—There is a theorem of +geometry to the effect that through any three points not +in the same straight line one circle, and only one, can be +drawn. Corresponding to this there is a theorem of celestial +mechanics, that through any three positions of a comet +one conic section, and +only one, can be passed +along which the comet +can move in accordance +with the law of gravitation. +This conic section +is, of course, its orbit, and +at the discovery of a comet +astronomers always +hasten to observe its position +in the sky on different +nights in order to +obtain the three positions +(right ascensions and declinations) +necessary for +determining the particular +orbit in which it +moves. The circle, to +which reference was made +above, is completely ascertained +and defined when we know its radius and the +position of its center. A parabola is not so simply defined, +and five numbers, called the <i>elements</i> of its orbit, are<span class="pagenum"><a name="Page_259" id="Page_259">[Pg 259]</a></span> +required to fix accurately a comet's path around the sun. +Two of these relate to the position of the line of nodes and +the angle which the orbit plane makes with the plane of the +ecliptic; a third fixes the direction of the axis of the orbit +in its plane, and the remaining two, which are of more +interest to us, are the date at which the comet makes its +nearest approach to the sun (<i>perihelion passage</i>) and its +distance from the sun at that date (<i>perihelion distance</i>). +The date, September 17th, placed near the center of <a href="#Fig_108">Fig. 108</a>, +is the former of these elements, while the latter, which +is too small to be accurately measured here, may be found +from <a href="#Fig_109">Fig. 109</a> to be 0.82 of the sun's diameter, or, in terms +of the earth's distance from the sun, 0.008.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_108" id="Fig_108"></a> +<img src="images/i293.png" width="500" height="402" alt="Fig. 108.—Orbits of the earth and the +Great Comet of 1882." title="Fig. 108.—Orbits of the earth and the +Great Comet of 1882." /> +<span class="caption"><span class="smcap">Fig. 108.</span>—Orbits of the earth and the +Great Comet of 1882.</span> +</div> + +<p><a href="#Fig_109">Fig. 109</a> shows on a large scale the shape of that part of +the orbit near the sun and gives the successive positions of +the comet, at intervals of 2/10 of a day, on September 16th +and 17th, showing that in less than 10 hours—17.0 to 17.4—the +comet swung around the sun through an angle of<span class="pagenum"><a name="Page_260" id="Page_260">[Pg 260]</a></span> +more than 240°. When at its perihelion it was moving +with a velocity of 300 miles per second! This very unusual +velocity was due to the comet's extraordinarily close approach +to the sun. The earth's velocity in its orbit is only +19 miles per second, and the velocity of any comet at any +distance from the sun, provided its orbit is a parabola, may +be found by dividing this number by the square root of +half the comet's distance—e. g., 300 miles per second equals +19 ÷ √ 0.004.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_109" id="Fig_109"></a> +<img src="images/i294.png" width="500" height="390" alt="Fig. 109.—Motion of the Great Comet of 1883 in passing around the sun." title="Fig. 109.—Motion of the Great Comet of 1883 in passing around the sun." /> +<span class="caption"><span class="smcap">Fig. 109.</span>—Motion of the Great Comet of 1883 in passing around the sun.</span> +</div> + +<p>Most of the visible comets have their perihelion distances +included between 1/3 and 4/3 of the earth's distance +from the sun, but occasionally one is found, like the +second comet of 1885, whose nearest approach to the sun +lies far outside the earth's orbit, in this case half-way +out to the orbit of Jupiter; but such a comet must be a +very large one in order to be seen at all from the earth.<span class="pagenum"><a name="Page_261" id="Page_261">[Pg 261]</a></span> +There is, however, some reason for believing that the number +of comets which move around the sun without ever +coming inside the orbit of Jupiter, or even that of Saturn, +is much larger than the number of those which come close +enough to be discovered from the earth. In any case we +are reminded of Kepler's saying, that comets in the sky are +as plentiful as fishes in the sea, which seems to be very little +exaggerated when we consider that, according to Kleiber, +out of all the comets which enter the solar system probably +not more than 2 or 3 per cent are ever discovered.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_110" id="Fig_110"></a> +<a href="images/i295-full.jpg"><img src="images/i295.jpg" width="500" height="393" alt="Fig. 110.—The Great Comet of 1843." title="Fig. 110.—The Great Comet of 1843." /></a> +<span class="caption"><span class="smcap">Fig. 110.</span>—The Great Comet of 1843.</span> +</div> + +<p><a name="S_163" id="S_163"></a>163. <b>Dimensions of comets.</b>—The comet whose orbit is +shown in Figs. <a href="#Fig_108">108</a> and <a href="#Fig_109">109</a> is the finest and largest that +has appeared in recent years. Its tail, which at its maximum +extent would have more than bridged the space between +sun and earth (100,000,000 miles), is made very much +too short in <a href="#Fig_109">Fig. 109</a>, but when at its best was probably not +inferior to that of the Great Comet of 1843, shown in <a href="#Fig_110">Fig. 110</a>.<span class="pagenum"><a name="Page_262" id="Page_262">[Pg 262]</a></span> +As we shall see later, there is a peculiar and special +relationship between these two comets.</p> + +<p>The head of the comet of 1882 was not especially large—about +twice the diameter of the ball of Saturn—but its +nucleus, according to an estimate made by Dr. Elkin when +it was very near perihelion, was as large as the moon. The +head of the comet shown in <a href="#Fig_107">Fig. 107</a> was too large to be +put in the space between the earth and the moon, and the +Great Comet of 1811 had a head considerably larger than +the sun itself. From these colossal sizes down to the +smallest shred just visible in the telescope, comets of all +dimensions may be found, but the smaller the comet the +less the chance of its being discovered, and a comet as small +as the earth would probably go unobserved unless it approached +very close to us.</p> + +<p><a name="S_164" id="S_164"></a>164. <b>The mass of a comet.</b>—There is no known case in +which the mass of a comet has ever been measured, yet +nothing about them is more sure than that they are bodies +with mass which is attracted by the sun and the planets, +and which in its turn attracts both sun and planets and +produces perturbations in their motion. These perturbations +are, however, too small to be measured, although the +corresponding perturbations in the comet's motion are +sometimes enormous, and since these mutual perturbations +are proportional to the masses of comet and planet, we are +forced to say that, by comparison with even such small +bodies as the moon or Mercury, the mass of a comet is +utterly insignificant, certainly not as great as a ten-thousandth +part of the mass of the earth. In the case of the +Great Comet of 1882, if we leave its hundred million miles +of tail out of account and suppose the entire mass condensed +into its head, we find by a little computation that the average +density of the head under these circumstances must +have been less than 1/1500 of the density of air. In +ordinary laboratory practice this would be called a pretty +good vacuum.<span class="pagenum"><a name="Page_263" id="Page_263">[Pg 263]</a></span> + +A striking observation made on September 17, 1882, +goes to confirm the very small density of this comet. It +is shown in <a href="#Fig_109">Fig. 109</a> that early on that day the comet +crossed the line joining earth and sun, and therefore passed +in transit over the sun's disk. Two observers at the Cape +of Good Hope saw the comet approach the sun, and followed +it with their telescopes until the nucleus actually +reached the edge of the sun and disappeared, behind it as +they supposed, for no trace of the comet, not even its +nucleus, could be seen against the sun, although it was carefully +looked for. Now, the figure shows that the comet +passed between the earth and sun, and its densest parts +were therefore too attenuated to cut off any perceptible +fraction of the sun's rays. In other cases stars have been +seen through the head of a comet, shining apparently with +undimmed luster, although in some cases they seem to +have been slightly refracted out of their true positions.</p> + +<p><a name="S_165" id="S_165"></a>165. <b>Meteors.</b>—Before proceeding further with the study +of comets it is well to turn aside and consider their humbler +relatives, the shooting stars. On some clear evening, +when the moon is absent from the sky, watch the heavens +for an hour and count the meteors visible during that time. +Note their paths, the part of the sky where they appear +and where they disappear, their brightness, and whether +they all move with equal swiftness. Out of such simple +observations with the unaided eye there has grown a large +and important branch of astronomical science, some parts +of which we shall briefly summarize here.</p> + +<p>A particular meteor is a local phenomenon seen over +only a small part of the earth's surface, although occasionally +a very big and bright one may travel and be visible +over a considerable territory. Such a one in December, +1876, swept over the United States from Kansas to Pennsylvania, +and was seen from eleven different States. But the +ordinary shooting star is much less conspicuous, and, as we +know from simultaneous observations made at neighboring<span class="pagenum"><a name="Page_264" id="Page_264">[Pg 264]</a></span> +places, it makes its appearance at a height of some 75 miles +above the earth's surface, occupies something like a second +in moving over its path, and then disappears at a height +of about 50 miles or more, although occasionally a big one +comes down to the very surface of the earth with force +sufficient to bury itself in the ground, from which it may +be dug up, handled, weighed, and turned over to the chemist +to be analyzed. The pieces thus found show that the +big meteors, at least, are masses of stone or mineral; iron +is quite commonly found in them, as are a considerable +number of other terrestrial substances combined in rather +peculiar ways. But no chemical element not found on the +earth has ever been discovered in a meteor.</p> + +<p><a name="S_166" id="S_166"></a>166. <b>Nature of meteors.</b>—The swiftness with which the +meteors sweep down shows that they must come from outside +the earth, for even half their velocity, if given to them +by some terrestrial volcano or other explosive agent, would +send them completely away from the earth never to return. +We must therefore look upon them as so many projectiles, +bullets, fired against the earth from some outside source +and arrested in their motion by the earth's atmosphere, +which serves as a cushion to protect the ground from the +bombardment which would otherwise prove in the highest +degree dangerous to both property and life. The speed of +the meteor is checked by the resistance which the atmosphere +offers to its motion, and the energy represented by +that speed is transformed into heat, which in less than a +second raises the meteor and the surrounding air to incandescence, +melts the meteor either wholly or in part, and +usually destroys its identity, leaving only an impalpable +dust, which cools off as it settles slowly through the lower +atmosphere to the ground. The heating effect of the air's +resistance is proportional to the square of the meteor's +velocity, and even at such a moderate speed as 1 mile per +second the effect upon the meteor is the same as if it stood +still in a bath of red-hot air. Now, the actual velocity of<span class="pagenum"><a name="Page_265" id="Page_265">[Pg 265]</a></span> +meteors through the air is often 30 or 40 times as great as +this, and the corresponding effect of the air in raising its +temperature is more than 1,000 times that of red heat. +Small wonder that the meteor is brought to lively incandescence +and consumed even in a fraction of a second.</p> + +<p><a name="S_167" id="S_167"></a>167. <b>The number of meteors.</b>—A single observer may +expect to see in the evening hours about one meteor every +10 minutes on the average, although, of course, in this +respect much irregularity may occur. Later in the night +they become more frequent, and after 2 <span class="smcap">A. M.</span> there are +about three times as many to be seen as in the evening +hours. But no one person can keep a watch upon the +whole sky, high and low, in front and behind, and experience +shows that by increasing the number of observers and +assigning to each a particular part of the sky, the total +number of meteors counted may be increased about five-fold. +So, too, the observers at any one place can keep an +effective watch upon only those meteors which come into the +earth's atmosphere within some moderate distance of their +station, say 50 or 100 miles, and to watch every part of that +atmosphere would require a large number of stations, estimated +at something more than 10,000, scattered systematically +over the whole face of the earth. If we piece together +the several numbers above considered, taking 14 as +a fair average of the hourly number of meteors to be seen +by a single observer at all hours of the night, we shall find +for the total number of meteors encountered by the earth +in 24 hours, 14 × 5 × 10,000 × 24 = 16,800,000. Without +laying too much stress upon this particular number, we +may fairly say that the meteors picked up by the earth +every day are to be reckoned by millions, and since they +come at all seasons of the year, we shall have to admit that +the region through which the earth moves, instead of being +empty space, is really a dust cloud, each individual particle +of dust being a prospective meteor.</p> + +<p>On the average these individual particles are very small<span class="pagenum"><a name="Page_266" id="Page_266">[Pg 266]</a></span> +and very far apart; a cloud of silver dimes each about 250 +miles from its nearest neighbor is perhaps a fair representation +of their average mass and distance from each other, +but, of course, great variations are to be expected both in the +size and in the frequency of the particles. There must be +great numbers of them that are too small to make shooting +stars visible to the naked eye, and such are occasionally +seen darting by chance across the field of view of a telescope.</p> + +<p><a name="S_168" id="S_168"></a>168. <b>The zodiacal light</b> is an effect probably due to the +reflection of sunlight from the myriads of these tiny meteors +which occupy the space inside the earth's orbit. It is a +faint and diffuse stream of light, something like the Milky +Way, which may be seen in the early evening or morning +stretching up from the sunrise or sunset point of the +horizon along the ecliptic and following its course for +many degrees, possibly around the entire circumference of +the sky. It may be seen at any season of the year, although +it shows to the best advantage in spring evenings and +autumn mornings. Look for it.</p> + +<p><a name="S_169" id="S_169"></a>169. <b>Great meteors.</b>—But there are other meteors, veritable +fireballs in appearance, far more conspicuous and imposing +than the ordinary shooting star. Such a one exploded +over the city of Madrid, Spain, on the morning of +February 10, 1896, giving in broad sunlight "a brilliant +flash which was followed ninety seconds later by a succession +of terrific noises like the discharge of a battery of +artillery." <a href="#Fig_111">Fig. 111</a> shows a large meteor which was seen +in California in the early evening of July 27, 1894, and +which left behind it a luminous trail or cloud visible for +more than half an hour.</p> + +<p>Not infrequently large meteors are found traveling +together, two or three or more in company, making their +appearance simultaneously as did the California meteor of +October 22, 1896, which is described as triple, the trio following +one another like a train of cars, and Arago cites an<span class="pagenum"><a name="Page_267" id="Page_267">[Pg 267]</a></span> +instance, from the year 1830, where within a short space of +time some forty brilliant meteors crossed the sky, all moving +in the same direction with a whistling noise and displaying +in their flight all the colors of the rainbow.</p> + +<p>The mass of great meteors such as these must be measured +in hundreds if not thousands of pounds, and stories +are current, although not +very well authenticated, of +even larger ones, many tons +in weight, having been found +partially buried in the ground. +Of meteors which have been +actually seen to fall from the +sky, the largest single fragment +recovered weighs about +500 pounds, but it is only a +fragment of the original meteor, +which must have been +much more massive before it +was broken up by collision +with the atmosphere.</p> + +<div class="figright" style="width: 300px;"><a name="Fig_111" id="Fig_111"></a> +<a href="images/i301-full.jpg"><img src="images/i301.jpg" width="300" height="562" alt="Fig. 111.—The California meteor of +July 27, 1894." title="Fig. 111.—The California meteor of +July 27, 1894." /></a> +<span class="caption"><span class="smcap">Fig. 111.</span>—The California meteor of +July 27, 1894.</span> +</div> + +<p><a name="S_170" id="S_170"></a>170. <b>The velocity of meteors.</b>—Every +meteor, big or +little, is subject to the law of +gravitation, and before it encounters +the earth must be +moving in some kind of orbit +having the sun at its focus, +the particular species of orbit—ellipse, parabola, hyperbola—depending +upon the velocity and direction of its motion. +Now, the direction in which a meteor is moving can be +determined without serious difficulty from observations of +its apparent path across the sky made by two or more observers, +but the velocity can not be so readily found, since +the meteors go too fast for any ordinary process of timing. +But by photographing one of them two or three times on<span class="pagenum"><a name="Page_268" id="Page_268">[Pg 268]</a></span> +the same plate, with an interval of only a tenth of a second +between exposures, Dr. Elkin has succeeded in showing, in +a few cases, that their velocities varied from 20 to 25 miles +per second, and must have been considerably greater than +this before the meteors encountered the earth's atmosphere. +This is a greater velocity than that of the earth in its orbit, +19 miles per second, as might have been anticipated, since +the mere fact that meteors can be seen at all in the evening +hours shows that some of them at least must travel considerably +faster than the earth, for, counting in the direction +of the earth's motion, the region of sunset and evening is +always on the rear side of the earth, and meteors in order +to strike this region must overtake it by their swifter +motion. We have here, in fact, the reason why meteors +are especially abundant in the morning hours; at this time +the observer is on the front side of the earth which catches +swift and slow meteors alike, while the rear is pelted only +by the swifter ones which follow it.</p> + +<p>A comparison of the relative number of morning and +evening meteors makes it probable that the average meteor +moves, relative to the sun, with a velocity of about 26 miles +per second, which is very approximately the average velocity +of comets when they are at the earth's distance from the +sun. Astronomers, therefore, consider meteors as well as +comets to have the parabola and the elongated ellipse as +their characteristic orbits.</p> + +<p><a name="S_171" id="S_171"></a>171. <b>Meteor showers</b>—<b>The radiant.</b>—There is evident +among meteors a distinct tendency for individuals, to the +number of hundreds or even hundreds of millions, to +travel together in flocks or swarms, all going the same way +in orbits almost exactly alike. This gregarious tendency is +made manifest not only by the fact that from time to time +there are unusually abundant meteoric displays, but also +by a striking peculiarity of their behavior at such times. +The meteors all seem to come from a particular part of the +heavens, as if here were a hole in the sky through which<span class="pagenum"><a name="Page_269" id="Page_269">[Pg 269]</a></span> +they were introduced, and from which they flow away in +every direction, even those which do not visibly start from +this place having paths among the stars which, if prolonged +backward, would pass through it. The cause of this appearance +may be understood from <a href="#Fig_112">Fig. 112</a>, which represents +a group of meteors moving together along parallel +paths toward an observer at <i>D</i>. Traveling unseen above +the earth until they encounter the upper strata of its atmosphere, +they here become incandescent and speed on in +parallel paths, <i>1</i>, <i>2</i>, <i>3</i>, <i>4</i>, <i>5</i>, <i>6</i>, which, as seen by the observer, +are projected back against the sky into luminous streaks +that, as is shown by the arrowheads, <i>b</i>, <i>c</i>, <i>d</i>, all seem to +radiate from the point <i>a</i>—i. e., from the point in the sky +whose direction from the observer is parallel to the paths +of the meteors.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_112" id="Fig_112"></a> +<img src="images/i303.jpg" width="500" height="304" alt="Fig. 112.—Explanation of the radiant of a meteoric shower.—Denning." title="Fig. 112.—Explanation of the radiant of a meteoric shower.—Denning." /> +<span class="caption"><span class="smcap">Fig. 112.</span>—Explanation of the radiant of a meteoric shower.—<span class="smcap">Denning.</span></span> +</div> + +<p>Such a display is called a meteor shower, and the point +<i>a</i> is called its radiant. Note how those meteors which +appear near the radiant all have short paths, while those +remote from it in the sky have longer ones. Query: As +the night wears on and the stars shift toward the west, will<span class="pagenum"><a name="Page_270" id="Page_270">[Pg 270]</a></span> +the radiant share in their motion or will it be left behind? +Would the luminous part of the path of any of these meteors +pass across the radiant from one side to the other? +Is such a crossing of the radiant possible under any circumstances? +<a href="#Fig_113">Fig. 113</a> shows how the meteor paths are grouped +around the radiant of a strongly marked shower. Select +from it the meteors which do not belong to this shower.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_113" id="Fig_113"></a> +<img src="images/i304.jpg" width="500" height="429" alt="Fig. 113.—The radiant of a meteoric shower, showing also the paths of three meteors +which do not belong to this shower.—Denning." title="Fig. 113.—The radiant of a meteoric shower, showing also the paths of three meteors +which do not belong to this shower.—Denning." /> +<span class="caption"><span class="smcap">Fig. 113.</span>—The radiant of a meteoric shower, showing also the paths of three meteors +which do not belong to this shower.—<span class="smcap">Denning.</span></span> +</div> + +<p>Many hundreds of these radiants have been observed in +the sky, each of which represents an orbit along which a +group of meteors moves, and the relation of one of these<span class="pagenum"><a name="Page_271" id="Page_271">[Pg 271]</a></span> +orbits to that of the earth is shown in <a href="#Fig_114">Fig. 114</a>. The orbit +of the meteors is an ellipse extending out beyond the orbit +of Uranus, but so eccentric that a part of it comes inside +the orbit of the earth, and the figure shows only that part +of it which lies nearest the sun. The Roman numerals +which are placed along the earth's orbit show the position +of the earth at the beginning of the tenth month, eleventh +month, etc. The meteors flow along their orbit in a long +procession, whose direction of motion is indicated by the +arrow heads, and the earth, coming in the opposite direction, +plunges into this stream and receives the meteor +shower when it reaches the intersection of the two orbits. +The long arrow at the left of the figure represents the +direction of motion of another meteor shower which +encounters the earth at this point.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_114" id="Fig_114"></a> +<img src="images/i305.jpg" width="500" height="449" alt="Fig. 114.—The orbits of the earth and the November meteors." title="Fig. 114.—The orbits of the earth and the November meteors." /> +<span class="caption"><span class="smcap">Fig. 114.</span>—The orbits of the earth and the November meteors.</span> +</div> + +<p>Can you determine from the figure answers to the following +questions? On what day of the year will the earth +meet each of these showers? Will the radiant points of +the showers lie above or below the plane of the earth's<span class="pagenum"><a name="Page_272" id="Page_272">[Pg 272]</a></span> +orbit? Will these meteors strike the front or the rear of +the earth? Can they be seen in the evening hours?</p> + +<p>From many of the radiants year after year, upon the +same day or week in each year, there comes a swarm of +shooting stars, showing that there must be a continuous +procession of meteors moving along this orbit, so that some +are always ready to strike the earth whenever it reaches +the intersection of its orbit with theirs. Such is the explanation +of the shower which appears each year in the first +half of August, and whose meteors are sometimes called +Perseids, because their radiant lies in the constellation +Perseus, and a similar explanation holds for all the star +showers which are repeated year after year.</p> + +<p><a name="S_172" id="S_172"></a>172. <b>The Leonids.</b>—There is, however, a kind of star +shower, of which the Leonids (radiant in Leo) is the most +conspicuous type, in which the shower, although repeated +from year to year, is much more striking in some years +than in others. Thus, to quote from the historian: "In +1833 the shower was well observed along the whole eastern +coast of North America from the Gulf of Mexico to Halifax. +The meteors were most numerous at about 5 <span class="smcap">A. M.</span> on +November 13th, and the rising sun could not blot out all +traces of the phenomena, for large meteors were seen now and +then in full daylight. Within the scope that the eye could +contain, more than twenty could be seen at a time shooting +in every direction. Not a cloud obscured the broad expanse, +and millions of meteors sped their way across in every +point of the compass. Their coruscations were bright, +gleaming, and incessant, and they fell thick as the flakes in +the early snows of December." But, so far as is known, none +of them reached the ground. An illiterate man on the following +day remarked: "The stars continued to fall until +none were left. I am anxious to see how the heavens will +appear this evening, for I believe we shall see no more stars."</p> + +<p>An eyewitness in the Southern States thus describes +the effect of this shower upon the plantation negroes:<span class="pagenum"><a name="Page_273" id="Page_273">[Pg 273]</a></span> +"Upward of a hundred lay prostrate upon the ground, +some speechless and some with the bitterest cries, but with +their hands upraised, imploring God to save the world and +them. The scene was truly awful, for never did rain fall +much thicker than the meteors fell toward the earth—east, +west, north, and south it was the same." In the preceding +year a similar but feebler shower from the same radiant +created much alarm in France, and through the old historic +records its repetitions may be traced back at intervals of 33 +or 34 years, although with many interruptions, to October +12, 902, O. S., when "an immense number of falling stars +were seen to spread themselves over the face of the sky +like rain."</p> + +<p>Such a star shower differs from the one repeated every +year chiefly in the fact that its meteors, instead of being +drawn out into a long procession, are mainly clustered in a +single flock which may be long enough to require two or +three or four years to pass a given point of its orbit, but +which is far from extending entirely around it, so that meteors +from this source are abundant only in those years in +which the flock is at or near the intersection of its orbit +with that of the earth. The fact that the Leonid shower is +repeated at intervals of 33 or 34 years (it appeared in 1799, +1832-'33, 1866-'67) shows that this is the "periodic time" +in its orbit, which latter must of course be an ellipse, and +presumably a long and narrow one. It is this orbit which +is shown in <a href="#Fig_114">Fig. 114</a>, and the student should note in this +figure that if the meteor stream at the point where it cuts +through the plane of the earth's orbit were either nearer to +or farther from the sun than is the earth there could be no +shower; the earth and the meteors would pass by without a +collision. Now, the meteors in their motion are subject to +perturbations, particularly by the large planets Jupiter, +Saturn, and Uranus, which slightly change the meteor orbit, +and it seems certain that the changes thus produced will +sometimes thrust the swarm inside or outside the orbit of<span class="pagenum"><a name="Page_274" id="Page_274">[Pg 274]</a></span> +the earth, and thus cause a failure of the shower at times +when it is expected. The meteors were due at the crossing +of the orbits in November, 1899 and 1900, and, although a +few were then seen, the shower was far from being a brilliant +one, and its failure was doubtless caused by the outer +planets, which switched the meteors aside from the path in +which they had been moving for a century. Whether they +will be again switched back so as to produce future showers +is at the present time uncertain.</p> + +<p><a name="S_173" id="S_173"></a>173. <b>Capture of the Leonids.</b>—But a far more striking +effect of perturbations is to be found in <a href="#Fig_115">Fig. 115</a>, which +shows the relation of the Leonid orbit to those of the principal +planets, and illustrates a curious chapter in the history +of the meteor swarm that has been worked out by +mathematical analysis, and is probably a pretty good account +of what actually befell them. Early in the second +century of the Christian era this flock of meteors came +down toward the sun from outer space, moving along a +parabolic orbit which would have carried it just inside the +orbit of Jupiter, and then have sent it off to return no +more. But such was not to be its fate. As it approached +the orbit of Uranus, in the year 126 <span class="smcap">A. D.</span>, that planet +chanced to be very near at hand and perturbed the motion +of the meteors to such an extent that the character of their +orbit was completely changed into the ellipse shown in the +figure, and in this new orbit they have moved from that +time to this, permanent instead of transient members of +the solar system. The perturbations, however, did not end +with the year in which the meteors were captured and annexed +to the solar system, but ever since that time Jupiter, +Saturn, and Uranus have been pulling together upon the +orbit, and have gradually turned it around into its present +position as shown in the figure, and it is chiefly this shifting +of the orbit's position in the thousand years that have +elapsed since 902 <span class="smcap">A. D.</span> that makes the meteor shower now +come in November instead of in October as it did then.<span class="pagenum"><a name="Page_275" id="Page_275">[Pg 275]</a></span></p> + +<div class="figcenter" style="width: 600px;"><a name="Fig_115" id="Fig_115"></a> +<a href="images/i309.png"><img src="images/i309.png" width="600" height="363" alt="Fig. 115.—Supposed capture of the November meteors by Uranus." title="Fig. 115.—Supposed capture of the November meteors by Uranus." /></a> +<span class="caption"><span class="smcap">Fig. 115.</span>—Supposed capture of the November meteors by Uranus.</span> +</div><p><span class="pagenum"><a name="Page_276" id="Page_276">[Pg 276]</a></span></p> + +<p><a name="S_174" id="S_174"></a>174. <b>Breaking up a meteor swarm.</b>—How closely packed +together these meteors were at the time of their annexation +to the solar system is unknown, but it is certain that ever +since that time the sun has been exerting upon them a +tidal influence tending to break up the swarm and distribute +its particles around the orbit, as the Perseids are distributed, +and, given sufficient time, it will accomplish this, but +up to the present the work is only partly done. A certain +number of the meteors have gained so much over the slower +moving ones as to have made an extra circuit of the orbit +and overtaken the rear of the procession, so that there is a +thin stream of them extending entirely around the orbit +and furnishing in every November a Leonid shower; but by +far the larger part of the meteors still cling together, although +drawn out into a stream or ribbon, which, though +very thin, is so long that it takes some three years to pass +through the perihelion of its orbit. It is only when the +earth plunges through this ribbon, as it should in 1899, +1900, 1901, that brilliant Leonid showers can be expected.</p> + +<p><a name="S_175" id="S_175"></a>175. <b>Relation of comets and meteors.</b>—It appears from +the foregoing that meteors and comets move in similar orbits, +and we have now to push the analogy a little further +and note that in some instances at least they move in identically +the same orbit, or at least in orbits so like that an +appreciable difference between them is hardly to be found. +Thus a comet which was discovered and observed early in +the year 1866, moves in the same orbit with the Leonid +meteors, passing its perihelion about ten months ahead of +the main body of the meteors. If it were set back in its +orbit by ten months' motion, <i>it would be a part of the meteor +swarm</i>. Similarly, the Perseid meteors have a comet moving +in their orbit actually immersed in the stream of meteor +particles, and several other of the more conspicuous star +showers have comets attending them.</p> + +<p>Perhaps the most remarkable case of this character is +that of a shower which comes in the latter part of November<span class="pagenum"><a name="Page_277" id="Page_277">[Pg 277]</a></span> +from the constellation Andromeda, and which from its +association with the comet called Biela (after the name of +its discoverer) is frequently referred to as the Bielid shower. +This comet, an inconspicuous one moving in an unusually +small elliptical orbit, had been observed at various times +from 1772 down to 1846 without presenting anything remarkable +in its appearance; but about the beginning of the +latter year, with very little warning, it broke in two, and +for three months the pieces were watched by astronomers +moving off, side by side, something more than half as far +apart as are the earth and moon. It disappeared, made the +circuit of its orbit, and six years later came back, with the +fragments nearly ten times as far apart as before, and after +a short stay near the earth once more disappeared in the distance, +never to be seen again, although the fragments should +have returned to perihelion at least half a dozen times since +then. In one respect the orbit of the comet was remarkable: +it passed through the place in which the earth stands +on November 27th of each year, so that if the comet were at +that particular part of its orbit on any November 27th, a +collision between it and the earth would be inevitable. So +far as is known, no such collision with the comet has ever +occurred, but the Bielid meteors which are strung along +its orbit do encounter the earth on that date, in greater or +less abundance in different years, and are watched with +much interest by the astronomers who look upon them as +the final appearance of the <i>débris</i> of a worn-out comet.</p> + +<p><a name="S_176" id="S_176"></a>176. <b>Periodic comets.</b>—The Biela comet is a specimen of +the type which astronomers call periodic comets—i. e., +those which move in small ellipses and have correspondingly +short periodic times, so that they return frequently +and regularly to perihelion. The comets which accompany +the other meteor swarms—Leonids, Perseids, etc.—also belong +to this class as do some 30 or 40 others which have +periodic times less than a century. As has been already +indicated, these deviations from the normal parabolic orbit<span class="pagenum"><a name="Page_278" id="Page_278">[Pg 278]</a></span> +call for some special explanation, and the substance of that +explanation is contained in the account of the Leonid +meteors and their capture by Uranus. Any comet may be +thus captured by the attraction of a planet near which it +passes. It is only necessary that the perturbing action +of the planet should result in a diminution of the comet's +velocity, for we have already learned that it is this velocity +which determines the character of the orbit, and anything +less than the velocity appropriate to a parabola must produce +an ellipse—i. e., a closed orbit around which the body +will revolve time after time in endless succession. We +note in <a href="#Fig_115">Fig. 115</a> that when the Leonid swarm encountered +Uranus it passed <i>in front of</i> the planet and had its velocity +diminished and its orbit changed into an ellipse thereby. +It might have passed behind Uranus, it would have passed +behind had it come a little later, and the effect would then +have been just the opposite. Its velocity would have been +increased, its orbit changed to a hyperbola, and it would +have left the solar system more rapidly than it came into +it, thrust out instead of held in by the disturbing planet. +Of such cases we can expect no record to remain, but the +captured comet is its own witness to what has happened, +and bears imprinted upon its orbit the brand of the planet +which slowed down its motion. Thus in <a href="#Fig_115">Fig. 115</a> the changed +orbit of the meteors has its <i>aphelion</i> (part remotest from +the sun) quite close to the orbit of Uranus, and one of its +nodes, ℧, the point in which it cuts through the plane of +the ecliptic from north to south side, is also very near to +the same orbit. It is these two marks, aphelion and node, +which by their position identify Uranus as the planet instrumental +in capturing the meteor swarm, and the date of +the capture is found by working back with their respective +periodic times to an epoch at which planet and comet were +simultaneously near this node.</p> + +<p>Jupiter, by reason of his great mass, is an especially efficient +capturer of comets, and <a href="#Fig_116">Fig. 116</a> shows his group of<span class="pagenum"><a name="Page_279" id="Page_279">[Pg 279]</a></span> +captives, his family of comets as they are sometimes called. +The several orbits are marked with the names commonly +given to the comets. Frequently this is the name of their +discoverer, but often a different system is followed—e. g., +the name 1886, IV, means the fourth comet to pass through +perihelion in the year 1886. The other great planets—Saturn, +Uranus, Neptune—have also their families of captured +comets, and according to Schulhof, who does not +entirely agree with the common opinion about captured +comets, the earth has caught no less than nine of these +bodies.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_116" id="Fig_116"></a> +<a href="images/i313-full.jpg"><img src="images/i313.jpg" width="500" height="469" alt="Fig. 116.—Jupiter's family of comets." title="Fig. 116.—Jupiter's family of comets." /></a> +<span class="caption"><span class="smcap">Fig. 116.</span>—Jupiter's family of comets.</span> +</div> + +<p><a name="S_177" id="S_177"></a>177. <b>Comet groups.</b>—But there is another kind of comet +family, or comet group as it is called, which deserves some +notice, and which is best exemplified by the Great Comet of +1882 and its relatives. No less than four other comets are +known to be traveling in substantially the same orbit with<span class="pagenum"><a name="Page_280" id="Page_280">[Pg 280]</a></span> +this one, the group consisting of comets 1668, I; 1843, I; +1880, I; 1882, II; 1887, I. The orbit itself is not quite a +parabola, but a very elongated ellipse, whose major axis +and corresponding periodic time can not be very accurately +determined from the available data, but it certainly +extends far beyond the orbit of Neptune, and requires not +less than 500 years for the comet to complete a revolution +in it. It was for a time supposed that some one of the +recent comets of this group of five might be a return of +the comet of 1668 brought back ahead of time by unknown +perturbations. There is still a possibility of this, but it is +quite out of the question to suppose that the last four +members of the group are anything other than separate +and distinct comets moving in practically the same orbit. +This common orbit suggests a common origin for the +comets, but leaves us to conjecture how they became separated.</p> + +<p>The observed orbits of these five comets present some +slight discordances among themselves, but if we suppose +each comet to move in the average of the observed paths it +is a simple matter to fix their several positions at the present +time. They have all receded from the sun nearly on +line toward the bright star Sirius, and were all of them, at +the beginning of the year 1900, standing nearly motionless +inside of a space not bigger than the sun and distant from +the sun about 150 radii of the earth's orbit. The great +rapidity with which they swept through that part of their +orbit near the sun (see <a href="#S_162">§ 162</a>) is being compensated by +the present extreme slowness of their motions, so that +the comets of 1668 and 1882, whose passages through the +solar system were separated by an interval of more than +two centuries, now stand together near the aphelion of their +orbits, separated by a distance only 50 per cent greater than +the diameter of the moon's orbit, and they will continue +substantially in this position for some two or three centuries +to come.<span class="pagenum"><a name="Page_281" id="Page_281">[Pg 281]</a></span></p> + +<p>The slowness with which these bodies move when far +from the sun is strikingly illustrated by an equation of +celestial mechanics which for parabolic orbits takes the +place of Kepler's Third Law—viz.:</p> + +<p class="center"><i>r</i><sup>3</sup> / <i>T</i><sup>2</sup> = 178,</p> + +<p>where <i>T</i> is the time, in years, required for the comet to +move from its perihelion to any remote part of the orbit, +whose distance from the sun is represented, in radii of the +earth's orbit, by <i>r</i>. If the comet of 1668 had moved in a +parabola instead of the ellipse supposed above, how many +years would have been required to reach its present distance +from the sun?</p> + +<p><a name="S_178" id="S_178"></a>178. <b>Relation of comets to the solar system.</b>—The orbits +of these comets illustrate a tendency which is becoming +ever more strongly marked. Because comet orbits are +nearly parabolas, it used to be assumed that they were +exactly parabolic, and this carried with it the conclusion +that comets have their origin outside the solar system. It +may be so, and this view is in some degree supported by +the fact that these nearly parabolic orbits of both comets +and meteors are tipped at all possible angles to the plane +of the ecliptic instead of lying near it as do the orbits of +the planets; and by the further fact that, unlike the planets, +the comets show no marked tendency to move around their +orbits in the direction in which the sun rotates upon his +axis. There is, in fact, the utmost confusion among them +in this respect, some going one way and some another. +The law of the solar system (gravitation) is impressed upon +their movements, but its order is not.</p> + +<p>But as observations grow more numerous and more +precise, and comet orbits are determined with increasing +accuracy, there is a steady gain in the number of elliptic +orbits at the expense of the parabolic ones, and if comets +are of extraneous origin we must admit that a very considerable<span class="pagenum"><a name="Page_282" id="Page_282">[Pg 282]</a></span> +percentage of them have their velocities slowed +down within the solar system, perhaps not so much by the +attraction of the planets as by the resistance offered to their +motion by meteor particles and swarms along their paths. +A striking instance of what may befall a comet in this way +is shown in <a href="#Fig_117">Fig. 117</a>, where the tail of a comet appears +sadly distorted and broken by what is presumed to have +been a collision with a meteor swarm. A more famous case +of impeded motion is offered by the comet which bears the +name of Encke. This has a periodic time less than that of +any other known comet, and at intervals of forty months +comes back to perihelion, each time moving in a little +smaller orbit than before, unquestionably on account of +some resistance which it has suffered.</p> + +<div class="figcenter" style="width: 400px;"><a name="Fig_117" id="Fig_117"></a> +<a href="images/i316-full.jpg"><img src="images/i316.jpg" width="400" height="421" alt="Fig. 117.—Brooks's comet, October 21, 1893.—Barnard." title="Fig. 117.—Brooks's comet, October 21, 1893.—Barnard." /></a> +<span class="caption"><span class="smcap">Fig. 117.</span>—Brooks's comet, October 21, 1893.—<span class="smcap">Barnard.</span></span> +</div> + +<p><a name="S_179" id="S_179"></a>179. <b>The development of a comet.</b>—We saw in <a href="#S_174">§ 174</a> +that the sun's action upon a meteor swarm tends to +break it up into a long stream, and the same tendency to<span class="pagenum"><a name="Page_283" id="Page_283">[Pg 283]</a></span> +break up is true of comets whose attenuated substance presents +scant resistance to this force. According to the +mathematical analysis of Roche, if the comet stood still +the sun's tidal force would tend first to draw it out on line +with the sun, just as the earth's tidal force pulled the +moon out of shape (<a href="#S_42">§ 42</a>), and then it would cause the +lighter part of the comet's substance to flow away from +both ends of this long diameter. This destructive action +of the sun is not limited to comets and meteor streams, +for it tends to tear the earth and moon to pieces as well; +but the densities and the resulting mutual attractions of +their parts are far too great to permit this to be accomplished.</p> + +<p>As a curiosity of mathematical analysis we may note +that a spherical cloud of meteors, or dust particles weighing +a gramme each, and placed at the earth's distance from +the sun, will be broken up and dissipated by the sun's tidal +action if the average distance between the particles exceeds +two yards. Now, the earth is far more dense than such a +cloud, whose extreme tenuity, however, suggests what we +have already learned of the small density of comets, and +prepares us in their case for an outflow of particles at both +ends of the diameter directed toward the sun. Something +of this kind actually occurs, for the tail of a comet +streams out on the side opposite to the sun, and in general +points away from the sun, as is shown in <a href="#Fig_109">Fig. 109</a>, and the +envelopes and jets rise up toward the sun; but an inspection +of <a href="#Fig_106">Fig. 106</a> will show that the tail and the envelope +are too unlike to be produced by one and the same set of +forces.</p> + +<p>It was long ago suggested that the sun possibly exerts +upon a comet's substance a repelling force in addition to +the attracting force which we call gravity. We think naturally +in this connection of the repelling force which a +charge of electricity exerts upon a similar charge placed +on a neighboring body, and we note that if both sun and<span class="pagenum"><a name="Page_284" id="Page_284">[Pg 284]</a></span> +comet carried a considerable store of electricity upon their +surfaces this would furnish just such a repelling force as +seems indicated by the phenomena of comets' tails; for the +force of gravity would operate between the substance of +sun and comet, and on the whole would be the controlling +force, while the electric charges would produce a repulsion, +relatively feeble for the big particles and strong for the +little ones, since an electric charge lies wholly on the surface, +while gravity permeates the whole mass of a body, +and the ratio of volume (gravity) to surface (electric +charge) increases rapidly with increasing size. The repelling +force would thrust back toward the comet those particles +which flowed out toward the sun, while it would urge +forward those which flowed away from it, thus producing +the difference in appearance between tail and envelopes, +the latter being regarded from this standpoint as stunted +tails strongly curved backward. In recent years the Russian +astronomer Bredichin has made a careful study of the +shape and positions of comets' tails and finds that they fit +with mathematical precision to the theories of electric +repulsion.</p> + +<p><a name="S_180" id="S_180"></a>180. <b>Comet tails.</b>—According to Bredichin, a comet's +tail is formed by something like the following process: In +the head of the comet itself a certain part of its matter is +broken up into fine bits, single molecules perhaps, which, +as they no longer cling together, may be described as in +the condition of vapor. By the repellent action of both +sun and comet these molecules are cast out from the head +of the comet and stream away in the direction opposite to +the sun with different velocities, the heavy ones slowly and +the light ones faster, much as particles of smoke stream +away from a smokestack, making for the comet a tail +which like a trail of smoke is composed of constantly +changing particles. The result of this process is shown +in <a href="#Fig_118">Fig. 118</a>, where the positions of the comet in its orbit +on successive days are marked by the Roman numerals, and<span class="pagenum"><a name="Page_285" id="Page_285">[Pg 285]</a></span> +the broken lines represent the paths of molecules <i>m<sup>I</sup></i>, <i>m<sup>II</sup></i>, +<i>m<sup>III</sup></i>, etc., expelled from it on their several dates and traveling +thereafter in +orbits determined +by the combined +effect of the sun's +attraction, the +sun's repulsion, +and the comet's +repulsion. The +comet's attraction +(gravity) is +too small to be +taken into account. +The line +drawn upward +from <i>VI</i> represents +the positions +of these +molecules on the +sixth day, and +shows that all of +them are arranged +in a tail pointing +nearly away from the sun. A similar construction for the +other dates gives the corresponding positions of the tail, +always pointing away from the sun.</p> + +<div class="figright" style="width: 350px;"><a name="Fig_118" id="Fig_118"></a> +<img src="images/i319.png" width="350" height="462" alt="Fig. 118.—Formation of a comet's tail." title="Fig. 118.—Formation of a comet's tail." /> +<span class="caption"><span class="smcap">Fig. 118.</span>—Formation of a comet's tail.</span> +</div> + +<p>Only the lightest kind of molecules—e. g., hydrogen—could +drift away from the comet so rapidly as is here shown. +The heavier ones, such as carbon and iron, would be repelled +as strongly by the electric forces, but they would be +more strongly pulled back by the gravitative forces, thus +producing a much slower separation between them and the +head of the comet. Construct a figure such as the above, +in which the molecules shall recede from the comet only +one eighth as fast as in <a href="#Fig_118">Fig. 118</a>, and note what a different<span class="pagenum"><a name="Page_286" id="Page_286">[Pg 286]</a></span> +position it gives to the comet's tail. Instead of pointing +directly away from the sun, it will be bent strongly to one +side, as is the large plume-shaped tail of the Donati comet +shown in <a href="#Fig_101">Fig. 101</a>. But observe that this comet has also a +nearly straight tail, like the theoretical one of <a href="#Fig_118">Fig. 118</a>. +We have here two distinct types of comet tails, and according +to Bredichin there is still another but unusual type, +even more strongly bent to one side of the line joining +comet and sun, and appearing quite short and stubby. +The existence of these three types, and their peculiarities +of shape and position, are all satisfactorily accounted for +by the supposition that they are made of different materials. +The relative molecular weights of hydrogen, some of +the hydrocarbons, and iron, are such that tails composed +of these molecules would behave just as do the actual tails +observed and classified into these three types. The spectroscope +shows that these materials—hydrogen, hydrocarbons, +and iron—are present in comets, and leaves little +room for doubt of the essential soundness of Bredichin's +theory.</p> + +<p><a name="S_181" id="S_181"></a>181. <b>Disintegration of comets.</b>—We must regard the tail +as waste matter cast off from the comet's head, and although +the amount of this matter is very small, it must in some +measure diminish the comet's mass. This process is, of +course, most active at the time of perihelion passage, and +if the comet returns to perihelion time after time, as the +periodic ones which move in elliptic orbits must do, this +waste of material may become a serious matter, leading +ultimately to the comet's destruction. It is significant in +this connection that the periodic comets are all small and +inconspicuous, not one of them showing a tail of any considerable +dimensions, and it appears probable that they are +far advanced along the road which, in the case of Biela's +comet, led to its disintegration. Their fragments are in +part strewn through the solar system, making some small +fraction of its cloud of cosmic dust, and in part they have<span class="pagenum"><a name="Page_287" id="Page_287">[Pg 287]</a></span> +been carried away from the sun and scattered throughout +the universe along hyperbolic orbits impressed upon them +at the time they left the comet.</p> + +<p>But it is not through the tail only that the disintegrating +process is worked out. While Biela's comet is perhaps +the most striking instance in which the head has +broken up, it is by no means the only one. The Great +Comet of 1882 cast off a considerable number of fragments +which moved away as independent though small comets +and other more recent comets have been seen to do the +same. An even more striking phenomenon was the gradual +breaking up of the nucleus of the same comet, 1882, +II, into a half dozen nuclei arranged in line like beads +upon a string, and pointing along the axis of the tail. See +<a href="#Fig_119">Fig. 119</a>, which shows the series of changes observed in +the head of this comet.</p> + +<p><a name="S_182" id="S_182"></a>182. <b>Comets and the spectroscope.</b>—The spectrum presented +by comets was long a puzzle, and still retains something +of that character, although much progress has been +made toward an understanding of it. In general it consists +of two quite distinct parts—first, a faint background +of continuous spectrum due to ordinary sunlight reflected +from the comet; and, second, superposed upon this, three +bright bands like the carbon band shown at the middle of +<a href="#Fig_48">Fig. 48</a>, only not so sharply defined. These bands make a +discontinuous spectrum quite similar to that given off by +compounds of hydrogen and carbon, and of course indicate +that a part of the comet's light originates in the body +itself, which must therefore be incandescent, or at least +must contain some incandescent portions.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_119" id="Fig_119"></a> +<a href="images/i322-full.jpg"><img src="images/i322.jpg" width="500" height="787" alt="October 9, 1882. + +November 21, 1882. + +February 1, 1883. + +March 3, 1883. + +Fig. 119.—The head of the Great Comet of 1882.—Winlock." title="October 9, 1882. + +November 21, 1882. + +February 1, 1883. + +March 3, 1883. + +Fig. 119.—The head of the Great Comet of 1882.—Winlock." /></a> +<span class="caption"><span class="smcap">Fig. 119.</span>—The head of the Great Comet of 1882.—<span class="smcap">Winlock.</span></span> +</div> + +<p>By heating hydrocarbons in our laboratories until they +become incandescent, something like the comet spectrum +may be artificially produced, but the best approximation +to it is obtained by passing a disruptive electrical discharge +through a tube in which fragments of meteors +have been placed. A flash of lightning is a disruptive<span class="pagenum"><a name="Page_289" id="Page_289">[Pg 289]</a></span> +electrical discharge upon a grand scale. Now, meteors +and electric phenomena have been independently brought +to our notice in connection with comets, and with this +suggestion it is easy to frame a general idea of the physical +condition of these objects—for example, a cloud of +meteors of different sizes so loosely clustered that the +average density of the swarm is very low indeed; the several +particles in motion relative to each other, as well as to +the sun, and disturbed in that motion by the sun's tidal +action. Each particle carries its own electric charge, +which may be of higher or lower tension than that of its +neighbor, and is ready to leap across the intervening gap +whenever two particles approach each other. To these +conditions add the inductive effect of the sun's electric +charge, which tends to produce a particular and artificial +distribution of electricity among the comet's particles, and +we may expect to find an endless succession of sparks, tiny +lightning flashes, springing from one particle to another, +most frequent and most vivid when the comet is near the +sun, but never strong enough to be separately visible. +Their number is, however, great enough to make the comet +in part self-luminous with three kinds of light—i. e., the three +bright bands of its spectrum, whose wave lengths show in +the comet the same elements and compounds of the elements—carbon, +hydrogen, and oxygen—which chemical +analysis finds in the fallen meteor. It is not to be supposed +that these are the only chemical elements in the +comet, as they certainly are not the only ones in the meteor. +They are the easy ones to detect under ordinary circumstances, +but in special cases, like that of the Great +Comet of 1882, whose near approach to the sun rendered +its whole substance incandescent, the spectrum glows with +additional bright lines of sodium, iron, etc.</p> + +<p><a name="S_183" id="S_183"></a>183. <b>Collisions.</b>—A question sometimes asked, What +would be the effect of a collision between the earth and a +comet? finds its answer in the results reached in the preceding<span class="pagenum"><a name="Page_290" id="Page_290">[Pg 290]</a></span> +sections. There would be a star shower, more or +less brilliant according to the number and size of the pieces +which made up the comet's head. If these were like the +remains of the Biela comet, the shower might even be a +very tame one; but a collision with a great comet would +certainly produce a brilliant meteoric display if its head +came in contact with the earth. If the comet were built of +small pieces whose individual weights did not exceed a few +ounces or pounds, the earth's atmosphere would prove a +perfect shield against their attacks, reducing the pieces to +harmless dust before they could reach the ground, and +leaving the earth uninjured by the encounter, although the +comet might suffer sadly from it. But big stones in the +comet, meteors too massive to be consumed in their flight +through the air, might work a very different effect, and by +their bombardment play sad havoc with parts of the earth's +surface, although any such result as the wrecking of the +earth, or the destruction of all life upon it, does not seem +probable. The 40 meteors of <a href="#S_169">§ 169</a> may stand for a collision +with a small comet. Consult the Bible (Joshua x, 11) +for an example of what might happen with a larger one.</p> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_291" id="Page_291">[Pg 291]</a></span></p> +<h2><a name="CHAPTER_XIII" id="CHAPTER_XIII"></a>CHAPTER XIII</h2> + +<h3>THE FIXED STARS</h3> + + +<p><a name="S_184" id="S_184"></a>184. <b>The constellations.</b>—In the earlier chapters the student +has learned to distinguish between wandering stars +(planets) and those fixed luminaries which remain year after +year in the same constellation, shining for the most part +with unvarying brilliancy, and presenting the most perfect +known image of immutability. Homer and Job and prehistoric +man saw Orion and the Pleiades much as we see +them to-day, although the precession, by changing their +relation to the pole of the heavens, has altered their risings +and settings, and it may be that their luster has changed +in some degree as they grew old with the passing centuries.</p> + +<div class="figcenter" style="width: 600px;"><a name="Fig_120" id="Fig_120"></a> +<a href="images/i326-full.jpg"><img src="images/i326.jpg" width="600" height="414" alt="Fig. 120.—Illustrating the division of the sky into constellations." title="Fig. 120.—Illustrating the division of the sky into constellations." /></a> +<span class="caption"><span class="smcap">Fig. 120.</span>—Illustrating the division of the sky into constellations.</span> +</div> + +<p>The division of the sky into constellations dates back to +the most primitive times, long before the Christian era, +and the crooked and irregular boundaries of these constellations, +shown by the dotted lines in <a href="#Fig_120">Fig. 120</a>, such +as no modern astronomer would devise, are an inheritance +from antiquity, confounded and made worse in its +descent to our day. The boundaries assigned to constellations +near the south pole are much more smooth and regular, +since this part of the sky, invisible to the peoples from +whom we inherit, was not studied and mapped until more +modern times. The old traditions associated with each +constellation a figure, often drawn from classical mythology, +which was supposed to be suggested by the grouping +of the stars: thus Ursa Major is a great bear, stalking across +the sky, with the handle of the Dipper for his tail; Leo is a +lion; Cassiopeia, a lady in a chair; Andromeda, a maiden<span class="pagenum"><a name="Page_293" id="Page_293">[Pg 293]</a></span> +chained to a rock, etc.; but for the most part the resemblances +are far-fetched and quite too fanciful to be followed +by the ordinary eye.</p> + +<p><a name="S_185" id="S_185"></a>185. <b>The number of stars.</b>—"As numerous as the stars +of heaven" is a familiar figure of speech for expressing the +idea of countless number, but as applied to the visible +stars of the sky the words convey quite a wrong impression, +for, under ordinary circumstances, in a clear sky every star +to be seen may be counted in the course of a few hours, +since they do not exceed 3,000 or 4,000, the exact number +depending upon atmospheric conditions and the keenness +of the individual eye. Test your own vision by counting +the stars of the Pleiades. Six are easily seen, and you may +possibly find as many as ten or twelve; but however many +are seen, there will be a vague impression of more just beyond +the limit of visibility, and doubtless this impression is +partly responsible for the popular exaggeration of the number +of the stars. In fact, much more than half of what we +call starlight comes from stars which are separately too +small to be seen, but whose number is so great as to more +than make up for their individual faintness.</p> + +<p>The Milky Way is just such a cloud of faint stars, and +the student who can obtain access to a small telescope, or +even an opera glass, should not fail to turn it toward the +Milky Way and see for himself how that vague stream of +light breaks up into shining points, each an independent +star. These faint stars, which are found in every part of +the sky as well as in the Milky Way, are usually called +<i>telescopic</i>, in recognition of the fact that they can be seen +only in the telescope, while the other brighter ones are +known as <i>lucid stars</i>.</p> + +<p><a name="S_186" id="S_186"></a>186. <b>Magnitudes.</b>—The telescopic stars show among themselves +an even greater range of brightness than do the lucid +ones, and the system of magnitudes (<a href="#S_9">§ 9</a>) has accordingly +been extended to include them, the faintest star visible in +the greatest telescope of the present time being of the sixteenth<span class="pagenum"><a name="Page_294" id="Page_294">[Pg 294]</a></span> +or seventeenth magnitude, while, as we have already +learned, stars on the dividing line between the telescopic and +the lucid ones are of the sixth magnitude. To compare the +amount of light received from the stars with that from the +planets, and particularly from the sun and moon, it has +been found necessary to prolong the scale of magnitudes +backward into the negative numbers, and we speak of the +sun as having a stellar magnitude represented by the number +-26.5. The full moon's stellar magnitude is -12, and +the planets range from -3 (Venus) to +8 (Neptune). +Even a very few of the stars are so bright that negative +magnitudes must be used to represent their true relation +to the fainter ones. Sirius, for example, the brightest of +the fixed stars, is of the -1 magnitude, and such stars as +Arcturus and Vega are of the 0 magnitude.</p> + +<p>The relation of these magnitudes to each other has been +so chosen that a star of any one magnitude is very approximately +2.5 times as bright as one of the next fainter magnitude, +and this ratio furnishes a convenient method of +comparing the amount of light received from different stars. +Thus the brightness of Venus is 2.5 × 2.5 times that of +Sirius. The full moon is (2.5)<sup>9</sup> times as bright as Venus, +etc.; only it should be observed that the number 2.5 is not +exactly the value of the <i>light ratio</i> between two consecutive +magnitudes. Strictly this ratio is the <sup>5</sup>√ 100 = 2.5119+, +so that to be entirely accurate we must say that a difference +of five magnitudes gives a hundredfold difference of brightness. +In mathematical symbols, if <i>B</i> represents the ratio of +brightness (quantity of light) of two stars whose magnitudes +are <i>m</i> and <i>n</i>, then</p> + +<p class="center"><i>B</i> = (100)<sup>(<i>m</i>-<i>n</i>)/5</sup></p> + +<p>How much brighter is an ordinary first-magnitude star, +such as Aldebaran or Spica, than a star just visible to the +naked eye? How many of the faintest stars visible in a +great telescope would be required to make one star just<span class="pagenum"><a name="Page_295" id="Page_295">[Pg 295]</a></span> +visible to the unaided eye? How many full moons must +be put in the sky in order to give an illumination as bright +as daylight? How large a part of the visible hemisphere +would they occupy?</p> + +<p><a name="S_187" id="S_187"></a>187. <b>Classification by magnitudes.</b>—The brightness of all +the lucid stars has been carefully measured with an instrument +(photometer) designed for that special purpose, and +the following table shows, according to the Harvard Photometry, +the number of stars in the whole sky, from pole to +pole, which are brighter than the several magnitudes +named in the table:</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left">The number</td><td align="center">of stars</td><td align="center">brighter</td><td align="center">than</td><td align="center">magnitude</td><td align="right">1.0</td><td align="center">is</td><td align="right">11</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="right">2.0</td><td align="center">"</td><td align="right">39</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="right">3.0</td><td align="center">"</td><td align="right">142</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="right">4.0</td><td align="center">"</td><td align="right">463</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="right">5.0</td><td align="center">"</td><td align="right">1,483</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td align="right">6.0</td><td align="center">"</td><td align="right">4,326</td></tr> +</table></div> + +<p>It must not be inferred from this table that there are +in the whole sky only 4,326 stars visible to the naked eye. +The actual number is probably 50 or 60 per cent greater +than this, and the normal human eye sees stars as faint as +the magnitude 6.4 or 6.5, the discordance between this number +and the previous statement, that the sixth magnitude is +the limit of the naked-eye vision, having been introduced +in the attempt to make precise and accurate a classification +into magnitudes which was at first only rough and approximate. +This same striving after accuracy leads to the introduction +of fractional numbers to represent gradations of +brightness intermediate between whole magnitudes. Thus +of the 2,843 stars included between the fifth and sixth +magnitudes a certain proportion are said to be of the 5.1 +magnitude, 5.2 magnitude, and so on to the 5.9 magnitude, +even hundredths of a magnitude being sometimes employed.</p> + +<p>We have found the number of stars included between +the fifth and sixth magnitudes by subtracting from the +last number of the preceding table the number immediately<span class="pagenum"><a name="Page_296" id="Page_296">[Pg 296]</a></span> +preceding it, and similarly we may find the number +included between each other pair of consecutive magnitudes, +as follows:</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left">Magnitude</td><td align="center">0</td><td align="right"> </td><td align="center">1</td><td align="right"> </td><td align="center">2</td><td align="right"> </td><td align="center">3</td><td align="right"> </td><td align="center">4</td><td align="right"> </td><td align="center">5</td><td align="right"> </td><td align="center">6</td></tr> +<tr><td align="left">Number of stars</td><td align="center"> </td><td align="right">11</td><td align="center"> </td><td align="right">28</td><td align="center"> </td><td align="right">103</td><td align="center"> </td><td align="right">321</td><td align="center"> </td><td align="right">1,020</td><td align="center"> </td><td align="right">2,843</td></tr> +<tr><td align="left">4 × 3<sup>m</sup></td><td align="center"> </td><td align="right">12</td><td align="center"> </td><td align="right">36</td><td align="center"> </td><td align="right">108</td><td align="center"> </td><td align="right">324</td><td align="center"> </td><td align="right">972</td><td align="center"> </td><td align="right">2,916</td></tr> +</table></div> + +<p>In the last line each number after the first is found by +multiplying the preceding one by 3, and the approximate +agreement of each such number with that printed above it +shows that on the whole, as far as the table goes, the fainter +stars are approximately three times as numerous as those +a magnitude brighter.</p> + +<p>The magnitudes of the telescopic stars have not yet +been measured completely, and their exact number is unknown; +but if we apply our principle of a threefold increase +for each successive magnitude, we shall find for the fainter +stars—those of the tenth and twelfth magnitudes—prodigious +numbers which run up into the millions, and even these +are probably too small, since down to the ninth or tenth +magnitude it is certain that the number of the telescopic +stars increases from magnitude to magnitude in more than +a threefold ratio. This is balanced in some degree by the +less rapid increase which is known to exist in magnitudes +still fainter; and applying our formula without regard to +these variations in the rate of increase, we obtain as a rude +approximation to the total number of stars down to the +fifteenth magnitude, 86,000,000. The Herschels, father +and son, actually counted the number of stars visible in +nearly 8,000 sample regions of the sky, and, inferring the +character of the whole sky from these samples, we find it +to contain 58,500,000 stars; but the magnitude of the faintest +star visible in their telescope, and included in their +count, is rather uncertain.</p> + +<p>How many first-magnitude stars would be needed to +give as much light as do the 2,843 stars of magnitude 5.0<span class="pagenum"><a name="Page_297" id="Page_297">[Pg 297]</a></span> +to 6.0? How many tenth-magnitude stars are required to +give the same amount of light?</p> + +<p>To the modern man it seems natural to ascribe the different +brilliancies of the stars to their different distances +from us; but such was not the case 2,000 years ago, when +each fixed star was commonly thought to be fastened to +a "crystal sphere," which carried them with it, all at the +same distance from us, as it turned about the earth. In +breaking away from this erroneous idea and learning to +think of the sky itself as only an atmospheric illusion +through which we look to stars at very different distances +beyond, it was easy to fall into the opposite error and to +think of the stars as being much alike one with another, +and, like pebbles on the beach, scattered throughout space +with some rough degree of uniformity, so that in every +direction there should be found in equal measure stars +near at hand and stars far off, each shining with a luster +proportioned to its remoteness.</p> + +<p><a name="S_188" id="S_188"></a>188. <b>Distances of the stars.</b>—Now, in order to separate +the true from the false in this last mode of thinking about +the stars, we need some knowledge of their real distances +from the earth, and in seeking it we encounter what is +perhaps the most delicate and difficult problem in the +whole range of observational astronomy. As shown in +<a href="#Fig_121">Fig. 121</a>, the principles involved in determining these distances +are not fundamentally different from those employed +in determining the moon's distance from the earth. +Thus, the ellipse at the left of the figure represents the +earth's orbit and the position of the earth at different +times of the year. The direction of the star <i>A</i> at these +several times is shown by lines drawn through <i>A</i> and prolonged +to the background apparently furnished by the sky. +A similar construction is made for the star <i>B</i>, and it is +readily seen that owing to the changing position of the +observer as he moves around the earth's orbit, both <i>A</i> and +<i>B</i> will appear to move upon the background in orbits<span class="pagenum"><a name="Page_298" id="Page_298">[Pg 298]</a></span> +shaped like that of the earth as seen from the star, but +having their size dependent upon the star's distance, the +apparent orbit of <i>A</i> being larger than that of <i>B</i>, because <i>A</i> +is nearer the earth. By measuring the angular distance +between <i>A</i> and <i>B</i> at opposite seasons of the year (e. g., the +angles <i>A—Jan.—B</i>, and <i>A—July—B</i>) the astronomer +determines from the change in this angle how much larger +is the one path than the other, and thus concludes how +much nearer is <i>A</i> than <i>B</i>. Strictly, the difference between +the January and July angles is equal to the difference between +the angles subtended at <i>A</i> and <i>B</i> by the diameter of +the earth's orbit, and if <i>B</i> were so far away that the angle +<i>Jan.—B—July</i> were nothing at all we should get immediately +from the observations the angle <i>Jan.—A—July</i>, +which would suffice to determine the stars' distance. Supposing +the diameter of the earth's orbit and the angle at <i>A</i> +to be known, can you make a graphical construction that +will determine the distance of <i>A</i> from the earth?</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_121" id="Fig_121"></a> +<img src="images/i332.png" width="500" height="287" alt="Fig. 121.—Determining a star's parallax." title="Fig. 121.—Determining a star's parallax." /> +<span class="caption"><span class="smcap">Fig. 121.</span>—Determining a star's parallax.</span> +</div> + +<p>The angle subtended at <i>A</i> by the radius of the earth's +orbit—i. e., 1/2 (<i>Jan.—A—July</i>)—is called the star's parallax, +and this is commonly used by astronomers as a measure +of the star's distance instead of expressing it in linear +units such as miles or radii of the earth's orbit. The distance<span class="pagenum"><a name="Page_299" id="Page_299">[Pg 299]</a></span> +of a star is equal to the radius of the earth's orbit +divided by the parallax, in seconds of arc, and multiplied +by the number 206265.</p> + +<p>A weak point of this method of measuring stellar distances +is that it always gives what is called a relative parallax—i. e., +the difference between the parallaxes of <i>A</i> and +<i>B</i>; and while it is customary to select for <i>B</i> a star or stars +supposed to be much farther off than <i>A</i>, it may happen, +and sometimes does happen, that these comparison stars +as they are called are as near or nearer than <i>A</i>, and give +a negative parallax—i. e., the difference between the angles +at <i>A</i> and <i>B</i> proves to be negative, as it must whenever the +star <i>B</i> is nearer than <i>A</i>.</p> + +<p>The first really successful determinations of stellar +parallax were made by Struve and Bessel a little prior to +1840, and since that time the distances of perhaps 100 stars +have been measured with some degree of reliability, although +the parallaxes themselves are so small—never as +great as 1''—that it is extremely difficult to avoid falling +into error, since even for the nearest star the problem of +its distance is equivalent to finding the distance of an object +more than 5 miles away by looking at it first with one +eye and then with the other. Too short a base line.</p> + +<p><a name="S_189" id="S_189"></a>189. <b>The sun and his neighbors.</b>—The distances of the +sun's nearer neighbors among the stars are shown in <a href="#Fig_122">Fig. 122</a>, +where the two circles having the sun at their center +represent distances from it equal respectively to 1,000,000 +and 2,000,000 times the distance between earth and sun. +In the figure the direction of each star from the sun corresponds +to its right ascension, as shown by the Roman +numerals about the outer circle; the true direction of the +star from the sun can not, of course, be shown upon the +flat surface of the paper, but it may be found by elevating +or depressing the star from the surface of the paper +through an angle, as seen from the sun, equal to its declination, +as shown in the fifth column of the following table,<span class="pagenum"><a name="Page_300" id="Page_300">[Pg 300]</a></span></p> + +<h4><i>The Sun's Nearest Neighbors</i></h4> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary="" rules="groups" frame="hsides"> +<colgroup></colgroup><colgroup></colgroup><colgroup></colgroup><colgroup></colgroup><colgroup></colgroup><colgroup></colgroup><colgroup></colgroup> +<thead> +<tr><th align="center">No.</th><th align="center"><span class="smcap">Star.</span></th><th align="center">Magnitude.</th><th align="center">R. A.</th><th align="center">Dec.</th><th align="center">Parallax.</th><th align="center">Distance.</th></tr> +</thead> +<tbody> +<tr><td align="right">1</td><td align="left">α Centauri</td><td align="right">0.7</td><td align="right">14.5h.</td><td align="right">-60°</td><td align="right">0.75"</td><td align="right">0.27</td></tr> +<tr><td align="right">2</td><td align="left">Ll. 21,185</td><td align="right">6.8</td><td align="right">11.0</td><td align="right">+37</td><td align="right">0.45</td><td align="right">0.46</td></tr> +<tr><td align="right">3</td><td align="left">61 Cygni</td><td align="right">5.0</td><td align="right">21.0</td><td align="right">+38</td><td align="right">0.40</td><td align="right">0.51</td></tr> +<tr><td align="right">4</td><td align="left">η Herculis</td><td align="right">3.6</td><td align="right">16.7</td><td align="right">+39</td><td align="right">0.40</td><td align="right">0.51</td></tr> +<tr><td align="right">5</td><td align="left">Sirius</td><td align="right">-1.4</td><td align="right">6.7</td><td align="right">-17</td><td align="right">0.37</td><td align="right">0.56</td></tr> +<tr><td align="right">6</td><td align="left">Σ 2,398</td><td align="right">8.2</td><td align="right">18.7</td><td align="right">+59</td><td align="right">0.35</td><td align="right">0.58</td></tr> +<tr><td align="right">7</td><td align="left">Procyon</td><td align="right">0.5</td><td align="right">7.6</td><td align="right">+5</td><td align="right">0.34</td><td align="right">0.60</td></tr> +<tr><td align="right">8</td><td align="left">γ Draconis</td><td align="right">4.8</td><td align="right">17.5</td><td align="right">+55</td><td align="right">0.30</td><td align="right">0.68</td></tr> +<tr><td align="right">9</td><td align="left">Gr. 34</td><td align="right">7.9</td><td align="right">0.2</td><td align="right">+43</td><td align="right">0.29</td><td align="right">0.71</td></tr> +<tr><td align="right">10</td><td align="left">Lac. 9,352</td><td align="right">7.5</td><td align="right">23.0</td><td align="right">-36</td><td align="right">0.28</td><td align="right">0.74</td></tr> +<tr><td align="right">11</td><td align="left">σ Draconis</td><td align="right">4.8</td><td align="right">19.5</td><td align="right">+69</td><td align="right">0.25</td><td align="right">0.82</td></tr> +<tr><td align="right">12</td><td align="left">A. O. 17,415-6</td><td align="right">9.0</td><td align="right">17.6</td><td align="right">+68</td><td align="right">0.25</td><td align="right">0.82</td></tr> +<tr><td align="right">13</td><td align="left">η Cassiopeię</td><td align="right">3.4</td><td align="right">0.7</td><td align="right">+57</td><td align="right">0.25</td><td align="right">0.82</td></tr> +<tr><td align="right">14</td><td align="left">Altair</td><td align="right">1.0</td><td align="right">19.8</td><td align="right">+9</td><td align="right">0.21</td><td align="right">0.97</td></tr> +<tr><td align="right">15</td><td align="left">ϵ Indi</td><td align="right">5.2</td><td align="right">21.9</td><td align="right">-57</td><td align="right">0.20</td><td align="right">1.03</td></tr> +<tr><td align="right">16</td><td align="left">Gr. 1,618</td><td align="right">6.7</td><td align="right">10.1</td><td align="right">+50</td><td align="right">0.20</td><td align="right">1.03</td></tr> +<tr><td align="right">17</td><td align="left">10 Ursę Majoris</td><td align="right">4.2</td><td align="right">8.9</td><td align="right">+42</td><td align="right">0.20</td><td align="right">1.03</td></tr> +<tr><td align="right">18</td><td align="left">Castor</td><td align="right">1.5</td><td align="right">7.5</td><td align="right">+32</td><td align="right">0.20</td><td align="right">1.03</td></tr> +<tr><td align="right">19</td><td align="left">Ll. 21,258</td><td align="right">8.5</td><td align="right">11.0</td><td align="right">+44</td><td align="right">0.20</td><td align="right">1.03</td></tr> +<tr><td align="right">20</td><td align="left">ο<sup>2</sup> Eridani</td><td align="right">4.5</td><td align="right">4.2</td><td align="right">-8</td><td align="right">0.19</td><td align="right">1.08</td></tr> +<tr><td align="right">21</td><td align="left">A. O. 11,677</td><td align="right">9.0</td><td align="right">11.2</td><td align="right">+66</td><td align="right">0.19</td><td align="right">1.08</td></tr> +<tr><td align="right">22</td><td align="left">Ll. 18,115</td><td align="right">8.0</td><td align="right">9.1</td><td align="right">+53</td><td align="right">0.18</td><td align="right">1.14</td></tr> +<tr><td align="right">23</td><td align="left">B. D. 36°, 3,883</td><td align="right">7.1</td><td align="right">20.0</td><td align="right">+36</td><td align="right">0.18</td><td align="right">1.14</td></tr> +<tr><td align="right">24</td><td align="left">Gr. 1,618</td><td align="right">6.5</td><td align="right">10.1</td><td align="right">+50</td><td align="right">0.17</td><td align="right">1.21</td></tr> +<tr><td align="right">25</td><td align="left">β Cassiopeię</td><td align="right">2.3</td><td align="right">0.1</td><td align="right">+59</td><td align="right">0.16</td><td align="right">1.28</td></tr> +<tr><td align="right">26</td><td align="left">70 Ophiuchi</td><td align="right">4.4</td><td align="right">18.0</td><td align="right">+2</td><td align="right">0.16</td><td align="right">1.28</td></tr> +<tr><td align="right">27</td><td align="left">Σ 1,516</td><td align="right">6.5</td><td align="right">11.2</td><td align="right">+74</td><td align="right">0.15</td><td align="right">1.38</td></tr> +<tr><td align="right">28</td><td align="left">Gr. 1,830</td><td align="right">6.6</td><td align="right">11.8</td><td align="right">+39</td><td align="right">0.15</td><td align="right">1.38</td></tr> +<tr><td align="right">29</td><td align="left">μ Cassiopeię</td><td align="right">5.4</td><td align="right">1.0</td><td align="right">+54</td><td align="right">0.14</td><td align="right">1.47</td></tr> +<tr><td align="right">30</td><td align="left">ϑ Eridani</td><td align="right">4.4</td><td align="right">3.5</td><td align="right">-10</td><td align="right">0.14</td><td align="right">1.47</td></tr> +<tr><td align="right">31</td><td align="left">ι Ursę Majoris</td><td align="right">3.2</td><td align="right">8.9</td><td align="right">+48</td><td align="right">0.13</td><td align="right">1.58</td></tr> +<tr><td align="right">32</td><td align="left">β Hydri</td><td align="right">2.9</td><td align="right">0.3</td><td align="right">-78</td><td align="right">0.1</td><td align="right">1.58</td></tr> +<tr><td align="right">33</td><td align="left">Fomalhaut</td><td align="right">1.0</td><td align="right">22.9</td><td align="right">-30</td><td align="right">0.13</td><td align="right">1.58</td></tr> +<tr><td align="right">34</td><td align="left">Br. 3,077</td><td align="right">6.0</td><td align="right">23.1</td><td align="right">+57</td><td align="right">0.13</td><td align="right">1.58</td></tr> +<tr><td align="right">35</td><td align="left">ϑ Cygni</td><td align="right">2.5</td><td align="right">20.8</td><td align="right">+33</td><td align="right">0.12</td><td align="right">1.71</td></tr> +<tr><td align="right">36</td><td align="left">β Comę</td><td align="right">4.5</td><td align="right">13.1</td><td align="right">+28</td><td align="right">0.11</td><td align="right">1.87</td></tr> +<tr><td align="right">37</td><td align="left">ψ<sup>5</sup> Aurigę</td><td align="right">8.8</td><td align="right">6.6</td><td align="right">+44</td><td align="right">0.11</td><td align="right">1.87</td></tr> +<tr><td align="right">38</td><td align="left">π Herculis</td><td align="right">3.3</td><td align="right">17.2</td><td align="right">+37</td><td align="right">0.11</td><td align="right">1.87</td></tr> +<tr><td align="right">39</td><td align="left">Aldebaran</td><td align="right">1.1</td><td align="right">4.5</td><td align="right">+16</td><td align="right">0.10</td><td align="right">2.06</td></tr> +<tr><td align="right">40</td><td align="left">Capella</td><td align="right">0.1</td><td align="right">5.1</td><td align="right">+46</td><td align="right">0.10</td><td align="right">2.06</td></tr> +<tr><td align="right">41</td><td align="left">B. D. 35°, 4,003</td><td align="right">9.2</td><td align="right">20.1</td><td align="right">+35</td><td align="right">0.10</td><td align="right">2.06</td></tr> +<tr><td align="right">42</td><td align="left">Gr. 1,646</td><td align="right">6.3</td><td align="right">10.3</td><td align="right">+49</td><td align="right">0.10</td><td align="right">2.06</td></tr> +<tr><td align="right">43</td><td align="left">γ Cygni</td><td align="right">2.3</td><td align="right">20.3</td><td align="right">+40</td><td align="right">0.10</td><td align="right">2.06</td></tr> +<tr><td align="right">44</td><td align="left">Regulus</td><td align="right">1.2</td><td align="right">10.0</td><td align="right">+12</td><td align="right">0.10</td><td align="right">2.06</td></tr> +<tr><td align="right">45</td><td align="left">Vega</td><td align="right">0.2</td><td align="right">18.6</td><td align="right">+39</td><td align="right">0.10</td><td align="right">2.06</td></tr> +</tbody> +</table><span class="pagenum"><a name="Page_301" id="Page_301">[Pg 301]</a></span></div> + +<p>in which the numbers in the first column are those placed +adjacent to the stars in the diagram to identify them.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_122" id="Fig_122"></a> +<img src="images/i335.png" width="500" height="506" alt="Fig. 122.—Stellar neighbors of the sun." title="Fig. 122.—Stellar neighbors of the sun." /> +<span class="caption"><span class="smcap">Fig. 122.</span>—Stellar neighbors of the sun.</span> +</div> + +<p><a name="S_190" id="S_190"></a>190. <b>Light years.</b>—The radius of the inner circle in <a href="#Fig_122">Fig. 122</a>, +1,000,000 times the earth's distance from the sun, is a +convenient unit in which to express the stellar distances, +and in the preceding table the distances of the stars from +the sun are expressed in terms of this unit. To express +them in miles the numbers in the table must be multiplied +by 93,000,000,000,000. The nearest star, α Centauri, +is 25,000,000,000,000 miles away. But there is another +unit in more common use—i. e., the distance traveled over<span class="pagenum"><a name="Page_302" id="Page_302">[Pg 302]</a></span> +by light in the period of one year. We have already found +(<a href="#S_141">§ 141</a>) that it requires light 8m. 18s. to come from the sun +to the earth, and it is a simple matter to find from this +datum that in a year light moves over a space equal to +63,368 radii of the earth's orbit. This distance is called a +<i>light year</i>, and the distance of the same star, α Centauri, +expressed in terms of this unit, is 4.26 years—i. e., it takes +light that long to come from the star to the earth.</p> + +<p>In <a href="#Fig_122">Fig. 122</a> the stellar magnitudes of the stars are indicated +by the size of the dots—the bigger the dot the brighter +the star—and a mere inspection of the figure will serve to +show that within a radius of 30 light years from the sun +bright stars and faint ones are mixed up together, and that, +so far as distance is concerned, the sun is only a member +of this swarm of stars, whose distances apart, each from its +nearest neighbor, are of the same order of magnitude as +those which separate the sun from the three or four stars +nearest it.</p> + +<p><a href="#Fig_122">Fig. 122</a> is not to be supposed complete. Doubtless +other stars will be found whose distance from the sun is less +than 2,000,000 radii of the earth's orbit, but it is not probable +that they will ever suffice to more than double or perhaps +treble the number here shown. The vast majority of +the stars lie far beyond the limits of the figure.</p> + +<p><a name="S_191" id="S_191"></a>191. <b>Proper motions.</b>—It is evident that these stars are too +far apart for their mutual attractions to have much influence +one upon another, and that we have here a case in which, +according to <a href="#S_34">§ 34</a>, each star is free to keep unchanged its +state of rest or motion with unvarying velocity along a +straight line. Their very name, <i>fixed stars</i>, implies that +they are at rest, and so astronomers long believed. Hipparchus +(125 <span class="smcap">B. C.</span>) and Ptolemy (130 <span class="smcap">A. D.</span>) observed and recorded +many allineations among the stars, in order to give +to future generations a means of settling this very question +of a possible motion of the stars and a resulting change in +their relative positions upon the sky. For example, they<span class="pagenum"><a name="Page_303" id="Page_303">[Pg 303]</a></span> +found at the beginning of the Christian era that the four +stars, Capella, ϑ Persei, α and β Arietis, stood in a straight +line—i. e., upon a great circle of the sky. Verify this by +direct reference to the sky, and see how nearly these stars +have kept the same position for nearly twenty centuries. +Three of them may be identified from the star maps, and the +fourth, ϑ Persei, is a third-magnitude star between Capella +and the other two.</p> + +<p>Other allineations given by Ptolemy are: Spica, Arcturus +and β Bootis; Spica, δ Corvi and γ Corvi; α Librę, +Arcturus and ζ Ursę Majoris. Arcturus does not now fit +very well to these alignments, and nearly two centuries +ago it, together with Aldebaran and Sirius, was on other +grounds suspected to have changed its place in the sky +since the days of Ptolemy. This discovery, long since +fully confirmed, gave a great impetus to observing with all +possible accuracy the right ascensions and declinations of the +stars, with a view to finding other cases of what was called +<i>proper motion</i>—i. e., a motion peculiar to the individual +star as contrasted with the change of right ascension and +declination produced for all stars by the precession.</p> + +<p>Since the middle of the eighteenth century there have +been made many thousands of observations of this kind, +whose results have gone into star charts and star catalogues, +and which are now being supplemented by a photographic +survey of the sky that is intended to record permanently +upon photographic plates the position and magnitude +of every star in the heavens down to the fourteenth +magnitude, with a view to ultimately determining all their +proper motions.</p> + +<p>The complete achievement of this result is, of course, a +thing of the remote future, but sufficient progress in determining +these motions has been made during the past century +and a half to show that nearly every lucid star possesses +some proper motion, although in most cases it is very +small, there being less than 100 known stars in which it<span class="pagenum"><a name="Page_304" id="Page_304">[Pg 304]</a></span> +amounts to so much as 1" per annum—i. e., a rate of motion +across the sky which would require nearly the whole +Christian era to alter a star's direction from us by so much +as the moon's angular diameter. The most rapid known +proper motion is that of a telescopic star midway between +the equator and the south pole, which changes its position +at the rate of nearly 9" per annum, and the next greatest is +that of another telescopic star, in the northern sky, No. 28 +of <a href="#Fig_122">Fig. 122</a>. It is not until we reach the tenth place in a +list of large proper motions that we find a bright lucid +star, No. 1 of <a href="#Fig_122">Fig. 122</a>. It is a significant fact that for the +most part the stars with large proper motions are precisely +the ones shown in <a href="#Fig_122">Fig. 122</a>, which is designed to show stars +near the earth. This connection between nearness and +rapidity of proper motions is indeed what we should expect +to find, since a given amount of real motion of the star +along its orbit will produce a larger angular displacement, +proper motion, the nearer the star is to the earth, and this +fact has guided astronomers in selecting the stars to be +observed for parallax, the proper motion being determined +first and the parallax afterward.</p> + +<p><a name="S_192" id="S_192"></a>192. <b>The paths of the stars.</b>—We have already seen reason +for thinking that the orbit along which a star moves is +practically a straight line, and from a study of proper motions, +particularly their directions across the sky, it appears +that these orbits point in all possible ways—north, south, +east, and west—so that some of them are doubtless directed +nearly toward or from the sun; others are square to the +line joining sun and star; while the vast majority occupy +some position intermediate between these two. Now, our +relation to these real motions of the stars is well illustrated +in <a href="#Fig_112">Fig. 112</a>, where the observer finds in some of the +shooting stars a tremendous proper motion across the sky, +but sees nothing of their rapid approach to him, while +others appear to stand motionless, although, in fact, they +are moving quite as rapidly as are their fellows. The fixed<span class="pagenum"><a name="Page_305" id="Page_305">[Pg 305]</a></span> +star resembles the shooting star in this respect, that its +proper motion is only that part of its real motion which +lies at right angles to the line of sight, and this needs to +be supplemented by that other part of the motion which +lies parallel to the line of sight, in order to give us any +knowledge of the star's real orbit.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_123" id="Fig_123"></a> +<a href="images/i339.jpg"><img src="images/i339.jpg" width="500" height="106" alt="Fig. 123.—Motion of Polaris in the line of sight as determined by the spectroscope. +Frost." title="Fig. 123.—Motion of Polaris in the line of sight as determined by the spectroscope. +Frost." /></a> +<span class="caption"><span class="smcap">Fig. 123.</span>—Motion of Polaris in the line of sight as determined by the spectroscope. +<span class="smcap">Frost.</span></span> +</div> + +<p><a name="S_193" id="S_193"></a>193. <b>Motion in the line of sight.</b>—It is only within the +last 25 years that anything whatever has been accomplished +in determining these stellar motions of approach or recession, +but within that time much progress has been made by +applying the Doppler principle (<a href="#S_89">§ 89</a>) to the study of stellar +spectra, and at the present time nearly every great telescope +in the world is engaged upon work of this kind. The +shifting of the lines of the spectrum toward the violet or +toward the red end of the spectrum indicates with certainty +the approach or recession of the star, but this shifting, +which must be determined by comparing the star's +spectrum with that of some artificial light showing corresponding +lines, is so small in amount that its accurate measurement +is a matter of extreme difficulty, as may be seen +from <a href="#Fig_123">Fig. 123</a>. This cut shows along its central line a part +of the spectrum of Polaris, between wave lengths 4,450 and +4,600 tenth meters, while above and below are the corresponding +parts of the spectrum of an electric spark whose +light passed through the same spectroscope and was photographed +upon the same plate with that of Polaris. This +comparison spectrum is, as it should be, a discontinuous or +bright-line one, while the spectrum of the star is a continuous<span class="pagenum"><a name="Page_306" id="Page_306">[Pg 306]</a></span> +one, broken only by dark gaps or lines, many of +which have no corresponding lines in the comparison spectrum. +But a certain number of lines in the two spectra +do correspond, save that the dark line is always pushed a +very little toward the direction of shorter wave lengths, +showing that this star is approaching the earth. This spectrum +was photographed for the express purpose of determining +the star's motion in the line of sight, and with it +there should be compared Figs. <a href="#Fig_124">124</a> and <a href="#Fig_125">125</a>, which show +in the upper part of each a photograph obtained without +comparison spectra by allowing the star's light to pass +through some prisms placed just in front of the telescope. +The lower section of each figure shows an enlargement of +the original photograph, bringing out its details in a way +not visible to the unaided eye. In the enlarged spectrum +of β Aurigę a rate of motion equal to that of the earth in +its orbit would be represented by a shifting of 0.03 of a +millimeter in the position of the broad, hazy lines.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_124" id="Fig_124"></a> +<a href="images/i340.jpg"><img src="images/i340.jpg" width="500" height="168" alt="Fig. 124.—Spectrum of β Aurigę.—Pickering." title="Fig. 124.—Spectrum of β Aurigę.—Pickering." /></a> +<span class="caption"><span class="smcap">Fig. 124.</span>—Spectrum of β Aurigę.—<span class="smcap">Pickering.</span></span> +</div> + +<p>Despite the difficulty of dealing with such small quantities +as the above, very satisfactory results are now obtained, +and from them it is known that the velocities of stars in +the line of sight are of the same order of magnitude as the +velocities of the planets in their orbits, ranging all the way +from 0 to 60 miles per second—more than 200,000 miles per +hour—which latter velocity, according to Campbell, is the +rate at which μ Cassiopeię is approaching the sun.<span class="pagenum"><a name="Page_307" id="Page_307">[Pg 307]</a></span></p> + +<p>The student should not fail to note one important +difference between proper motions and the motions determined +spectroscopically: the latter are given directly in +miles per second, or per hour, while the former are expressed +in angular measure, seconds of arc, and there can +be no direct comparison between the two until by means +of the known distances of the stars their proper motions +are converted from angular into linear measure. We are +brought thus to the very heart of the matter; parallax, +proper motion, and motion in the line of sight are intimately +related quantities, all of which are essential to a +knowledge of the real motions of the stars.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_125" id="Fig_125"></a> +<a href="images/i341.jpg"><img src="images/i341.jpg" width="500" height="168" alt="Fig. 125.—Spectrum of Pollux.—Pickering." title="Fig. 125.—Spectrum of Pollux.—Pickering." /></a> +<span class="caption"><span class="smcap">Fig. 125.</span>—Spectrum of Pollux.—<span class="smcap">Pickering.</span></span> +</div> + +<p><a name="S_194" id="S_194"></a>194. <b>Star drift.</b>—An illustration of how they may be +made to work together is furnished by some of the stars—which +make up the Great Dipper—β, γ, ϑ, and ζ Ursę Majoris, +whose proper motions have long been known to point +in nearly the same direction across the sky and to be nearly +equal in amount. More recently it has been found that +these stars are all moving toward the sun with approximately +the same velocity—18 miles per second. One other +star of the Dipper, δ Ursę Majoris, shares in the common +proper motion, but its velocity in the line of sight has not +yet been determined with the spectroscope. These similar +motions make it probable that the stars are really traveling +together through space along parallel lines; and on the<span class="pagenum"><a name="Page_308" id="Page_308">[Pg 308]</a></span> +supposition that such is the case it is quite possible to +write out a set of equations which shall involve their +known proper motions and motions in the line of sight, +together with their unknown distances and the unknown +direction and velocity of their real motion along their +orbits. Solving these equations for the values of the unknown +quantities, it is found that the five stars probably +lie in a plane which is turned nearly edgewise toward us, +and that in this plane they are moving about twice as fast +as the earth moves around the sun, and are at a distance +from us represented by a parallax of less than 0.02"—i. e., +six times as great as the outermost circle in <a href="#Fig_122">Fig. 122</a>. A +most extraordinary system of stars which, although separated +from each other +by distances as +great as the whole +breadth of <a href="#Fig_122">Fig. 122</a>, +yet move along in +parallel paths which +it is difficult to regard +as the result +of chance, and for +which it is equally +difficult to frame an +explanation.</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_126" id="Fig_126"></a> +<a href="images/i342-full.jpg"><img src="images/i342.jpg" width="350" height="435" alt="Fig. 126.—The Great Dipper, past, present, and +future." title="Fig. 126.—The Great Dipper, past, present, and +future." /></a> +<span class="caption"><span class="smcap">Fig. 126.</span>—The Great Dipper, past, present, and +future.</span> +</div> + +<p>The stars α and +η of the Great Dipper +do not share +in this motion, and +must ultimately part +company with the +other five, to the +complete destruction +of the Dipper's shape. <a href="#Fig_126">Fig. 126</a> illustrates this change of +shape, the upper part of the figure (<i>a</i>) showing these seven +stars as they were grouped at a remote epoch in the past,<span class="pagenum"><a name="Page_309" id="Page_309">[Pg 309]</a></span> +while the lower section (<i>c</i>) shows their position for an +equally remote epoch in the future. There is no resemblance +to a dipper in either of these configurations, but it +should be observed that in each of them the stars α and η +keep their relative position unaltered, and the other five +stars also keep together, the entire change of appearance +being due to the changing positions of these two groups +with respect to each other.</p> + +<p>This phenomenon of groups of stars moving together is +called <i>star drift</i>, and quite a number of cases of it are +found in different parts of the sky. The Pleiades are perhaps +the most conspicuous one, for here some sixty or +more stars are found traveling together along similar paths. +Repeated careful measurements of the relative positions of +stars in this cluster show that one of the lucid stars and +four or five of the telescopic ones do not share in this +motion, and therefore are not to be considered as members +of the group, but rather as isolated stars which, for a time, +chance to be nearly on line with the Pleiades, and probably +farther off, since their proper motions are smaller.</p> + +<p>To rightly appreciate the extreme slowness with which +proper motions alter the constellations, the student should +bear in mind that the changes shown in passing from one +section of <a href="#Fig_126">Fig. 126</a> to the next represent the effect of the +present proper motions of the stars accumulated for a period +of 200,000 years. Will the stars continue to move in +straight paths for so long a time?</p> + +<p><a name="S_195" id="S_195"></a>195. <b>The sun's way.</b>—Another and even more interesting +application of proper motions and motions in the line +of sight is the determination from them of the sun's orbit +among the stars. The principle involved is simple enough. +If the sun moves with respect to the stars and carries the +earth and the other planets year after year into new regions +of space, our changing point of view must displace in some +measure every star in the sky save those which happen to +be exactly on the line of the sun's motion, and even these<span class="pagenum"><a name="Page_310" id="Page_310">[Pg 310]</a></span> +will show its effect by their apparent motion of approach +or recession along the line of sight. So far as their own +orbital motions are concerned, there is no reason to suppose +that more stars move north than south, or that more +go east than west; and when we find in their proper motions +a distinct tendency to radiate from a point somewhere +near the bright star Vega and to converge toward +a point on the opposite side of the sky, we infer that this +does not come from any general drift of the stars in that +direction, but that it marks the course of the sun among +them. That it is moving along a straight line pointing +toward Vega, and that at least a part of the velocities +which the spectroscope shows in the line of sight, comes +from the motion of the sun and earth. Working along +these lines, Kapteyn finds that the sun is moving through +space with a velocity of 11 miles per second, which is decidedly +below the average rate of stellar motion—19 miles +per second.</p> + +<p><a name="S_196" id="S_196"></a>196. <b>Distance of Sirian and solar stars.</b>—By combining +this rate of motion of the sun with the average proper motions +of the stars of different magnitudes, it is possible to +obtain some idea of the average distance from us of a first-magnitude +star or a sixth-magnitude star, which, while it +gives no information about the actual distance of any particular +star, does show that on the whole the fainter stars +are more remote. But here a broad distinction must be +drawn. By far the larger part of the stars belong to one of +two well-marked classes, called respectively Sirian and solar +stars, which are readily distinguished from each other by +the kind of spectrum they furnish. Thus β Aurigę belongs +to the Sirian class, as does every other star which has a spectrum +like that of <a href="#Fig_124">Fig. 124</a>, while Pollux is a solar star presenting +in <a href="#Fig_125">Fig. 125</a> a spectrum like that of the sun, as do +the other stars of this class.</p> + +<p>Two thirds of the sun's near neighbors, shown in <a href="#Fig_122">Fig. 122</a>, +have spectra of the solar type, and in general stars of<span class="pagenum"><a name="Page_311" id="Page_311">[Pg 311]</a></span> +this class are nearer to us than are the stars with spectra +unlike that of the sun. The average distance of a solar +star of the first magnitude is very approximately represented +by the outer circle in <a href="#Fig_122">Fig. 122</a>, 2,000,000 times the +distance of the sun from the earth; while the corresponding +distance for a Sirian star of the first magnitude is represented +by the number 4,600,000.</p> + +<p>A third-magnitude star is on the average twice as far +away as one of the first magnitude, a fifth-magnitude star +four times as far off, etc., each additional two magnitudes +doubling the average distance of the stars, at least down to +the eighth magnitude and possibly farther, although beyond +this limit we have no certain knowledge. Put in +another way, the naked eye sees many Sirian stars which +<i>may</i> have "gone out" and ceased to shine centuries ago, +for the light by which we now see them left those stars +before the discovery of America by Columbus. For the +student of mathematical tastes we note that the results of +Kapteyn's investigation of the mean distances (<i>D</i>) of the +stars of magnitude (<i>m</i>) may be put into two equations:</p> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align="left">For Solar Stars,</td><td align="left"><i>D</i> = 23 × 2<sup><i>m</i>/2</sup></td></tr> +<tr><td align="left">For Sirian Stars,</td><td align="left"><i>D</i> = 52 × 2<sup><i>m</i>/2</sup></td></tr> +</table></div> + +<p>where the coefficients 23 and 52 are expressed in light +years. How long a time is required for light to come from +an average solar star of the sixth magnitude?</p> + +<p><a name="S_197" id="S_197"></a>197. <b>Consequences of stellar distance.</b>—The amount of +light which comes to us from any luminous body varies +inversely as the square of its distance, and since many of +the stars are changing their distance from us quite rapidly, +it must be that with the lapse of time they will grow +brighter or fainter by reason of this altered distance. +But the distances themselves are so great that the most +rapid known motion in the line of sight would require +more than 1,000 years (probably several thousand) to produce +any perceptible change in brilliancy.<span class="pagenum"><a name="Page_312" id="Page_312">[Pg 312]</a></span></p> + +<p>The law in accordance with which this change of brilliancy +takes place is that the distance must be increased or +diminished tenfold in order to produce a change of five +magnitudes in the brightness of the object, and we may +apply this law to determine the sun's rank among the stars. +If it were removed to the distance of an average first-, or +second-, or third-magnitude star, how would its light compare +with that of the stars? The average distance of a +third-magnitude star of the solar type is, as we have seen +above, 4,000,000 times the sun's distance from the earth, +and since 4,000,000 = 10<sup>6.6</sup>, we find that at this distance the +sun's stellar magnitude would be altered by 6.6 × 5 magnitudes, +and would therefore be -26.5 + 33.0 = 6.5—i. e., the +sun if removed to the average distance of the third-magnitude +stars of its type would be reduced to the very limit +of naked-eye visibility. It must therefore be relatively +small and feeble as compared with the brightness of the +average star. It is only its close proximity to us that +makes the sun look brighter than the stars.</p> + +<p>The fixed stars may have planets circling around them, +but an application of the same principles will show how +hopeless is the prospect of ever seeing them in a telescope. +If the sun's nearest neighbor, α Centauri, were attended by +a planet like Jupiter, this planet would furnish to us no +more light than does a star of the twenty-second magnitude—i. e., +it would be absolutely invisible, and would remain +invisible in the most powerful telescope yet built, +even though its bulk were increased to equal that of the +sun. Let the student make the computation leading to +this result, assuming the stellar magnitude of Jupiter to +be -1.7.</p> + +<p><a name="S_198" id="S_198"></a>198. <b>Double stars.</b>—In the constellation Taurus, not far +from Aldebaran, is the fourth-magnitude star θ Tauri, +which can readily be seen to consist of two stars close +together. The star α Capricorni is plainly double, and a +sharp eye can detect that one of the faint stars which with<span class="pagenum"><a name="Page_313" id="Page_313">[Pg 313]</a></span> +Vega make a small equilateral triangle, is also a double +star. Look for them in the sky.</p> + +<p>In the strict language of astronomy the term double +star would not be applied to the first two of these objects, +since it is usually restricted to those stars whose angular +distance from each other is so small that in the telescope +they appear much as do the stars named above to the naked +eye—i. e., their angular separation is measured by a few +seconds or fractions of a single second, instead of the six +minutes which separate the component stars of θ Tauri or +α Capricorni. There are found in the sky many thousands +of these close double stars, of which some are only optically +double—i. e., two stars nearly on line with the earth +but at very different distances from it—while more of them +are really what they seem, stars near each other, and in +many cases near enough to influence each other's motion. +These are called <i>binary</i> systems, and in cases of this kind +the principles of celestial mechanics set forth in <a href="#CHAPTER_IV">Chapter IV</a> +hold true, and we may expect to find each component +of a double star moving in a conic section of some kind, +having its focus at the common center of gravity of the +two stars. We are thus presented with problems of orbital +motion quite similar to those which occur in the solar system, +and careful telescopic observations are required year +after year to fix the relative positions of the two stars—i. e., +their angular separation, which it is customary to call their +<i>distance</i>, and their direction one from the other, which is +called <i>position angle</i>.</p> + +<p><a name="S_199" id="S_199"></a>199. <b>Orbits of double stars.</b>—The sun's nearest neighbor, +α Centauri, is such a double star, whose position angle and +distance have been measured by successive generations of +astronomers for more than a century, and <a href="#Fig_127">Fig. 127</a> shows +the result of plotting their observations. Each black dot +that lies on or near the circumference of the long ellipse +stands for an observed direction and distance of the fainter +of the two stars from the brighter one, which is represented<span class="pagenum"><a name="Page_314" id="Page_314">[Pg 314]</a></span> +by the small circle at the intersection of the lines inside +the ellipse. It appears from the figure that during this +time the one star has +gone completely around +the other, as a planet +goes around the sun, +and the true orbit must +therefore be an ellipse +having one of its foci +at the center of gravity +of the two stars. The +other star moves in an +ellipse of precisely similar +shape, but probably +smaller size, since the +dimensions of the two +orbits are inversely proportional +to the masses +of the two bodies, but it is customary to neglect this motion +of the larger star and to give to the smaller one an orbit +whose diameter is equal to the sum of the diameters of the +two real orbits. This practice, which has been followed in +<a href="#Fig_127">Fig. 127</a>, gives correctly the relative positions of the two +stars, and makes one orbit do the work of two.</p> + +<div class="figleft" style="width: 350px;"><a name="Fig_127" id="Fig_127"></a> +<a href="images/i348-full.jpg"><img src="images/i348.jpg" width="350" height="360" alt="Fig. 127.—The orbit of α Centauri.—See." title="Fig. 127.—The orbit of α Centauri.—See." /></a> +<span class="caption"><span class="smcap">Fig. 127.</span>—The orbit of α Centauri.—<span class="smcap">See.</span></span> +</div> + +<p>In <a href="#Fig_127">Fig. 127</a> the bright star does not fall anywhere near +the focus of the ellipse marked out by the smaller one, and +from this we infer that the figure does not show the true +shape of the orbit, which is certainly distorted, foreshortened, +by the fact that we look obliquely down upon its +plane. It is possible, however, by mathematical analysis, +to find just how much and in what direction that plane +should be turned in order to bring the focus of the +ellipse up to the position of the principal star, and thus +give the true shape and size of the orbit. See <a href="#Fig_128">Fig. 128</a> +for a case in which the true orbit is turned exactly edgewise +toward the earth, and the small star, which really<span class="pagenum"><a name="Page_315" id="Page_315">[Pg 315]</a></span> +moves in an ellipse like that shown in the figure, appears +to oscillate to and fro along a straight line drawn through +the principal star, as shown at the left of the figure.</p> + +<p>In the case of α Centauri +the true orbit +proves to have a major +axis 47 times, and a +minor axis 40 times, +as great as the distance +of the earth from the +sun. The orbit, in +fact, is intermediate +in size between the +orbits of Uranus and +Neptune, and the periodic +time of the star +in this orbit is 81 +years, a little less than +the period of Uranus.</p> + +<div class="figright" style="width: 350px;"><a name="Fig_128" id="Fig_128"></a> +<a href="images/i349-full.jpg"><img src="images/i349.jpg" width="350" height="341" alt="Fig. 128.—Apparent orbit and real orbit of the +double star 42 Comę Berenicis.—See." title="Fig. 128.—Apparent orbit and real orbit of the +double star 42 Comę Berenicis.—See." /></a> +<span class="caption"><span class="smcap">Fig. 128.</span>—Apparent orbit and real orbit of the +double star 42 Comę Berenicis.—<span class="smcap">See.</span></span> +</div> + +<p><a name="S_200" id="S_200"></a>200. <b>Masses of double stars.</b>—If we apply to this orbit +Kepler's Third Law in the form given it at <a href="#Page_179">page 179</a>, we +shall find—</p> + +<p class="center"><i>a</i><sup>3</sup> / <i>T</i><sup>2</sup> = (23.5)<sup>3</sup> / (81)<sup>2</sup> = <i>k</i> (<i>M</i> + <i>m</i>),</p> + +<p>where <i>M</i> and <i>m</i> represent the masses of the two stars. We +have already seen that <i>k</i>, the gravitation constant, is equal +to 1 when the masses are measured in terms of the sun's +mass taken as unity, and when <i>T</i> and <i>a</i> are expressed in +years and radii of the earth's orbit respectively, and with +this value of <i>k</i> we may readily find from the above equation, +<i>M</i> + <i>m</i> = 2.5—i. e., the combined mass of the two components +of α Centauri is equal to rather more than twice +the mass of the sun. It is not every double star to which +this process of weighing can be applied. The major axis +of the orbit, <i>a</i>, is found from the observations in angular +measure, 35" in this case, and it is only when the parallax<span class="pagenum"><a name="Page_316" id="Page_316">[Pg 316]</a></span> +of the star is known that this can be converted into the +required linear units, radii of the earth's orbit, by dividing +the angular major axis by the parallax; 47 = 35" ÷ 0.75".</p> + +<p>Our list of distances (<a href="#S_189">§ 189</a>) contains four double stars +whose periodic times and major axes have been fairly well +determined, and we find in the accompanying table the information +which they give about the masses of double stars +and the size of the orbits in which they move:</p> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary="" rules="groups" frame="hsides"> +<colgroup></colgroup><colgroup></colgroup><colgroup></colgroup><colgroup></colgroup><colgroup></colgroup> +<thead> +<tr><th align="center"><span class="smcap">Star.</span></th><th align="center">Major axis.</th><th align="center">Minor axis.</th><th align="center">Periodic<br />time.</th><th align="center">Mass.</th></tr> +</thead> +<tbody> +<tr><td align="left">α Centauri</td><td align="center">47</td><td align="center">40</td><td align="center">81 y.</td><td align="center">2</td></tr> +<tr><td align="left">70 Ophiuchi</td><td align="center">56</td><td align="center">48</td><td align="center">88</td><td align="center">3</td></tr> +<tr><td align="left">Procyon</td><td align="center">34</td><td align="center">31</td><td align="center">40</td><td align="center">3</td></tr> +<tr><td align="left">Sirius</td><td align="center">43</td><td align="center">34</td><td align="center">52</td><td align="center">4</td></tr> +</tbody> +</table></div> + +<p>The orbit of Uranus, diameter = 38, and Neptune, diameter += 60, are of much the same size as these double-star +orbits; but the planetary orbits are nearly circular, while +in every case the double stars show a substantial difference +between the long and short diameters of their orbits. This +is a characteristic feature of most double-star orbits, and +seems to stand in some relation to their periodic times, for, +on the average, the longer the time required by a star to +make its orbital revolution the more eccentric is its orbit +likely to prove.</p> + +<p>Another element of the orbits of double stars, which +stands in even closer relation to the periodic time, is the +major axis; the smaller the long diameter of the orbit the +more rapid is the motion and the shorter the periodic time, +so that astronomers in search of interesting double-star +orbits devote themselves by preference to those stars whose +distance apart is so small that they can barely be distinguished +one from the other in the telescope.</p> + +<p>Although the half-dozen stars contained in the table +all have orbits of much the same size and with much the<span class="pagenum"><a name="Page_317" id="Page_317">[Pg 317]</a></span> +same periodic time as those in which Uranus and Neptune +move, this is by no means true of all the double stars, many +of which have periods running up into the hundreds if not +thousands of years, while a few complete their orbital revolutions +in periods comparable with, or even shorter than, +that of Jupiter.</p> + +<p><a name="S_201" id="S_201"></a>201. <b>Dark stars.</b>—Procyon, the next to the last star of +the preceding table, calls for some special mention, as the +determination of its mass and orbit stands upon a rather +different basis from that of the other stars. More than +half a century ago it was discovered that its proper motion +was not straight and uniform after the fashion of ordinary +stars, but presented a series of loops like those marked out +by a bright point on the rim of a swiftly running bicycle +wheel. The hub may move straight forward with uniform +velocity, but the point near the tire goes up and down, and, +while sharing in the forward motion of the hub, runs sometimes +ahead of it, sometimes behind, and such seemed to +be the motion of Procyon and of Sirius as well. Bessel, +who discovered it, did not hesitate to apply the laws of motion, +and to affirm that this visible change of the star's +motion pointed to the presence of an unseen companion, +which produced upon the motions of Sirius and Procyon +just such effects as the visible companions produce in the +motions of double stars. A new kind of star, dark instead +of bright, was added to the astronomer's domain, and its +discoverer boldly suggested the possible existence of many +more. "That countless stars are visible is clearly no argument +against the existence of as many more invisible ones." +"There is no reason to think radiance a necessary property +of celestial bodies." But most astronomers were incredulous, +and it was not until 1862 that, in the testing of a new +and powerful telescope just built, a dark star was brought +to light and the companion of Sirius actually seen. The +visual discovery of the dark companion of Procyon is +of still more recent date (November, 1896), when it was<span class="pagenum"><a name="Page_318" id="Page_318">[Pg 318]</a></span> +detected with the great telescope of the Lick Observatory. +This discovery is so recent that the orbit is still very uncertain, +being based almost wholly upon the variations in the +proper motion of the star, and while the periodic time must +be very nearly correct, the mass of the stars and dimensions +of the orbit may require considerable correction.</p> + +<p>The companion of Sirius is about ten magnitudes and +that of Procyon about twelve magnitudes fainter than the +star itself. How much more light does the bright star give +than its faint companion? Despite the tremendous difference +of brightness represented by the answer to this question, +the mass of Sirius is only about twice as great as +that of its companion, and for Procyon the ratio does not +exceed five or six.</p> + +<p>The visual discovery of the companions to Sirius and +Procyon removes them from the list of dark stars, but +others still remain unseen, although their existence is indicated +by variable proper motions or by variable orbital +motion, as in the case of ζ Cancri, where one of the components +of a triple star moves around the other two in a series +of loops whose presence indicates a disturbing body which +has never yet been seen.</p> + +<p><a name="S_202" id="S_202"></a>202. <b>Multiple stars.</b>—Combinations of three, four, or +more stars close to each other, like ζ Cancri, are called multiple +stars, and while they are far from being as common as +are double stars, there is a considerable number of them in +the sky, 100 or more as against the more than 10,000 double +stars that are known. That their relative motions are +subject to the law of gravitation admits of no serious doubt, +but mathematical analysis breaks down in face of the difficulties +here presented, and no astronomer has ever been +able to determine what will be the general character of +the motions in such a system.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_129" id="Fig_129"></a> +<img src="images/i353.png" width="500" height="267" alt="Fig. 129.—Illustrating the motion of a spectroscopic binary." title="Fig. 129.—Illustrating the motion of a spectroscopic binary." /> +<span class="caption"><span class="smcap">Fig. 129.</span>—Illustrating the motion of a spectroscopic binary.</span> +</div> + +<p><a name="S_203" id="S_203"></a>203. <b>Spectroscopic binaries.</b>—In the year 1890 Professor +Pickering, of the Harvard Observatory, announced the discovery +of a new class of double stars, invisible as such in<span class="pagenum"><a name="Page_319" id="Page_319">[Pg 319]</a></span> +even the most powerful telescope, and producing no perturbations +such as have been considered above, but showing +in their spectrum that two or more bodies must be +present in the source of light which to the eye is indistinguishable +from a single star. In <a href="#Fig_129">Fig. 129</a> we suppose <i>A</i> +and <i>B</i> to be the two components of a double star, each +moving in its own orbit about their common center of +gravity, <i>C</i>, whose distance from the earth is several million +times greater than the distance between the stars themselves. +Under such circumstances no telescope could distinguish +between the two stars, which would appear fused +into one; but the smaller the orbit the more rapid would +be their motion in it, and if this orbit were turned edgewise +toward the earth, as is supposed in the figure, whenever +the stars were in the relative position there shown, <i>A</i> would +be rapidly approaching the earth by reason of its orbital +motion, while <i>B</i> would move away from it, so that in +accordance with the Doppler principle the lines composing +their respective spectra would be shifted in opposite directions, +thus producing a doubling of the lines, each single +line breaking up into two, like the double-sodium line <i>D</i>, +only not spaced so far apart. When the stars have moved +a quarter way round their orbit to the points <i>A'</i>, <i>B'</i>, their +velocities are turned at right angles to the line of sight<span class="pagenum"><a name="Page_320" id="Page_320">[Pg 320]</a></span> +and the spectrum returns to the normal type with single +lines, only to break up again when after another quarter +revolution their velocities are again parallel with the line +of sight. The interval of time between consecutive doublings +of the lines in the spectrum thus furnishes half +the time of a revolution in the orbit. The distance between +the components of a double line shows by means of +the Doppler principle how fast the stars are traveling, and +this in connection with the periodic times fixes the size +of the orbit, provided we assume that it is turned exactly +edgewise to the earth. This assumption may not be quite +true, but even though the orbit should deviate considerably +from this position, it will still present the phenomenon +of the double lines whose displacement will now show something +less than the true velocities of the stars in their orbits, +since the spectroscope measures only that component +of the whole velocity which is directed toward the earth, +and it is important to note that the real orbits and masses +of these <i>spectroscopic binaries</i>, as they are called, will usually +be somewhat larger than those indicated by the spectroscope, +since it is only in exceptional cases that the orbit +will be turned exactly edgewise to us.</p> + +<p>The bright star Capella is an excellent illustration of +these spectroscopic binaries. At intervals of a little less +than a month the lines of its spectrum are alternately +single and double, their maximum separation corresponding +to a velocity in the line of sight amounting to 37 miles +per second. Each component of a doubled line appears to +be shifted an equal amount from the position occupied by +the line when it is single, thus indicating equal velocities +and equal masses for the two component stars whose periodic +time in their orbit is 104 days. From this periodic +time, together with the velocity of the star's motion, let the +student show that the diameter of the orbit—i. e., the distance +of the stars from each other—is approximately 53,000,000 +miles, and that their combined mass is a little less than<span class="pagenum"><a name="Page_321" id="Page_321">[Pg 321]</a></span> +that of α Centauri, provided that their orbit plane is turned +exactly edgewise toward the earth.</p> + +<p>There are at the present time (1901) 34 spectroscopic +binaries known, including among them such stars as Polaris, +Capella, Algol, Spica, β Aurigę, ζ Ursę Majoris, etc., +and their number is rapidly increasing, about one star out of +every seven whose motion in the line of sight is determined +proving to be a binary or, as in the case of Polaris, possibly +triple. On account of smaller distance apart their periodic +times are much shorter than those of the ordinary double +stars, and range from a few days up to several months—more +than two years in the case of η Pegasi, which has the +longest known period of any star of this class.</p> + +<p>Spectroscopic binaries agree with ordinary double stars +in having masses rather greater than that of the sun, but +there is as yet no assured case of a mass ten times as great +as that of the sun.</p> + +<p><a name="S_204" id="S_204"></a>204. <b>Variable stars.</b>—Attention has already been drawn +(<a href="#S_23">§ 23</a>) to the fact that some stars shine with a changing +brightness—e. g., Algol, the most famous of these <i>variable +stars</i>, at its maximum of brightness furnishes three times +as much light as when at its minimum, and other variable +stars show an even greater range. The star ο Ceti has been +named Mira (Latin, <i>the wonderful</i>), from its extraordinary +range of brightness, more than six-hundred-fold. For the +greater part of the time this star is invisible to the naked +eye, but during some three months in every year it brightens +up sufficiently to be seen, rising quite rapidly to its +maximum brilliancy, which is sometimes that of a second-magnitude +star, but more frequently only third or even +fourth magnitude, and, after shining for a few weeks with +nearly maximum brilliancy, falling off to become invisible +for a time and then return to its maximum brightness +after an interval of eleven months from the preceding +maximum. In 1901 it should reach its greatest brilliancy +about midsummer, and a month earlier than this for each<span class="pagenum"><a name="Page_322" id="Page_322">[Pg 322]</a></span> +succeeding year. Find it by means of the star map, and +by comparing its brightness from night to night with +neighboring stars of about the same magnitude see how it +changes with respect to them.</p> + +<p>The interval of time from maximum to maximum of +brightness—331.6 days for Mira—is called the star's period, +and within its period a star regularly variable runs +through all its changes of brilliancy, much as the weather +runs through its cycle of changes in the period of a year. +But, as there are wet years and dry ones, hot years and cold, +so also with variable stars, many of them show differences +more or less pronounced between different periods, and +one such difference has already been noted in the case of +Mira; its maximum brilliancy is different in different years. +So, too, the length of the period fluctuates in many cases, +as does every other circumstance connected with it, and +predictions of what such a variable star will do are notoriously +unreliable.</p> + +<p><a name="S_205" id="S_205"></a>205. <b>The Algol variables.</b>—On the other hand, some variable +stars present an almost perfect regularity, repeating +their changes time after time with a precision like that of +clockwork. Algol is one type of these regular variables, +having a period of 68.8154 hours, during six sevenths of +which time it shines with unchanging luster as a star of +the 2.3 magnitude, but during the remaining 9 hours of +each period it runs down to the 3.5 magnitude, and comes +back again, as is shown by a curve in <a href="#Fig_130">Fig. 130</a>. The horizontal +scale here represents hours, reckoned from the time of +the star's minimum brightness, and the vertical scale shows +stellar magnitudes. Such a diagram is called the star's +light curve, and we may read from it that at any time between +5h. and 32h. after the time of minimum the star's +magnitude is 2.32; at 2h. after a minimum the magnitude +is 2.88, etc. What is the magnitude an hour and a +half before the time of minimum? What is the magnitude +43 days after a minimum?<span class="pagenum"><a name="Page_323" id="Page_323">[Pg 323]</a></span></p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_130" id="Fig_130"></a> +<img src="images/i357.png" width="500" height="239" alt="Fig. 130.—The light curve of Algol." title="Fig. 130.—The light curve of Algol." /> +<span class="caption"><span class="smcap">Fig. 130.</span>—The light curve of Algol.</span> +</div> + +<p>The arrows shown in <a href="#Fig_130">Fig. 130</a> are a feature not usually +found with light curves, but in this case each one represents +a spectroscopic determination of the motion of Algol +in the line of sight. These observations extended over a +period of more than two years, but they are plotted in the +figure with reference to the number of hours each one preceded +or followed a minimum of the star's light, and each +arrow shows not only the direction of the star's motion +along the line of sight, the arrows pointing down denoting +approach of the star toward the earth, but also its velocity, +each square of the ruling corresponding to 10 kilometers +(6.2 miles per second). The differences of velocity shown +by adjacent arrows come mainly from errors of observation +and furnish some idea of how consistent among themselves +such observations are, but there can be no doubt that before +minimum the star is moving away from the earth, and after +minimum is approaching it. It is evident from these observations +that in Algol we have to do with a spectroscopic +binary, one of whose components is a dark star which, once +in each revolution, partially eclipses the bright star and +produces thus the variations in its light. By combining +the spectroscopic observations with the variations in the +star's light, Vogel finds that the bright star, Algol, itself +has a diameter somewhat greater than that of the sun, but<span class="pagenum"><a name="Page_324" id="Page_324">[Pg 324]</a></span> +is of low density, so that its mass is less than half that of +the sun, while the dark star is a very little smaller than the +sun and has about a quarter of its mass. The distance between +the two stars, dark and bright, is 3,200,000 miles. +<a href="#Fig_129">Fig. 129</a>, which is drawn to scale, shows the relative positions +and sizes of these stars as well as the orbits in which +they move.</p> + +<p>The mere fact already noted that close binary systems +exist in considerable numbers is sufficient to make it +probable that a certain proportion of these stars would +have their orbit planes turned so nearly edgewise toward +the earth as to produce eclipses, and corresponding to this +probability there are already known no less than 15 stars of +the Algol type of eclipse variables, and only a beginning +has been made in the search for them.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_131" id="Fig_131"></a> +<img src="images/i358.png" width="500" height="252" alt="Fig. 131.—The light curve of β Lyrę." title="Fig. 131.—The light curve of β Lyrę." /> +<span class="caption"><span class="smcap">Fig. 131.</span>—The light curve of β Lyrę.</span> +</div> + +<p><a name="S_206" id="S_206"></a>206. <b>Variables of the β Lyrę type.</b>—In addition to these +there is a certain further number of binary variables in +which both components are bright and where the variation +of brightness follows a very different course. Capella +would be such a variable if its orbit plane were directed +exactly toward the earth, and the fact that its light is not +variable shows conclusively that such is not the position of +the orbit. <a href="#Fig_131">Fig. 131</a> represents the light curve of one of the<span class="pagenum"><a name="Page_325" id="Page_325">[Pg 325]</a></span> +best-known variable systems of this second type, that of +β Lyrę, whose period is 12 days 21.8 hours, and the student +should read from the curve the magnitude of the star for +different times during this interval. According to Myers, +this light curve and the spectroscopic observations of the +star point to the existence of a binary star of very remarkable +character, such as is shown, together with its orbit and +a scale of miles, in <a href="#Fig_132">Fig. 132</a>. Note the tide which each of +these stars raises in the other, thus changing their shapes +from spheres into ellipsoids. The astonishing dimensions +of these stars are in part compensated by their very low +density, which is less than that of air, so that their masses +are respectively only 10 times and 21 times that of the +sun! But these dimensions and masses perhaps require +confirmation, since they depend upon spectroscopic observations +of doubtful interpretation. In <a href="#Fig_132">Fig. 132</a> what relative +positions must the stars occupy in their orbit in order +that their combined light should give β Lyrę its maximum +brightness? What position will furnish a minimum +brightness?</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_132" id="Fig_132"></a> +<img src="images/i359.png" width="500" height="246" alt="Fig. 132.—The system of β Lyrę.—Myers." title="Fig. 132.—The system of β Lyrę.—Myers." /> +<span class="caption"><span class="smcap">Fig. 132.</span>—The system of β Lyrę.—<span class="smcap">Myers.</span></span> +</div> + +<p><a name="S_207" id="S_207"></a>207. <b>Variables of long and short periods.</b>—It must not be +supposed that all variable stars are binaries which eclipse +each other. By far the larger part of them, like Mira, are +not to be accounted for in this way, and a distinction which<span class="pagenum"><a name="Page_326" id="Page_326">[Pg 326]</a></span> +is pretty well marked in the length of their periods is significant +in this connection. There is a considerable number +of variable stars with periods shorter than a month, and +there are many having periods longer than 6 months, but +there are very few having periods longer than 18 months, +or intermediate between 1 month and 6 months, so that it +is quite customary to divide variable stars into two classes—those +of long period, 6 months or more, and those of +short period less than 6 months, and that this distinction +corresponds to some real difference in the stars themselves +is further marked by the fact that the long-period variables +are prevailingly red in color, while the short-period stars +are almost without exception white or very pale yellow. +In fact, the longer the period the redder the star, although +it is not to be inferred that all red stars are variable; a +considerable percentage of them shine with constant light. +The eclipse explanation of variability holds good only for +short-period variables, and possibly not for all of them, +while for the long-period variables there is no explanation +which commands the general assent of astronomers, although +unverified hypotheses are plenty.</p> + +<p>The number of stars known to be variable is about 400, +while a considerable number of others are "suspected," +and it would not be surprising if a large fraction of all the +stars should be found to fluctuate a little in brightness. +The sun's spots may suffice to make it a variable star with +a period of 11 years.</p> + +<p>The discovery of new variables is of frequent occurrence, +and may be expected to become more frequent when +the sky is systematically explored for them by the ingenious +device suggested by Pickering and illustrated in <a href="#Fig_133">Fig. 133</a>. +A given region of the sky—e. g., the Northern Crown—is +photographed repeatedly upon the same plate, which is +shifted a little at each new exposure, so that the stars shall +fall at new places upon it. The finally developed plate +shows a row of images corresponding to each star, and if<span class="pagenum"><a name="Page_327" id="Page_327">[Pg 327]</a></span> +the star's light is constant the images in any given row will +all be of the same size, as are most of those in <a href="#Fig_133">Fig. 133</a>; +but a variable star such as is shown by the arrowhead +reveals its presence by the broken aspect of its row of +dots, a minimum brilliancy being shown by smaller and a +maximum by larger ones. In this particular case, at two +exposures the star was too faint to print its image upon +the plate.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_133" id="Fig_133"></a> +<img src="images/i361.jpg" width="500" height="501" alt="Fig. 133.—Discovery of a variable star by means of photography.—Pickering." title="Fig. 133.—Discovery of a variable star by means of photography.—Pickering." /> +<span class="caption"><span class="smcap">Fig. 133.</span>—Discovery of a variable star by means of photography.—<span class="smcap">Pickering.</span></span> +</div> + +<p><a name="S_208" id="S_208"></a>208. <b>New stars.</b>—Next to the variable stars of very long +or very irregular period stand the so-called <i>new</i> or <i>temporary +stars</i>, which appear for the most part suddenly, and +after a brief time either vanish altogether or sink to comparative +insignificance. These were formerly thought to +be very remarkable and unusual occurrences—"the birth +of a new world"—and it is noteworthy that no new star +is recorded to have been seen from 1670 to 1848 <span class="smcap">A. D.</span>, for +since that time there have been no less than five of them<span class="pagenum"><a name="Page_328" id="Page_328">[Pg 328]</a></span> +visible to the naked eye and others telescopic. In so far +as these new stars are not ordinary variables (Mira, first +seen in 1596, was long counted as a new star), they are commonly +supposed due to chance encounters between stars +or other cosmic bodies moving with considerable velocities +along orbits which approach very close to each other. The +actual collision of two dark bodies moving with high velocities +is clearly sufficient to produce a luminous star—e. g., +meteors—and even the close approach of two cooled-off +stars, might result in tidal actions which would rend +open their crusts and pour out the glowing matter from +within so as to produce temporarily a very great accession +of brightness.</p> + +<p>The most famous of all new stars is that which, according +to Tycho Brahe's report, appeared in the year 1572, and +was so bright when at its best as to be seen with the naked +eye in broad daylight. It continued visible, though with +fading light, for about 16 months, and finally disappeared +to the naked eye, although there is some reason to suppose +that it can be identified with a ruddy star of the eleventh +magnitude in the constellation Cassiopeia, whose light still +shows traces of variability.</p> + +<p>No modern temporary star approaches that of Tycho +in splendor, but in some respects the recent ones surpass +it in interest, since it has been possible to apply the spectroscope +to the analysis of their light and to find thereby +a much more complex set of conditions in the star than +would have been suspected from its light changes alone.</p> + +<p>One of the most extraordinary of new stars, and the +most brilliant one since that of Tycho, appeared suddenly +in the constellation Perseus in February, 1901, and for a +short time equaled Capella in brightness. But its light +rapidly waned, with periodic fluctuations of brightness like +those of a variable star, and at the present time (September, +1902) it is lost to the naked eye, although in the telescope +it still shines like a star of the ninth or tenth magnitude.<span class="pagenum"><a name="Page_329" id="Page_329">[Pg 329]</a></span></p> + +<p>By the aid of powerful photographic apparatus, during +the period of its waning brilliancy a ring of faint nebulous +matter was detected surrounding the star and drifting +around and away from it much as if a series of nebulę had +been thrown off by the star at the time of its sudden outburst +of light. But the extraordinary velocity of this nebular +motion, nearly a billion miles per hour, makes such an +explanation almost incredible, and astronomers are more inclined +to believe that the ring was merely a reflection of the +star's own light from a cloud of meteoric matter, into which +a rapidly moving dark star plunged and, after the fashion of +terrestrial meteors, was raised to brilliant incandescence by +the collision. If we assume this to be the true explanation +of these extraordinary phenomena, it is possible to show +from the known velocity with which light travels through +space and from the rate at which the nebula spread, that +the distance of Nova Persei, as the new star is called, corresponds +to a parallax of about one one-hundredth of a second, +a result that is, in substance, confirmed by direct telescopic +measurements of its parallax.</p> + +<p>Another modern temporary star is Nova Aurigę, which +appeared suddenly in December, 1891, waned, and in the +following April vanished, only to reappear three months +later for another season of renewed brightness. The spectra +of both these modern Novę contain both dark and +bright lines displaced toward opposite ends of the spectrum, +and suggesting the Doppler effect that would be +produced by two or more glowing bodies having rapid and +opposite motions in the line of sight. But the most recent +investigations cast discredit on this explanation and leave +the spectra of temporary stars still a subject of debate +among astronomers, with respect both to the motion they +indicate and the intrinsic nature of the stars themselves. +The varying aspect of the spectra suggested at one time +the sun's chromosphere, at another time the conditions that +are present in nebulę, etc.</p> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_330" id="Page_330">[Pg 330]</a></span></p> +<h2><a name="CHAPTER_XIV" id="CHAPTER_XIV"></a>CHAPTER XIV</h2> + +<h3>STARS AND NEBULĘ</h3> + + +<p><a name="S_209" id="S_209"></a>209. <b>Stellar colors.</b>—We have already seen that one star +differs from another in respect of color as well as brightness, +and the diligent student of the sky will not fail to +observe for himself how the luster of Sirius and Rigel is +more nearly a pure white than is that of any other stars in +the heavens, while at the other end of the scale α Orionis +and Aldebaran are strongly ruddy, and Antares presents an +even deeper tone of red. Between these extremes the +light of every star shows a mixture of the rainbow hues, in +which a very pale yellow is the predominant color, shading +off, as we have seen, to white at one end of the scale and +red at the other. There are no green stars, or blue stars, +or violet stars, save in one exceptional class of cases—viz., +where the two components of a double star are of very different +brightness, it is quite the usual thing for them to +have different colors, and then, almost without exception, +the color of the fainter star lies nearer to the violet end +of the spectrum than does the color of the bright one, +and sometimes shows a distinctly blue or green hue. A +fine type of such double star is β Cygni, in which the +components are respectively yellow and blue, and the yellow +star furnishes eight times as much light as the blue +one.</p> + +<p>The exception which double stars thus make to the general +rule of stellar colors, yellow and red, but no color of +shorter wave length, has never been satisfactorily explained,<span class="pagenum"><a name="Page_331" id="Page_331">[Pg 331]</a></span> +but the rule itself presents no difficulties. Each star is an +incandescent body, giving off radiant energy of every wave +length within the limits of the visible spectrum, and, indeed, +far beyond these limits. If this radiant energy could +come unhindered to our eyes every star would appear white, +but they are all surrounded by atmospheres—analogous to +the chromosphere and reversing layer of the sun—which +absorb a portion of their radiant energy and, like the earth's +atmosphere, take a heavier toll from the violet than from +the red end of the spectrum. The greater the absorption +in the star's atmosphere, therefore, the feebler and the ruddier +will be its light, and corresponding to this the red stars +are as a class fainter than the white ones.</p> + +<p><a name="S_210" id="S_210"></a>210. <b>Chemistry of the stars.</b>—The spectroscope is pre-eminently +the instrument to deal with this absorption of light +in the stellar atmospheres, just as it deals with that absorption +in the sun's atmosphere to which are due the dark lines +of the solar spectrum, although the faintness of starlight, +compared with that of the sun, presents a serious obstacle +to its use. Despite this difficulty most of the lucid stars +and many of the telescopic ones have been studied with +the spectroscope and found to be similar to the sun and +the earth as respects the material of which they are made. +Such familiar chemical elements as hydrogen and iron, carbon, +sodium, and calcium are scattered broadcast throughout +the visible universe, and while it would be unwarranted +by the present state of knowledge to say that the stars contain +nothing not found in the earth and the sun, it is evident +that in a broad way their substance is like rather than +unlike that composing the solar system, and is subject to +the same physical and chemical laws which obtain here. +Galileo and Newton extended to the heavens the terrestrial +sciences of mathematics and mechanics, but it remained to +the nineteenth century to show that the physics and chemistry +of the sky are like the physics and chemistry of the +earth.<span class="pagenum"><a name="Page_332" id="Page_332">[Pg 332]</a></span></p> + +<p><a name="S_211" id="S_211"></a>211. <b>Stellar spectra.</b>—When the spectra of great numbers +of stars are compared one with another, it is found that +they bear some relation to the colors of the stars, as, indeed, +we should expect, since spectrum and color are both produced +by the stellar atmospheres, and it is found useful to +classify these spectra into three types, as follows:</p> + +<p><i>Type I. Sirian stars.</i>—Speaking generally, the stars +which are white or very faintly tinged with yellow, furnish +spectra like that of Sirius, from which they take their +name, or that of β Aurigę (<a href="#Fig_124">Fig. 124</a>), which is a continuous +spectrum, especially rich in energy of short wave length—i. e., +violet and ultra-violet light, and is crossed by a relatively +small number of heavy dark lines corresponding to +the spectrum of hydrogen. Sometimes, however, these lines +are much fainter than is here shown, and we find associated +with them still other faint ones pointing to the presence of +other metallic substances in the star's atmosphere. These +metallic lines are not always present, and sometimes even +the hydrogen lines themselves are lacking, but the spectrum +is always rich in violet and ultra-violet light.</p> + +<p>Since with increasing temperature a body emits a continually +increasing proportion of energy of short wave +length (<a href="#S_118">§ 118</a>), the richness of these spectra in such energy +points to a very high temperature in these stars, probably +surpassing in some considerable measure that of the sun. +Stars with this type of spectrum are more numerous than +all others combined, but next to them in point of numbers +stands—</p> + +<p><i>Type II. Solar stars.</i>—To this type of spectrum belong +the yellow stars, which show spectra like that of the sun, +or of Pollux (<a href="#Fig_125">Fig. 125</a>). These are not so rich in violet +light as are those of Type I, but in complexity of spectrum +and in the number of their absorption lines they far surpass +the Sirian stars. They are supposed to be at a lower +temperature than the Sirian stars, and a much larger number +of chemical elements seems present and active in the<span class="pagenum"><a name="Page_333" id="Page_333">[Pg 333]</a></span> +reversing layer of their atmospheres. The strong resemblance +which these spectra bear to that of the sun, together +with the fact that most of the sun's stellar neighbors have +spectra of this type, justify us in ranking both them and it +as members of one class, called <i>solar stars</i>.</p> + +<p><i>Type III. Red stars.</i>—A small number of stars show +spectra comparable with that of α Herculis (<a href="#Fig_134">Fig. 134</a>), in +which the blue and the violet part of the spectrum is almost +obliterated, and the remaining yellow and red parts +show not only dark lines, but also numerous broad dark +bands, sharp at one edge, and gradually fading out at the +other. It is this <i>selective absorption</i>, extinguishing the blue +and leaving the red end of the spectrum, which produces +the ruddy color of these stars, while the bands in their +spectra "are characteristic of chemical combinations, and +their presence ... proves that at certain elevations in the +atmospheres of these stars the temperature has sunk so low +that chemical combinations can be formed and maintained" +(Scheiner-Frost). One of the chemical compounds here indicated +is a hydrocarbon similar to that found in comets. +In the white and yellow stars the temperatures are so high +that the same chemical elements, although present, can not +unite one with another to form compound substances.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_134" id="Fig_134"></a> +<a href="images/i367.jpg"><img src="images/i367.jpg" width="500" height="70" alt="Fig. 134.—The spectrum of α Herculis.—Espin." title="Fig. 134.—The spectrum of α Herculis.—Espin." /></a> +<span class="caption"><span class="smcap">Fig. 134.</span>—The spectrum of α Herculis.—<span class="smcap">Espin.</span></span> +</div> + +<p>Most of the variable stars are red and have spectra of +the third type; but this does not hold true for the eclipse +variables like Algol, all of which are white stars with spectra +of the first type. The ordinary variable star is therefore +one with a dense atmosphere of relatively low temperature +and complex structure, which produces the prevailing +red color of these stars by absorbing the major part of<span class="pagenum"><a name="Page_334" id="Page_334">[Pg 334]</a></span> +their radiant energy of short wave length while allowing +the longer, red waves to escape. Although their exact +nature is not understood, there can be little doubt that the +fluctuation in the light of these stars is due to processes +taking place within the star itself, but whether above or +below its photosphere is still uncertain.</p> + +<p><a name="S_212" id="S_212"></a>212. <b>Classes of stars.</b>—There is no hard-and-fast dividing +line between these types of stellar spectra, but the change +from one to another is by insensible gradations, like the +transition from youth to manhood and from manhood to +old age, and along the line of transition are to be found +numberless peculiarities and varieties of spectra not enumerated +above—e. g., a few stars show not only dark absorption +lines in their spectra but bright lines as well, which, +like those in <a href="#Fig_48">Fig. 48</a>, point to the presence of incandescent +vapors, even in the outer parts of their atmospheres. Among +the lucid stars about 75 per cent have spectra of the first +type, 23 per cent are of the second type, 1 per cent of the +third type, and the remaining 1 per cent are peculiar or of +doubtful classification. Among the telescopic stars it is +probable that much the same distribution holds, but in the +present state of knowledge it is not prudent to speak with +entire confidence upon this point.</p> + +<p>That the great number of stars whose spectra have been +studied should admit of a classification so simple as the +above, is an impressive fact which, when supplemented by +the further fact of a gradual transition from one type of +spectrum to the next, leaves little room for doubt that in +the stars we have an innumerable throng of individuals belonging +to the same species but in different stages of development, +and that the sun is only one of these individuals, +of something less than medium size and in a stage of development +which is not at all peculiar, since it is shared by +nearly a fourth of all the stars.</p> + +<div class="figright" style="width: 350px;"><a name="Fig_135" id="Fig_135"></a> +<a href="images/i369.jpg"><img src="images/i369.jpg" width="350" height="288" alt="Fig 135.—Star cluster in Hercules." title="Fig 135.—Star cluster in Hercules." /></a> +<span class="caption"><span class="smcap">Fig 135.</span>—Star cluster in Hercules.</span> +</div> + + +<p><a name="S_213" id="S_213"></a>213. <b>Star clusters.</b>—In previous chapters we have noted +the Pleiades and Pręsepe as star clusters visible to the +<span class="pagenum"><a name="Page_335" id="Page_335">[Pg 335]</a></span> +naked eye, and to them we may add the Hyades, near Aldebaran, +and the little constellation Coma Berenices. But +more impressive than any of these, although visible only +in a telescope, is the splendid cluster in Hercules, whose +appearance in a telescope +of moderate size +is shown in <a href="#Fig_135">Fig. 135</a>, +while <a href="#Fig_136">Fig. 136</a> is a photograph +of the same +cluster taken with a +very large reflecting +telescope. This is only +a type of many telescopic +clusters which +are scattered over the +sky, and which are made +up of stars packed so +closely together as to become indistinguishable, one from +another, at the center of the cluster. Within an area +which could be covered by a third of the full moon's face +are crowded in this cluster more than five thousand stars +which are unquestionably close neighbors, but whose apparent +nearness to each other is doubtless due to their +great distance from us. It is quite probable that even at +the center of this cluster, where more than a thousand stars +are included within a radius of 160", the actual distances +separating adjoining stars are much greater than that separating +earth and sun, but far less than that separating the +sun from its nearest stellar neighbor.</p> + +<p>An interesting discovery of recent date, made by Professor +Bailey in photographing star clusters, is that some +few of them, which are especially rich in stars, contain an +extraordinary number of variable stars, mostly very faint +and of short period. Two clusters, one in the northern and +one in the southern hemisphere, contain each more than a +hundred variables, and an even more extraordinary case is<span class="pagenum"><a name="Page_336" id="Page_336">[Pg 336]</a></span> +presented by a cluster, called Messier 5, not far from the +star α Serpentis, which contains no less than sixty-three +variables, all about of the fourteenth magnitude, all having +light periods which differ but little from half a day, all +having light curves of about the same shape, and all having +a range of brightness from maximum to minimum of about +one magnitude. An extraordinary set of coincidences +which "points unmistakably to a common origin and cause +of variability."</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_136" id="Fig_136"></a> +<a href="images/i370-full.jpg"><img src="images/i370.jpg" width="500" height="542" alt="Fig. 136.—Star cluster in Hercules.—Keeler." title="Fig. 136.—Star cluster in Hercules.—Keeler." /></a> +<span class="caption"><span class="smcap">Fig. 136.</span>—Star cluster in Hercules.—<span class="smcap">Keeler.</span></span> +</div><p><span class="pagenum"><a name="Page_337" id="Page_337">[Pg 337]</a></span></p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_137" id="Fig_137"></a> +<a href="images/i371a-full.jpg"><img src="images/i371a.jpg" width="500" height="330" alt="Fig. 137.—The Andromeda nebula as seen in a very small telescope." title="Fig. 137.—The Andromeda nebula as seen in a very small telescope." /></a> +<span class="caption"><span class="smcap">Fig. 137.</span>—The Andromeda nebula as seen in a very small telescope.</span> +</div> + +<div class="figcenter" style="width: 500px;"><a name="Fig_138" id="Fig_138"></a> +<a href="images/i371b-full.jpg"><img src="images/i371b.jpg" width="500" height="508" alt="Fig. 138.—The Andromeda nebula and Holmes's comet. +Photographed by Barnard." title="Fig. 138.—The Andromeda nebula and Holmes's comet. +Photographed by Barnard." /></a> +<span class="caption"><span class="smcap">Fig. 138.</span>—The Andromeda nebula and Holmes's comet. +Photographed by <span class="smcap">Barnard</span>.</span> +</div> + +<div class="figcenter" style="width: 500px;"><a name="Fig_139" id="Fig_139"></a> +<a href="images/i372a-full.jpg"><img src="images/i372a.jpg" width="500" height="385" alt="Fig. 139.—A drawing of the Andromeda nebula." title="Fig. 139.—A drawing of the Andromeda nebula." /></a> +<span class="caption"><span class="smcap">Fig. 139.</span>—A drawing of the Andromeda nebula.</span> +</div> + +<div class="figcenter" style="width: 500px;"><a name="Fig_140" id="Fig_140"></a> +<a href="images/i372b-full.jpg"><img src="images/i372b.jpg" width="500" height="445" alt="Fig. 140.—A photograph of the Andromeda nebula.—Roberts." title="Fig. 140.—A photograph of the Andromeda nebula.—Roberts." /></a> +<span class="caption"><span class="smcap">Fig. 140.</span>—A photograph of the Andromeda nebula.—<span class="smcap">Roberts.</span></span> +</div> + +<div class="figright" style="width: 300px;"><a name="Fig_141" id="Fig_141"></a> +<a href="images/i373-full.jpg"><img src="images/i373.jpg" width="300" height="456" alt="Fig. 141.—Types of nebulę." title="Fig. 141.—Types of nebulę." /></a> +<span class="caption"><span class="smcap">Fig. 141.</span>—Types of nebulę.</span> +</div> + +<p><a name="S_214" id="S_214"></a>214. <b>Nebulę.</b>—Returning to <a href="#Fig_136">Fig. 136</a>, we note that its +background has a hazy appearance, and that at its center +the stars can no longer be distinguished, but blend one +with another so as to appear like a bright cloud. The<span class="pagenum"><a name="Page_338" id="Page_338">[Pg 338]</a></span> +outer part of the cluster is <i>resolved</i> into stars, while in the +picture the inner portion is not so resolved, although in +the original photographic plate the individual stars can be +distinguished to the very center of the cluster. In many<span class="pagenum"><a name="Page_339" id="Page_339">[Pg 339]</a></span> +cases, however, this is not possible, and we have an <i>irresolvable +cluster</i> which it is customary to call a <i>nebula</i> +(Latin, <i>little cloud</i>).</p> + +<p>The most conspicuous example of this in the northern +heavens is the great nebula in Andromeda (R. A. 0<sup>h</sup> 37<sup>m</sup>, +Dec. +41°), which may be seen with the naked eye as a +faint patch of foggy light. Look for it. This appears in +an opera glass or very small telescope not unlike <a href="#Fig_137">Fig. 137</a>, +which is reproduced from a sketch. <a href="#Fig_138">Fig. 138</a> is from a +photograph of the same object showing essentially the same +shape as in the preceding figure, but bringing out more +detail. Note the two small nebulę adjoining the large +one, and at the bottom of the picture an object which might +easily be taken for another nebula but which is in fact +a tailless comet that chanced to be passing that part of +the sky when the picture was taken. <a href="#Fig_139">Fig. 139</a> is from another +drawing of this nebula, +although it is hardly to be +recognized as a representation +of the same thing; but +its characteristic feature, the +two dark streaks near the center +of the picture, is justified +in part by <a href="#Fig_140">Fig. 140</a>, which is +from a photograph made with +a large reflecting telescope.</p> + +<p>A comparison of these several +representations of the +same thing will serve to illustrate +the vagueness of its outlines, +and how much the impressions +to be derived from +nebulę depend upon the telescopes +employed and upon the +observer's own prepossessions. The differences among the +pictures can not be due to any change in the nebula itself,<span class="pagenum"><a name="Page_340" id="Page_340">[Pg 340]</a></span> +for half a century ago it was sketched much as shown in +the latest of them (<a href="#Fig_140">Fig. 140</a>).</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_142" id="Fig_142"></a> +<a href="images/i374-full.jpg"><img src="images/i374.jpg" width="500" height="550" alt="Fig. 142.—The Trifid nebula.—Keeler." title="Fig. 142.—The Trifid nebula.—Keeler." /></a> +<span class="caption"><span class="smcap">Fig. 142.</span>—The Trifid nebula.—<span class="smcap">Keeler.</span></span> +</div> + +<p><a name="S_215" id="S_215"></a>215. <b>Typical nebulę.</b>—Some of the fantastic forms which +nebulę present in the telescope are shown on a small scale +in <a href="#Fig_141">Fig. 141</a>, but in recent years astronomers have learned to +place little reliance upon drawings such as these, which are +now almost entirely supplanted by photographs made with +long exposures in powerful telescopes. One of the most +exquisite of these modern photographs is that of the Trifid<span class="pagenum"><a name="Page_341" id="Page_341">[Pg 341]</a></span> +nebula in Sagittarius (<a href="#Fig_142">Fig. 142</a>). Note especially the dark +lanes that give to this nebula its name, Trifid, and which run +through its brightest parts, breaking it into seemingly independent +sections. The area of the sky shown in this cut is +about 15 per cent less than that covered by the full moon.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_143" id="Fig_143"></a> +<a href="images/i375-full.jpg"><img src="images/i375.jpg" width="500" height="546" alt="Fig. 143.—A nebula in Cygnus.—Keeler." title="Fig. 143.—A nebula in Cygnus.—Keeler." /></a> +<span class="caption"><span class="smcap">Fig. 143.</span>—A nebula in Cygnus.—<span class="smcap">Keeler.</span></span> +</div> + +<p><a href="#Fig_143">Fig. 143</a> shows a very different type of nebula, found in +the constellation Cygnus, which appears made up of filaments +closely intertwined, and stretches across the sky for +a distance considerably greater than the moon's diameter.<span class="pagenum"><a name="Page_342" id="Page_342">[Pg 342]</a></span></p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_144" id="Fig_144"></a> +<a href="images/i376-full.jpg"><img src="images/i376.jpg" width="500" height="536" alt="Fig. 144.—Spiral nebula in Canes Venatici.—Keeler." title="Fig. 144.—Spiral nebula in Canes Venatici.—Keeler." /></a> +<span class="caption"><span class="smcap">Fig. 144.</span>—Spiral nebula in Canes Venatici.—<span class="smcap">Keeler.</span></span> +</div> + +<p>A much smaller but equally striking nebula is that in +the constellation Canes Venatici (<a href="#Fig_144">Fig. 144</a>), which shows a +most extraordinary spiral structure, as if the stars composing +it were flowing in along curved lines toward a center of +condensation. The diameter of the circular part of this +nebula, omitting the projection toward the bottom of the +picture, is about five minutes of arc, a sixth part of the +diameter of the moon, and its thickness is probably very +small compared with its breadth, perhaps not much exceeding<span class="pagenum"><a name="Page_343" id="Page_343">[Pg 343]</a></span> +the width of the spiral streams which compose it. Note +how the bright stars that appear within the area of this +nebula fall on the streams of nebulous matter as if they +were part of them. This characteristic grouping of the +stars, which is followed in many other nebulę, shows that +they are really part and parcel of the nebula and not merely +on line with it. <a href="#Fig_145">Fig. 145</a> shows how a great nebula is associated +with the star ρ Ophiuchi.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_145" id="Fig_145"></a> +<a href="images/i377-full.jpg"><img src="images/i377.jpg" width="500" height="483" alt="Fig. 145.—Great nebula about the star ρ Ophiuchi.—Barnard." title="Fig. 145.—Great nebula about the star ρ Ophiuchi.—Barnard." /></a> +<span class="caption"><span class="smcap">Fig. 145.</span>—Great nebula about the star ρ Ophiuchi.—<span class="smcap">Barnard.</span></span> +</div> + +<p>Probably the most impressive of all nebulę is the great +one in Orion (<a href="#Fig_146">Fig. 146</a>), whose position is shown on the +star map between Rigel and ζ Orionis. Look for it with +an opera glass or even with the unaided eye. This is sometimes +called an <i>amorphous</i>—i. e., shapeless—nebula, because +it presents no definite form which the eye can grasp and +little trace of structure or organization. It is "without +form and void" at least in its central portions, although on +its edges curved filaments may be traced streaming away<span class="pagenum"><a name="Page_344" id="Page_344">[Pg 344]</a></span> +from the brighter parts of the central region. This nebula, +as shown in <a href="#Fig_146">Fig. 146</a>, covers an area about equal to that of +the full moon, without counting as any part of this the +companion nebula shown at one side, but photographs +made with suitable exposures show that faint outlying parts +of the nebula extend in curved lines over the larger part of +the constellation Orion. Indeed, over a large part of the +entire sky the background is faintly covered with nebulous +light whose brighter portions, if each were counted as a +separate nebula, would carry the total number of such objects +well into the hundreds of thousands.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_146" id="Fig_146"></a> +<a href="images/i378-full.jpg"><img src="images/i378.jpg" width="500" height="378" alt="Fig. 146.—The Orion nebula." title="Fig. 146.—The Orion nebula." /></a> +<span class="caption"><span class="smcap">Fig. 146.</span>—The Orion nebula.</span> +</div> + +<p>The Pleiades (<a href="#PLATE_IV">Plate IV</a>) present a case of a resolvable +star cluster projected against such a nebulous background +whose varying intensity should be noted in the figure. A +part of this nebulous matter is shown in wisps extending +from one star to the next, after the fashion of a bridge, and +leaving little doubt that the nebula is actually a part of the +cluster and not merely a background for it.</p> + +<div class="figcenter" style="width: 600px;"><a name="PLATE_IV" id="PLATE_IV"></a> +<a href="images/i379-full.jpg"><img src="images/i379.jpg" width="600" height="489" alt="THE PLEIADES + +(AFTER A PHOTOGRAPH)" title="THE PLEIADES + +(AFTER A PHOTOGRAPH)" /></a> +<span class="caption">THE PLEIADES + +(AFTER A PHOTOGRAPH)</span> +</div> + +<p><a href="#Fig_147">Fig. 147</a> shows a series of so-called double nebulę perhaps +comparable with double stars, although the most +recent photographic work seems to indicate that they are<span class="pagenum"><a name="Page_345" id="Page_345">[Pg 345]</a></span> +really faint spiral nebulę in which only the brightest parts +are shown by the telescope.</p> + +<p>According to Keeler, the spiral is the prevailing type +of nebulę, and while <a href="#Fig_144">Fig. 144</a> presents the most perfect example +of such a nebula, the +student should not fail to +note that the Andromeda nebula +(<a href="#Fig_140">Fig. 140</a>) shows distinct +traces of a spiral structure, +only here we do not see its +true shape, the nebula being +turned nearly edgewise toward +us so that its presumably circular +outline is foreshortened +into a narrow ellipse.</p> + +<div class="figright" style="width: 300px;"><a name="Fig_147" id="Fig_147"></a> +<a href="images/i381.jpg"><img src="images/i381.jpg" width="300" height="413" alt="Fig. 147.—Double nebulę. +Herschel." title="Fig. 147.—Double nebulę. +Herschel." /></a> +<span class="caption"><span class="smcap">Fig. 147.</span>—Double nebulę. +<span class="smcap">Herschel.</span></span> +</div> + +<p>Another type of nebula of +some consequence presents in +the telescope round disks like +those of Uranus or Neptune, +and this appearance has given +them the name <i>planetary nebulę</i>. +The comet in <a href="#Fig_138">Fig. 138</a>, if smaller, would represent +fairly well the nebulę of this type. Sometimes a planetary +nebula has a star at its center, and sometimes it appears +hollow, like a smoke ring, and is then called a ring nebula. +The most famous of these is in the constellation Lyra, not +far from Vega.</p> + +<p><a name="S_216" id="S_216"></a>216. <b>Spectra of nebulę.</b>—A star cluster, like the one in +Hercules, shows, of course, stellar spectra, and even when +irresolvable the spectrum is a continuous one, testifying to +the presence of stars, although they stand too close together +to be separately seen. But in a certain number of +nebulę the spectrum is altogether different, a discontinuous +one containing only a few bright lines, showing that +here the nebular light comes from glowing gases which +are subject to no considerable pressure. The planetary<span class="pagenum"><a name="Page_346" id="Page_346">[Pg 346]</a></span> +nebulę all have spectra of this kind and make up about +half of all the known gaseous nebulę. It is worthy of +note that a century ago Sir William Herschel had observed +a green shimmer in the light of certain nebulę which led +him to believe that they were "not of a starry nature," a +conclusion which has been abundantly confirmed by the +spectroscope. The green shimmer is, in fact, caused by a +line in the green part of the spectrum that is always present +and is always the brightest part of the spectrum of +gaseous nebulę.</p> + +<p>In faint nebulę this line constitutes the whole of their +visible spectrum, but in brighter ones two or three other +and fainter lines are usually associated with it, and a very +bright nebula, like that in Orion, may show a considerable +number of extra lines, but for the most part they can not +be identified in the spectrum of any terrestrial substances. +An exception to this is found in the hydrogen lines, which +are well marked in most spectra of gaseous nebulę, and +there are indications of one or two other known substances.</p> + +<p><a name="S_217" id="S_217"></a>217. <b>Density of nebulę.</b>—It is known from laboratory +experiments that diminishing the pressure to which an incandescent +gas is subject, diminishes the number of lines +contained in its spectrum, and we may surmise from the +very simple character and few lines of these nebular spectra +that the gas which produces them has a very small +density. But this is far from showing that the nebula +itself is correspondingly attenuated, for we must not assume +that this shining gas is all that exists in the nebula; +so far as telescope or camera are concerned, there may be +associated with it any amount of dark matter which can +not be seen because it sends to us no light. It is easy +to think in this connection of meteoric dust or the stuff of +which comets are made, for these seem to be scattered +broadcast on every side of the solar system and may, perchance, +extend out to the region of the nebulę.<span class="pagenum"><a name="Page_347" id="Page_347">[Pg 347]</a></span></p> + +<p>But, whatever may be associated in the nebula with the +glowing gas which we see, the total amount of matter, invisible +as well as visible, must be very small, or rather its +average density must be very small, for the space occupied +by such a nebula as that of Orion is so great that if the +average density of its matter were equal to that of air the +resulting mass by its attraction would exert a sensible effect +upon the motion of the sun through space. The brighter +parts of this nebula as seen from the earth subtend an angle +of about half a degree, and while we know nothing of its +distance from us, it is easy to see that the farther it is away +the greater must be its real dimensions, and that this increase +of bulk and mass with increasing distance will just +compensate the diminishing intensity of gravity at great +distances, so that for a given angular diameter—e. g., half +a degree—the force with which this nebula attracts the sun +depends upon its density but not at all upon its distance. +Now, the nebula must attract the sun in some degree, and +must tend to move it and the planets in an orbit about +the attracting center so that year after year we should see +the nebula from slightly different points of view, and this +changed point of view should produce a change in the apparent +direction of the nebula from us—i. e., a proper motion, +whose amount would depend upon the attracting force, +and therefore upon the density of the attracting matter. +Observations of the Orion nebula show that its proper +motion is wholly inappreciable, certainly far less than half +a second of arc per year, and corresponding to this amount +of proper motion the mean density of the nebula must be +some millions of times (10<sup>10</sup> according to Ranyard) less than +that of air at sea level—i. e., the average density throughout +the nebula is comparable with that of those upper parts +of the earth's atmosphere in which meteors first become +visible.</p> + +<p><a name="S_218" id="S_218"></a>218. <b>Motion of nebulę.</b>—The extreme minuteness of +their proper motions is a characteristic feature of all<span class="pagenum"><a name="Page_348" id="Page_348">[Pg 348]</a></span> +nebulę. Indeed, there is hardly a known case of sensible +proper motion of one of these bodies, although a dozen or +more of them show velocities in the line of sight ranging +in amount from +30 to -40 miles per second, the plus +sign indicating an increasing distance. While a part of +these velocities may be only apparent and due to the motion +of earth and sun through space, a part at least is real +motion of the nebulę themselves. These seem to move +through the celestial spaces in much the same way and +with the same velocities as do the stars, and their smaller +proper motions across the line of sight (angular motions) +are an index of their great distance from us. No one has +ever succeeded in measuring the parallax of a nebula or +star cluster.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_148" id="Fig_148"></a> +<a href="images/i384-full.jpg"><img src="images/i384.jpg" width="500" height="445" alt="Fig. 148.—A part of the Milky Way." title="Fig. 148.—A part of the Milky Way." /></a> +<span class="caption"><span class="smcap">Fig. 148.</span>—A part of the Milky Way.</span> +</div> + +<p>The law of gravitation presumably holds sway within +these bodies, and the fact that their several parts and the +stars which are involved within them, although attracted +by each other, have shown little or no change of position<span class="pagenum"><a name="Page_349" id="Page_349">[Pg 349]</a></span> +during the past century, is further evidence of their low +density and feeble attraction. In a few cases, however, +there seem to be in progress within a nebula changes of +brightness, so that what was formerly a faint part has become +a brighter one, or <i>vice versa</i>; but, on the whole, even +these changes are very small.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_149" id="Fig_149"></a> +<a href="images/i385-full.jpg"><img src="images/i385.jpg" width="500" height="499" alt="Fig. 149.—The Milky Way near θ Ophiuchi.—Barnard." title="Fig. 149.—The Milky Way near θ Ophiuchi.—Barnard." /></a> +<span class="caption"><span class="smcap">Fig. 149.</span>—The Milky Way near θ Ophiuchi.—<span class="smcap">Barnard.</span></span> +</div> + +<p><a name="S_219" id="S_219"></a>219. <b>The Milky Way.</b>—Closely related to nebulę and +star clusters is another feature of the sky, the <i>galaxy</i> or +<i>Milky Way</i>, with whose appearance to the unaided eye the +student should become familiar by direct study of the thing +itself. Figs. <a href="#Fig_148">148</a> and <a href="#Fig_149">149</a> are from photographs of two +small parts of it, and serve to bring out the small stars of +which it is composed. Every star shown in these pictures +is invisible to the naked eye, although their combined light +is easily seen. The general course of the galaxy across the +heavens is shown in the star maps, but these contain no +indication of the wealth of detail which even the naked eye +may detect in it. Bright and faint parts, dark rifts which<span class="pagenum"><a name="Page_350" id="Page_350">[Pg 350]</a></span> +cut it into segments, here and there a hole as if the ribbon +of light had been shot away—such are some of the features +to be found by attentive examination.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_150" id="Fig_150"></a> +<a href="images/i386-full.jpg"><img src="images/i386.jpg" width="500" height="498" alt="Fig. 150.—The Milky Way near β Cygni.—Barnard." title="Fig. 150.—The Milky Way near β Cygni.—Barnard." /></a> +<span class="caption"><span class="smcap">Fig. 150.</span>—The Milky Way near β Cygni.—<span class="smcap">Barnard.</span></span> +</div> + +<p>Speaking generally, the course of the Milky Way is a +great circle completely girdling the sky and having its +north pole in the constellation Coma Berenices. The +width of this stream of light is very different in different +parts of the heavens, amounting where it is widest, in Lyra +and Cygnus, to something more than 30°, although its +boundaries are too vague and ill defined to permit much +accuracy of measurement. Observe the very bright part +between β and γ Cygni, nearly opposite Vega, and note +how even an opera glass will partially resolve the nebulous +light into a great number of stars, which are here rather +brighter than in other parts of its course. But the resolution +into stars is only partial, and there still remains a +background of unresolved shimmer. <a href="#Fig_150">Fig. 150</a> is a photograph<span class="pagenum"><a name="Page_351" id="Page_351">[Pg 351]</a></span> +of a small part of this region in which, although +each fleck of light represents a separate star, the galaxy is +not completely resolved. Compare with this region, rich +in stars, the nearly empty space between the branches of +the galaxy a little west of Altair. Another hole in the +Milky Way may be found a little north and east of α Cygni, +and between the extremes of abundance and poverty here +noted there may be found every gradation of nebulous +light.</p> + +<p>The Milky Way is not so simple in its structure as might +at first be thought, but a clear and moonless night is +required to bring out its details. The nature of these +details, the structure of the galaxy, its shape and extent, +the arrangement of its parts, and their relation to stars +and nebulę in general, have been subjects of much speculation +by astronomers and others who have sought to trace +out in this way what is called the <i>construction of the +heavens</i>.</p> + +<p><a name="S_220" id="S_220"></a>220. <b>Distribution of the stars.</b>—How far out into space +do the stars extend? Are they limited or infinite in number? +Do they form a system of mutually related parts, or +are they bunched promiscuously, each for itself, without +reference to the others? Here is what has been well called +"the most important problem of stellar astronomy, the +acquisition of well-founded ideas about the distribution of +the stars." While many of the ideas upon this subject +which have been advanced by eminent astronomers and +which are still current in the books are certainly wrong, +and few of their speculations along this line are demonstrably +true, the theme itself is of such grandeur and permanent +interest as to demand at least a brief consideration. +But before proceeding to its speculative side we +need to collect facts upon which to build, and these, however +inadequate, are in the main simple and not far to seek.</p> + +<p>Parallaxes, proper motions, motions in the line of sight, +while pertinent to the problem of stellar distribution, are<span class="pagenum"><a name="Page_352" id="Page_352">[Pg 352]</a></span> +of small avail, since they are far too scanty in number and +relate only to limited classes of stars, usually the very +bright ones or those nearest to the sun. Almost the sole +available data are contained in the brightness of the stars +and the way in which they seem scattered in the sky. The +most casual survey of the heavens is enough to show that +the stars are not evenly sprinkled upon it. The lucid stars +are abundant in some regions, few in others, and the laborious +star gauges, actual counting of the stars in sample +regions of the sky, which have been made by the Herschels, +Celoria, and others, suffice to show that this lack of uniformity +in distribution is even more markedly true of the +telescopic stars.</p> + +<p>The rate of increase in the number of stars from one +magnitude to the next, as shown in <a href="#S_187">§ 187</a>, is proof of +another kind of irregularity in their distribution. It is not +difficult to show, mathematically, that if in distant regions +of space the stars were on the average as numerous and as +bright as they are in the regions nearer to the sun, then +the stars of any particular magnitude ought to be four +times as numerous as those of the next brighter magnitude—e. g., +four times as many sixth-magnitude stars as there +are fifth-magnitude ones. But, as we have already seen in +<a href="#S_187">§ 187</a>, by actual count there are only three times as many, +and from the discrepancy between these numbers, an actual +threefold increase instead of a fourfold one, we must conclude +that on the whole the stars near the sun are either +bigger or brighter or more numerous than in the remoter +depths of space.</p> + +<p><a name="S_221" id="S_221"></a>221. <b>The stellar system.</b>—But the arrangement of the +stars is not altogether lawless and chaotic; there are traces +of order and system, and among these the Milky Way is the +dominant feature. Telescope and photographic plate alike +show that it is made up of stars which, although quite irregularly +scattered along its course, are on the average +some twenty times as numerous in the galaxy as at its<span class="pagenum"><a name="Page_353" id="Page_353">[Pg 353]</a></span> +poles, and which thin out as we recede from it on either +side, at first rapidly and then more slowly. This tendency +to cluster along the Milky Way is much more pronounced +among the very faint telescopic stars than among the +brighter ones, for the lucid stars and the telescopic ones +down to the tenth or eleventh magnitude, while very +plainly showing the clustering tendency, are not more than +three times as numerous in the galaxy as in the constellations +most remote from it. It is remarkable as showing +the condensation of the brightest stars that one half of all +the stars in the sky which are brighter than the second +magnitude are included within a belt extending 12° on +either side of the center line of the galaxy.</p> + +<p>In addition to this general condensation of stars toward +the Milky Way, there are peculiarities in the distribution of +certain classes of stars which are worth attention. Planetary +nebulę and new stars are seldom, if ever, found far +from the Milky Way, and stars with bright lines in their +spectra especially affect this region of the sky. Stars with +spectra of the first type—Sirian stars—are much more +strongly condensed toward the Milky Way than are stars +of the solar type, and in consequence of this the Milky +Way is peculiarly rich in light of short wave lengths. Resolvable +star clusters are so much more numerous in the +galaxy than elsewhere, that its course across the sky would +be plainly indicated by their grouping upon a map showing +nothing but clusters of this kind.</p> + +<p>On the other hand, nebulę as a class show a distinct +aversion for the galaxy, and are found most abundantly in +those parts of the sky farthest from it, much as if they +represented raw material which was lacking along the +Milky Way, because already worked up to make the stars +which are there so numerous.</p> + +<p><a name="S_222" id="S_222"></a>222. <b>Relation of the sun to the Milky Way.</b>—The fact +that the galaxy is a <i>great circle</i> of the sky, but only of moderate +width, shows that it is a widely extended and comparatively<span class="pagenum"><a name="Page_354" id="Page_354">[Pg 354]</a></span> +thin stratum of stars within which the solar system +lies, a member of the galactic system, and probably not +very far from its center. This position, however, is not to +be looked upon as a permanent one, since the sun's motion, +which lies nearly in the plane of the Milky Way, is ceaselessly +altering its relation to the center of that system, and +may ultimately carry us outside its limits.</p> + +<p>The Milky Way itself is commonly thought to be a +ring, or series of rings, like the coils of the great spiral +nebula in Andromeda, and separated from us by a space far +greater than the thickness of the ring itself. Note in Figs. <a href="#Fig_149">149</a> +and <a href="#Fig_150">150</a> how the background is made up of bright and +dark parts curiously interlaced, and presenting much the +appearance of a thin sheet of cloud through which we look +to barren space beyond. While, mathematically, this appearance +can not be considered as proof that the galaxy +is in fact a distant ring, rather than a sheet of starry +matter stretching continuously from the nearer stellar +neighbors of the sun into the remotest depths of space, +nevertheless, most students of the question hold it to be +such a ring of stars, which are relatively close together +while its center is comparatively vacant, although even +here are some hundreds of thousands of stars which on the +whole have a tendency to cluster near its plane and to +crowd together a little more densely than elsewhere in the +region where the sun is placed.</p> + +<p><a name="S_223" id="S_223"></a>223. <b>Dimensions of the galaxy.</b>—The dimensions of this +stellar system are wholly unknown, but there can be no +doubt that it extends farther in the plane of the Milky +Way than at right angles to that plane, for stars of the fifteenth +and sixteenth magnitudes are common in the galaxy, +and testify by their feeble light to their great distance +from the earth, while near the poles of the Milky Way there +seem to be few stars fainter than the twelfth magnitude. +Herschel, with his telescope of 18 inches aperture, could +count in the Milky Way more than a dozen times as many<span class="pagenum"><a name="Page_355" id="Page_355">[Pg 355]</a></span> +stars per square degree as could Celoria with a telescope of +4 inches aperture; but around the poles of the galaxy the +two telescopes showed practically the same number of stars, +indicating that here even the smaller telescope reached to +the limits of the stellar system. Very recently, indeed, the +telescope with which <a href="#Fig_140">Fig. 140</a> was photographed seems to +have reached the farthest limit of the Milky Way, for on a +photographic plate of one of its richest regions Roberts +finds it completely resolved into stars which stand out upon +a black background with no trace of nebulous light between +them.</p> + +<p><a name="S_224" id="S_224"></a>224. <b>Beyond the Milky Way.</b>—Each additional step into +the depths of space brings us into a region of which less is +known, and what lies beyond the Milky Way is largely a +matter of conjecture. We shrink from thinking it an infinite +void, endless emptiness, and our intellectual sympathies +go out to Lambert's speculation of a universe filled +with stellar systems, of which ours, bounded by the galaxy, +is only one. There is, indeed, little direct evidence that +other such systems exist, but the Andromeda nebula is not +altogether unlike a galaxy with a central cloud of stars, +and in the southern hemisphere, invisible in our latitudes, +are two remarkable stellar bodies like the Milky Way in +appearance, but cut off from all apparent connection with +it, much as we might expect to find independent stellar +systems, if such there be.</p> + +<p>These two bodies are known as the Magellanic clouds, +and individually bear the names of Major and Minor Nubecula. +According to Sir John Herschel, "the Nubecula +Major, like the Minor, consists partly of large tracts and +ill-defined patches of irresolvable nebula, and of nebulosity +in every stage of resolution up to perfectly resolved stars +like the Milky Way, as also of regular and irregular nebulę ... of +globular clusters in every stage of resolvability, and +of clustering groups sufficiently insulated and condensed to +come under the designation of clusters of stars." Its outlines<span class="pagenum"><a name="Page_356" id="Page_356">[Pg 356]</a></span> +are vague and somewhat uncertain, but surely include +an area of more than 40 square degrees—i. e., as much as +the bowl of the Big Dipper—and within this area Herschel +counted several hundred nebulę and clusters "which far +exceeds anything that is to be met with in any other region +of the heavens." Although its excessive complexity of detail +baffled Herschel's attempts at artistic delineation, it +has yielded to the modern photographic processes, which +show the Nubecula Major to be an enormous spiral nebula +made up of subordinate stars, nebulę, and clusters, as is +the Milky Way.</p> + +<p>Compared with the Andromeda nebula, its greater angular +extent suggests a smaller distance, although for the +present all efforts at determining the parallax of either +seem hopeless. But the spiral form which is common to +both suggests that the Milky Way itself may be a gigantic +spiral nebula near whose center lies the sun, a humble +member of a great cluster of stars which is roughly globular +in shape, but flattened at the poles of the galaxy +and completely encircled by its coils. However plausible +such a view may appear, it is for the present, at least, pure +hypothesis, although vigorously advocated by Easton, who +bases his argument upon the appearance of the galaxy +itself.</p> + +<p><a name="S_225" id="S_225"></a>225. <b>Absorption of starlight.</b>—We have had abundant +occasion to learn that at least within the confines of the +solar system meteoric matter, cosmic dust, is profusely scattered, +and it appears not improbable that the same is true, +although in smaller degree, in even the remoter parts of +space. In this case the light which comes from the farther +stars over a path requiring many centuries to travel, must +be in some measure absorbed and enfeebled by the obstacles +which it encounters on the way. Unless celestial space is +transparent to an improbable degree the remoter stars do +not show their true brightness; there is a certain limit +beyond which no star is able to send its light, and beyond<span class="pagenum"><a name="Page_357" id="Page_357">[Pg 357]</a></span> +which the universe must be to us a blank. A lighthouse +throws into the fog its beams only to have them extinguished +before a single mile is passed, and though the +celestial lights shine farther, a limit to their reach is none +the less certain if meteoric dust exists outside the solar +system. If there is such an absorption of light in space, +as seems plausible, the universe may well be limitless and +the number of stellar systems infinite, although the most +attenuated of dust clouds suffices to conceal from us and +to shut off from our investigation all save a minor fraction +of it and them.</p> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_358" id="Page_358">[Pg 358]</a></span></p> +<h2><a name="CHAPTER_XV" id="CHAPTER_XV"></a>CHAPTER XV</h2> + +<h3>GROWTH AND DECAY</h3> + + +<p><a name="S_226" id="S_226"></a>226. <b>Nature of the problem.</b>—To use a common figure of +speech, the universe is alive. We have found it filled with +an activity that manifests itself not only in the motions of +the heavenly bodies along their orbits, but which extends +to their minutest parts, the molecules and atoms, whose +vibrations furnish the radiant energy given off by sun and +stars. Some of these activities, such as the motions of the +heavenly bodies in their orbits, seem fitted to be of endless +duration; while others, like the radiation of light and heat, +are surely temporary, and sooner or later must come to an +end and be replaced by something different. The study of +things as they are thus leads inevitably to questions of +what has been and what is to be. A sound science should +furnish some account of the universe of yesterday and +to-morrow as well as of to-day, and we need not shrink +from such questions, although answers to them must be +vague and in great measure speculative.</p> + +<p>The historian of America finds little difficulty with events +of the nineteenth century or even the eighteenth, but the +sources of information about America in the fifteenth century +are much less definite; the tenth century presents +almost a blank, and the history of American mankind in +the first century of the Christian era is wholly unknown. +So, as we attempt to look into the past or the future of the +heavens, we must expect to find the mists of obscurity grow +denser with remoter periods until even the vaguest outlines +of its development are lost, and we are compelled to say,<span class="pagenum"><a name="Page_359" id="Page_359">[Pg 359]</a></span> +beyond this lies the unknown. Our account of growth and +decay in the universe, therefore, can not aspire to cover the +whole duration of things, but must be limited in its scope +to certain chapters whose epochs lie near to the time in +which we live, and even for these we need to bear constantly +in mind the logical bases of such an inquiry and +the limitations which they impose upon us.</p> + +<p><a name="S_227" id="S_227"></a>227. <b>Logical bases and limitations.</b>—The first of these +bases is: An adequate knowledge of the present universe. +Our only hope of reading the past and future lies in an +understanding of the present; not necessarily a complete +knowledge of it, but one which is sound so far as it goes. +Our position is like that of a detective who is called upon +to unravel a mystery or crime, and who must commence +with the traces that have been left behind in its commission. +The foot print, the blood stain, the broken glass must +be examined and compared, and fashioned into a theory of +how they came to be; and as a wrong understanding of +these elements is sure to vitiate the theories based upon +them, so a false science of the universe as it now is, will +surely give a false account of what it has been; while a +correct but incomplete knowledge of the present does not +wholly bar an understanding of the past, but only puts us +in the position of the detective who correctly understands +what he sees but fails to take note of other facts which +might greatly aid him.</p> + +<p>The second basis of our inquiry is: The assumed permanence +of natural laws. The law of gravitation certainly +held true a century ago as well as a year ago, and for aught +we know to the contrary it may have been a law of the universe +for untold millions of years; but that it has prevailed +for so long a time is a pure assumption, although a necessary +one for our purpose. So with those other laws of +mathematics and mechanics and physics and chemistry to +which we must appeal; if there was ever a time or place +in which they did not hold true, that time and place lie<span class="pagenum"><a name="Page_360" id="Page_360">[Pg 360]</a></span> +beyond the scope of our inquiry, and are in the domain +inaccessible to scientific research. It is for this reason +that science knows nothing and can know nothing of a +creation or an end of the universe, but considers only its +orderly development within limited periods of time. What +kind of a past universe would, under the operation of +known laws, develop into the present one, is the question +with which we have to deal, and of it we may say with +Helmholtz: "From the standpoint of science this is no +idle speculation but an inquiry concerning the limitations +of its methods and the scope of its known laws."</p> + +<p>To ferret out the processes by which the heavenly bodies +have been brought to their present condition we seek first +of all for lines of development now in progress which tend +to change the existing order of things into something different, +and, having found these, to trace their effects into +both past and future. Any force, however small, or any +process, however slow, may produce great results if it works +always and ceaselessly in the same direction, and it is in +these processes, whose trend is never reversed, that we find +a partial clew to both past and future.</p> + +<p><a name="S_228" id="S_228"></a>228. <b>The sun's development.</b>—The first of these to claim +our attention is the shrinking of the sun's diameter which, +as we have seen in <a href="#CHAPTER_X">Chapter X</a>, is the means by which the +solar output of radiant energy is maintained from year to +year. Its amount, only a few feet per annum, is far too +small to be measured with any telescope; but it is cumulative, +working century after century in the same direction, +and, given time enough, it will produce in the future, and +must have produced in the past, enormous transformations +in the sun's bulk and equally significant changes in its +physical condition.</p> + +<p>Thus, as we attempt to trace the sun's history into the +past, the farther back we go the greater shall we expect to +find its diameter and the greater the space (volume) +through which its molecules are spread. By reason of this<span class="pagenum"><a name="Page_361" id="Page_361">[Pg 361]</a></span> +expansion its density must have been less then than now, +and by going far enough back we may even reach a time at +which the density was comparable with what we find in the +nebulę of to-day. If our ideas of the sun's present mechanism +are sound, then, as a necessary consequence of these, +its past career must have been a process of condensation in +which its component particles were year by year packed +closer together by their own attraction for each other. As +we have seen in <a href="#S_126">§ 126</a>, this condensation necessarily developed +heat, a part of which was radiated away as fast as produced, +while the remainder was stored up, and served to +raise the temperature of the sun to what we find it now. +At the present time this temperature is a chief obstacle to +further shrinkage, and so powerfully opposes the gravitative +forces as to maintain nearly an equilibrium with them, +thus causing a very slow rate of further condensation. But +it is not probable that this was always so. In the early +stages of the sun's history, when the temperature was low, +contraction of its bulk must have been more rapid, and +attempts have been made by the mathematicians to measure +its rate of progress and to determine how long a time has +been consumed in the development of the present sun from +a primitive nebulous condition in which it filled a space of +greater diameter than Neptune's orbit. Of course, numerical +precision is not to be expected in results of this kind, +but, from a consideration of the greatest amount of heat +that could be furnished by the shrinkage of a mass equal to +that of the sun, it seems that the period of this development +is to be measured in tens of millions or possibly hundreds +of millions of years, but almost certainly does not +reach a thousand millions.</p> + +<p><a name="S_229" id="S_229"></a>229. <b>The sun's future.</b>—The future duration of the sun +as a source of radiant energy is surely to be measured in +far smaller numbers than these. Its career as a dispenser +of light and heat is much more than half spent, for the +shrinkage results in an ever-increasing density, which<span class="pagenum"><a name="Page_362" id="Page_362">[Pg 362]</a></span> +makes its gaseous substance approximate more and more +toward the behavior of a liquid or solid, and we recall that +these forms of matter can not by any further condensation +restore the heat whose loss through radiation caused them +to contract. They may continue to shrink, but their temperature +must fall, and when the sun's substance becomes +too dense to obey the laws of gaseous matter its surface +must cool rapidly as a consequence of the radiation into +surrounding space, and must congeal into a crust which, +although at first incandescent, will speedily become dark +and opaque, cutting off the light of the central portions, +save as it may be rent from time to time by volcanic +outbursts of the still incandescent mass beneath. But +such outbursts can be of short duration only, and its final +condition must be that of a dark body, like the earth or +moon, no longer available as a source of radiant energy. +Even before the formation of a solid crust it is quite possible +that the output of light and heat may be seriously +diminished by the formation of dense vapors completely +enshrouding it, as is now the case with Jupiter and Saturn. +It is believed that these planets were formerly incandescent, +and at the present time are in a state of development +through which the earth has passed and toward which the +sun is moving. According to Newcomb, the future during +which the sun can continue to furnish light and heat at its +present rate is not likely to exceed 10,000,000 years.</p> + +<p>This idea of the sun as a developing body whose present +state is only temporary, furnishes a clew to some of the +vexing problems of solar physics. Thus the sun-spot period, +the distribution of the spots in latitude, and the peculiar +law of rotation of the sun in different latitudes, may be, +and very probably are, results not of anything now operating +beneath its photosphere, but of something which happened +to it in the remote past—e. g., an unsymmetrical +shrinkage or possibly a collision with some other body. At +sea the waves continue to toss long after the storm which<span class="pagenum"><a name="Page_363" id="Page_363">[Pg 363]</a></span> +produced them has disappeared, and, according to the +mathematical researches of Wilsing, a profound agitation +of the sun's mass might well require tens of thousands, or +even hundreds of thousands of years to subside, and during +this time its effects would be visible, like the waves, as phenomena +for which the actual condition of things furnishes +no apparent cause.</p> + +<p><a name="S_230" id="S_230"></a>230. <b>The nebular hypothesis.</b>—The theory of the sun's +progressive contraction as a necessary result of its radiation +of energy is comparatively modern, but more than a century +ago philosophic students of Nature had been led in +quite a different way to the belief that in the earlier stages +of its career the sun must have been an enormously extended +body whose outer portions reached even beyond the +orbit of the remotest planet. Laplace, whose speculations +upon this subject have had a dominant influence during +the nineteenth century, has left, in a popular treatise upon +astronomy, an admirable statement of the phenomena of +planetary motion, which suggest and lead up to the nebular +theory of the sun's development, and in presenting this +theory we shall follow substantially his line of thought, +but with some freedom of translation and many omissions.</p> + +<p>He says: "To trace out the primitive source of the planetary +movements, we have the following five phenomena: +(1) These movements all take place in the same direction +and nearly in the same plane. (2) The movements of the +satellites are in the same direction as those of the planets. +(3) The rotations of the planets and the sun are in the +same direction as the orbital motions and nearly in the same +plane. (4) Planets and satellites alike have nearly circular +orbits. (5) The orbits of comets are wholly unlike these by +reason of their great eccentricities and inclinations to the +ecliptic." That these coincidences should be purely the +result of chance seemed to Laplace incredible, and, seeking +a cause for them, he continues: "Whatever its nature may +be, since it has produced or controlled the motions of the<span class="pagenum"><a name="Page_364" id="Page_364">[Pg 364]</a></span> +planets, it must have reached out to all these bodies, and, in +view of the prodigious distances which separate them, the +cause can have been nothing else than a fluid of great extent +which must have enveloped the sun like an atmosphere. +A consideration of the planetary motions leads us to think +that ... the sun's atmosphere formerly extended far beyond +the orbits of all the planets and has shrunk by degrees +to its present dimensions." This is not very different from +the idea developed in <a href="#S_228">§ 228</a> from a consideration of the +sun's radiant energy; but in Laplace's day the possibility +of generating the sun's heat by contraction of its bulk was +unknown, and he was compelled to assume a very high temperature +for the primitive nebulous sun, while we now know +that this is unnecessary. Whether the primitive nebula +was hot or cold the shrinkage would take place in much +the same way, and would finally result in a star or sun of +very high temperature, but its development would be slower +if it were hot in the beginning than if it were cold.</p> + +<p>But again Laplace: "How did the sun's atmosphere +determine the rotations and revolutions of planets and +satellites? If these bodies had been deeply immersed in +this atmosphere its resistance to their motion would have +made them fall into the sun, and we may therefore conjecture +that the planets were formed, one by one, at the outer +limits of the solar atmosphere by the condensation of zones +of vapor which were cast off in the plane of the sun's equator." +Here he proceeds to show by an appeal to dynamical +principles that something of this kind must happen, and +that the matter sloughed off by the nebula in the form of a +ring, perhaps comparable to the rings of Saturn or the +asteroid zone, would ultimately condense into a planet, +which in its turn might shrink and cast off rings to produce +satellites.</p> + +<div class="figcenter" style="width: 500px;"><a name="LAPLACE" id="LAPLACE"></a> +<a href="images/i401-full.jpg"><img src="images/i401.jpg" width="500" height="620" alt="PIERRE SIMON LAPLACE (1749-1827)." title="PIERRE SIMON LAPLACE (1749-1827)." /></a> +<span class="caption">PIERRE SIMON LAPLACE (1749-1827).</span> +</div> + +<p>Planets and satellites would then all have similar motions, +as noted at the beginning of this section, since in +every case this motion is an inheritance from a common<span class="pagenum"><a name="Page_365" id="Page_365">[Pg 365]</a></span> +source, the rotation of the primitive nebula about its own +axis. "All the bodies which circle around a planet having +been thus formed from rings which its atmosphere successively +abandoned as rotation became more and more rapid, +this rotation should take place in less time than is required +for the orbital revolution of any of the bodies which have +been cast off, and this holds true for the sun as compared +with the planets."</p> + +<p><a name="S_231" id="S_231"></a>231. <b>Objections to the nebular hypothesis.</b>—In Laplace's +time this slower rate of motion was also supposed to hold +true for Saturn's rings as compared with the rotation of +Saturn itself, but, as we have seen in <a href="#CHAPTER_XI">Chapter XI</a>, this ring is +made up of a great number of independent particles which +move at different rates of speed, and comparing, through +Kepler's Third Law, the motion of the inner edge of the +ring with the known periodic time of the satellites, we may +find that these particles must rotate about Saturn more +rapidly than the planet turns upon its axis. Similarly the +inner satellite of Mars completes its revolution in about +one third of a Martian day, and we find in cases like this +grounds for objection to the nebular theory. Compare also +Laplace's argument with the peculiar rotations of Uranus, +Neptune, and their satellites (<a href="#CHAPTER_XI">Chapter XI</a>). Do these fortify +or weaken his case?</p> + +<p>Despite these objections and others equally serious that +have been raised, the nebular theory agrees with the facts +of Nature at so many points that astronomers upon the +whole are strongly inclined to accept its major outlines as +being at least an approximation to the course of development +actually followed by the solar system; but at some +points—e. g., the formation of planets and satellites through +the casting off of nebulous rings—the objections are so +many and strong as to call for revision and possibly serious +modification of the theory.</p> + +<p>One proposed modification, much discussed in recent +years, consists in substituting for the primitive <i>gaseous</i><span class="pagenum"><a name="Page_366" id="Page_366">[Pg 366]</a></span> +nebula imagined by Laplace, a very diffuse cloud of meteoric +matter which in the course of its development would +become transformed into the gaseous state by rising temperature. +From this point of view much of the meteoric +dust still scattered throughout the solar system may be +only the fragments left over in fashioning the sun and +planets. Chamberlin and Moulton, who have recently +given much attention to this subject, in dissenting from +some of Laplace's views, consider that the primitive nebulous +condition must have been one in which the matter of +the system was "so brought together as to give low mass, +high momentum, and irregular distribution to the outer +part, and high mass, low momentum, and sphericity to the +central part," and they suggest a possible oblique collision +of a small nebula with the outer parts of a large one.</p> + +<p><a name="S_232" id="S_232"></a>232. <b>Bode's law.</b>—We should not leave the theory of +Laplace without noting the light it casts upon one point +otherwise obscure—the meaning of Bode's law (<a href="#S_134">§ 134</a>). +This law, stated in mathematical form, makes a geometrical +series, and similar geometrical series apply to the +distances of the satellites of Jupiter and Saturn from +these planets. Now, Roche has shown by the application +of physical laws to the shrinkage of a gaseous body that +its radius at any time may be expressed by means of a +certain mathematical formula very similar to Bode's law, +save that it involves the amount of time that has elapsed +since the beginning of the shrinking process. By comparing +this formula with the one corresponding to Bode's law +he reaches the conclusion that the peculiar spacing of the +planets expressed by that law means that they were formed +at successive <i>equal</i> intervals of time—i. e., that Mars is as +much older than the earth as the earth is older than +Venus, etc. The failure of Bode's law in the case of +Neptune would then imply that the interval of time between +the formation of Neptune and Uranus was shorter +than that which has prevailed for the other planets. But<span class="pagenum"><a name="Page_367" id="Page_367">[Pg 367]</a></span> +too much stress should not be placed upon this conclusion. +So long as the manner in which the planets came into being +continues an open question, conclusions about their time +of birth must remain of doubtful validity.</p> + +<p><a name="S_233" id="S_233"></a>233. <b>Tidal friction between earth and moon.</b>—An important +addition to theories of development within the solar +system has been worked out by Prof. G. H. Darwin, who, +starting with certain very simple assumptions as to the +present condition of things in earth and moon, derives +from these, by a strict process of mathematical reasoning, +far-reaching conclusions of great interest and importance. +The key to these conclusions lies in recognition of the fact +that through the influence of the tides (<a href="#S_42">§ 42</a>) there is now +in progress and has been in progress for a very long time, a +gradual transfer of motion (moment of momentum) from +the earth to the moon. The earth's motion of rotation is +being slowly destroyed by the friction of the tides, as the +motion of a bicycle is destroyed by the friction of a brake, +and, in consequence of this slowing down, the moon is +pushed farther and farther away from the earth, so that +it now moves in a larger orbit than it had some millions +of years ago.</p> + +<p><a href="#Fig_24">Fig. 24</a> has been used to illustrate the action of the +moon in raising tides upon the earth, but in accordance +with the third law of motion (<a href="#S_36">§ 36</a>) this action must be +accompanied by an equal and contrary reaction whose +nature may readily be seen from the same figure. The +moon moves about its orbit from west to east and the +earth rotates about its axis in the same direction, as +shown by the curved arrow in the figure. The tidal wave, +<i>I</i>, therefore points a little <i>in advance</i> of the moon's position +in its orbit and by its attraction must tend to pull the +moon ahead in its orbital motion a little faster than it +would move if the whole substance of the earth were +placed inside the sphere represented by the broken circle +in the figure. It is true that the tidal wave at <i>I''</i> pulls<span class="pagenum"><a name="Page_368" id="Page_368">[Pg 368]</a></span> +back and tends to neutralize the effect of the wave at <i>I</i>, +but on the whole the tidal wave nearer the moon has the +stronger influence, and the moon on the whole moves a +very little faster, and by virtue of this added impetus +draws continually a little farther away from the earth +than it would if there were no tides.</p> + +<p><a name="S_234" id="S_234"></a>234. <b>Consequences of tidal friction upon the earth.</b>—This +process of moving the moon away from the earth is a +cumulative one, going on century after century, and with +reference to it the moon's orbit must be described not as +a circle or ellipse, or any other curve which returns into +itself, but as a spiral, like the balance spring of a watch, +each of whose coils is a little larger than the preceding +one, although this excess is, to be sure, very small, because +the tides themselves are small and the tidal influence +feeble when compared with the whole attraction +of the earth for the moon. But, given time enough, +even this small force may accomplish great results, and +something like 100,000,000 years of past opportunity +would have sufficed for the tidal forces to move the moon +from close proximity with the earth out to its present position.</p> + +<p>For millions of years to come, if moon and earth endure +so long, the distance between them must go on increasing, +although at an ever slower rate, since the farther away the +moon goes the smaller will be the tides and the slower the +working out of their results. On the other hand, when +the moon was nearer the earth than now, tidal influences +must have been greater and their effects more rapidly +produced than at the present time, particularly if, as +seems probable, at some past epoch the earth was hot and +plastic like Jupiter and Saturn. Then, instead of tides in +the water of the sea, such as we now have, the whole substance +of the earth would respond to the moon's attraction +in <i>bodily tides</i> of semi-fluid matter not only higher, but with +greater internal friction of their molecules one upon another,<span class="pagenum"><a name="Page_369" id="Page_369">[Pg 369]</a></span> +and correspondingly greater effect in checking the +earth's rotation.</p> + +<p>But, whether the tide be a bodily one or confined to the +waters of the sea, so long as the moon causes it to flow +there will be a certain amount of friction which will affect +the earth much as a brake affects a revolving wheel, slowing +down its motion, and producing thus a longer day as +well as a longer month on account of the moon's increased +distance. Slowing down the earth's rotation is the direct +action of the moon upon the earth. Pushing the moon +away is the form in which the earth's equal and contrary +reaction manifests itself.</p> + +<p><a name="S_235" id="S_235"></a>235. <b>Consequences of tidal friction upon the moon.</b>—When +the moon was plastic the earth must have raised in it a +bodily tide manifold greater than the lunar tides upon the +earth, and, as we have seen in <a href="#CHAPTER_IX">Chapter IX</a>, this tide has +long since worn out the greater part of the moon's rotation +and brought our satellite to the condition in which it presents +always the same face toward the earth.</p> + +<p>These two processes, slowing down the rotation and +pushing away the disturbing body, are inseparable—one +requires the other; and it is worth noting in this connection +that when for any reason the tide ceases to flow, and +the tidal wave takes up a permanent position, as it has in +the moon (<a href="#S_99">§ 99</a>), its work is ended, for when there is no +motion of the wave there can be no friction to further +reduce the rate of rotation of the one body, and no reaction +to that friction to push away the other. But this permanent +and stationary tidal wave in the moon, or elsewhere, +means that the satellite presents always the same face +toward its planet, moving once about its orbit in the time +required for one revolution upon its axis, and the tide +raised by the moon upon the earth tends to produce here +the result long since achieved in our satellite, to make our +day and month of equal length, and to make the earth +turn always the same side toward the moon. But the<span class="pagenum"><a name="Page_370" id="Page_370">[Pg 370]</a></span> +moon's tidal force is small compared with that of the earth, +and has a vastly greater momentum to overcome, so that +its work upon the earth is not yet complete. According +to Thomson and Tait, the moon must be pushed off another +hundred thousand miles, and the day lengthened out +by tidal influence to seven of our present weeks before the +day and the lunar month are made of equal length, and +the moon thereby permanently hidden from one hemisphere +of the earth.</p> + +<p><a name="S_236" id="S_236"></a>236. <b>The earth-moon system.</b>—Retracing into the past +the course of development of the earth and moon, it is possible +to reach back by means of the mathematical theory +of tidal friction to a time at which these bodies were much +nearer to each other than now, but it has not been found +possible to trace out the mode of their separation from one +body into two, as is supposed in the nebular theory. In +the earliest part of their history accessible to mathematical +analysis they are distinct bodies at some considerable distance +from each other, with the earth rotating about an +axis more nearly perpendicular to the moon's orbit and to +the ecliptic than is now the case. Starting from such a +condition, the lunar tides, according to Darwin, have been +instrumental in tipping the earth's rotation axis into its +present oblique position, and in determining the eccentricity +of the moon's orbit and its position with respect to +the ecliptic as well as the present length of day and month.</p> + +<p><a name="S_237" id="S_237"></a>237. <b>Tidal friction upon the planets.</b>—The satellites of the +outer planets are equally subject to influences of this kind, +and there appears to be independent evidence that some of +them, at least, turn always the same face toward their +respective planets, indicating that the work of tidal friction +has here been accomplished. We saw in <a href="#CHAPTER_XI">Chapter XI</a> that +it is at present an open question whether the inner planets, +Venus and Mercury, do not always turn the same face +toward the sun, their day and year being of equal length. +In addition to the direct observational evidence upon this<span class="pagenum"><a name="Page_371" id="Page_371">[Pg 371]</a></span> +point, Schiaparelli has sought to show by an appeal to tidal +theory that such is probably the case, at least for Mercury, +since the tidal forces which tend to bring about this result +in that planet are about as great as the forces which have +certainly produced it in the case of the moon and Saturn's +satellite, Japetus. The same line of reasoning would show +that every satellite in the solar system, save possibly the +newly discovered ninth satellite of Saturn, must, as a consequence +of tidal friction, turn always the same face toward +its planet.</p> + +<p><a name="S_238" id="S_238"></a>238. <b>The solar tide.</b>—The sun also raises tides in the +earth, and their influence must be similar in character to +that of the lunar tides, checking the rotation of the earth +and thrusting earth and sun apart, although quantitatively +these effects are small compared with those of the moon. +They must, however, continue so long as the solar tide +lasts, possibly until the day and year are made of equal +length—i. e., they may continue long after the lunar tidal +influence has ceased to push earth and moon apart. Should +this be the case, a curious inverse effect will be produced. +The day being then longer than the month, the moon will +again raise a tide in the earth which will run around it +<i>from west to east</i>, opposite to the course of the present tide, +thus tending to accelerate the earth's rotation, and by its +reaction to bring the moon back toward the earth again, +and ultimately to fall upon it.</p> + +<p>We may note that an effect of this kind must be in +progress now between Mars and its inner satellite, Phobos, +whose time of orbital revolution is only one third of a Martian +day. It seems probable that this satellite is in the last +stages of its existence as an independent body, and must +ultimately fall into Mars.</p> + +<p><a name="S_239" id="S_239"></a>239. <b>Roche's limit.</b>—In looking forward to such a catastrophe, +however, due regard must be paid to a dynamical +principle of a different character. The moon can never be +precipitated upon the earth entire, since before it reaches<span class="pagenum"><a name="Page_372" id="Page_372">[Pg 372]</a></span> +us it will have been torn asunder by the excess of the +earth's attraction for the near side of its satellite over that +which it exerts upon the far side. As the result of Roche's +mathematical analysis we are able to assign a limiting distance +between any planet and its satellite within which the +satellite, if it turns always the same face toward the planet, +can not come without being broken into fragments. If we +represent the radius of the planet by <i>r</i>, and the quotient +obtained by dividing the density of the planet by the density +of the satellite by <i>q</i>, then</p> + +<p class="center">Roche's limit = 2.44 <i>r</i> ∛ <i>q</i>.</p> + +<p>Thus in the case of earth and moon we find from the densities +given in <a href="#S_95">§ 95</a>, <i>q</i> = 1.65, and with <i>r</i> = 3,963 miles we +obtain 11,400 miles as the nearest approach which the moon +could make to the earth without being broken up by the +difference of the earth's attractions for its opposite sides.</p> + +<p>We must observe, however, that Roche's limit takes no +account of molecular forces, the adhesion of one molecule +to another, by virtue of which a stick or stone resists fracture, +but is concerned only with the gravitative forces by +which the molecules are attracted toward the moon's center +and toward the earth. Within a stone or rock of moderate +size these gravitative forces are insignificant, and cohesion +is the chief factor in preserving its integrity, but in a large +body like the moon, the case is just reversed, cohesion plays +a small part and gravitation a large one in holding the +body together. We may conclude, therefore, that at a +proper distance these forces are capable of breaking up the +moon, or any other large body, into fragments of a size +such that molecular cohesion instead of gravitation is the +chief agent in preserving them from further disintegration.</p> + +<p><a name="S_240" id="S_240"></a>240. <b>Saturn's rings.</b>—Saturn's rings are of peculiar interest +in this connection. The outer edge of the ring system +lies just inside of Roche's limit for this planet, and we +have already seen that the rings are composed of small fragments<span class="pagenum"><a name="Page_373" id="Page_373">[Pg 373]</a></span> +independent of each other. Whatever may have +been the process by which the nine satellites of Saturn +came into existence, we have in Roche's limit the explanation +why the material of the ring was not worked up into +satellites; the forces exerted by Saturn would tear into +pieces any considerable satellite thus formed and equally +would prevent the formation of one from raw material.</p> + +<p>Saturn's rings present the only case within the solar +system where matter is known to be revolving about a +planet at a distance less than Roche's limit, and it is an +interesting question whether these rings can remain as a +permanent part of the planet's system or are only a temporary +feature. The drawings of Saturn made two centuries +ago agree among themselves in representing the rings as +larger than they now appear, and there is some reason to +suppose that as a consequence of mutual disturbances—collisions—their +momentum is being slowly wasted so that +ultimately they must be precipitated into the planet. But +the direct evidence of such a progress that can be drawn +from present data is too scanty to justify positive conclusions +in the matter. On the other hand, Nolan suggests +that in the outer parts of the ring small satellites might be +formed whose tidal influence upon Saturn would suffice to +push them away from the ring beyond Roche's limit, and +that the very small inner satellites of Saturn may have +been thus formed at the expense of the ring.</p> + +<p>The inner satellite of Mars is very close to Roche's limit +for that planet, and, as we have seen above, must be approaching +still nearer to the danger line.</p> + +<p><a name="S_241" id="S_241"></a>241. <b>The moon's development.</b>—The fine series of photographs +of the moon obtained within the last few years at +Paris, have been used by the astronomers of that observatory +for a minute study of the lunar formations, much as +geologists study the surface of the earth to determine something +about the manner in which it was formed. Their +conclusions are, in general, that at some past time the moon<span class="pagenum"><a name="Page_374" id="Page_374">[Pg 374]</a></span> +was a hot and fluid body which, as it cooled and condensed, +formed a solid crust whose further shrinkage compressed +the liquid nucleus and led to a long series of fractures in +the crust and outbursts of liquid matter, whose latest and +feeblest stages produced the lunar craters, while traces of +the earlier ones, connected with a general settling of the +crust, although nearly obliterated, are still preserved in certain +large but vague features of the lunar topography, such +as the distribution of the seas, etc. They find also in certain +markings of the surface what they consider convincing +evidence of the existence in past times of a lunar atmosphere. +But this seems doubtful, since the force of gravity +at the moon's surface is so small that an atmosphere similar +to that of the earth, even though placed upon the moon, +could not permanently endure, but would be lost by the +gradual escape of its molecules into the surrounding space.</p> + +<p>The molecules of a gas are quite independent one of +another, and are in a state of ceaseless agitation, each one +darting to and fro, colliding with its neighbors or with +whatever else opposes its forward motion, and traveling +with velocities which, on the average, amount to a good +many hundreds of feet per second, although in the case of +any individual molecule they may be much less or much +greater than the average value, an occasional molecule having +possibly a velocity several times as great as the average. +In the upper regions of our own atmosphere, if one of these +swiftly moving particles of oxygen or nitrogen were headed +away from the earth with a velocity of seven miles per second, +the whole attractive power of the earth would be +insufficient to check its motion, and it would therefore, +unless stopped by some collision, escape from the earth and +return no more. But, since this velocity of seven miles per +second is more than thirty times as great as the average +velocity of the molecules of air, it must be very seldom indeed +that one is found to move so swiftly, and the loss of +the earth's atmosphere by leakage of this sort is insignificant.<span class="pagenum"><a name="Page_375" id="Page_375">[Pg 375]</a></span> +But upon the moon, or any other body where the +force of gravity is small, conditions are quite different, and +in our satellite a velocity of little more than one mile per +second would suffice to carry a molecule away from the +outer limits of its atmosphere. This velocity, only five times +the average, would be frequently attained, particularly in +former times when the moon's temperature was high, for +then the average velocity of all the molecules would be considerably +increased, and the amount of leakage might become, +and probably would become, a serious matter, steadily +depleting the moon's atmosphere and leading finally to +its present state of exhaustion. It is possible that the +moon may at one time have had an atmosphere, but if so it +could have been only a temporary possession, and the same +line of reasoning may be applied to the asteroids and to +most of the satellites of the solar system, and also, though +in less degree, to the smaller planets, Mercury and Mars.</p> + +<p><a name="S_242" id="S_242"></a>242. <b>Stellar development.</b>—We have already considered +in this chapter the line of development followed by one +star, the sun, and treating this as a typical case, it is commonly +believed that the life history of a star, in so far as it +lies within our reach, begins with a condition in which its +matter is widely diffused, and presumably at a low temperature. +Contracting in bulk under the influence of its own +gravitative forces, the star's temperature rises to a maximum, +and then falls off in later stages until the body ceases +to shine and passes over to the list of dark stars whose +existence can only be detected in exceptional cases, such +as are noted in <a href="#CHAPTER_XIII">Chapter XIII</a>. The most systematic development +of this idea is due to Lockyer, who looks upon all +the celestial bodies—sun, moon and planets, stars, nebulę, +and comets—as being only collections of meteoric matter in +different stages of development, and who has sought by +means of their spectra to classify these bodies and to determine +their stage of advancement. While the fundamental +ideas involved in this "meteoritic hypothesis" are not seriously<span class="pagenum"><a name="Page_376" id="Page_376">[Pg 376]</a></span> +controverted, the detailed application of its principles +is open to more question, and for the most part those +astronomers who hold that in the present state of knowledge +stellar spectra furnish a key to a star's age or degree +of advancement do not venture beyond broad general statements.</p> + +<div class="figcenter" style="width: 500px;"><a name="Fig_151" id="Fig_151"></a> +<a href="images/i414-full.jpg"><img src="images/i414.jpg" width="500" height="349" alt="Fig. 151.—Types of stellar spectra substantially according to Secchi." title="Fig. 151.—Types of stellar spectra substantially according to Secchi." /></a> +<span class="caption"><span class="smcap">Fig. 151.</span>—Types of stellar spectra substantially according to <span class="smcap">Secchi</span>.</span> +</div> + +<p><a name="S_243" id="S_243"></a>243. <b>Stellar spectra.</b>—Thus the types of stellar spectra +shown in <a href="#Fig_151">Fig. 151</a> are supposed to illustrate successive +stages in the development of an average star. Type I corresponds +to the period in which its temperature is near the +maximum; Type II belongs to a later stage in which the +temperature has commenced to fall; and Type III to the +period immediately preceding extinction.</p> + +<p>While human life, or even the duration of the human +race, is too short to permit a single star to be followed +through all the stages of its career, an adequate picture of +that development might be obtained by examining many +stars, each at a different stage of progress, and, following<span class="pagenum"><a name="Page_377" id="Page_377">[Pg 377]</a></span> +this idea, numerous subdivisions of the types of stellar +spectra shown in <a href="#Fig_151">Fig. 151</a> have been proposed in order to +represent with more detail the process of stellar growth +and decay; but for the most part these subdivisions and +their interpretation are accepted by astronomers with much +reserve.</p> + +<p>It is significant that there are comparatively few stars +with spectra of Type III, for this is what we should expect +to find if the development of a star through the last stages +of its visible career occupied but a small fraction of its +total life. From the same point of view the great number +of stars with spectra of the first type would point to a long +duration of this stage of life. The period in which the +sun belongs, represented by Type II, probably has a duration +intermediate between the others. Since most of the +variable stars, save those of the Algol class, have spectra of +the third type, we conclude that variability, with its associated +ruddy color and great atmospheric absorption of light, +is a sign of old age and approaching extinction. The Algol +or eclipse variables, on the other hand, having spectra of the +first type, are comparatively young stars, and, as we shall +see a little later, the shortness of their light periods in some +measure confirms this conclusion drawn from their spectra.</p> + +<p>We have noted in <a href="#S_196">§ 196</a> that the sun's near neighbors +are prevailingly stars with spectra of the second type, +while the Milky Way is mainly composed of first-type stars, +and from this we may now conclude that in our particular +part of the entire celestial space the stars are, as a rule, +somewhat further developed than is the case elsewhere.</p> + +<p><a name="S_244" id="S_244"></a>244. <b>Double stars.</b>—The double stars present special +problems of development growing out of the effects of tidal +friction, which must operate in them much as it does between +earth and moon, tending steadily to increase the distance +between the components of such a star. So, too, +in such a system as is shown in <a href="#Fig_132">Fig. 132</a>, gravity must +tend to make each component of the double star shrink to<span class="pagenum"><a name="Page_378" id="Page_378">[Pg 378]</a></span> +smaller dimensions, and this shrinkage must result in +faster rotation and increased tidal friction, which in turn +must push the components apart, so that in view of the +small density and close proximity of those particular stars +we may fairly regard a star like β Lyrę as in the early stages +of its career and destined with increasing age to lose its +variability of light, since the eclipses which now take place +must cease with increasing distance between the components +unless the orbit is turned exactly edgewise toward the +earth. Close proximity and the resulting shortness of periodic +time in a double star seem, therefore, to be evidence +of its youth, and since this shortness of periodic time is +characteristic of both Algol variables and spectroscopic +binaries as a class, we may set them down as being, upon +the whole, stars in the early stages of their career. On +the other hand, it is generally true that the larger the orbit, +and the greater the periodic time in the orbit, the +farther is the star advanced in its development.</p> + +<p>In his theory of tidal friction, Darwin has pointed out +that whenever the periodic time in the orbit is more than +twice as long as the time required for rotation about the +axis, the effect of the tides is to increase the eccentricity of +the orbit, and, following this indication, See has urged that +with increasing distance between the components of a +double star their orbits about the common center of gravity +must grow more and more eccentric, so that we have in +the shape of such orbits a new index of stellar development; +the more eccentric the orbit, the farther advanced +are the stars. It is important to note in this connection +that among the double stars whose orbits have been computed +there seems to run a general rule—the larger the +orbit the greater is its eccentricity—a relation which must +hold true if tidal friction operates as above supposed, and +which, being found to hold true, confirms in some degree +the criteria of stellar age which are furnished by the theory +of tidal friction.<span class="pagenum"><a name="Page_379" id="Page_379">[Pg 379]</a></span></p> + +<p><a name="S_245" id="S_245"></a>245. <b>Nebulę.</b>—The nebular hypothesis of Laplace has +inclined astronomers to look upon nebulę in general as +material destined to be worked up into stars, but which is +now in a very crude and undeveloped stage. Their great +bulk and small density seem also to indicate that gravitation +has not yet produced in them results at all comparable with +what we see in sun and stars. But even among nebulę +there are to be found very different stages of development. +The irregular nebula, shapeless and void like that of +Orion; the spiral, ring, and planetary nebulę and the star +cluster, clearly differ in amount of progress toward their +final goal. But it is by no means sure that these several +types are different stages in one line of development; for +example, the primitive nebula which grows into a spiral +may never become a ring or planetary nebula, and <i>vice +versa</i>. So too there is no reason to suppose that a star +cluster will ever break up into isolated stars such as those +whose relation to each other is shown in <a href="#Fig_122">Fig. 122</a>.</p> + +<p><a name="S_246" id="S_246"></a>246. <b>Classification.</b>—Considering the heavenly bodies +with respect to their stage of development, and arranging +them in due order, we should probably find lowest down in +the scale of progress the irregular nebulę of chaotic appearance +such as that represented in <a href="#Fig_146">Fig. 146</a>. Above +these in point of development stand the spiral, ring, and +planetary nebulę, although the exact sequence in which +they should be arranged remains a matter of doubt. Still +higher up in the scale are star clusters whose individual +members, as well as isolated stars, are to be classified by +means of their spectra, as shown in <a href="#Fig_151">Fig. 151</a>, where the +order of development of each star is probably from Type I, +through II, into III and beyond, to extinction of its light +and the cutting off of most of its radiant energy. Jupiter +and Saturn are to be regarded as stars which have recently +entered this dark stage. The earth is further developed +than these, but it is not so far along as are Mars and Mercury; +while the moon is to be looked upon as the most<span class="pagenum"><a name="Page_380" id="Page_380">[Pg 380]</a></span> +advanced heavenly body accessible to our research, having +reached a state of decrepitude which may almost be called +death—a stage typical of that toward which all the others +are moving.</p> + +<p>Meteors and comets are to be regarded as fragments of +celestial matter, chips, too small to achieve by themselves +much progress along the normal lines of development, but +destined sooner or later, by collision with some larger body, +to share thenceforth in its fortunes.</p> + +<p><a name="S_247" id="S_247"></a>247. <b>Stability of the universe.</b>—It was considered a great +achievement in the mathematical astronomy of a century +ago when Laplace showed that the mutual attractions of +sun and planets might indeed produce endless perturbations +in the motions and positions of these bodies, but +could never bring about collisions among them or greatly +alter their existing orbits. But in the proof of this great +theorem two influences were neglected, either of which is +fatal to its validity. One of these—tidal friction—as we +have already seen, tends to wreck the systems of satellites, +and the same effect must be produced upon the planets by +any other influence which tends to impede their orbital +motion. It is the inertia of the planet in its forward movement +that balances the sun's attraction, and any diminution +of the planet's velocity will give this attraction the +upper hand and must ultimately precipitate the planet +into the sun. The meteoric matter with which the earth +comes ceaselessly into collision must have just this influence, +although its effects are very small, and something +of the same kind may come from the medium +which transmits radiant energy through the interstellar +spaces.</p> + +<p>It seems incredible that the luminiferous ether, which +is supposed to pervade all space, should present absolutely +no resistance to the motion of stars and planets rushing +through it with velocities which in many cases exceed +50,000 miles per hour. If there is a resistance to this motion,<span class="pagenum"><a name="Page_381" id="Page_381">[Pg 381]</a></span> +however small, we may extend to the whole visible +universe the words of Thomson and Tait, who say in their +great Treatise on Natural Philosophy, "We have no data in +the present state of science for estimating the relative importance +of tidal friction and of the resistance of the resisting +medium through which the earth and moon move; +but, whatever it may be, there can be but one ultimate +result for such a system as that of the sun and planets, +if continuing long enough under existing laws and not +disturbed by meeting with other moving masses in +space. That result is the falling together of all into +one mass, which, although rotating for a time, must in +the end come to rest relatively to the surrounding medium."</p> + +<p>Compare with this the words of a great poet who in +The Tempest puts into the mouth of Prospero the lines:</p> + +<div class="poem"><div class="stanza"> +<span class="i0">"The cloud-capp'd towers, the gorgeous palaces,<br /></span> +<span class="i0">The solemn temples, the great globe itself,<br /></span> +<span class="i0">Yea, all which it inherit, shall dissolve;<br /></span> +<span class="i0">And, like this insubstantial pageant faded,<br /></span> +<span class="i0">Leave not a rack behind."<br /></span> +</div></div> + +<p><a name="S_248" id="S_248"></a>248. <b>The future.</b>—In spite of statements like these, it +lies beyond the scope of scientific research to affirm that +the visible order of things will ever come to naught, and +the outcome of present tendencies, as sketched above, may +be profoundly modified in ages to come, by influences of +which we are now ignorant. We have already noted that +the farther our speculation extends into either past or +future, the more insecure are its conclusions, and the remoter +consequences of present laws are to be accepted with +a corresponding reserve. But the one great fact which +stands out clear in this connection is that of <i>change</i>. The +old concept of a universe created in finished form and destined +so to abide until its final dissolution, has passed away +from scientific thought and is replaced by the idea of slow<span class="pagenum"><a name="Page_382" id="Page_382">[Pg 382]</a></span> +development. A universe which is ever becoming something +else and is never finished, as shadowed forth by +Goethe in the lines:</p> + +<div class="poem"><div class="stanza"> +<span class="i0">"Thus work I at the roaring loom of Time,<br /></span> +<span class="i0">And weave for Deity a living robe sublime."<br /></span> +</div></div> + + +<div class="footnotes"> +<h4>FOOTNOTES</h4> +<div class="footnote"><p><a name="Footnote_A_1" id="Footnote_A_1"></a><a href="#FNanchor_A_1"><span class="label">[A]</span></a> The circle and straight line are considered to be special cases of +these curves, which, taken collectively, are called the conic sections.</p></div> + +<div class="footnote"><p><a name="Footnote_B_2" id="Footnote_B_2"></a><a href="#FNanchor_B_2"><span class="label">[B]</span></a> Aristophanes, The Clouds, Whewell's translation.</p></div> + +<div class="footnote"><p><a name="Footnote_C_3" id="Footnote_C_3"></a><a href="#FNanchor_C_3"><span class="label">[C]</span></a> Schiaparelli, Osservazioni sulle Stelle Doppie.</p></div> +</div> + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_383" id="Page_383">[Pg 383]</a></span></p> +<h2><a name="APPENDIX" id="APPENDIX"></a>APPENDIX</h2> + + +<h3><span class="smcap">The Greek Alphabet</span></h3> + +<p>The Greek letters are so much used by astronomers in +connection with the names of the stars, and for other purposes, +that the Greek alphabet is printed below—not necessarily +to be learned, but for convenient reference:</p> + + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><th colspan="2">Greek.</th><th align="left">Name.</th><th align="center">English.</th></tr> +<tr><td align="center">Α</td><td align="left">α</td><td align="left">Alpha</td><td align="center">a</td></tr> +<tr><td align="center">Β</td><td align="left">β</td><td align="left">Beta</td><td align="center">b</td></tr> +<tr><td align="center">Γ</td><td align="left">γ</td><td align="left">Gamma</td><td align="center">g</td></tr> +<tr><td align="center">Δ</td><td align="left">δ</td><td align="left">Delta</td><td align="center">d</td></tr> +<tr><td align="center">Ε</td><td align="left">ε or ϵ</td><td align="left">Epsilon</td><td align="center">ĕ</td></tr> +<tr><td align="center">Ζ</td><td align="left">ζ</td><td align="left">Zeta</td><td align="center">z</td></tr> +<tr><td align="center">Η</td><td align="left">η</td><td align="left">Eta</td><td align="center">ē</td></tr> +<tr><td align="center">Θ</td><td align="left">ϑ or θ</td><td align="left">Theta</td><td align="center">th</td></tr> +<tr><td align="center">Ι</td><td align="left">ι</td><td align="left">Iota</td><td align="center">i</td></tr> +<tr><td align="center">Κ</td><td align="left">κ</td><td align="left">Kappa</td><td align="center">k</td></tr> +<tr><td align="center">Λ</td><td align="left">λ</td><td align="left">Lambda</td><td align="center">l</td></tr> +<tr><td align="center">Μ</td><td align="left">μ</td><td align="left">Mu</td><td align="center">m</td></tr> +<tr><td align="center">Ν</td><td align="left">ν</td><td align="left">Nu</td><td align="center">n</td></tr> +<tr><td align="center">Ξ</td><td align="left">ξ</td><td align="left">Xi</td><td align="center">x</td></tr> +<tr><td align="center">Ο</td><td align="left">ο</td><td align="left">Omicron</td><td align="center">ŏ</td></tr> +<tr><td align="center">Π</td><td align="left">π</td><td align="left">Pi</td><td align="center">p</td></tr> +<tr><td align="center">Ρ</td><td align="left">ρ</td><td align="left">Rho</td><td align="center">r</td></tr> +<tr><td align="center">Σ</td><td align="left">σ or ς</td><td align="left">Sigma</td><td align="center">s</td></tr> +<tr><td align="center">Τ</td><td align="left">τ</td><td align="left">Tau</td><td align="center">t</td></tr> +<tr><td align="center">Υ</td><td align="left">υ</td><td align="left">Upsilon</td><td align="center">u</td></tr> +<tr><td align="center">Φ</td><td align="left">φ</td><td align="left">Phi</td><td align="center">ph</td></tr> +<tr><td align="center">Χ</td><td align="left">χ</td><td align="left">Chi</td><td align="center">ch</td></tr> +<tr><td align="center">Ψ</td><td align="left">ψ</td><td align="left">Psi</td><td align="center">ps</td></tr> +<tr><td align="center">Ω</td><td align="left">ω</td><td align="left">Omega</td><td align="center">ō</td></tr> +</table></div> + + +<hr style="width: 25%;" /> +<p><span class="pagenum"><a name="Page_384" id="Page_384">[Pg 384]</a></span></p> +<h3><span class="smcap">Popular Literature of Astronomy</span></h3> + +<p>The following brief bibliography, while making no +pretense at completeness, may serve as a useful guide to +supplementary reading:</p> + + +<h4><i>General Treatises</i></h4> + +<p><span class="smcap">Young.</span> <i>General Astronomy.</i> An admirable general survey of the +entire field.</p> + +<p><span class="smcap">Newcomb.</span> <i>Popular Astronomy.</i> The second edition of a German +translation of this work by Engelmann and Vogel is especially valuable.</p> + +<p><span class="smcap">Ball.</span> <i>Story of the Heavens.</i> Somewhat easier reading than either +of the preceding.</p> + +<p><span class="smcap">Chambers.</span> <i>Descriptive Astronomy.</i> An elaborate but elementary +work in three volumes.</p> + +<p><span class="smcap">Langley.</span> <i>The New Astronomy.</i> Treats mainly of the physical +condition of the celestial bodies.</p> + +<p><span class="smcap">Proctor</span> and <span class="smcap">Ranyard</span>. <i>Old and New Astronomy.</i></p> + + +<h4><i>Special Treatises</i></h4> + +<p><span class="smcap">Proctor.</span> <i>The Moon.</i> A general treatment of the subject.</p> + +<p><span class="smcap">Nasmyth</span> and <span class="smcap">Carpenter</span>. <i>The Moon.</i> An admirably illustrated +but expensive work dealing mainly with the topography and physical +conditions of the moon. There is a cheaper and very good edition in +German.</p> + +<p><span class="smcap">Young.</span> <i>The Sun.</i> International Scientific Series. The most recent +and authoritative treatise on this subject.</p> + +<p><span class="smcap">Proctor.</span> <i>Other Worlds than Ours.</i> An account of planets, comets, +etc.</p> + +<p><span class="smcap">Newton.</span> <i>Meteor.</i> Encyclopędia Britannica.</p> + +<p><span class="smcap">Airy.</span> <i>Gravitation.</i> A non-mathematical exposition of the laws +of planetary motion.</p> + +<p><span class="smcap">Stokes.</span> <i>On Light as a Means of Investigation.</i> Burnett Lectures. +II. The basis of spectrum analysis.</p> + +<p><span class="smcap">Schellen.</span> <i>Spectrum Analysis.</i></p> + +<p><span class="smcap">Thomson</span> (Sir W., Lord <span class="smcap">Kelvin</span>), <i>Popular Lectures, etc.</i> Lectures +on the Tides, The Sun's Heat, etc.<span class="pagenum"><a name="Page_385" id="Page_385">[Pg 385]</a></span></p> + +<p><span class="smcap">Ball.</span> <i>Time and Tide.</i> An exposition of the researches of G. H. +Darwin upon tidal friction.</p> + +<p><span class="smcap">Gore.</span> <i>The Visible Universe.</i> Deals with a class of problems inadequately +treated in most popular astronomies.</p> + +<p><span class="smcap">Darwin.</span> <i>The Tides.</i> An admirable elementary exposition.</p> + +<p><span class="smcap">Clerke.</span> <i>The System of the Stars.</i> Stellar astronomy.</p> + +<p><span class="smcap">Newcomb.</span> Chapters on the Stars, in <i>Popular Science Monthly</i> for +1900.</p> + +<p><span class="smcap">Clerke.</span> <i>History of Astronomy during the Nineteenth Century.</i> +An admirable work.</p> + +<p><span class="smcap">Wolf.</span> <i>Geschichte der Astronomie.</i> München, 1877. An excellent +German work.</p> + +<hr style="width: 25%;" /> + +<p><span class="pagenum"><a name="Page_386" id="Page_386">[Pg 386]</a></span></p> + + +<h3><span class="smcap">A List of Stars for Time Observations</span></h3> + +<p class="center">See <a href="#S_20">§ 20</a>.</p> + + +<div class="center"> +<table border="1" cellpadding="4" cellspacing="0" summary="" rules="groups" frame="hsides"> +<colgroup></colgroup><colgroup></colgroup><colgroup span="2"></colgroup><colgroup></colgroup> +<thead> +<tr><th align="center"><span class="smcap">Name.</span></th><th align="center">Magnitude.</th><th align="center" colspan="2">Right Ascension.</th><th align="center">Declination.</th></tr> +</thead> +<tbody> +<tr><td align="left"> </td><td align="right"> </td><td align="right">h.</td><td align="right">m. </td><td align="right">° </td></tr> +<tr><td align="left">β Ceti</td><td align="right">2</td><td align="right">0</td><td align="right">38.6</td><td align="right">-18.5</td></tr> +<tr><td align="left">η Ceti</td><td align="right">3</td><td align="right">1</td><td align="right">3.6</td><td align="right">-10.7</td></tr> +<tr><td align="left">α Ceti</td><td align="right">3</td><td align="right">2</td><td align="right">57.1</td><td align="right">+3.7</td></tr> +<tr><td align="left">γ Eridani</td><td align="right">3</td><td align="right">3</td><td align="right">53.4</td><td align="right">-13.8</td></tr> +<tr><td align="left"><i>Aldebaran</i></td><td align="right">1</td><td align="right">4</td><td align="right">30.2</td><td align="right">+16.3</td></tr> +<tr><td> </td><td> </td><td> </td><td> </td></tr> +<tr><td align="left"><i>Rigel</i></td><td align="right">0</td><td align="right">5</td><td align="right">9.7</td><td align="right">-8.3</td></tr> +<tr><td align="left">κ Orionis</td><td align="right">2</td><td align="right">5</td><td align="right">43.0</td><td align="right">-9.7</td></tr> +<tr><td align="left">β Canis Majoris</td><td align="right">2</td><td align="right">6</td><td align="right">18.3</td><td align="right">-17.9</td></tr> +<tr><td align="left"><i>Sirius</i></td><td align="right">-1</td><td align="right">6</td><td align="right">40.7</td><td align="right">-16.6</td></tr> +<tr><td align="left"><i>Procyon</i></td><td align="right">0</td><td align="right">7</td><td align="right">34.1</td><td align="right">+5.5</td></tr> +<tr><td> </td><td> </td><td> </td><td> </td></tr> +<tr><td align="left">α Hydrę</td><td align="right">2</td><td align="right">9</td><td align="right">22.7</td><td align="right">-8.2</td></tr> +<tr><td align="left"><i>Regulus</i></td><td align="right">1</td><td align="right">10</td><td align="right">3.0</td><td align="right">+12.5</td></tr> +<tr><td align="left">ν Hydrę</td><td align="right">3</td><td align="right">10</td><td align="right">44.7</td><td align="right">-15.7</td></tr> +<tr><td align="left">ϵ Corvi</td><td align="right">3</td><td align="right">12</td><td align="right">5.0</td><td align="right">-22.1</td></tr> +<tr><td align="left">γ Corvi</td><td align="right">3</td><td align="right">12</td><td align="right">10.7</td><td align="right">-17.0</td></tr> +<tr><td> </td><td> </td><td> </td><td> </td></tr> +<tr><td align="left"><i>Spica</i></td><td align="right">1</td><td align="right">13</td><td align="right">19.9</td><td align="right">-10.6</td></tr> +<tr><td align="left">ζ Virginis</td><td align="right">3</td><td align="right">13</td><td align="right">29.6</td><td align="right">-0.1</td></tr> +<tr><td align="left">α Librę</td><td align="right">3</td><td align="right">14</td><td align="right">45.3</td><td align="right">-15.6</td></tr> +<tr><td align="left">β Librę</td><td align="right">3</td><td align="right">15</td><td align="right">11.6</td><td align="right">-9.0</td></tr> +<tr><td align="left"><i>Antares</i></td><td align="right">1</td><td align="right">16</td><td align="right">23.3</td><td align="right">-26.2</td></tr> +<tr><td> </td><td> </td><td> </td><td> </td></tr> +<tr><td align="left">α Ophiuchi</td><td align="right">2</td><td align="right">17</td><td align="right">30.3</td><td align="right">+12.6</td></tr> +<tr><td align="left">ϵ Sagittarii</td><td align="right">2</td><td align="right">18</td><td align="right">17.5</td><td align="right">-34.4</td></tr> +<tr><td align="left">δ Aquilę</td><td align="right">3</td><td align="right">19</td><td align="right">20.5</td><td align="right">+2.9</td></tr> +<tr><td align="left"><i>Altair</i></td><td align="right">1</td><td align="right">19</td><td align="right">45.9</td><td align="right">+8.6</td></tr> +<tr><td align="left">β Aquarii</td><td align="right">3</td><td align="right">21</td><td align="right">26.3</td><td align="right">-6.0</td></tr> +<tr><td> </td><td> </td><td> </td><td> </td></tr> +<tr><td align="left">α Aquarii</td><td align="right">3</td><td align="right">22</td><td align="right">0.6</td><td align="right">-0.8</td></tr> +<tr><td align="left"><i>Fomalhaut</i></td><td align="right">1</td><td align="right">22</td><td align="right">52.1</td><td align="right">-30.2</td></tr> +</tbody> +</table> +</div> + + + +<hr style="width: 65%;" /> +<p><span class="pagenum"><a name="Page_387" id="Page_387">[Pg 387]</a></span></p> +<h2><a name="INDEX" id="INDEX"></a>INDEX</h2> + + +<p class="center">The references are to section numbers.</p> + + +<ul id="index"> +<li>Absorption of starlight, <a href="#S_225">225</a>.</li> + +<li>Absorption spectra, <a href="#S_87">87</a>.</li> + +<li>Accelerating force, <a href="#S_35">35</a>.</li> + +<li>Adjustment of observations, <a href="#S_2">2</a>.</li> + +<li>Albedo of moon, <a href="#S_97">97</a>. +<ul> +<li>of Venus, <a href="#S_148">148</a>.</li> +</ul> +</li> + +<li>Algol, <a href="#S_205">205</a>.</li> + +<li>Altitudes, <a href="#S_4">4</a>, <a href="#S_21">21</a>.</li> + +<li>Andromeda nebula, <a href="#S_214">214</a>.</li> + +<li>Angles, measurement of, <a href="#S_2">2</a>.</li> + +<li>Angular diameter, <a href="#S_7">7</a>.</li> + +<li>Annular eclipse, <a href="#S_64">64</a>.</li> + +<li>Asteroids, <a href="#S_156">156</a>.</li> + +<li>Atmosphere of the earth, <a href="#S_49">49</a>. +<ul> +<li>of the moon, <a href="#S_103">103</a>.</li> +<li>of Jupiter, <a href="#S_139">139</a>.</li> +<li>of Mars, <a href="#S_153">153</a>.</li> +</ul> +</li> + +<li>Aurora, <a href="#S_51">51</a>.</li> + +<li>Azimuth, <a href="#S_5">5</a>, <a href="#S_21">21</a>.</li> + +<li> </li> + +<li>Biela's comet, <a href="#S_181">181</a>.</li> + +<li>Bode's law, <a href="#S_134">134</a>, <a href="#S_232">232</a>.</li> + +<li>Bredichin's theory of comet tails, <a href="#S_180">180</a>.</li> + +<li> </li> + +<li>Calendar, O. S. and N. S., <a href="#S_61">61</a>.</li> + +<li>Capture of comets and meteors, <a href="#S_176">176</a>.</li> + +<li>Canals of Mars, <a href="#S_154">154</a>.</li> + +<li>Celestial mechanics, <a href="#S_32">32</a>.</li> + +<li>Changes upon the moon, <a href="#S_108">108</a>.</li> + +<li>Chemical constitution of sun, <a href="#S_116">116</a>. +<ul><li>of stars, <a href="#S_210">210</a>.</li></ul></li> + +<li>Chromosphere, the sun's, <a href="#S_124">124</a>.</li> + +<li>Chronology, <a href="#S_59">59</a>.</li> + +<li>Classification of stars, <a href="#S_212">212</a>.</li> + +<li>Clocks and watches, <a href="#S_74">74</a>. +<ul><li>sidereal clock, <a href="#S_12">12</a>.</li></ul></li> + +<li>Collisions with comets, <a href="#S_183">183</a>.</li> + +<li>Colors of stars, <a href="#S_209">209</a>.</li> + +<li>Comets, general characteristics, <a href="#S_158">158</a>-<a href="#S_164">164</a>. +<ul><li>development of, <a href="#S_179">179</a>, <a href="#S_181">181</a>.</li> +<li>groups, <a href="#S_177">177</a>.</li> +<li>orbits, <a href="#S_161">161</a>.</li> +<li>periodic, <a href="#S_176">176</a>.</li> +<li>spectra, <a href="#S_182">182</a>.</li> +<li>tails, <a href="#S_180">180</a>.</li></ul></li> + +<li>Comets and meteors, relation of, <a href="#S_175">175</a>.</li> + +<li>Conic sections, <a href="#S_38">38</a>.</li> + +<li>Constellations, <a href="#S_184">184</a>.</li> + +<li>Corona, the sun's, <a href="#S_123">123</a>.</li> + +<li>Craters, lunar, <a href="#S_105">105</a>.</li> + +<li> </li> + +<li>Dark stars, <a href="#S_201">201</a>.</li> + +<li>Day, <a href="#S_52">52</a>, <a href="#S_62">62</a>.</li> + +<li>Declination, <a href="#S_21">21</a>.</li> + +<li>Development of comet, <a href="#S_179">179</a>. +<ul><li>of moon, <a href="#S_241">241</a>.</li> +<li>of nebulę, <a href="#S_245">245</a>.</li> +<li>of stars, <a href="#S_242">242</a>, <a href="#S_244">244</a>.<span class="pagenum"><a name="Page_388" id="Page_388">[Pg 388]</a></span></li> +<li>of sun, <a href="#S_228">228</a>.</li> +<li>of universe, <a href="#S_226">226</a>.</li></ul></li> + +<li>Distribution of stars and nebulę, <a href="#S_220">220</a>.</li> + +<li>Diurnal motion, <a href="#S_10">10</a>, <a href="#S_15">15</a>.</li> + +<li>Doppler principle, <a href="#S_89">89</a>.</li> + +<li>Double nebulę, <a href="#S_215">215</a>.</li> + +<li>Double stars, <a href="#S_198">198</a>. +<ul><li>development of, <a href="#S_244">244</a>.</li></ul></li> + +<li>Driving clock, <a href="#S_80">80</a>.</li> + +<li> </li> + +<li>Earth, atmosphere, <a href="#S_48">48</a>. +<ul><li>mass, <a href="#S_45">45</a>.</li> +<li>size and shape, <a href="#S_44">44</a>.</li> +<li>warming of the earth, <a href="#S_47">47</a>.</li></ul></li> + +<li>Eclipses, nature of, <a href="#S_63">63</a>. +<ul><li>annular eclipse, <a href="#S_64">64</a>.</li> +<li>eclipse limits, <a href="#S_68">68</a>.</li> +<li>eclipse maps, <a href="#S_70">70</a>, <a href="#S_71">71</a>.</li> +<li>number of, in a year, <a href="#S_69">69</a>.</li> +<li>partial eclipse, <a href="#S_64">64</a>.</li> +<li>prediction of, <a href="#S_70">70</a>, <a href="#S_71">71</a>.</li> +<li>recurrence of, <a href="#S_72">72</a>.</li> +<li>shadow cone, <a href="#S_64">64</a>, <a href="#S_66">66</a>.</li> +<li>total eclipse, <a href="#S_64">64</a>.</li> +<li>uses of, <a href="#S_73">73</a>.</li></ul></li> + +<li>Eclipses of Jupiter's satellites, <a href="#S_141">141</a>.</li> + +<li>Eclipse theory of variable stars, <a href="#S_205">205</a>.</li> + +<li>Ecliptic, <a href="#S_26">26</a>. +<ul><li>obliquity of, <a href="#S_25">25</a>.</li></ul></li> + +<li>Ellipse, <a href="#S_33">33</a>.</li> + +<li>Epochs for planetary motion, <a href="#S_30">30</a>.</li> + +<li>Energy, radiant, <a href="#S_75">75</a>. +<ul><li>condensation of, <a href="#S_76">76</a>.</li></ul></li> + +<li>Epicycle, <a href="#S_32">32</a>.</li> + +<li>Equation of time, <a href="#S_53">53</a>.</li> + +<li>Equator, <a href="#S_16">16</a>, <a href="#S_21">21</a>.</li> + +<li>Equatorial mounting, <a href="#S_80">80</a>.</li> + +<li>Equinoxes, <a href="#S_25">25</a>.</li> + +<li>Ether, <a href="#S_75">75</a>.</li> + +<li>Evening star, <a href="#S_31">31</a>.</li> + +<li> </li> + +<li>Faculę, <a href="#S_122">122</a>.</li> + +<li>Falling bodies, law of, <a href="#S_35">35</a>.</li> + +<li>Finding the stars, <a href="#S_14">14</a>.</li> + +<li>Fraunhofer lines, <a href="#S_87">87</a>.</li> + +<li> </li> + +<li>Galaxy, <a href="#S_219">219</a>.</li> + +<li>Geography of the sky, <a href="#S_16">16</a>.</li> + +<li>Graphical representation, <a href="#S_6">6</a>.</li> + +<li>Grating, diffraction, <a href="#S_84">84</a>.</li> + +<li>Gravitation, law of, <a href="#S_37">37</a>.</li> + +<li> </li> + +<li>Harvest moon, <a href="#S_93">93</a>.</li> + +<li>Heat of the sun, <a href="#S_118">118</a>, <a href="#S_126">126</a>.</li> + +<li>Helmholtz, contraction theory of the sun, <a href="#S_126">126</a>, <a href="#S_228">228</a>.</li> + +<li>Horizon, <a href="#S_4">4</a>, <a href="#S_21">21</a>.</li> + +<li>Hour angle, <a href="#S_21">21</a>.</li> + +<li>Hour circle, <a href="#S_21">21</a>.</li> + +<li>Hyperbola, <a href="#S_38">38</a>.</li> + +<li> </li> + +<li>Japetus, satellite of Saturn, <a href="#S_145">145</a>.</li> + +<li>Jupiter, <a href="#S_136">136</a>. +<ul><li>atmosphere, <a href="#S_139">139</a>.</li> +<li>belts, <a href="#S_137">137</a>.</li> +<li>invisible from fixed stars, <a href="#S_197">197</a>.</li> +<li>orbit of, <a href="#S_29">29</a>.</li> +<li>physical condition, <a href="#S_139">139</a>.</li> +<li>rotation and flattening, <a href="#S_138">138</a>.</li> +<li>satellites, <a href="#S_140">140</a>.</li> +<li>surface markings, <a href="#S_137">137</a>.</li></ul></li> + +<li> </li> + +<li>Kepler's laws, <a href="#S_233">33</a>, <a href="#S_111">111</a>.</li> + +<li> </li> + +<li>Latitude, determination of, <a href="#S_18">18</a>.</li> + +<li>Leap year, <a href="#S_61">61</a>.</li> + +<li>Lenses, <a href="#S_77">77</a>.</li> + +<li>Leonid meteor shower, <a href="#S_172">172</a>. +<ul><li>perturbations of, <a href="#S_174">174</a>.</li></ul></li> + +<li>Librations of moon, <a href="#S_98">98</a>.</li> + +<li>Life upon the planets, <a href="#S_157">157</a>.</li> + +<li>Light curves, <a href="#S_205">205</a>.</li> + +<li>Light, nature of, <a href="#S_75">75</a>.<span class="pagenum"><a name="Page_389" id="Page_389">[Pg 389]</a></span></li> + +<li>Light year, <a href="#S_190">190</a>.</li> + +<li>Limits of eclipses, <a href="#S_68">68</a>.</li> + +<li>Longitude, <a href="#S_56">56</a>. +<ul><li>determination of, <a href="#S_58">58</a>.</li></ul></li> + +<li>Lunation, <a href="#S_60">60</a>.</li> + +<li> </li> + +<li>Magnifying power of telescope, <a href="#S_79">79</a>.</li> + +<li>Magnitude, stellar, <a href="#S_9">9</a>, <a href="#S_186">186</a>.</li> + +<li>Mars, atmosphere, temperature, <a href="#S_150">150</a>. +<ul><li>canals, <a href="#S_154">154</a>.</li> +<li>orbit, <a href="#S_30">30</a>.</li> +<li>polar caps, <a href="#S_152">152</a>.</li> +<li>rotation, <a href="#S_151">151</a>.</li> +<li>satellites, <a href="#S_155">155</a>.</li> +<li>surface markings, <a href="#S_150">150</a>.</li></ul></li> + +<li>Mass, determination of, <a href="#S_37">37</a>. +<ul><li>of comets, <a href="#S_164">164</a>.</li> +<li>of double stars, <a href="#S_200">200</a>.</li> +<li>of moon, <a href="#S_94">94</a>.</li> +<li>of planets, <a href="#S_40">40</a>, <a href="#S_133">133</a>.</li></ul></li> + +<li>Measurements, accurate, <a href="#S_1">1</a>.</li> + +<li>Mercury, <a href="#S_149">149</a>. +<ul><li>motion of its perihelion, <a href="#S_43">43</a>.</li> +<li>orbit of, <a href="#S_30">30</a>.</li></ul></li> + +<li>Meridian, <a href="#S_19">19</a>, <a href="#S_21">21</a>.</li> + +<li><a name="Meteor" id="Meteor"></a>Meteors, nature of, <a href="#S_165">165</a>, <a href="#S_169">169</a>. +<ul><li>number of, <a href="#S_167">167</a>.</li> +<li>velocity, <a href="#S_170">170</a>.</li></ul></li> + +<li>Meteors and comets, relation of, <a href="#S_175">175</a>.</li> + +<li>Meteor showers, radiant, <a href="#S_171">171</a>. +<ul><li>Leonids, capture of, <a href="#S_172">172</a>, <a href="#S_173">173</a>.</li> +<li>perturbations, <a href="#S_174">174</a>.</li></ul></li> + +<li>Milky Way, <a href="#S_219">219</a>.</li> + +<li>Mira, ο Ceti, <a href="#S_204">204</a>.</li> + +<li>Mirrors, <a href="#S_77">77</a>.</li> + +<li>Month, <a href="#S_60">60</a>.</li> + +<li>Moon, <a href="#S_91">91</a>. +<ul><li>albedo, <a href="#S_97">97</a>.</li> +<li>atmosphere, <a href="#S_103">103</a>.</li> +<li>changes in, <a href="#S_108">108</a>.</li> +<li>density, surface gravity, <a href="#S_95">95</a>.</li> +<li>development of, <a href="#S_241">241</a>.</li> +<li>harvest moon, <a href="#S_93">93</a>.</li> +<li>influence upon the earth, <a href="#S_109">109</a>, <a href="#S_233">233</a>.</li> +<li>librations, <a href="#S_198">98</a>.</li> +<li>map of, <a href="#S_101">101</a>.</li> +<li>mass and size, <a href="#S_94">94</a>.</li> +<li>motion, <a href="#S_24">24</a>, <a href="#S_92">92</a>.</li> +<li>mountains and craters, <a href="#S_104">104</a>.</li> +<li>phases, <a href="#S_91">91</a>, <a href="#S_92">92</a>.</li> +<li>physical condition, <a href="#S_100">100</a>, <a href="#S_107">107</a>.</li></ul></li> + +<li>Month, <a href="#S_60">60</a>.</li> + +<li>Morning star, <a href="#S_31">31</a>.</li> + +<li>Motion in line of sight, <a href="#S_89">89</a>, <a href="#S_193">193</a>.</li> + +<li>Multiple stars, <a href="#S_202">202</a>.</li> + +<li> </li> + +<li>Names of stars, <a href="#S_8">8</a>.</li> + +<li>Nebulę, <a href="#S_214">214</a>. +<ul><li>density, <a href="#S_217">217</a>.</li> +<li>development of, <a href="#S_245">245</a>.</li> +<li>motion, <a href="#S_218">218</a>.</li> +<li>spectra, <a href="#S_216">216</a>.</li> +<li>types and classes of, <a href="#S_215">215</a>.</li></ul></li> + +<li>Nebular hypothesis, <a href="#S_230">230</a>. +<ul><li>objections to, <a href="#S_231">231</a>.</li></ul></li> + +<li>Neptune, <a href="#S_146">146</a>. +<ul><li>discovery of, <a href="#S_41">41</a>.</li></ul></li> + +<li>Newton's laws of motion, <a href="#S_34">34</a>. +<ul><li>law of gravitation, <a href="#S_37">37</a>, <a href="#S_43">43</a>.</li></ul></li> + +<li>Nodes, <a href="#S_39">39</a>. +<ul><li>relation to eclipses, <a href="#S_67">67</a>, <a href="#S_71">71</a>.</li></ul></li> + +<li>Nucleus, of comet, <a href="#S_160">160</a>.</li> + +<li> </li> + +<li>Objective, of telescope, <a href="#S_78">78</a>.</li> + +<li>Obliquity of ecliptic, <a href="#S_25">25</a>.</li> + +<li>Observations, of stars, <a href="#S_10">10</a>.</li> + +<li>Occultation of stars, <a href="#S_103">103</a>.</li> + +<li>Orbits, of comets, <a href="#S_161">161</a>. +<ul><li>of double stars, <a href="#S_199">199</a>.</li> +<li>of moon, <a href="#S_92">92</a>.<span class="pagenum"><a name="Page_390" id="Page_390">[Pg 390]</a></span></li> +<li>of planets, <a href="#S_28">28</a>.</li></ul></li> + +<li>Orion nebula, <a href="#S_215">215</a>.</li> + +<li> </li> + +<li>Parabola, <a href="#S_35">35</a>, <a href="#S_38">38</a>, <a href="#S_161">161</a>.</li> + +<li>Parabolic velocity, <a href="#S_38">38</a>.</li> + +<li>Parallax, <a href="#S_114">114</a>, <a href="#S_188">188</a>.</li> + +<li>Penumbra, <a href="#S_64">64</a>, <a href="#S_121">121</a>.</li> + +<li>Perihelion, <a href="#S_38">38</a>.</li> + +<li>Periodic comets, <a href="#S_176">176</a>.</li> + +<li>Personal equation, <a href="#S_82">82</a>.</li> + +<li>Perturbations, <a href="#S_39">39</a>. +<ul><li>of meteors, <a href="#S_174">174</a>.</li></ul></li> + +<li>Phases, of the moon, <a href="#S_91">91</a>, <a href="#S_92">92</a>.</li> + +<li>Photography, <a href="#S_81">81</a>. +<ul><li>of stars, <a href="#S_13">13</a>.</li></ul></li> + +<li>Photosphere, of sun, <a href="#S_121">121</a>.</li> + +<li>Planets, <a href="#S_26">26</a>, <a href="#S_133">133</a>. +<ul><li>distances from the sun, <a href="#S_134">134</a>.</li> +<li>how to find, <a href="#S_29">29</a>.</li> +<li>mass, density, size, <a href="#S_133">133</a>.</li> +<li>motion of, <a href="#S_27">27</a>, <a href="#S_38">38</a>.</li> +<li>periodic times of, <a href="#S_30">30</a>.</li></ul></li> + +<li>Planetary nebulę, <a href="#S_215">215</a>.</li> + +<li>Pleiades, <a href="#S_16">16</a>, <a href="#S_215">215</a>.</li> + +<li>Plumb-line apparatus, <a href="#S_11">11</a>, <a href="#S_18">18</a>.</li> + +<li>Poles, <a href="#S_21">21</a>.</li> + +<li>Precession, <a href="#S_46">46</a>.</li> + +<li>Prisms, <a href="#S_84">84</a>.</li> + +<li>Problem of three bodies, <a href="#S_39">39</a>.</li> + +<li>Prominences, solar, <a href="#S_125">125</a>.</li> + +<li>Proper motions, <a href="#S_191">191</a>.</li> + +<li>Protractor, <a href="#S_2">2</a>.</li> + +<li>Ptolemaic system, <a href="#S_32">32</a>.</li> + +<li> </li> + +<li>Radiant energy, <a href="#S_75">75</a>.</li> + +<li>Radiant, of meteor shower, <a href="#S_171">171</a>.</li> + +<li>Radius <span title="typo for vector">victor</span>, <a href="#S_33">33</a>.</li> + +<li>Reference lines and circles, <a href="#S_17">17</a>.</li> + +<li>Refraction, <a href="#S_50">50</a>.</li> + +<li>Right ascension, <a href="#S_16">16</a>, <a href="#S_20">20</a>, <a href="#S_21">21</a>.</li> + +<li>Roche's limit, <a href="#S_239">239</a>.</li> + +<li>Rotation, of earth, <a href="#S_55">55</a>. +<ul><li>of Mars, <a href="#S_151">151</a>.</li> +<li>of moon, <a href="#S_99">99</a>.</li> +<li>of Jupiter, <a href="#S_138">138</a>.</li> +<li>of Saturn, <a href="#S_144">144</a>.</li> +<li>of sun, <a href="#S_120">120</a>, <a href="#S_132">132</a>.</li></ul></li> + +<li> </li> + +<li>Saros, <a href="#S_72">72</a>.</li> + +<li>Satellites, of Jupiter, <a href="#S_136">136</a>, <a href="#S_140">140</a>. +<ul><li>of Mars, <a href="#S_155">155</a>.</li> +<li>of Saturn, <a href="#S_145">145</a>.</li></ul></li> + +<li>Saturn, <a href="#S_142">142</a>. +<ul><li>ball of, <a href="#S_144">144</a>.</li> +<li>orbit, <a href="#S_29">29</a>.</li> +<li>rings, <a href="#S_142">142</a>.</li> +<li>rotation, <a href="#S_144">144</a>.</li> +<li>satellites, <a href="#S_145">145</a>.</li></ul></li> + +<li>Seasons, on the earth, <a href="#S_47">47</a>. +<ul><li>on Mars, <a href="#S_151">151</a>.</li></ul></li> + +<li>Shadow cone, <a href="#S_64">64</a>, <a href="#S_66">66</a>.</li> + +<li>Sidereal time, <a href="#S_20">20</a>, <a href="#S_54">54</a>.</li> + +<li>Shooting stars, <a href="#S_158">158</a>. (See <a href="#Meteor">Meteor</a>.)</li> + +<li>Spectroscope, <a href="#S_84">84</a>.</li> + +<li>Spectroscopic binaries, <a href="#S_203">203</a>.</li> + +<li>Spectrum, <a href="#S_84">84</a>, <a href="#S_87">87</a>. +<ul><li>of comets, <a href="#S_182">182</a>.</li> +<li>of nebulę, <a href="#S_216">216</a>.</li> +<li>of stars, <a href="#S_211">211</a>.</li> +<li>types of, <a href="#S_88">88</a>.</li></ul></li> + +<li>Spectrum analysis, <a href="#S_85">85</a>.</li> + +<li>Spiral nebulę, <a href="#S_215">215</a>.</li> + +<li>Standard time, <a href="#S_57">57</a>.</li> + +<li>Stars, <a href="#S_8">8</a>, <a href="#S_184">184</a>. +<ul><li>classes of, <a href="#S_212">212</a>.</li> +<li>clusters, <a href="#S_213">213</a>.</li> +<li>colors, <a href="#S_209">209</a>.</li> +<li>dark stars, <a href="#S_201">201</a>.</li> +<li>development of, <a href="#S_242">242</a>.</li> +<li>distances from the sun, <a href="#S_188">188</a>, <a href="#S_196">196</a>.</li> +<li>distribution of, <a href="#S_220">220</a>.</li> +<li>double stars, <a href="#S_198">198</a>, <a href="#S_203">203</a>.</li> +<li>drift, <a href="#S_194">194</a>.</li> +<li>magnitudes, <a href="#S_9">9</a>, <a href="#S_196">196</a>.<span class="pagenum"><a name="Page_391" id="Page_391">[Pg 391]</a></span></li> +<li>number of, <a href="#S_185">185</a>.</li> +<li>spectra, <a href="#S_211">211</a>.</li> +<li>temporary, <a href="#S_208">208</a>.</li> +<li>variable, <a href="#S_204">204</a>.</li></ul></li> + +<li>Starlight, absorption of, <a href="#S_225">225</a>.</li> + +<li>Star maps, construction of, <a href="#S_23">23</a>.</li> + +<li>Stellar system, extent of, <a href="#S_223">223</a>.</li> + +<li>Sun's apparent motion, <a href="#S_25">25</a>. +<ul><li>real motion, <a href="#S_195">195</a>.</li></ul></li> + +<li>Sun, <a href="#S_110">110</a>. +<ul><li>chemical composition, <a href="#S_116">116</a>.</li> +<li>chromosphere, <a href="#S_124">124</a>.</li> +<li>corona, <a href="#S_123">123</a>.</li> +<li>distance from the earth, <a href="#S_111">111</a>.</li> +<li>faculę, <a href="#S_119">119</a>, <a href="#S_122">122</a>.</li> +<li>gaseous constitution, <a href="#S_127">127</a>.</li> +<li>heat of, <a href="#S_117">117</a>.</li> +<li>mechanism of, <a href="#S_126">126</a>.</li> +<li>physical properties, <a href="#S_115">115</a>-<a href="#S_120">120</a>.</li> +<li>prominences, <a href="#S_125">125</a>.</li> +<li>rotation, <a href="#S_120">120</a>, <a href="#S_132">132</a>.</li> +<li>surface of, <a href="#S_119">119</a>.</li> +<li>temperature, <a href="#S_118">118</a>.</li></ul></li> + +<li>Sun spots, <a href="#S_119">119</a>, <a href="#S_121">121</a>. +<ul><li>period, <a href="#S_129">129</a>, <a href="#S_131">131</a>.</li> +<li>zones, <a href="#S_130">130</a>.</li></ul></li> + +<li> </li> + +<li>Telescopes, <a href="#S_78">78</a>. +<ul><li>equatorial mounting for, <a href="#S_80">80</a>.</li> +<li>magnifying power of, <a href="#S_79">79</a>.</li></ul></li> + +<li>Temperature of Jupiter, <a href="#S_139">139</a>. +<ul><li>of Mars, <a href="#S_152">152</a>.</li> +<li>of Mercury, <a href="#S_149">149</a>.</li> +<li>of moon, <a href="#S_107">107</a>.</li> +<li>of sun, <a href="#S_118">118</a>.</li></ul></li> + +<li>Temporary stars, <a href="#S_208">208</a>.</li> + +<li>Terminator, <a href="#S_91">91</a>.</li> + +<li>Tenth meter, <a href="#S_75">75</a>.</li> + +<li>Tidal friction, <a href="#S_233">233</a>-<a href="#S_238">238</a>.</li> + +<li>Tides, <a href="#S_42">42</a>.</li> + +<li>Time, sidereal, <a href="#S_120">20</a>, <a href="#S_54">54</a>. +<ul><li>solar, <a href="#S_52">52</a>.</li> +<li>determination of, <a href="#S_20">20</a>.</li> +<li>equation of, <a href="#S_53">53</a>.</li> +<li>standard, <a href="#S_57">57</a>.</li></ul></li> + +<li>Triangulation, <a href="#S_3">3</a>.</li> + +<li>Trifid nebula, <a href="#S_215">215</a>.</li> + +<li>Twilight, <a href="#S_51">51</a>.</li> + +<li>Twinkling, of stars, <a href="#S_48">48</a>.</li> + +<li> </li> + +<li>Universe, development of, <a href="#S_226">226</a>. +<ul><li>stability of, <a href="#S_247">247</a>.</li></ul></li> + +<li>Uranus, <a href="#S_146">146</a>.</li> + +<li> </li> + +<li>Variable stars, <a href="#S_204">204</a>.</li> + +<li>Velocity, its relation to orbital motion, <a href="#S_38">38</a>.</li> + +<li>Venus, <a href="#S_148">148</a>. +<ul><li>orbit of, <a href="#S_30">30</a>.</li></ul></li> + +<li>Vernal equinox, <a href="#S_21">21</a>, <a href="#S_25">25</a>.</li> + +<li>Vertical circle, <a href="#S_21">21</a>.</li> + +<li> </li> + +<li>Wave front, <a href="#S_76">76</a>.</li> + +<li>Wave lengths, <a href="#S_75">75</a>, <a href="#S_86">86</a>.</li> + +<li> </li> + +<li>Year, <a href="#S_25">25</a>. +<ul><li>leap year, <a href="#S_61">61</a>.</li> +<li>sidereal year, <a href="#S_59">59</a>.</li> +<li>tropical year, <a href="#S_60">60</a>.</li></ul></li> + +<li> </li> + +<li>Zenith, <a href="#S_21">21</a>.</li> + +<li>Zodiac, <a href="#S_26">26</a>.</li> + +<li>Zodiacal light, <a href="#S_168">168</a>.</li> +</ul> + + + +<h4>THE END</h4> + + + +<div class="figcenter" style="width: 600px;"><a name="PROTRACTOR" id="PROTRACTOR"></a> +<img src="images/i431.jpg" width="600" height="303" alt="PROTRACTOR + +TO ACCOMPANY COMSTOCK'S ASTRONOMY" title="PROTRACTOR + +TO ACCOMPANY COMSTOCK'S ASTRONOMY" /> +</div> + + + + + + + + +<pre> + + + + + +End of Project Gutenberg's A Text-Book of Astronomy, by George C. 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