diff options
| author | Roger Frank <rfrank@pglaf.org> | 2025-10-14 20:02:28 -0700 |
|---|---|---|
| committer | Roger Frank <rfrank@pglaf.org> | 2025-10-14 20:02:28 -0700 |
| commit | f8f75bdccc8f1f125aa65962fc0b1e0213ffd2da (patch) | |
| tree | 5e152f96799c0beb973d3db41a515b2a89180cf0 /34834.txt | |
Diffstat (limited to '34834.txt')
| -rw-r--r-- | 34834.txt | 11939 |
1 files changed, 11939 insertions, 0 deletions
diff --git a/34834.txt b/34834.txt new file mode 100644 index 0000000..77fb971 --- /dev/null +++ b/34834.txt @@ -0,0 +1,11939 @@ +Project Gutenberg's A Text-Book of Astronomy, by George C. 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: ASCII + +*** START OF THIS PROJECT GUTENBERG EBOOK A TEXT-BOOK OF ASTRONOMY *** + + + + + Transcriber's Note: The angle symbol has been replaced + with [angle]. Greek letters have been replaced with their + transliterations in brackets, e. g. [a] for alpha. The + upside-down Omega symbol has been replaced with [mho]. + + + + + TWENTIETH CENTURY TEXT-BOOKS + + + EDITED BY + A. F. NIGHTINGALE, PH.D., LL.D. + FORMERLY SUPERINTENDENT OF HIGH SCHOOLS, CHICAGO + + + + [Illustration: A TOTAL SOLAR ECLIPSE. + After Burckhalter's photographs of the eclipse of May 28, 1900.] + + + + TWENTIETH CENTURY TEXT-BOOKS + + + A TEXT-BOOK OF + ASTRONOMY + + BY + GEORGE C. COMSTOCK + + + DIRECTOR OF THE WASHBURN OBSERVATORY AND + PROFESSOR OF ASTRONOMY IN THE + UNIVERSITY OF WISCONSIN + + + [Illustration] + + + NEW YORK + D. APPLETON AND COMPANY + 1903 + + + + COPYRIGHT, 1901 + BY D. APPLETON AND COMPANY + + + + +PREFACE + + +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. + +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 weather for a direct +study of the sky and cloudy days for book work. + +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. + +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. + +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. + + GEORGE C. COMSTOCK. + + UNIVERSITY OF WISCONSIN, _February, 1901_. + + + + +CONTENTS + + + CHAPTER PAGE + I.--DIFFERENT KINDS OF MEASUREMENT 1 + The measurement of angles and time. + + II.--THE STARS AND THEIR DIURNAL MOTION 10 + Finding the stars--Their apparent motion-- + Latitude--Direction of the meridian--Sidereal + time--Definitions. + + III.--FIXED AND WANDERING STARS 29 + Apparent motion of the sun, moon, and + planets--Orbits of the planets--How to find + the planets. + + IV.--CELESTIAL MECHANICS 46 + Kepler's laws--Newton's laws of motion--The law + of gravitation--Orbital motion--Perturbations-- + Masses of the planets--Discovery of Neptune-- + The tides. + + V.--THE EARTH AS A PLANET 70 + Size--Mass--Precession--The warming of the + earth--The atmosphere--Twilight. + + VI.--THE MEASUREMENT OF TIME 86 + Solar and sidereal time--Longitude--The + calendar--Chronology. + + VII.--ECLIPSES 101 + Their cause and nature--Eclipse limits--Eclipse + maps--Recurrence and prediction of eclipses. + + VIII.--INSTRUMENTS AND THE PRINCIPLES INVOLVED IN THEIR USE 121 + The clock--Radiant energy--Mirrors and lenses-- + The telescope--Camera--Spectroscope--Principles + of spectrum analysis. + + IX.--THE MOON 150 + Numerical data--Phases--Motion--Librations--Lunar + topography--Physical condition. + + X.--THE SUN 178 + Numerical data--Chemical nature--Temperature-- + Visible and invisible parts--Photosphere--Spots-- + Faculæ--Chromosphere--Prominences--Corona--The + sun-spot period--The sun's rotation--Mechanical + theory of the sun. + + XI.--THE PLANETS 212 + Arrangement of the solar system--Bode's law-- + Physical condition of the planets--Jupiter-- + Saturn--Uranus and Neptune--Venus--Mercury-- + Mars--The asteroids. + + XII.--COMETS AND METEORS 251 + 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. + + XIII.--THE FIXED STARS 291 + Number of the stars--Brightness--Distance--Proper + motion--Motion in line of sight--Double stars-- + Variable stars--New stars. + + XIV.--STARS AND NEBULÆ 330 + Stellar colors and spectra--Classes of stars-- + Clusters--Nebulæ--Their spectra and physical + condition--The Milky Way--Construction of the + heavens--Extent of the stellar system. + + XV.--GROWTH AND DECAY 358 + Logical bases and limitations--Development of the + sun--The nebular hypothesis--Tidal friction--Roche's + limit--Development of the moon--Development of stars + and nebulæ--The future. + + APPENDIX 383 + + INDEX 387 + + + + +LIST OF LITHOGRAPHIC PLATES + + + FACING PAGE + I.--Northern Constellations 124 + II.--Equatorial Constellations 190 + III.--Map of Mars 246 + IV.--The Pleiades 344 + Protractor _In pocket at back of book_ + + + + +LIST OF FULL-PAGE ILLUSTRATIONS + + + FACING PAGE + A Total Solar Eclipse _Frontispiece_ + The Harvard College Observatory, Cambridge, Mass. 24 + Isaac Newton 46 + Galileo Galilei 52 + The Lick Observatory, Mount Hamilton, Cal. 60 + The Yerkes Observatory, Williams Bay, Wis. 100 + The Moon, one day after First Quarter 150 + William Herschel 234 + Pierre Simon Laplace 364 + + + + +ASTRONOMY + + + + +CHAPTER I + +DIFFERENT KINDS OF MEASUREMENT + + +1. ACCURATE MEASUREMENT.--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 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. + +EXERCISE 1.--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: + + 2h. 44.5m. First tap. 2h. 46.4m. 1.9m. + 2h. 44.9m. Second tap. 2h. 46.7m. 1.8m. + 2h. 46.6m. Third tap. 2h. 48.6m. 2.0m. + +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. + +2. ANGLES AND THEIR USE.--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 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. + +A watch may be used to measure angles. How? But a more convenient +instrument is the protractor, which is shown in Fig. 1, applied to the +angle _A B C_ and showing that _A B C_ = 85° as nearly as the protractor +scale can be read. + +The student should have and use a protractor, such as is furnished with +this book, for the numerous exercises which are to follow. + +[Illustration: FIG. 1.--A protractor.] + +EXERCISE 2.--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: + + Measured angles. Correction. Corrected angles. + ° ° ° + A 73.4 + 0.1 73.5 + B 49.3 + 0.1 49.4 + C 57.0 + 0.1 57.1 + ----- ----- + Sum 179.7 180.0 + Defect + 0.3 + +This process is in very common use among astronomers, and is called +"adjusting" the observations. + +[Illustration: FIG. 2.--Triangulation.] + +3. TRIANGLES.--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 +Fig. 2. A surveyor at _A_ desires to know the distance to _C_, 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 _A B_ = 100 yards and +then, with a suitable instrument, measures the angle at _A_ between the +points _C_ and _B_, and the angle at _B_ between _C_ and _A_, finding _B +A C_ = 73.4°, _A B C_ = 49.3°. To determine the distance _A C_ he draws +upon paper a line 100 millimeters long, and marks the ends _a_ and _b_; +with a protractor he constructs at _a_ the angle _b a c_ = 73.4°, and at +_b_ the angle _a b c_ = 49.3°, and marks by _c_ the point where the two +lines thus drawn meet. With the millimeter scale he now measures the +distance _a c_ = 90.2 millimeters, which determines the distance _A C_ +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 _A B_ in the surveyor's +problem is called a base line. + +EXERCISE 3.--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. + +[Illustration: FIG. 3.--Finding the moon's distance from the earth.] + +In the same manner, by sighting at the moon from widely different parts +of the earth, as in Fig. 3, 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? + +4. THE HORIZON--ALTITUDES.--In their observations astronomers and +sailors make much use of the _plane of the horizon_, 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 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. + +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. + +5. TAKING THE SUN'S ALTITUDE. EXERCISE 4.--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 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 Fig. 4, 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. + +[Illustration: FIG. 4.--Taking the sun's altitude.] + +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 _azimuth_. When the sun is south, its azimuth is zero; +when west, it is 90°; when east, 270°, etc. + +EXERCISE 5.--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. + +6. GRAPHICAL REPRESENTATIONS.--Make a graph (drawing) of all the +observations, similar to Fig. 5, and find by bisecting a set of chords +_g_ to _g_, _e_ to _e_, _d_ to _d_, drawn parallel to _B B_, the time at +which the sun's altitude was greatest. In Fig. 5 we see from the +intersection of _M M_ with _B B_ that this time was 11h. 50m. + +The method of graphs which is here introduced is of great importance in +physical science, and the student should carefully observe in Fig. 5 +that the line _B B_ is a scale of times, which may be made long or +short, provided only the intervals between consecutive hours 9 to 10, 10 +to 11, 11 to 12, etc., are equal. The distance of each little circle +from _B B_ 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 +A. M. and 3 P. M. In Fig. 5 the sun's altitude at noon was 57°. What was +it at half past two? + +[Illustration: FIG. 5.--A graph of the sun's altitude.] + +7. DIAMETER OF A DISTANT OBJECT.--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 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. + +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? + + + + +CHAPTER II + +THE STARS AND THEIR DIURNAL MOTION + + +8. THE STARS.--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 Plate I, opposite page 124. +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. + +_The names of the stars._--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.) + +9. MAGNITUDES OF THE STARS.--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, which the modern astronomers still use, calling each group a +_magnitude_. 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. + +10. OBSERVING THE STARS.--Find on the map and in the sky the stars +[a] Ursæ Minoris, [a] Ursæ Majoris, [b] Ursæ Majoris. What geometrical +figure will fit on to these stars? In addition to its regular name, +[a] Ursæ 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? + +EXERCISE 6.--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 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. + +The motion of the stars which the student has here detected is called +their "diurnal" motion. What is the significance of the word diurnal? + +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. + +Repeat Exercise 6 night after night, and note whether the stars come +back to the same position at the same hour and minute every night. + +[Illustration: FIG. 6. The plumb-line apparatus.] + +[Illustration: FIG. 7. The plumb-line apparatus.] + +11. THE PLUMB-LINE APPARATUS.--This experiment, and many others, may be +conveniently and accurately made with no other apparatus than a plumb +line, and a device for sighting past it. In Figs. 6 and 7 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. 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 Fig. 6, for measuring altitudes; or to the box, as in +Fig. 7, 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. + +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 § 10, it should be leveled, and +the board with the screw eyes, attached as in Fig. 7, 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. + +12. A SIDEREAL CLOCK.--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? + +[Illustration: FIG. 8.--Photographing the circumpolar stars.--BARNARD.] + +13. PHOTOGRAPHING THE STARS.--EXERCISE 7.--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 Fig. 8, only longer. Each one of these is produced 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 Fig. 8? + +14. FINDING THE STARS.--On Plate I, opposite page 124, the pole of the +heavens is at the center of the map, near Polaris, and the heavy trail +near the center of Fig. 8 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. + +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? + +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? + +In what part of the sky do the stars move most rapidly, near the pole or +far from it? + +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? + +15. RISING AND SETTING OF THE STARS.--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 Fig. 9). 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 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. + +[Illustration: FIG. 9.--Diurnal motion of the northern constellations.] + +How much time do stars which are more than 90° from the pole spend above +the horizon? + +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. + +16. THE GEOGRAPHY OF THE SKY.--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? + +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 _declination_, +in place of longitude he says _right ascension_, in place of meridian he +says _hour circle_, but he means by these new names the same ideas that +the geographer expresses by the old ones. + +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 _celestial equator_. +Trace its position along the middle of the map opposite page 190 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? + +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 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. + +[Illustration: FIG. 10.--From a photograph of the Pleiades.] + +Find on Plate II, opposite page 190, the Pleiades (Pl[=e]ad[=e]s), +R. A. = 3h. 42m., Dec. = +23.8°. Why do they not show on Plate I, +opposite page 124? 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 Fig. 10. 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? + +Find the R. A. and Dec. of [a] Ursæ Majoris; of [b] Ursæ Majoris; of +Polaris. Find the Northern Crown, _Corona Borealis_, R. A. = 15h. 30m., +Dec. = +27.0°; the Beehive, _Præsepe_, R. A. = 8h. 33m., Dec. = +20.4°. + +These should be looked up, not only on the map, but also in the sky. + +17. REFERENCE LINES AND CIRCLES.--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. + +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 Fig. 11 +the inner circle represents the terrestrial meridian of a certain +place, _O_, as seen from the center of the earth, _C_, and the outer +circle represents the celestial meridian of _O_ as seen from _C_, 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 _C P_ represents the direction in which the +earth's axis passes through the center, then _C E_ at right angles to it +must be the direction of the equator which we suppose to be turned +edgewise toward us; and if _C O_ is the direction of some particular +point on the earth's surface, then _Z_ directly overhead is called the +_zenith_ of that point, upon the celestial sphere. The line _C H_ +represents a direction parallel to the horizon plane at _O_, and _H C P_ +is the angle which the axis of the earth makes with this horizon plane. +The arc _O E_ measures the latitude of _O_, and the arc _Z E_ measures +the declination of _Z_, and since by elementary geometry each of these +arcs contains the same number of degrees as the angle _E C Z_, we have +the + +_Theorem._--The latitude of any place is equal to the declination of its +zenith. + +_Corollary._--Any star whose declination is equal to your latitude will +once in each day pass through your zenith. + +[Illustration: FIG. 11.--Reference lines and circles.] + +18. LATITUDE.--From the construction of the figure + + [angle] _E C Z_ + [angle] _Z C P_ = 90° + [angle] _H C P_ + [angle] _Z C P_ = 90° + +from which we find by subtraction and transposition + + [angle] _E C Z_ = [angle] _H C P_ + +and this gives the further + +_Theorem._--The latitude of any place is equal to the elevation of the +pole above its horizon plane. + +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? + +[Illustration: FIG. 12.--Diurnal path of Polaris.] + +EXERCISE 8.--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 +Fig. 12. When it is at _1_ it is said to be at upper culmination, and +the star [z] Ursæ Majoris in the handle of the Big Dipper will be +directly below it. When at _2_ it is at western elongation, and the +star Castor is near the meridian. When it is at _3_ it is at lower +culmination, and the star Spica is on the meridian. When it is at _4_ 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 _2_ +or _4_ may be considered equal to the latitude of the place, but the +altitude observed when Polaris is at the positions marked _1_ and _3_ +must be corrected for the star's distance from the pole, which may be +assumed equal to 1.3°. + +The plumb-line apparatus described at page 12 is shown in Fig. 6 +slightly modified, so as to adapt it to measuring the altitudes of +stars. Note that the board with the screw 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. + +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. + +19. THE MERIDIAN LINE.--To establish a true north and south line upon +the ground, use the apparatus as described at page 13, 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. + +20. TIME.--What is _the time_ at which school begins in the morning? +What do you mean by "_the time_"? + +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 "_on the meridian_" 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. + +[Illustration: THE HARVARD COLLEGE OBSERVATORY, CAMBRIDGE, MASS.] + +EXERCISE 9.--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 § 19, 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 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. + +A more accurate mode of performing the experiment consists in using the +plumb-line apparatus carefully adjusted, as in Fig. 7, 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. + +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 +Chapter V), 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. + +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 is expressed in the following +equation, with which the student should become thoroughly familiar: + + A = T ± U + +_T_ stands for the time by the clock at which the star crossed the +meridian. _A_ is the right ascension of the star, and _U_ 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. _U_ may be found +from this equation when _A_ and _T_ are given, or _A_ may be found when +_T_ and _U_ are given. It is in this way that astronomers measure the +right ascensions of the stars and planets. + +Determine _U_ from each star you have observed, and note how the several +results agree one with another. + +21. DEFINITIONS.--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. + +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. + +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: + +_The Poles_ 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. + +_The Celestial Equator_ is a great circle of the sky distant 90° from +the poles. + +_The Zenith_ 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? + +_The Horizon_ is a great circle of the sky 90° distant from the zenith. + +_An Hour Circle_ is any great circle of the sky which passes through the +poles. Every star has its own hour circle. + +_The Meridian_ is that hour circle which passes through the zenith. + +_A Vertical Circle_ is any great circle that passes through the zenith. +Is the meridian a vertical circle? + +_The Declination_ of a star is its angular distance north or south of +the celestial equator. + +_The Right Ascension_ 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 _Vernal Equinox_. 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 page 124, 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. + +_The Altitude_ of a star is its angular distance above the horizon. + +_The Azimuth_ 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°. + +What is the azimuth of Polaris in degrees? + +What is the azimuth of the sun at sunrise? At sunset? At noon? Are these +azimuths the same on different days? + +_The Hour Angle_ 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. + +What is the hour angle of the sun at noon? What is the hour angle of +Polaris when it is at the lowest point in its daily motion? + +22. EXERCISES.--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? + + + + +CHAPTER III + +FIXED AND WANDERING STARS + + +23. STAR MAPS.--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. + +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 Fig. 13. + +So, too, a sharp eye may detect that some stars do not remain always of +the same magnitude, but change their 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 _variable stars_, as they are called. + +[Illustration: FIG. 13.--Star map of the region about Orion.] + +24. THE MOON'S MOTION AMONG THE STARS.--Whenever the moon is visible +note its position among the stars by allineations, and plot it on the +key map opposite page 190. 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. + +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? + +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. + +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? + +Each of these questions can be correctly answered from the student's own +observations without recourse to any book. + +25. THE SUN AND ITS MOTION.--Examine the face of the sun through a +smoked glass to see if there is anything there that you can sketch. + +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 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. + +EXERCISE 10.--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 § 20, and substitute in place of _U_ the value of the +clock correction found from observations of stars on a preceding or +following night. If the clock gains or loses _with respect to sidereal +time_, take this into account in the value of _U_. + +EXERCISE 11.--To determine the sun's declination, measure its altitude +at the time it crosses the meridian. Use either the method of Exercise +4, or that used with Polaris in Exercise 8. The student should be able +to show from Fig. 11 that the declination is equal to the sum of the +altitude and the latitude of the place diminished by 90°, or in an +equation + + Declination = Altitude + Latitude - 90°. + +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. + +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. + +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. + +If observations of the sun's right ascension and declination 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. + +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? + +EXERCISE 12.--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 _tropical year_, is 365 days 5 hours 48 +minutes 46 seconds. Is this the same as the ordinary year of our +calendars? + +26. THE PLANETS.--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? + +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 mediæval literature are +permeated with this idea, which was displaced only after a long struggle +begun by Copernicus (1543 A. D.), 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 _zodiac_, a word which may be regarded as +the name of a narrow street (16° wide) within which all the wanderings +of the visible 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. + +[Illustration: FIG. 14.--The apparent motion of a planet.] + +27. A TYPICAL CASE OF PLANETARY MOTION.--The Copernican theory, +enormously extended and developed through the Newtonian law of +gravitation (see Chapter IV), 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. 14 and 15, the first of which represents the +apparent motion of the planet Mars through the constellations Aries and +Pisces during the latter part of the 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 Fig. 14, 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 Fig. 15 +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 Fig. 14 show that +the orbit of Mars does not lie exactly in the same plane with the orbit +of the earth? + +EXERCISE 13.--Find from Fig. 15 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 Fig. 14. The apparent position +of Mars among the stars is merely its direction from the earth, and this +direction is represented in Fig. 14 by the distance of the planet from +the ecliptic and by its longitude. + +[Illustration: FIG. 15.--The real motion of a planet.] + +The longitude of Mars for each date can be found from Fig. 15 by +measuring the angle between the straight line _S V_ 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 _S V_ and the line joining +the earth to Mars is a little more than 30°, and in Fig. 14 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 Fig. 15, which +from necessity is constructed as if the orbits of Mars and the earth lay +in the same plane, and Mars in this case would always appear to stand +exactly on the ecliptic and to oscillate back and forth as shown in Fig. +14, but without the up-and-down motion there shown. In this way plot in +Fig. 14 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. + +[Illustration: FIG. 16.--The orbits of Jupiter and Saturn.] + +28. THE ORBITS OF THE PLANETS.--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 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. 16 and 17, 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. + +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. + +29. JUPITER AND SATURN.--In Fig. 16 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_), first day of February (_II_), 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 orbits for something more +than the first decade of the twentieth century. + +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. + +[Illustration: FIG. 17.--The orbits of the inner planets.] + +EXERCISE 14.--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. + +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. + +EXERCISE 15.--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. + +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? + +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. + +EXERCISE 16.--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? + +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 _opposition_--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 _conjunction_ 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? + + +30. MERCURY, VENUS, AND MARS.--Fig. 17, which represents the orbits of +the inner planets, differs from Fig. 16 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, _V_, 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 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 + + 1900, July 4 - 1899, September 23 = 284 days, + +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. + +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? + +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: + + TABLE OF EPOCHS + + ----------------------------------------------------------- + A. D. | Mercury. | Venus. | Earth. | Mars. + --------+------------+-----------+------------+------------ + Period | 88.0 days. |224.7 days.|365.25 days.| 687.1 days. + 1900 | Feb. 18th. | Jan. 11th.| Sept. 23d. | April 28th. + 1901 | Feb. 5th. | April 5th.| Sept. 23d. | ... + 1902 | Jan. 23d. | June 29th.| Sept. 23d. | March 16th. + 1903 | April 8th. | Feb. 8th. | Sept. 23d. | ... + 1904 | March 25th.| May 3d. | Sept. 23d. | Feb. 1st. + 1905 | March 12th.| July 26th.| Sept. 23d. | Dec. 19th. + 1906 | Feb. 27th. | March 8th.| Sept. 23d. | ... + 1907 | Feb. 14th. | May 31st. | Sept. 23d. | Nov. 6th. + 1908 | Feb. 1st. | Jan. 11th.| Sept. 23d. | ... + 1909 | Jan. 18th. | April 4th.| Sept. 23d. | Sept. 23d. + 1910 | Jan. 5th. | June 28th.| Sept. 23d. | ... + ----------------------------------------------------------- + +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 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. + +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. + +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. + +31. EXERCISES.--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 Fig. 16 or Fig. 17 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. + +What planet is the evening star _now_? Is there more than one evening +star at a time? What is the morning star now? + +Do Mercury, Venus, or Mars ever appear in opposition? 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? + +The earth always comes to the same longitude on the same day of each +year. Why is not this true of the other planets? + +The student should remember that in one respect Figs. 16 and 17 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. + + + + +CHAPTER IV + +CELESTIAL MECHANICS + + +32. THE BEGINNINGS OF CELESTIAL MECHANICS.--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. + +[Illustration: ISAAC NEWTON (1643-1727).] + +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 upon +and moved along a circular orbit, called the deferent, within which the +earth was placed, as is shown in Fig. 18, where the small circle is the +epicycle, the large circle is the deferent, _P_ is the planet, and _E_ +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. + +[Illustration: FIG. 18.--Epicycle and deferent.] + +33. KEPLER'S LAWS.--Two generations later came Kepler with his three +famous laws of planetary motion: + +I. Every planet moves in an ellipse which has the sun at one of its +foci. + +II. The radius vector of each planet moves over equal areas in equal +times. + +III. The squares of the periodic times of the planets are proportional +to the cubes of their mean distances from the sun. + +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. + +EXERCISE 17.--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. + +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 Fig. 17 the dot, inside the orbit of Mercury, which is +marked _a_, shows the position of the vacant focus of the orbit of Mars, +and the dot _b_ 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 _radius vector_. The point midway between the pins is the +_center_ of the ellipse, and the distance of either pin from the center +measures the _eccentricity_ of the ellipse. + +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. + +If both pins were driven into the same hole, what kind of an ellipse +would you get? + +The Second Law was worked out by Kepler as his answer to a problem +suggested by the first law. In Fig. 17 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 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 Fig. 17 +was done by means of this law. + +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 _a_ and the second by _T_, we have, +as the mathematical equivalent of the law, + + a^{3} ÷ T^{2} = C + +where the quotient, _C_, 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, +_C_ = 1. Applying this value to any other planet we shall find in the +same units, _a_ = _T_^{2/3}, by means of which we may determine the +distance of any planet from the sun when its periodic time, _T_, has +been learned from observation. + +EXERCISE 18.--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 Chapter III for their +periodic times.) Would it be possible for two planets at different +distances from the sun to move around their orbits in the same time? + +A circle is an ellipse in which the two foci have been brought together. +Would Kepler's laws hold true for such an orbit? + +34. NEWTON'S LAWS OF MOTION.--Kepler studied and described the motion of +the planets. Newton, three generations later (1727 A. D.), 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. + +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 + +THE FIRST LAW OF MOTION.--"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. + +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 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. + +35. THE SECOND LAW OF MOTION, which is also due to Galileo and Newton, +is: + +"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 _v_ 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 _d_, 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 +_s_ in the table, is found by taking the sum of all the preceding values +of _d_. The velocity, 32 feet per second, which measures the change of +motion in each second, also measures the _accelerating force_ which +produces this motion, and it is usually represented in formulæ by the +letter _g_. Let the student show from the numbers in the table that the +accelerating force, the time, _t_, during which it operates, and the +space, _s_, fallen through, satisfy the relation + + s = 1/2 gt^{2}, + +which is usually called the law of falling bodies. How does the table +show that _g_ is equal to 32? + + TABLE + + _t_ _v_ _d_ _s_ + + 0 0 0 0 + 1 32 16 16 + 2 64 48 64 + 3 96 80 144 + 4 128 112 256 + 5 160 144 400 + etc. etc. etc. etc. + +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? + +[Illustration: GALILEO GALILEI (1564-1642).] + +Fig. 19 shows the path through the air of a ball which has been struck +by a bat at the point _A_, and started off in the direction _A B_ 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 _A B_ at the +uniform rate of 200 feet per second, and at the end of the fourth second +it should be 800 feet from _A_, 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 _A C_. No +matter how far the ball may go before striking the ground, it can not +get back to the point _A_, and the curve _A C_ therefore can not be a +part of a circle, since that curve returns into itself. It is, in fact, +a part of a _parabola_, 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. + +[Illustration: FIG. 19.--The path of a ball.] + +36. THE THIRD LAW OF MOTION.--"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. + +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-- + +37. NEWTON'S LAW OF GRAVITATION.--"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, _gravitas_, 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. + +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 sponsor for them, even though they are justified by a +rigorous interpretation of the Newtonian law. + +The word _mass_, in the statement of the law of gravitation, means the +quantity of matter contained in the body, and if we represent by the +letters _mŽ_ and _mŽŽ_ the respective quantities of matter contained in +the two bodies whose distance from each other is _r_, we shall have, in +accordance with the law of gravitation, the following mathematical +expression for the force, _F_, which acts between them: + + F = k {mŽmŽŽ/r^{2}}. + +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 + + F = k {(1 × 1)/1^{2}} = k, + +from which it appears that the coefficient _k_ 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 _mŽ_, _mŽŽ_ are very great that the force of gravity becomes +large, and the weight of bodies at the 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. + +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. + +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? + +38. THE MOTION OF A PLANET.--In Fig. 20 _S_ represents the sun and _P_ a +planet or other celestial body, which for the moment is moving along the +straight line _P 1_. 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 +_P 1_. + +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 _perihelion_. + +Without any formal application of mathematics we may readily see that +the swifter the motion of the body at _P_ 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 _P 1_ and _P 2_. + +On the other hand, _P 5_ and _P 6_ represent orbits in which the +velocity at _P_ was comparatively small, and the resulting change of +motion greater than would be possible for a more swiftly moving body. + +What would be the orbit if the velocity at _P_ were reduced to nothing +at all? + +What would be the effect if the body starting at _P_ moved directly away +from _1_? + +[Illustration: FIG. 20.--Different kinds of orbits.] + +The student should not fail to observe that the sun's attraction tends +to pull the body at _P_ 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 turns in different parts of the orbit, +as given by the second law, depends upon the changes in this force. + +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 _P_, +moving in the same direction and with the same speed as before--i. e., +it has gone around the sun in an orbit like _P 6_ or _P 4_, 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 _P 2_, 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 _P 3_, a parabola, along +which the body moves with _parabolic velocity_, 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. + +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. + +It is sometimes a source of wonder that the planets move in ellipses +instead of circles, but it is easily seen from Fig. 20 that the planet, +_P_, could not by any possibility move in a circle, since the direction +of its motion at _P_ 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 (Fig. 17), which is much more +eccentric than that of the earth, might almost pass for a circle. + +[Illustration: FIG. 21. An impossible orbit.] + +The orbit _P 2_, 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.[1] 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 Fig. 21. If the +body passes a second time through any point of its orbit, such as _P_ in +the figure, then it must retrace, time after time, the whole path that +it first traversed in getting from _P_ around to _P_ again--i. e., the +orbit must be an ellipse. + + [1] The circle and straight line are considered to be special cases + of these curves, which, taken collectively, are called the conic + sections. + +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. + +39. PERTURBATIONS.--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 _perturbations_, 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, +_P_, 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. + +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. + +[Illustration: THE LICK OBSERVATORY, MOUNT HAMILTON, CAL.] + +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 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. + +The precession (Chapter V) 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 _nodes_, 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. + +[Illustration: FIG. 22.--A planet subject to great perturbations by +Jupiter.] + +40. WEIGHING THE PLANETS.--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 _F_ which it exerts contains +this mass, _mŽ_, as a factor. So, too, the divisor _r^{2}_ 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 is +presented in Fig. 22, 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 the mass of Jupiter expressed as a fractional +part of the mass of the sun. + +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: + + Mercury 7,000,000 (?) + Venus 408,000 + Earth 329,000 + Mars 3,093,500 + Jupiter 1,047.4 + Saturn 3,502 + Uranus 22,800 + Neptune 19,700 + +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. + +41. DISCOVERY OF NEPTUNE.--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 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. + +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. + +42. THE SHAPE OF A PLANET.--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 _centrifugal_, +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. + +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 Fig. 23 where _1_, _2_, and _3_ represent +pieces of iron of equal mass placed in line on a table near a horseshoe +magnet, _H_. 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, _P_, 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. _2_. It is clear that under this arrangement No. +_2_ will move 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. _1_, however, the magnet pulls harder than upon No. _2_, +because it is nearer and its pull therefore more than balances the force +exerted by the weight, so that No. _1_ will be pulled away from No. _2_ +and will stretch the elastic cords, which are represented by the lines +joining _1_ and _2_, until their tension, together with the force +exerted by the weight, just balances the attraction of the magnet. For +No. _3_, the force exerted by the magnet is less than that of the +weight, and it will also be pulled away from No. _2_ 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. + +[Illustration: FIG. 23.--Tide-raising forces.] + +An entirely analogous set of forces produces a similar effect upon the +shape of the moon. The elastic cords of Fig. 23 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 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. + +[Illustration: FIG. 24.--The tides.] + +THE TIDES.--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 Fig. 24 +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 _tide_. If _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 position _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 _IŽŽ_, +half a day later, they will again rise in flood tide, and midway between +these points, at _IŽ_, the waters must subside, giving low or ebb tide. + +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? + +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. + +43. THE SCOPE OF THE LAW OF GRAVITATION.--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 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. + + + + +CHAPTER V + +THE EARTH AS A PLANET + + +44. THE SIZE OF THE EARTH.--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. + +[Illustration: FIG. 25.--Measuring the size of the earth.] + +In Fig. 25 the circle represents a meridian section of the earth; _P PŽ_ +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 _1_, _2_, _3_, +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 +Chapter II, how these angles may be measured, and it is apparent from +the figure that the difference between any two of these angles--e. g., +the angles at _1_ and _2_--is equal to the angle at the center, _O_, +between the points _1_ and _2_. 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 _1_, _2_, _3_, 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. + +Neglecting the _compression_, 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 _1_--_2_ along the +surface and by combining with this the angle _1 O 2_ obtained through +measuring the meridian altitudes of any star as seen from _1_ and _2_. +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 _1_ and _2_. This distance from the vertex +will be the earth's radius. + +EXERCISE 19.--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., 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. + +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 Chapter +II and determined within a small percentage of its true value. + +45. THE MASS OF THE EARTH.--We have seen in Chapter IV 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. + +[Illustration: FIG. 26.--Illustrating the principles involved in +weighing the earth.] + +In Fig. 26 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, +_C_, by a force whose intensity is (Chapter IV) + + F = k mE/R^{2}, + +where _E_ denotes the mass of the earth, which is to be determined by +experiment, and _R_ is the radius of the earth, 3,963 miles. If there is +no disturbing influence present, the plumb line will point directly +downward, but if a massive ball of lead or other heavy substance is +placed at one side, _1_, it will attract the plumb line with a force +equal to + + f = k mB/r^{2}, + +where _r_ is the distance of its center from the plumb bob and _B_ 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 _l_ the +length of the plumb line and by _d_ the distance between the original +and the disturbed positions of the plumb bob we may write the proportion + + F : f :: l : d; + +and introducing the values of _F_ and _f_ given above, and solving for +_E_ the proportion thus transformed, we find + + E = B × l/d × (R/r)^{2}. + +In this equation the mass of the ball, _B_, the length of the plumb +line, _l_, the distance between the center of the ball and the center of +the plumb bob, _r_, and the radius of the earth, _R_, can all be +measured directly, and _d_, 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 _2_, and measuring with a microscope how far the +plumb bob moves. This distance will, of course, be equal to _2 d_. + +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^{18}--i. e., 6,642 followed by 18 ciphers, or in +kilogrammes 60,258 × 10^{20}. The earth's atmosphere makes up about a +millionth part of this mass. + +If the length of the plumb line were 100 feet, the weight of the ball a +ton, and the distance between the two positions of the ball, _1_ and +_2_, six feet, how many inches, _d_, would the plumb bob be pulled out +of place? + +Find from the mass of the earth and the data of § 40 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. + +46. PRECESSION.--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? + +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 Exercise 7, 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. + +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 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. + +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 Chapter +IV), 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 motion, first in one +way and then in another, without in the long run producing any results +of consequence. + +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°. + +EXERCISE 20.--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: + +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? + +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. + +Will the precession ever bring back the right ascensions and +declinations to be again what they now are? + +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? + +47. THE WARMING OF THE EARTH.--Winter and summer alike the day is on the +average warmer than the night, and it is 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. + +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 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. + +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. + +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. + +We have seen in Chapter III 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 +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. + +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. + +48. RELATION OF THE SUN TO CLIMATE.--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 winter reigns at the +time we are enjoying summer, while six months later the conditions are +reversed. + +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. + +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. + +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? + +Does the precession of the equinoxes have any effect upon the seasons or +upon the climate of different parts of the earth? + +If the axis of the earth pointed toward Arcturus instead of Polaris, +would the seasons be any different from what they are now? + +49. THE ATMOSPHERE.--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. 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. + +50. REFRACTION.--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 Fig. 27, 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. + +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. + +[Illustration: FIG. 27.--Flattening of the sun's disk by refraction and +by reflection from the surface of the sea.] + +51. THE TWILIGHT.--Another effect of the atmosphere, even more marked +than the preceding, is the twilight. As 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. + +[Illustration: FIG. 28.--Twilight phenomena.] + +Fig. 28 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 _1_ 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 _2_, 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 _3_, 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 _3 L_. 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. + +Let the student redraw Fig. 28 on a large scale, so that the points _1_ +and _3_ shall be only 18° apart, as seen from the earth's center. He +will find that the point _L_ is brought down much closer to the surface +of the earth, and measuring the length of the line _2 L_, 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. + +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. + +[Illustration: FIG. 29.--The cause of long and short twilights.] + +_Duration of twilight._--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 _a_, Fig. 29, a much +shorter time will suffice to carry it to a depression of 18° than is +needed in the case shown at _b_ 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 of +circumstance from _a_ to _b_, 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, + + "The sun's rim dips; the stars rush out: + At one stride comes the dark." + _The Ancient Mariner._ + +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. + +How long does twilight last at the north pole? + +_The Aurora._--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. + + + + +CHAPTER VI + +THE MEASUREMENT OF TIME + + +52. SOLAR TIME.--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. + +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. + +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 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. + +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 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. + +[Illustration: FIG. 30.--The equation of time.] + +53. MEAN SOLAR TIME.--To remedy these inconveniences there has been +invented and brought into common use what is called _mean solar time_, +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 Fig. 30, in which the part of the curve above the +line marked _0m_ 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 _equation of time_, but in the almanacs it is +frequently marked "sun fast" or "sun slow." In sidereal time and true +solar time the distinction between A. M. hours (_ante meridiem_ = +before the sun reaches the meridian) and P. M. hours (_post meridiem_ = +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. + +54. TO FIND (APPROXIMATELY) THE SIDEREAL TIME AT ANY MOMENT.--RULE I. +When the mean solar time is known. Let _W_ represent the time shown by +an ordinary watch, and represent by _S_ the corresponding sidereal time +and by _D_ the number of days that have elapsed from March 23d to the +date in question. Then + + S = W + 69/70 × D × 4. + +The last term is expressed in minutes, and should be reduced to hours +and minutes. Thus at 4 P. M. on July 4th-- + + _D_ = 103 days. + 69/70 × _D_ × 4 = 406m. + = 6h. 46m. + _W_ = 4h. 0m. + _S_ = 10h. 46m. + +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. + +RULE II. When the stars in the northern sky can be seen. Find [b] +Cassiopeiæ, and imagine a line drawn from it 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. + +55. THE EARTH'S ROTATION.--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. + +56. LONGITUDE AND TIME.--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 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 Fig. 31, 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 _O_ 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 page 36. From Fig. 31 we obtain +the + +_Theorem._--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°. + +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. + +[Illustration: FIG. 31.--Longitude and time] + +[Illustration: FIG. 32.--Standard time.] + +57. STANDARD TIME.--The requirements of railroad traffic have led to the +use throughout the United States and 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. + + Eastern time is 5 hours slower than that of Greenwich. + Central " 6 " " " " " + Mountain " 7 " " " " " + Pacific " 8 " " " " " + +In Fig. 32 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. + +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. + +58. TO DETERMINE THE LONGITUDE.--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 Fig. 30. 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. + +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. + +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? + +59. CHRONOLOGY.--The Century Dictionary defines chronology as "the +science of time"--that is, "the method of measuring or computing time +by regular divisions or periods according to the revolutions of the sun +or moon." + +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 Chapter V, 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. + +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 +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? + +One of the Greek poets[2] 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: + + "The moon by us to you her greeting sends, + But bids us say that she's an ill-used moon + And takes it much amiss that you will still + Shuffle her days and turn them topsy-turvy, + So that when gods, who know their feast days well, + By your false count are sent home supperless, + They scold and storm at her for your neglect." + + [2] Aristophanes, The Clouds, Whewell's translation. + +60. DAY, MONTH, AND YEAR.--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. + +According to Professor Harkness, for the epoch 1900 A. D.-- + + One tropical year = 365.242197 mean solar days. + " " " = 365d. 5h. 48m. 45.8s. + One lunation = 29.530588 mean solar days. + " " = 29d. 12h. 44m. 2.8s. + +The word _lunation_ 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. + +A very ancient device was to call a year equal to 365 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: + + "Thirty days hath September, + April, June, and November; + All the rest have thirty-one + Save February, + Which alone hath twenty-eight, + Till leap year gives it twenty-nine." + + +61. THE CALENDAR.--The foundations of our calendar may fairly be +ascribed to Julius Cæsar, 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 +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 Cæsar's reformation, and also their places in some of the +subsequent calendars, for the widest diversity of practice existed +during mediæval 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. + +The system of leap years introduced by Cæsar 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 _any_ 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 mediæval Europe found here ground for objection to Cæsar'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 A. D. 325, the time of the Council of Nicæa, which Gregory +adopted as the fundamental epoch of his calendar. + +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 Cæsar's leap-year 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. + +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 + + G = J + (N - 2) - N/4, + +where _G_ and _J_ are the respective dates, _N_ 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 + + J = Sept. 3 + N - 2 = + 15 + - N/4 = - 4 + ------------------ + G = Sept. 14 + +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? + +62. THE DAY OF THE WEEK.--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. + +The formula for this case is + + 7q + r = Y + D + (Y - 1)/4 - (Y - 1)/100 + (Y - 1)/400 + +where _Y_ denotes the given year, _D_ the number of the day (date) in +that year, and _q_ and _r_ are respectively the quotient and the +remainder obtained by dividing the second member of the equation by 7. +If _r_ = 1 the date falls on Sunday, etc., and if _r_ = 0 the day is +Saturday. For the example suggested above we have + + Jan. 31 + Feb. 29 + Mch. 31 + April 30 + May 31 + June 30 + July 31 + Aug. 31 + Sept. 30 + Oct. 21 + --- + D = 295 + + Y = 1492 + + D = + 295 + + (Y - 1) ÷ 4 = + 372 + - (Y - 1) ÷ 100 = - 14 + + (Y - 1) ÷ 400 = + 3 + ------- + 7) 2148 + + _q_ = 306 + _r_ = 6 = Friday. + +Find from some history the day of the week on which Columbus first saw +America, and compare this with the above. + +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 _q_ have +the coefficient 7? What principles in the calendar give rise to the +divisors 4, 100, 400? + +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 encyclopædia. + +[Illustration: THE YERKES OBSERVATORY, WILLIAMS BAY, WIS.] + + + + +CHAPTER VII + +ECLIPSES + + +63. THE NATURE OF ECLIPSES.--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. + +But the eclipses of most interest to us are those of the sun and moon, +called respectively solar and lunar eclipses. In Fig. 33 the full moon, +_MŽ_, is shown immersed in the shadow cast by the earth, and therefore +eclipsed, and in the same figure the new moon, _M_, 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, _MŽ_, 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 the eclipsed sun +will present very different aspects from different parts of the earth. +Thus, at _L_, 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 _J_ and _K_ 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 _J_ and +_L_ or _K_ and _L_ 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. + +[Illustration: FIG. 33.--Different kinds of eclipse.] + +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 _MŽ M_ produced. But it frequently +happens that this plane is turned to one side of the sun, along some +such line as _P Q_, 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. + +In what parts of the earth would this eclipse be visible? What kinds of +solar eclipse would be produced by the new moon at _Q_? In what parts of +the earth would they be visible? + +64. THE SHADOW CONE.--The shape and position of the earth's shadow are +indicated in Fig. 33 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. + +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 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 +_annular_, 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 +_penumbra_--i. e., partial shadow--which is shown in Fig. 33 by the +broken lines tangent to the sun and moon, and crossing at the point _V_, +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. + +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 eclipse will be visible in +those parts of the earth nearest the axis of the shadow? + +65. DIFFERENT CHARACTERISTICS OF LUNAR AND SOLAR ECLIPSES.--One marked +difference between lunar and solar eclipses which has been already +suggested, may be learned from Fig. 33. The full moon, _MŽ_, 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 Fig. 33, 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 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 § 50). + +QUERY.--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? + +66. THE TRACK OF THE SHADOW.--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 (Fig. 34), 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 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. + +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. + +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 _MŽ_, Fig. 33, 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 _P_, the total phase of the +eclipse may fail altogether, and between these extremes the duration of +totality may be anything from two hours downward. + +[Illustration: FIG. 34.--Relation of the lunar nodes to eclipses.] + +67. RELATION OF THE LUNAR NODES TO ECLIPSES.--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 Fig. 34, +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, _M MŽ_, +is also shown, with the new moon, _M_, casting its shadow toward the +earth and the full moon, _MŽ_, apparently immersed in the earth's +shadow. But here appearances are deceptive, and the student who has +made the observations set forth in Chapter III 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, _NŽ NŽŽ_, 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, _MŽ_, must have passed below the shadow, and the new +moon, _M_, 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 +_NŽ NŽŽ_ points almost directly toward the sun, in line with the shadow +cones which hide it. Note that the line _NŽ NŽŽ_ remains very nearly +parallel to its original position, while the earth is moving along 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. + +_NŽ NŽŽ_ is called the line of nodes of the moon's orbit (§ 39), and the +two positions of the earth in its orbit, diametrically opposite each +other, at which _NŽ NŽŽ_ points exactly toward the sun, we shall call +the _nodes_ 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: + + _Eclipses of the Year 1900_ + + Total solar eclipse May 28th. + Partial lunar eclipse June 12th. + Annular (solar) eclipse November 21st. + +68. ECLIPSE LIMITS.--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 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: + + _Solar Eclipse Limits_ + + If at any new moon the earth is + + Less than 10 days away from a node, a central eclipse is certain. + Between 10 and 16 days " " " some kind of eclipse is certain. + Between 16 and 19 days " " " a partial eclipse is possible. + More than 19 days " " " no eclipse is possible. + + _Lunar Eclipse Limits_ + + If at any full moon the earth is + + Less than 4 days away from a node, a total eclipse is certain. + Between 4 and 10 days " " " some kind of eclipse is certain. + Between 10 and 14 days " " " a partial eclipse is possible. + More than 14 days " " " no eclipse is possible. + +From this table of eclipse limits we may draw some interesting +conclusions about the frequency with which eclipses occur. + +69. NUMBER OF ECLIPSES IN A YEAR.--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? + +A similar line of reasoning will not hold true for eclipses of the moon, +since it is quite possible that no full 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. + +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. + +[Illustration: FIG. 35.--The eclipse of May 28, 1900.] + +70. ECLIPSE MAPS.--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 Fig. 35. 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 +presents 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 P. M., 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. + +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. + +Let the student make these "predictions" for Washington, Chicago, +London, and Algiers. + +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. + +[Illustration: FIG. 36.--Central eclipses for the first two decades of +the twentieth century. OPPOLZER.] + +71. FUTURE ECLIPSES.--An eclipse map of a different kind is shown in +Fig. 36, which represents the shadow paths of all the central eclipses +of the sun, visible during the period 1900-1918 A. D., 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 B. C. to 2160 A. D., a period of more +than three thousand years. + +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, _NŽ NŽŽ_, of Fig. 34, 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 _NŽ NŽŽ_ is made to revolve westward, +opposite to the arrowheads in Fig. 34, 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. + +72. RECURRENCE OF ECLIPSES.--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 (Fig. 36), we find that a total solar +eclipse will occur on June 8, 1918, 18 years and 11 days after the one +illustrated in Fig. 35. This period of 18 years and 11 days is called +_saros_, an ancient word which means cycle or repetition, and since +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 (§ 67), 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. + +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 § 60) 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, 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 Fig. 37, 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 _0_, to the end, _72_. 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." + +[Illustration: FIG. 37.--Graphical illustration of the saros.] + +A similar figure may be constructed to represent the recurrence of lunar +eclipses; but here, in consequence of the smaller 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. + +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 Fig. 36 the regions in which the eclipses of 1900 +and 1918 are visible. + +Is this change in the region where the repeated eclipse is visible, true +of lunar eclipses as well as solar? + +73. USE OF ECLIPSES.--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. + +But to the astronomer an eclipse is more than a beautiful illustration +of the working of natural laws; it is in 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. + +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 Chapter +X. + +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. 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 B. C. 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. + + + + +CHAPTER VIII + +INSTRUMENTS AND THE PRINCIPLES INVOLVED IN THEIR USE + + +74. TWO FAMILIAR INSTRUMENTS.--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. + +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 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. + +75. RADIANT ENERGY.--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 of light +and heat, and this energy is called _radiant_ 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: + +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. + +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 _ether_, +which serves everywhere as a medium for the transmission of radiant +energy 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. + +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^{10} equal parts. 10^{10} = +10,000,000,000. + + Color. Wave length. + + Extreme limit of visible violet 3,900 + Middle of the violet 4,060 + " " blue 4,730 + " " green 5,270 + " " yellow 5,810 + " " orange 5,970 + " " red 7,000 + Extreme limit of visible red 7,600 + +[Illustration: PLATE I. THE NORTHERN CONSTELLATIONS] + +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 a photographic plate will be strongly affected by energy of +shorter wave length than 3,900 tenth meters. + +76. REFLECTION AND CONDENSATION OF WAVES.--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 _at any point_ a +condensation of energy? + +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? + +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. + +The student will note that for the sake of greater precision we here +say _wave front_ 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. + +77. MIRRORS AND LENSES.--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. + +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. + +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 _A B_ in Fig. 38. If we suppose _E G +D_ 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 by the straight line _E D_, 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, +_G_, in its onward motion will be retarded by the thick center of the +lens, more than _E_ or _D_ will be retarded by the comparatively thin +outer edges of _A B_. 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 _F_ and the whole energy of the +wave front, _E G D_, will then be condensed at _F_, 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 _F_ from _A B_ is called the focal length of the lens, and _F_ itself +is called the focus. The significance of this last word (Latin, _focus_ += 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. + +[Illustration: FIG. 38.--Illustrating the theory of lenses.] + +All the energy transmitted by the lens in the direction _G F_ is +concentrated upon a very small area at _F_, 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 _focal plane_, +_F H_, passed through the focus, _F_, perpendicular to the line, _F G_, +and we shall find in this plane a picture of all the stars or other +objects within the range of the lens. + +[Illustration: FIG. 39.--Essential parts of a reflecting telescope.] + +78. TELESCOPES.--The simplest kind of telescope consists of a concave +mirror to produce images, and a magnifying glass, called an _eyepiece_, +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 _H_ in Fig. 39, 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 _F_, where they may be examined from one side through the magnifying +glass _E_. + +[Illustration: FIG. 40.--A simple form of refracting telescope.] + +Such a combination of parts is called a _reflecting_ telescope, while +one in which the images are produced by a lens or combination of lenses +is called a _refracting_ 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 Fig. 40, where the part marked _O_ is +called the objective and _V E_ (the magnifying glass) is the eyepiece, +or ocular, as it is sometimes called. + +Most objects with which we have to deal in using a telescope send to it +not light of one color only, but a mixture 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 _O_ in +Fig. 40. The two pieces of glass thus mounted in one frame constitute a +compound lens having its own focal plane, shown at _F_ 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 _F_, 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. + +79. MAGNIFYING POWER.--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 Fig. 40 the distance of the objective from the focal +plane _F_ 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 _area_ of +an object seems increased; and since areas are proportional to the +squares of lines, the 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. + +The part played by the eyepiece in determining magnifying power will be +readily understood from the following experiment: + +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. + +80. THE EQUATORIAL MOUNTING.--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 shown in Fig. 41. It +is not customary to place a driving clock on so small a telescope as +this: + +(_a_) A supporting pier or tripod. + +(_b_) An axis placed parallel to the axis of the earth. + +(_c_) Another axis at right angles to _b_ and capable of revolving upon +_b_ as an axle. + +(_d_) The telescope tube attached to _c_ and capable of revolving about +_c_. + +(_e_) Graduated circles attached to _c_ and _b_ to measure the amount by +which the telescope is turned on these axes. + +(_f_) A driving clock so connected with _b_ as to make _c_ (and _d_) +revolve about _b_ with an angular velocity equal and opposite to that +with which the earth turns upon its axis. + +[Illustration: FIG. 41.--A simple equatorial mounting.] + +[Illustration: FIG. 42.--Equatorial mounting of the great telescope of +the Yerkes Observatory.] + +Such a support is called an equatorial mounting, and the student should +note from the figure that the circles, _e_, 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 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 Fig. 42, 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 Fig. 43 trace out the corresponding parts in the mounting +of a reflecting telescope. + +[Illustration: FIG. 43.--The reflecting telescope of the Paris +Observatory.] + +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 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. + +81. PHOTOGRAPHY.--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. Fig. 44 shows such a telescope, or rather two +telescopes, one photographic, the other visual, supported side by side +upon the same equatorial mounting. + +[Illustration: FIG. 44.--Photographic telescope of the Paris +Observatory.] + +One of the great advantages of photography is found in connection with +what is called-- + +82. PERSONAL EQUATION.--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. + +These minor deceptions of the senses are included in the term _personal +equation_, 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. + +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: + +"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."[3] A regimen suggestive of preparation for an +athletic contest rather than for the more quiet labors of an astronomer. + + [3] Schiaparelli, Osservazioni sulle Stelle Doppie. + +83. VISUAL AND PHOTOGRAPHIC WORK.--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 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 Chapter XIV. 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 _vice versa_. + +84. THE SPECTROSCOPE.--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 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 Fig. 38. + +[Illustration: FIG. 45.--Resolution of light into its component colors.] + +The course of a beam of light in passing through such a prism is shown +in Fig. 45. 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 +same cause, the slower velocity of light in glass than in air. It takes +the light-waves as long to move over the path _A B_ in glass as over the +longer path _1_, _2_, _3_, _4_, of which only the middle section lies in +the glass. + +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, _S S_. 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 _Roygbiv_, and by means of it their order is +easily remembered. + +[Illustration: FIG. 46.--Principal parts of a spectroscope.] + +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 _spectrum_, 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 _view telescope_ superposed +and confused one with another in a very objectionable manner. To avoid +this difficulty there is placed between the prism and the source of +light an opaque screen, _S_, 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, _A_, placed between the slit and the prism, as shown in Fig. 46. +The slit and lens, together with the tube in which they are usually +supported, are called a _collimator_. 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 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. Fig. 47 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. Fig. 48 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. + +[Illustration: FIG. 47.--Green and blue part of the spectrum of an +electric arc light.] + +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 _analyzing +spectroscope_ while one without the lens is called an _integrating +spectroscope_, 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 done (see Fig. 49), 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 _spectrograph_. + +[Illustration: FIG. 48.--Violet and ultraviolet parts of spectrum of an +arc lamp.] + +[Illustration: FIG. 49.--A spectroscope attached to the Yerkes +telescope.] + +85. SPECTRUM ANALYSIS.--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: + +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 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 Fig. 47, +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. 47 and 48, +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: + +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. + +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 +Fig. 47 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. + +[Illustration: FIG. 50.--The chief lines in the spectrum of +sunlight.--HERSCHEL.] + +86. WAVE LENGTHS.--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 +(§ 75) is the unit employed, and a scale of wave lengths expressed in +this unit is presented in Fig. 50. 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. + +87. ABSORPTION SPECTRA.--There is another kind of spectrum, of greater +importance than either of those above considered, which is well +illustrated by the spectrum of sunlight (Fig. 50). This is a nearly +continuous spectrum crossed by numerous _dark_ 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 _D_, 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 _D_ +and bears a very intimate relation to the dark _D_ line of the solar +spectrum. + +The student who has access to colored crayons should color one edge of +Fig. 50 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. + +Fig. 50 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. + +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 Fig. 51 shows a magnified representation of a small part of such a +spectrum adjacent to the _D_ (sodium) lines. Down the middle of each of +these lines runs a black streak whose position (wave length) is +precisely that of the _D_ lines in the spectrum of sunlight, and whose +presence is explained as follows: + +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 (Fig. 50) 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 _emission_ and _absorption_ +spectra. + +[Illustration: FIG. 51.--The lines reversed.] + +88. TYPES OF SPECTRUM.--The sun presents by far the most complex +spectrum known, and Fig. 50 shows only a small number of the more +conspicuous lines which appear in it. Spectra of stars, _per contra_, +appear relatively simple, since their feeble light is insufficient to +bring out faint details. In Chapters XIII and XIV 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 [b] Aurigæ 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 +[a] 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. + +89. THE DOPPLER PRINCIPLE.--This important principle of the spectrum +analysis is most readily appreciated through the following experiment: + +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 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. + +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 _D_ in Fig. 50. 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 _D_ 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. + +90. OTHER INSTRUMENTS.--Other instruments of importance to the +astronomer, but of which only casual mention can here be made, are the +meridian-circle; the transit, one form of which is shown in Fig. 52, 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. + +[Illustration: FIG. 52.--A combined transit instrument and zenith +telescope.] + + + + +CHAPTER IX + +THE MOON + + +91. RESULTS OF OBSERVATION WITH THE UNAIDED EYE.--The student who has +made the observations of the moon which are indicated in Chapter III 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: + +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. + +[Illustration: THE MOON, ONE DAY AFTER FIRST QUARTER. From a photograph +made at the Paris Observatory.] + +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 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 _terminator_, as it +is called, is the dividing line between day and night upon the moon. + +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? + +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 _synodical_ 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. + +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. + +[Illustration: FIG. 53.--Motion of moon and earth relative to the sun.] + +92. THE MOON'S MOTION.--The student should compare the results of his +own observations, as well as the preceding section, with Fig. 53, 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 Fig. 34 (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 Fig. 53 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 is to be especially noted that this +real orbit of the moon is everywhere concave toward the sun. + +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? + +We may find in Fig. 53 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 Fig. 53, with the protractor, the moon's angular distance +from the meridian at noon on July 3d. When will the meridian overtake +the moon? + +93. HARVEST MOON.--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 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. + +94. SIZE AND MASS OF THE MOON.--It has been shown in Chapter I 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 Chapter VII, 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. + +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. + +We have seen that the moon moves around the sun in a path differing but +little from the smooth curve shown in Fig. 53, 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 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 _center of gravity_, 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 +(Chapter IV), 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. + +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 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-- + + Mass of earth : Mass of moon :: 237,075 : 2,925, + +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. + +95. DENSITY OF THE MOON.--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. + +We know the mass of the earth (§ 45), 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 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. + +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. + +96. FORCE OF GRAVITY UPON THE MOON.--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-- + + W = k × (m mŽ) / (3963)^{2}; + +and for the moon-- + + w = k × {m (mŽ/81)} / (1081)^{2}; + +from which we find by division-- + + w = (W / 81) (3963 / 1081)^{2} = (W / 6) (approximately). + +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 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. + +97. ALBEDO.--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 _albedo_ (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. + +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. + +98. LIBRATIONS.--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 +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 Fig. 55 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. + +This turning is called a _libration_, 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, 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. + +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. + +[Illustration: FIG. 54.--Illustrating the moon's rotation.] + +99. CAUSE OF LIBRATIONS.--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 Fig. 54, 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 from the +figure at the center of its orbit while moving around it. + +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 (Fig. 17), 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. + +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. + +The attraction of the earth for the moon has very slightly pulled the +latter out of shape (§ 42), 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. + +100. THE MOON AS A WORLD.--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. 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 Fig. 55 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 +_terminator_--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 Fig. 55 +with reference to these features. + +[Illustration: FIG. 55.--The moon at first and last quarter. Lick +Observatory photographs.] + +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 Fig. 55. 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 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. + +A subordinate feature of the moon's surface is the system of _rays_ +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 Fig. 55, 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. + +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 cañons of our +Western country. + +101. THE MAP OF THE MOON.--Fig. 55 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. Fig. 56 +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 much foreshortened in the direction of the +moon's radius. + +[Illustration: FIG. 56.--Relief map of the moon's surface.--After +NASMYTH and CARPENTER.] + +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. + +The student should pick out upon the map those features which he has +learned to know in the photograph (Fig. 55)--the Apennines, Copernicus, +and the continuation of the Apennines, extending into the dark part of +the moon. + +[Illustration: FIG. 57.--Mare Imbrium. Photographed by G. W. RITCHEY.] + +102. SIZE OF THE LUNAR FEATURES.--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-- + + Diameter of Copernicus in miles : 2,163 :: 2.1 : 79.7, + +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, _ma-re_ += sea). Measure its length. The large crater to the northwest of the +Apennines is called Archimedes. Measure its diameter both in the map and +in the photograph (Fig. 55), 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? Fig. 57 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. + +[Illustration: FIG. 58.--Mare Crisium. Lick Observatory photographs.] + +Fig. 58 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. + +With these pictures of the smoother parts of the moon's surface we may +compare Fig. 59, which shows a region near the north pole of the moon, +and Fig. 60, giving an early morning view of Archimedes and the +Apennines. Note how long and sharp are the shadows. + +[Illustration: FIG. 59.--Illustrating the rugged character of the moon's +surface.--NASMYTH and CARPENTER.] + +103. THE MOON'S ATMOSPHERE.--Upon the earth the sun casts no shadows so +sharp and black as those of Fig. 60, because his rays are here scattered +and reflected in all directions by the dust and vapors of the +atmosphere (§ 51), so that the place from which direct sunlight is cut +off is at least partially illumined by this reflected light. The shadows +of Fig. 60 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 (_occults_ is +the technical word), and if the moon had an atmosphere such as is shown +in Fig. 61, the light from the star _A_ 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 _B_) 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. 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. + +[Illustration: FIG. 60.--Archimedes and Apennines. NASMYTH and +CARPENTER.] + +104. HEIGHT OF THE LUNAR MOUNTAINS.--Attention has already been called +to the detached mountain peaks, which in Fig. 55 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: Fig. 62 +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 _T_ and barely +illuminates the top of the mountain, _M_, whose height, _h_, is to be +determined. If we let _R_ stand for the radius of the moon and _s_ for +the distance, _T M_, we shall have in the right-angled triangle _M T C_, + + R^{2} + s^{2} = (R + h)^{2}, + +and we need only to measure _s_--that is, the distance from the +terminator to the detached mountain peak--to make this equation +determine _h_, since _R_ 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 form, which the student who is expert in +algebra may show to be very nearly equivalent to it: + + _h_ (miles) = s^{2} / 2163, + or _h_ (feet) = 2.44 s^{2}. + +The distance _s_ must be expressed in miles in all of these equations. +In Fig. 55 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. + +[Illustration: FIG. 61.--Occultations and the moon's atmosphere.] + +[Illustration: FIG. 62.--Determining the height of a lunar mountain.] + +Two things, however, need to be borne in mind in this connection. On the +earth we measure the heights of mountains _above sea level_, 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 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 Fig. 55 as the brightest part of the +Caucasus range. + +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. + +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. + +105. CRATERS.--Fig. 63 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: + +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. + +B. Craters are shallow, their diameters ranging from 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. + +[Illustration: FIG. 63.--A typical lunar crater.--NASMYTH and +CARPENTER.] + +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. + +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. + +106. MOON AND EARTH.--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 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. + +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. + +107. TEMPERATURE OF THE MOON.--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 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." + +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. + +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. + +108. CHANGES IN THE MOON.--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 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. Fig. 64 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. + +[Illustration: FIG. 64.--Archimedes in the lunar morning and +afternoon.--WEINEK.] + +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. + +109. THE MOON'S INFLUENCE UPON THE EARTH.--There is a widespread popular +belief that in many ways the moon exercises 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. + + + + +CHAPTER X + +THE SUN + + +110. DEPENDENCE OF THE EARTH UPON THE SUN.--There is no better +introduction to the study of the sun than Byron's Ode to Darkness, +beginning with the lines-- + + "I dreamed a dream + That was not all a dream. + The bright sun was extinguished," + +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. + +111. THE SUN'S DISTANCE FROM THE EARTH.--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, 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 (Chapter IV) 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. + +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 § 38 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-- + +_T_ = Periodic time of any planet; + +_a_ = One half the major axis of its orbit; + +_m_ = Its mass; + +_M_ = The mass of the sun; + +_k_ = The gravitation constant corresponding to the particular set of +units in which _T_, _a_, _m_, and _M_ are expressed. + + (Kepler) a^{3}/T^{2} = h; + (Newton) a^{3}/T^{2} = k (M + m). + +Kepler's idea was: For every planet which moves around the sun, _a^{3}_ +divided by _T^{2}_ always gives the same quotient, _h_; and he did not +concern himself with the significance of this quotient further than to +note that if the particular _a_ and _T_ 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. + +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-- + + (240,000^{3})/(27.32^{2}) = k (1 + 1/81), + +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-- + + k = 1830 × 10^{10}. + +If we introduce this value of _k_ into the corresponding equation, which +represents the motion of the earth around the sun, we shall have-- + + a^{3}/(365.25)^{2} = 1830 × 10^{10} (333,000 + 1), + +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 _a_, the mean distance of the sun from the +earth, is very approximately 93,000,000 miles. + +113. ANOTHER METHOD OF DETERMINING THE SUN'S DISTANCE.--This will be +best appreciated by a reference to Fig. 17. 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 _D_, would be the difference of the radii of +these orbits-- + + D = aŽŽ - aŽ, + +where the accents ŽŽ, Ž represent Mars and the earth respectively. +Kepler's Third Law furnishes the relation-- + + (aŽŽ)^{3}/(TŽŽ)^{2} = (aŽ)^{3}/(TŽ)^{2}; + +and since the periodic times of the earth and Mars, _TŽ_, _TŽŽ_, are +known to a high degree of accuracy, these two equations are sufficient +to determine the two unknown quantities, _aŽ_, _aŽŽ_--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. + +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 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). + +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 _D_ 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. + +114. PARALLAX AND DISTANCE.--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. + +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 A. D. down to the present moment 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. + +115. SIZE AND DENSITY OF THE SUN.--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 _orbit_ 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 Fig. 65. + +[Illustration: FIG. 65.--The sun's size.--YOUNG.] + +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 is +just about one quarter of the average density of the earth. + +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. + +116. MATERIAL OF WHICH THE SUN IS MADE.--As to the first of these +alternatives, the spectroscope comes to our aid and shows in the sun's +spectrum (Fig. 50) the characteristic line marked _D_, 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 _C_ and _F_ are produced by hydrogen, which is one of +the constituents of water, _E_ shows calcium to be present in the sun, +_b_ 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 spectrum, says: "Were the whole earth heated to +the temperature of the sun, its spectrum would probably resemble that of +the sun very closely." + +Some of the common terrestrial elements found in the sun are: + + Aluminium. + Calcium. + Carbon. + Copper. + Hydrogen. + Iron. + Lead. + Nickel. + Potassium. + Silicon. + Silver. + Sodium. + Tin. + Zinc. + Oxygen (?) + +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-- + +117. THE HEAT OF THE SUN.--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. + +Before we inquire more closely into the sun's temperature, 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. + +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. + +118. DETERMINING THE SUN'S TEMPERATURE.--One ingenious method which has +been used for determining this temperature 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. + +Paschen's law has been shown to hold true, at least approximately, for +lower temperatures and longer wave 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. + +[Illustration: FIG. 66.--The sun, August 11, 1894. Photographed at the +Goodsell Observatory.] + +[Illustration: FIG. 67.--The sun, August 14, 1894. Photographed at the +Goodsell Observatory.] + +119. THE SUN'S SURFACE.--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 _sun spots_, such as are shown in Figs. +66 to 69, and 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 Fig. 69, by vague +patches called _faculæ_ (Latin, _facula_ = 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 Fig. 70, where it is 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. + +[Illustration: FIG. 68.--The sun, August 18, 1894. Photographed at the +Goodsell Observatory.] + +Examine the sun spots in the four photographs, Figs. 66 to 69, 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. + +[Illustration: PLATE II. THE EQUATORIAL CONSTELLATIONS] + +120. THE SUN'S ROTATION.--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 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. + +[Illustration: FIG. 69.--The sun, August 21, 1894. Photographed at the +Goodsell Observatory.] + +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? + +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 _N S_ mark the direction of a north and south line across the +face of the sun, and 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. + +[Illustration: FIG. 70.--Absorption at the sun's edge.] + +121. SUN SPOTS.--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 Fig. 67 determine in miles the length of +the group on August 14th. Fig. 71 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 _nucleus_ or _umbra_ (Latin, shadow), which is +surrounded by an irregular border called the _penumbra_ (partial +shadow), which is intermediate in brightness between the nucleus and +the 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. + +[Illustration: FIG. 71.--Sun spots, August 17, 1894. Goodsell +Observatory.] + +[Illustration: FIG. 72.--Sun spot of March 5, 1873.--From LANGLEY, The +New Astronomy. By permission of the publishers.] + +The bright shining surface of the sun, the background for the spots, is +called the _photosphere_ (Greek, light sphere), and, as Fig. 71 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 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 Fig. 72. 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. + +[Illustration: FIG. 73.--Spectroheliograph, showing distribution of +faculæ upon the sun.--HALE.] + +[Illustration: FIG. 74.--Eclipse of July 20, 1878.--TROUVELOT.] + +122. FACULÆ.--We have seen in Fig. 69 a few of the bright spots called +faculæ. 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 +faculæ 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 Fig. +73. The faculæ 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 faculæ seem to be produced. It is significant of their connection +with sun spots that the spots occur in these particular zones and are +rarely found outside them. + +[Illustration: FIG. 75.--Eclipse of April 16, 1893.--SCHAEBERLE.] + +123. INVISIBLE PARTS OF THE SUN. THE CORONA.--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. + +[Illustration: FIG. 76.--Eclipse of January 21, 1898.--CAMPBELL.] + +Fig. 74 is from a drawing, and Figs. 75 and 76 are from eclipse +photographs showing this region, in which the most conspicuous object +is the halo of soft light called the _corona_, 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, 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 _the +corona is not hot_, its effective temperature being lower than that of +the instrument used for the observation. + +[Illustration: FIG. 77.--Solar prominence of March 25, 1895.--HALE.] + +124. THE CHROMOSPHERE.--Between the corona and the photosphere there is +a thin separating layer called the _chromosphere_ (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 _prominences_ 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 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, +faculæ, 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. 74 to 76) show the chromosphere, +because the color effect is lacking in them, but a great curving +prominence may be seen near the bottom of Fig. 75, and smaller ones at +other parts of the sun's edge. + +[Illustration: FIG. 78.--A solar prominence.--HALE.] + +125. PROMINENCES.--Fig. 77 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 faculæ to diminish the brightness of the +background without much enfeebling the brilliancy of the prominence +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. + +Fig. 78 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 Fig. 77. + +[Illustration: FIG. 79.--Contrasted forms of solar +prominences.--ZOELLNER.] + +The preceding pictures are from photographs, and with them the student +may compare Fig. 79, 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 _eruptive_ 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 +_quiescent_ prominence. These quiescent prominences are, as a rule, much +longer-lived than the eruptive ones. One more picture of prominences +(Fig. 80) is introduced to show the continuous stretch of chromosphere +out of which they spring. + +[Illustration: FIG. 80.--Prominences and chromosphere.--HALE.] + +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 faculæ as if all three were +intimately related phenomena. + +126. THE SUN AS A MACHINE.--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 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. + +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. + +Every boy who has inflated a bicycle tire with a hand pump knows that +the pump grows warm during the operation, 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. + +127. GASEOUS CONSTITUTION OF THE SUN.--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. + +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 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. + +128. THE SUN'S CIRCULATION.--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. + +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 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 faculæ 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. + +129. THE SUN-SPOT PERIOD.--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 Fig. 81, 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 records +curves (which may be found in Young's, The Sun) have been plotted, +showing a succession of waves extending back for many years. + +[Illustration: FIG. 81.--The curve of sun-spot frequency.] + +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 Fig. 81 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. + +Determine from Fig. 81 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 from its intersections with the curve--e. g., in 1874 and 1885? + +[Illustration: FIG. 82.--Illustrating change of the sun-spot zones.] + +130. THE SUN-SPOT ZONES.--It has been already noted that sun spots are +found only in certain zones of latitude upon the sun, and that faculæ +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 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 Fig. 82 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. + +131. INFLUENCE OF THE SUN-SPOT PERIOD.--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 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. + +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 Fig. 81 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. + +132. THE LAW OF THE SUN'S ROTATION.--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 circle, upon the surface of +the earth, while Fig. 83 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. + +[Illustration: FIG. 83.--Effect of the sun's peculiar rotation in +warping a meridian, originally straight.] + +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 faculæ which have +also been observed for this purpose. + +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 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. + + + + +CHAPTER XI + +THE PLANETS + + +133. PLANETS.--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 Chapter III, and Figs. 16 +and 17 of that chapter may be completed so as to represent all of the +planets by drawing in Fig. 16 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. 84 and 85 their relative sizes. The earth, _E_, is introduced +into Fig. 85 as a connecting link between the two figures. + +Some of these planets, like the earth, are attended by 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. + +[Illustration: FIG. 84.--The inner planets and the moon.] + +[Illustration: FIG. 85.--The outer planets.] + +134. DISTANCES OF THE PLANETS FROM THE SUN.--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, _T_, 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-- + + a^{3} / (4333^{2}) = (93,000,000^{3}) / (365.25^{2}), + +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. + + Mercury. Venus. Earth. Mars. Jupiter. Saturn. Uranus. Neptune. + 0 3 6 12 24 48 96 192 384 + 4 4 4 4 4 4 4 4 4 + ----------------------------------------------------------------------- + 0.4 0.7 1.0 1.6 2.8 5.2 10.0 19.6 38.8 + 0.4 0.7 1.0 1.5 2.8 5.2 9.5 19.2 30.1 + +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. + +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. + +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. + +135. THE PLANETS COMPARED WITH EACH OTHER.--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. + +Figs. 84 and 85 show the relative sizes of the planets composing the +inner and outer groups respectively, and furnish 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. + + +JUPITER + +136. APPEARANCE.--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 Fig. 86 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 _1_, _2_, +_3_, _4_, in order to preserve their identity in the successive +pictures. + +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 Fig. 16, 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? + +137. THE BELTS.--Even upon the small scale of Fig. 86 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 Fig. 87 these same dark bands may be recognized amid the +abundance 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. + +[Illustration: FIG. 86.--Jupiter and his satellites.] + +[Illustration: FIG. 87.--Drawings of Jupiter made at the 36-inch +telescope of the Lick Observatory.--KEELER.] + +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 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. + +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 _great red spot_, +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. + +138. ROTATION AND FLATTENING AT THE POLES.--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. + +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 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. + +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. + +139. PHYSICAL CONDITION.--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. + +_Appearance._--The formations which we see in Fig. 87 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 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. + +_Density._--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 Fig. 88, +where the line marked _E_ 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 _J_ in the same figure shows 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? + +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. + +[Illustration: FIG. 88.--Increase of density in the atmospheres of +Jupiter and the earth.] + +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. + +_Temperature._--The temperature of Jupiter must, of 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. + +140. THE SATELLITES OF JUPITER.--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 Fig. 86 the position of satellite No. _1_ 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. _4_ +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. _1_ is +nearer to Jupiter than No. _4_, 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. + +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, A. D. 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 used, and, following the custom of astronomers, we +shall designate them by the Roman numerals I, II, III, IV. + +[Illustration: FIG. 89.--Orbits of Jupiter's satellites.] + +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 Fig. 89 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 +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 § 111 how much more massive is +Jupiter than the earth. + +Small as these satellites seem in Fig. 86, they are really bodies of +considerable size, as appears from Fig. 90, 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. + +[Illustration: FIG. 90.--Jupiter's satellites compared with the earth +and moon.] + +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. + +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 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. + +141. ECLIPSES OF THE SATELLITES.--It may be seen from Fig. 89 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 +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. + +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 Chapter X; 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. + +It is worthy of note in this connection that both methods of obtaining +the sun's distance which were given in Chapter X 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 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. + + +SATURN + +142. THE RING OF SATURN.--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." + +[Illustration: FIG. 91.--Aspects of Saturn's rings.] + +Compare with this description Fig. 91, 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. Fig. 92 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 _N_ side of the ring when +the planet is at _N_ and the _S_ side when it is at _S_, as is shown in +the first and third pictures of Fig. 91, while midway between these +positions the edge of the ring will be presented to the earth. + +[Illustration: FIG. 92.--Aspects of the ring in their relation to +Saturn's orbital motion.] + +The last occasion of this kind was in October, 1891, and with the large +telescope of the Washburn Observatory the 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 Fig. 92 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? + +143. NATURE OF THE RING.--It is apparent from Figs. 91 and 93 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 _dusky ring_ or +_crape ring_. 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. + +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 (Chapter IX), +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. + +[Illustration: FIG. 93.--Saturn.] + +From theoretical reasons based upon the law of gravitation astronomers +have held that the rings of Saturn could 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. + +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. + +The curious darkness of the inner or crape ring is easily 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. + +144. THE BALL OF SATURN.--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. + +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. + +145. THE SATELLITES.--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 _seen_. + +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 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? + +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. + + +URANUS AND NEPTUNE + +146. CHIEF CHARACTERISTICS.--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 Chapter IV, 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. + +[Illustration: WILLIAM HERSCHEL (1738-1822).] + +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 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°. + +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. + +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. + +147. THE INNER PLANETS.--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 +Fig. 84, 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. + + +VENUS + +[Illustration: FIG. 94.--The phases of Venus.--ANTONIADI.] + +148. APPEARANCE.--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 Fig. 94. These drawings bring out well the phases of the planet, +and the student should determine from Fig. 17 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 +Fig. 94 about 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 Fig. 17 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 Fig. 94. 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? + +The irregularities in the shading of the illuminated parts of the disk +are too conspicuous in Fig. 94, 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. + +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. + +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. + + +MERCURY + +149. CHIEF CHARACTERISTICS.--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 Fig. 16 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. + +Mercury, as the smallest of the planets, is best compared 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. + +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. + + +MARS + +150. APPEARANCE.--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 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. + +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 Fig. 17 that this can only happen in the months +of August and September. The last favorable epoch of this kind was in +1894. From Fig. 17 the student should determine when the next one will +come. + +[Illustration: FIG. 95.--Mars.--SCHAEBERLE.] + +Fig. 95 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 of the second drawing was seen and sketched by Huyghens, 1659 +A. D. In Fig. 96 some of these markings are shown much more plainly, but +Fig. 95 gives a better idea of their usual appearance in the telescope. + +[Illustration: FIG. 96.--Four views of Mars differing 90° in +longitude.--BARNARD.] + +151. ROTATION.--It may be seen readily enough, from a comparison of the +first two sketches of Fig. 95, 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 in the _southern_ +hemisphere of Mars when the planet, as seen from the sun, lies in the +direction of Pisces. + +152. THE POLAR CAPS.--One effect of the changing seasons upon Mars is +shown in Fig. 97, 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 Fig. 17 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. + +[Illustration: FIG. 97.--The south polar cap of Mars in 1894.--BARNARD.] + +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 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. + +153. ATMOSPHERE AND CLIMATE.--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 Fig. 98 +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 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. + +[Illustration: FIG. 98.--The same face of Mars at three different +seasons.--LOWELL.] + +154. THE CANALS.--In Fig. 98 the lower part of the disk of Mars shows +certain faint dark lines which are generally called canals, and in Plate +III 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 Plate III +with Fig. 99, in which the projection represents very well the +equatorial parts of the planet, but enormously exaggerates the region +around the poles. + +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. + +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. + +[Illustration: FIG. 99.--A chart of Mars, 1898-'99.--CERULLI.] + +[Illustration: PLATE III. MAP OF MARS (AFTER SCHIAPARELLI)] + +155. SATELLITES.--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 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. + + +THE ASTEROIDS + +156. MINOR PLANETS.--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., [circle 1] = 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 Fig. 100. The +great majority of them must be much smaller than the smallest of these, +perhaps not more than a score of miles in diameter. + +A few of the asteroids present problems of special interest, such as +Eros, on account of its close approach to the 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. + +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. + +[Illustration: FIG. 100.--The size of the first four +asteroids.--BARNARD.] + +157. LIFE ON THE PLANETS.--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. + +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 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. + +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. + +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 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. + +On Mars we encounter the fundamental difficulty of temperature already +noted in § 152. 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. + +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. + + + + +CHAPTER XII + +COMETS AND METEORS + + +158. VISITORS IN THE SOLAR SYSTEM.--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 mediæval 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. + +The comet of 1618 A. D. inspired the lines-- + + "Eight things there be a Comet brings, + When it on high doth horrid range: + Wind, Famine, Plague, and Death to Kings, + War, Earthquakes, Floods, and Direful Change," + +which, according to White (History of the Doctrine of Comets), were to +be taught in all seriousness to peasants and school children. + +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 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. + +[Illustration: FIG. 101.--Donati's comet.--BOND.] + +159. COMETS.--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 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 (Fig. 101), 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. + +[Illustration: FIG. 102.--Some famous comets.] + +Note in Fig. 102 the great variety of aspect presented by some of the +more famous comets, which are here represented upon a very small scale. + +Fig. 103 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. + +A more striking representation of a moderately bright telescopic comet +is contained in Figs. 104 and 105, which present two different views of +the same comet, showing a considerable change in its appearance. A +striking feature of Fig. 105 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, 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. + +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 _head_ of the comet, while the brushlike appendage that +streams away from it is called the comet's _tail_. + +[Illustration: FIG. 103.--Brooks's comet, November 13, 1893. BARNARD.] + +160. THE PARTS OF A COMET.--It is not every comet that has a tail, +though all the large ones do, and in Fig. 103 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. 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 Fig. 106, +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. 106 and +107, 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. + +[Illustration: FIG. 104.--Swift's comet, April 17, 1892.--BARNARD.] + +The amount of detail shown in Figs. 106 and 107 is, however, quite +exceptional, and the ordinary comet is much more like Fig. 103 or 104. +Even a great comet when it first appears is not unlike the detached +fragment in Fig. 103, 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. + +[Illustration: FIG. 105.--Swift's comet, April 24, 1892.--BARNARD.] + +161. THE ORBITS OF COMETS.--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 of comet orbit, and to regard a comet whose +motion differs much from a parabola as being abnormal and calling for +some special explanation. + +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. + +[Illustration: FIG. 106.--Head of Coggia's comet, July 13, +1874.--TROUVELOT.] + +Fig. 108 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 _S V_ shows the direction from the sun to the vernal +equinox, and _S_ [Ô] is the line 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 _S_ [Ô], 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. + +[Illustration: FIG. 107.--Head of Donati's comet, September 30, October +2, 1858.--BOND.] + +162. ELEMENTS OF A COMET'S ORBIT.--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 _elements_ of its orbit, are 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 (_perihelion passage_) and its distance from the sun +at that date (_perihelion distance_). The date, September 17th, placed +near the center of Fig. 108, is the former of these elements, while the +latter, which is too small to be accurately measured here, may be found +from Fig. 109 to be 0.82 of the sun's diameter, or, in terms of the +earth's distance from the sun, 0.008. + +[Illustration: FIG. 108.--Orbits of the earth and the Great Comet of +1882.] + +Fig. 109 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 +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^{1/2}. + +[Illustration: FIG. 109.--Motion of the Great Comet of 1883 in passing +around the sun.] + +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 +halfway 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. 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. + +[Illustration: FIG. 110.--The Great Comet of 1843.] + +163. DIMENSIONS OF COMETS.--The comet whose orbit is shown in Figs. 108 +and 109 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 Fig. 109, but when at its best was probably not inferior to that of +the Great Comet of 1843, shown in Fig. 110. As we shall see later, +there is a peculiar and special relationship between these two comets. + +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 Fig. 107 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. + +164. THE MASS OF A COMET.--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. A striking observation made +on September 17, 1882, goes to confirm the very small density of this +comet. It is shown in Fig. 109 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. + +165. METEORS.--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. + +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 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. + +166. NATURE OF METEORS.--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 +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. + +167. THE NUMBER OF METEORS.--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 A. M. 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. + +On the average these individual particles are very small 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. + +168. THE ZODIACAL LIGHT 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. + +169. GREAT METEORS.--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." Fig. 111 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. + +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 +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. + +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. + +[Illustration: FIG. 111.--The California meteor of July 27, 1894.] + +170. THE VELOCITY OF METEORS.--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 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. + +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. + +171. METEOR SHOWERS--THE RADIANT.--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 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 Fig. +112, which represents a group of meteors moving together along parallel +paths toward an observer at _D_. Traveling unseen above the earth until +they encounter the upper strata of its atmosphere, they here become +incandescent and speed on in parallel paths, _1_, _2_, _3_, _4_, _5_, +_6_, which, as seen by the observer, are projected back against the sky +into luminous streaks that, as is shown by the arrowheads, _b_, _c_, +_d_, all seem to radiate from the point _a_--i. e., from the point in +the sky whose direction from the observer is parallel to the paths of +the meteors. + +[Illustration: FIG. 112.--Explanation of the radiant of a meteoric +shower.--DENNING.] + +Such a display is called a meteor shower, and the point _a_ 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 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? Fig. 113 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. + +[Illustration: FIG. 113.--The radiant of a meteoric shower, showing +also the paths of three meteors which do not belong to this +shower.--DENNING.] + +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 orbits to that of the earth is shown in Fig. +114. 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. + +[Illustration: FIG. 114.--The orbits of the earth and the November +meteors.] + +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 orbit? Will these meteors strike the front or the rear of the +earth? Can they be seen in the evening hours? + +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. + +172. THE LEONIDS.--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 A. M. 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." + +An eyewitness in the Southern States thus describes the effect of this +shower upon the plantation negroes: "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." + +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 Fig. 114, 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 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. + +173. CAPTURE OF THE LEONIDS.--But a far more striking effect of +perturbations is to be found in Fig. 115, 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 A. D., 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 A. D. that makes the +meteor shower now come in November instead of in October as it did +then. + +[Illustration: FIG. 115.--Supposed capture of the November meteors by +Uranus.] + +174. BREAKING UP A METEOR SWARM.--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. + +175. RELATION OF COMETS AND METEORS.--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, _it would be a part of the meteor swarm_. +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. + +Perhaps the most remarkable case of this character is that of a shower +which comes in the latter part of November 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 _débris_ of a worn-out +comet. + +176. PERIODIC COMETS.--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 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 Fig. 115 that when the +Leonid swarm encountered Uranus it passed _in front of_ 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 Fig. 115 +the changed orbit of the meteors has its _aphelion_ (part remotest from +the sun) quite close to the orbit of Uranus, and one of its nodes, +[mho], 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. + +Jupiter, by reason of his great mass, is an especially efficient +capturer of comets, and Fig. 116 shows his group of 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. + +[Illustration: FIG. 116.--Jupiter's family of comets.] + +177. COMET GROUPS.--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 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. + +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 § 162) 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. + +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.: + + r^3 / T^2 = 178, + +where _T_ 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 _r_. 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? + +178. RELATION OF COMETS TO THE SOLAR SYSTEM.--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. + +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 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 Fig. 117, 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. + +[Illustration: FIG. 117.--Brooks's comet, October 21, 1893.--BARNARD.] + +179. THE DEVELOPMENT OF A COMET.--We saw in § 174 that the sun's action +upon a meteor swarm tends to break it up into a long stream, and the +same tendency to 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 (§ 42), 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. + +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 Fig. 109, and the envelopes and jets rise +up toward the sun; but an inspection of Fig. 106 will show that the tail +and the envelope are too unlike to be produced by one and the same set +of forces. + +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 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. + +180. COMET TAILS.--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 Fig. 118, where the positions of the comet +in its orbit on successive days are marked by the Roman numerals, and +the broken lines represent the paths of molecules _m^{I}_, _m^{II}_, +_m^{III}_, 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 _VI_ 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. + +[Illustration: FIG. 118.--Formation of a comet's tail.] + +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 Fig. 118, and +note what a different 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 +Fig. 101. But observe that this comet has also a nearly straight tail, +like the theoretical one of Fig. 118. 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. + +181. DISINTEGRATION OF COMETS.--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 been carried away from the sun and scattered throughout +the universe along hyperbolic orbits impressed upon them at the time +they left the comet. + +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 Fig. 119, which shows the +series of changes observed in the head of this comet. + +182. COMETS AND THE SPECTROSCOPE.--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 Fig. 48, 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. + +[Illustration: FIG. 119.--The head of the Great Comet of +1882.--WINLOCK.] + +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 +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. + +183. COLLISIONS.--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 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 § 169 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. + + + + +CHAPTER XIII + +THE FIXED STARS + + +184. THE CONSTELLATIONS.--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. + +[Illustration: FIG. 120.--Illustrating the division of the sky into +constellations.] + +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 Fig. 120, 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 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. + +185. THE NUMBER OF STARS.--"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. + +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 _telescopic_, in +recognition of the fact that they can be seen only in the telescope, +while the other brighter ones are known as _lucid stars_. + +186. MAGNITUDES.--The telescopic stars show among themselves an even +greater range of brightness than do the lucid ones, and the system of +magnitudes (§ 9) has accordingly been extended to include them, the +faintest star visible in the greatest telescope of the present time +being of the sixteenth 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. + +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^{9} times as bright as Venus, etc.; only it should be +observed that the number 2.5 is not exactly the value of the _light +ratio_ between two consecutive magnitudes. Strictly this ratio is the +100^{1/5} = 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 _B_ represents the ratio of +brightness (quantity of light) of two stars whose magnitudes are _m_ and +_n_, then + + B = (100)^{(m-n)/5} + +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 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? + +187. CLASSIFICATION BY MAGNITUDES.--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: + + The number of stars brighter than magnitude 1.0 is 11 + " " " " " 2.0 " 39 + " " " " " 3.0 " 142 + " " " " " 4.0 " 463 + " " " " " 5.0 " 1,483 + " " " " " 6.0 " 4,326 + +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. + +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 preceding it, and similarly we may find the +number included between each other pair of consecutive magnitudes, as +follows: + + Magnitude 0 1 2 3 4 5 6 + Number of stars 11 28 103 321 1,020 2,843 + 4 × 3^{m} 12 36 108 324 972 2,916 + +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. + +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. + +How many first-magnitude stars would be needed to give as much light as +do the 2,843 stars of magnitude 5.0 to 6.0? How many tenth-magnitude +stars are required to give the same amount of light? + +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. + +188. DISTANCES OF THE STARS.--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 Fig. 121, 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 _A_ at these several times is shown by +lines drawn through _A_ and prolonged to the background apparently +furnished by the sky. A similar construction is made for the star _B_, +and it is readily seen that owing to the changing position of the +observer as he moves around the earth's orbit, both _A_ and _B_ will +appear to move upon the background in orbits 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 _A_ being larger than that of +_B_, because _A_ is nearer the earth. By measuring the angular distance +between _A_ and _B_ at opposite seasons of the year (e. g., the angles +_A--Jan.--B_, and _A--July--B_) 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 _A_ than _B_. Strictly, the difference +between the January and July angles is equal to the difference between +the angles subtended at _A_ and _B_ by the diameter of the earth's +orbit, and if _B_ were so far away that the angle _Jan.--B--July_ were +nothing at all we should get immediately from the observations the angle +_Jan.--A--July_, which would suffice to determine the stars' distance. +Supposing the diameter of the earth's orbit and the angle at _A_ to be +known, can you make a graphical construction that will determine the +distance of _A_ from the earth? + +[Illustration: FIG. 121.--Determining a star's parallax.] + +The angle subtended at _A_ by the radius of the earth's orbit--i. e., +1/2 (_Jan.--A--July_)--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 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. + +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 _A_ and _B_; and while it is customary to +select for _B_ a star or stars supposed to be much farther off than _A_, +it may happen, and sometimes does happen, that these comparison stars as +they are called are as near or nearer than _A_, and give a negative +parallax--i. e., the difference between the angles at _A_ and _B_ proves +to be negative, as it must whenever the star _B_ is nearer than _A_. + +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. + +189. THE SUN AND HIS NEIGHBORS.--The distances of the sun's nearer +neighbors among the stars are shown in Fig. 122, 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, + + _The Sun's Nearest Neighbors_ + + ---+------------------+----------+-------+-----+----------+--------- + No.| STAR. |Magnitude.| R. A. |Dec. | Parallax.|Distance. + ---+------------------+----------+-------+-----+----------+--------- + 1 | [a] Centauri | 0.7 | 14.5h.| -60°| 0.75" | 0.27 + | | | | | | + 2 | Ll. 21,185 | 6.8 | 11.0 | +37 | 0.45 | 0.46 + | | | | | | + 3 | 61 Cygni | 5.0 | 21.0 | +38 | 0.40 | 0.51 + | | | | | | + 4 | [ê] Herculis | 3.6 | 16.7 | +39 | 0.40 | 0.51 + | | | | | | + 5 | Sirius | -1.4 | 6.7 | -17 | 0.37 | 0.56 + | | | | | | + 6 | [S] 2,398 | 8.2 | 18.7 | +59 | 0.35 | 0.58 + | | | | | | + 7 | Procyon | 0.5 | 7.6 | + 5 | 0.34 | 0.60 + | | | | | | + 8 | [g] Draconis | 4.8 | 17.5 | +55 | 0.30 | 0.68 + | | | | | | + 9 | Gr. 34 | 7.9 | 0.2 | +43 | 0.29 | 0.71 + | | | | | | + 10 | Lac. 9,352 | 7.5 | 23.0 | -36 | 0.28 | 0.74 + | | | | | | + 11 | [s] Draconis | 4.8 | 19.5 | +69 | 0.25 | 0.82 + | | | | | | + 12 | A. O. 17,415-6 | 9.0 | 17.6 | +68 | 0.25 | 0.82 + | | | | | | + 13 | [ê] Cassiopeiæ | 3.4 | 0.7 | +57 | 0.25 | 0.82 + | | | | | | + 14 | Altair | 1.0 | 19.8 | + 9 | 0.21 | 0.97 + | | | | | | + 15 | [e] Indi | 5.2 | 21.9 | -57 | 0.20 | 1.03 + | | | | | | + 16 | Gr. 1,618 | 6.7 | 10.1 | +50 | 0.20 | 1.03 + | | | | | | + 17 | 10 Ursæ Majoris | 4.2 | 8.9 | +42 | 0.20 | 1.03 + | | | | | | + 18 | Castor | 1.5 | 7.5 | +32 | 0.20 | 1.03 + | | | | | | + 19 | Ll. 21,258 | 8.5 | 11.0 | +44 | 0.20 | 1.03 + | | | | | | + 20 | [o]^{2} Eridani | 4.5 | 4.2 | - 8 | 0.19 | 1.08 + | | | | | | + 21 | A. O. 11,677 | 9.0 | 11.2 | +66 | 0.19 | 1.08 + | | | | | | + 22 | Ll. 18,115 | 8.0 | 9.1 | +53 | 0.18 | 1.14 + | | | | | | + 23 | B. D. 36°, 3,883 | 7.1 | 20.0 | +36 | 0.18 | 1.14 + | | | | | | + 24 | Gr. 1,618 | 6.5 | 10.1 | +50 | 0.17 | 1.21 + | | | | | | + 25 | [b] Cassiopeiæ | 2.3 | 0.1 | +59 | 0.16 | 1.28 + | | | | | | + 26 | 70 Ophiuchi | 4.4 | 18.0 | + 2 | 0.16 | 1.28 + | | | | | | + 27 | [S] 1,516 | 6.5 | 11.2 | +74 | 0.15 | 1.38 + | | | | | | + 28 | Gr. 1,830 | 6.6 | 11.8 | +39 | 0.15 | 1.38 + | | | | | | + 29 | [m] Cassiopeiæ | 5.4 | 1.0 | +54 | 0.14 | 1.47 + | | | | | | + 30 | [e] Eridani | 4.4 | 3.5 | -10 | 0.14 | 1.47 + | | | | | | + 31 | [i] Ursæ Majoris | 3.2 | 8.9 | +48 | 0.13 | 1.58 + | | | | | | + 32 | [b] Hydri | 2.9 | 0.3 | -78 | 0.13 | 1.58 + | | | | | | + 33 | Fomalhaut | 1.0 | 22.9 | -30 | 0.13 | 1.58 + | | | | | | + 34 | Br. 3,077 | 6.0 | 23.1 | +57 | 0.13 | 1.58 + | | | | | | + 35 | [e] Cygni | 2.5 | 20.8 | +33 | 0.12 | 1.71 + | | | | | | + 36 | [b] Comæ | 4.5 | 13.1 | +28 | 0.11 | 1.87 + | | | | | | + 37 | [ps]^{5} Aurigæ | 8.8 | 6.6 | +44 | 0.11 | 1.87 + | | | | | | + 38 | [p] Herculis | 3.3 | 17.2 | +37 | 0.11 | 1.87 + | | | | | | + 39 | Aldebaran | 1.1 | 4.5 | +16 | 0.10 | 2.06 + | | | | | | + 40 | Capella | 0.1 | 5.1 | +46 | 0.10 | 2.06 + | | | | | | + 41 | B. D. 35°, 4,003 | 9.2 | 20.1 | +35 | 0.10 | 2.06 + | | | | | | + 42 | Gr. 1,646 | 6.3 | 10.3 | +49 | 0.10 | 2.06 + | | | | | | + 43 | [g] Cygni | 2.3 | 20.3 | +40 | 0.10 | 2.06 + | | | | | | + 44 | Regulus | 1.2 | 10.0 | +12 | 0.10 | 2.06 + | | | | | | + 45 | Vega | 0.2 | 18.6 | +39 | 0.10 | 2.06 + ---+------------------+----------+-------+-----+----------+--------- + +in which the numbers in the first column are those placed adjacent to +the stars in the diagram to identify them. + +[Illustration: FIG. 122.--Stellar neighbors of the sun.] + +190. LIGHT YEARS.--The radius of the inner circle in Fig. 122, 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, [a] Centauri, is +25,000,000,000,000 miles away. But there is another unit in more common +use--i. e., the distance traveled over by light in the period of one +year. We have already found (§ 141) 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 _light year_, and the +distance of the same star, [a] 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. + +In Fig. 122 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. + +Fig. 122 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. + +191. PROPER MOTIONS.--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 § 34, each star is +free to keep unchanged its state of rest or motion with unvarying +velocity along a straight line. Their very name, _fixed stars_, implies +that they are at rest, and so astronomers long believed. Hipparchus (125 +B. C.) and Ptolemy (130 A. D.) 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 found at the beginning of the Christian era that the four stars, +Capella, [e] Persei, [a] and [b] 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, [e] Persei, is a third-magnitude +star between Capella and the other two. + +Other allineations given by Ptolemy are: Spica, Arcturus and [b] Bootis; +Spica, [d] Corvi and [g] Corvi; [a] Libræ, Arcturus and [z] Ursæ +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 _proper motion_--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. + +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. + +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 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 Fig. 122. 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 Fig. 122. It is a significant fact that for the most part +the stars with large proper motions are precisely the ones shown in Fig. +122, 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. + +192. THE PATHS OF THE STARS.--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 Fig. 112, 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 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. + +[Illustration: FIG. 123.--Motion of Polaris in the line of sight as +determined by the spectroscope. FROST.] + +193. MOTION IN THE LINE OF SIGHT.--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 (§ 89) 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 Fig. 123. 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 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. +124 and 125, 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 [b] Aurigæ 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. + +[Illustration: FIG. 124.--Spectrum of [b] Aurigæ.--PICKERING.] + +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 [m] Cassiopeiæ is approaching the sun. + +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. + +[Illustration: FIG. 125.--Spectrum of Pollux.--PICKERING.] + +194. STAR DRIFT.--An illustration of how they may be made to work +together is furnished by some of the stars--which make up the Great +Dipper--[b], [g], [e], and [z] Ursæ 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, [d] Ursæ +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 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 Fig. 122. A most extraordinary system of +stars which, although separated from each other by distances as great as +the whole breadth of Fig. 122, 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. + +[Illustration: FIG. 126.--The Great Dipper, past, present, and future.] + +The stars [a] and [ê] 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. Fig. 126 illustrates this change of +shape, the upper part of the figure (_a_) showing these seven stars as +they were grouped at a remote epoch in the past, while the lower +section (_c_) 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 +[a] and [ê] 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. + +This phenomenon of groups of stars moving together is called _star +drift_, 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. + +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 Fig. 126 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? + +195. THE SUN'S WAY.--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 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. + +196. DISTANCE OF SIRIAN AND SOLAR STARS.--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 [b] Aurigæ +belongs to the Sirian class, as does every other star which has a +spectrum like that of Fig. 124, while Pollux is a solar star presenting +in Fig. 125 a spectrum like that of the sun, as do the other stars of +this class. + +Two thirds of the sun's near neighbors, shown in Fig. 122, have spectra +of the solar type, and in general stars of 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 Fig. 122, 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. + +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 _may_ 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 (_D_) of the stars of magnitude +(_m_) may be put into two equations: + + For Solar Stars, D = 23 × 2^{m/2} + + For Sirian Stars, D = 52 × 2^{m/2} + +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? + +197. CONSEQUENCES OF STELLAR DISTANCE.--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. + +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^{6.6}, 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. + +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, [a] 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. + +198. DOUBLE STARS.--In the constellation Taurus, not far from Aldebaran, +is the fourth-magnitude star [th] Tauri, which can readily be seen to +consist of two stars close together. The star [a] Capricorni is plainly +double, and a sharp eye can detect that one of the faint stars which +with Vega make a small equilateral triangle, is also a double star. +Look for them in the sky. + +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 [th] Tauri or [a] 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 _binary_ +systems, and in cases of this kind the principles of celestial mechanics +set forth in Chapter IV 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 _distance_, and their direction one from the other, which +is called _position angle_. + +199. ORBITS OF DOUBLE STARS.--The sun's nearest neighbor, [a] 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 Fig. 127 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 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 Fig. 127, gives correctly the relative positions of the +two stars, and makes one orbit do the work of two. + +[Illustration: FIG. 127.--The orbit of [a] Centauri.--SEE.] + +In Fig. 127 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 Fig. 128 +for a case in which the true orbit is turned exactly edgewise toward the +earth, and the small star, which really 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. + +In the case of [a] 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. + +[Illustration: FIG. 128.--Apparent orbit and real orbit of the double +star 42 Comæ Berenicis.--SEE.] + +200. MASSES OF DOUBLE STARS.--If we apply to this orbit Kepler's Third +Law in the form given it at page 179, we shall find-- + + a^3 / T^2 = (23.5)^3 / (81)^2 = k (M + m), + +where _M_ and _m_ represent the masses of the two stars. We have already +seen that _k_, the gravitation constant, is equal to 1 when the masses +are measured in terms of the sun's mass taken as unity, and when _T_ and +_a_ are expressed in years and radii of the earth's orbit respectively, +and with this value of _k_ we may readily find from the above equation, +_M_ + _m_ = 2.5--i. e., the combined mass of the two components of +[a] 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, _a_, is found from the +observations in angular measure, 35" in this case, and it is only when +the parallax 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". + +Our list of distances (§ 189) 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: + + ---------------------+-------+-------+----------+------- + STAR. | Major | Minor | Periodic | Mass. + | axis. | axis. | time. | + ---------------------+-------+-------+----------+------- + [a] Centauri | 47 | 40 | 81 y. | 2 + 70 Ophiuchi | 56 | 48 | 88 | 3 + Procyon | 34 | 31 | 40 | 3 + Sirius | 43 | 34 | 52 | 4 + ---------------------+-------+-------+----------+------- + +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. + +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. + +Although the half-dozen stars contained in the table all have orbits of +much the same size and with much the 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. + +201. DARK STARS.--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 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. + +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. + +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 [z] 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. + +202. MULTIPLE STARS.--Combinations of three, four, or more stars close +to each other, like [z] 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. + +[Illustration: FIG. 129.--Illustrating the motion of a spectroscopic +binary.] + +203. SPECTROSCOPIC BINARIES.--In the year 1890 Professor Pickering, of +the Harvard Observatory, announced the discovery of a new class of +double stars, invisible as such in 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 Fig. 129 we suppose _A_ and _B_ to be the two components of a +double star, each moving in its own orbit about their common center of +gravity, _C_, 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, _A_ would be rapidly +approaching the earth by reason of its orbital motion, while _B_ 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 _D_, only not spaced +so far apart. When the stars have moved a quarter way round their orbit +to the points _AŽ_, _BŽ_, their velocities are turned at right angles to +the line of sight 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 _spectroscopic binaries_, 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. + +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 that of [a] Centauri, provided +that their orbit plane is turned exactly edgewise toward the earth. + +There are at the present time (1901) 34 spectroscopic binaries known, +including among them such stars as Polaris, Capella, Algol, Spica, [b] +Aurigæ, [z] Ursæ 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 [ê] Pegasi, which has the longest known period of any star of +this class. + +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. + +204. VARIABLE STARS.--Attention has already been drawn (§ 23) to the +fact that some stars shine with a changing brightness--e. g., Algol, the +most famous of these _variable stars_, 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 [o] Ceti has +been named Mira (Latin, _the wonderful_), 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 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. + +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. + +205. THE ALGOL VARIABLES.--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 +Fig. 130. 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? + +[Illustration: FIG. 130.--The light curve of Algol.] + +The arrows shown in Fig. 130 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 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. Fig. 129, which is drawn to scale, shows the +relative positions and sizes of these stars as well as the orbits in +which they move. + +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. + +[Illustration: FIG. 131.--The light curve of [b] Lyræ.] + +206. VARIABLES OF THE [b] LYRÆ TYPE.--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. +Fig. 131 represents the light curve of one of the best-known variable +systems of this second type, that of [b] Lyræ, 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 Fig. 132. 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 Fig. 132 what relative +positions must the stars occupy in their orbit in order that their +combined light should give [b] Lyræ its maximum brightness? What +position will furnish a minimum brightness? + +[Illustration: FIG. 132.--The system of [b] Lyræ.--MYERS.] + +207. VARIABLES OF LONG AND SHORT PERIODS.--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 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. + +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. + +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 Fig. 133. 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 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 Fig. 133; 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. + +[Illustration: FIG. 133.--Discovery of a variable star by means of +photography.--PICKERING.] + +208. NEW STARS.--Next to the variable stars of very long or very +irregular period stand the so-called _new_ or _temporary stars_, 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 A. D., for since that time there have been +no less than five of them 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. + +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. + +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. + +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. + +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 nebulæ 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. + +Another modern temporary star is Nova Aurigæ, 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 Novæ 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 nebulæ, etc. + + + + +CHAPTER XIV + +STARS AND NEBULÆ + + +209. STELLAR COLORS.--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 +[a] 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 [b] Cygni, in which the components are respectively +yellow and blue, and the yellow star furnishes eight times as much light +as the blue one. + +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, 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. + +210. CHEMISTRY OF THE STARS.--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. + +211. STELLAR SPECTRA.--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: + +_Type I. Sirian stars._--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 [b] Aurigæ (Fig. 124), which +is a continuous spectrum, especially rich in energy of short wave +length--i. e., violet and ultraviolet 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 ultraviolet light. + +Since with increasing temperature a body emits a continually increasing +proportion of energy of short wave length (§ 118), 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-- + +_Type II. Solar stars._--To this type of spectrum belong the yellow +stars, which show spectra like that of the sun, or of Pollux (Fig. 125). +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 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 _solar stars_. + +_Type III. Red stars._--A small number of stars show spectra comparable +with that of [a] Herculis (Fig. 134), 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 +_selective absorption_, 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. + +[Illustration: FIG. 134.--The spectrum of [a] Herculis.--ESPIN.] + +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 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. + +212. CLASSES OF STARS.--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 Fig. 48, 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. + +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. + +213. STAR CLUSTERS.--In previous chapters we have noted the Pleiades and +Præsepe as star clusters visible to the 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 Fig. 135, while Fig. 136 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. + +[Illustration: FIG 135.--Star cluster in Hercules.] + +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 presented by +a cluster, called Messier 5, not far from the star [a] 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." + +[Illustration: FIG. 136.--Star cluster in Hercules.--KEELER.] + +[Illustration: FIG. 137.--The Andromeda nebula as seen in a very small +telescope.] + +[Illustration: FIG. 138.--The Andromeda nebula and Holmes's comet. +Photographed by BARNARD.] + +[Illustration: FIG. 139.--A drawing of the Andromeda nebula.] + +[Illustration: FIG. 140.--A photograph of the Andromeda +nebula.--ROBERTS.] + +214. NEBULÆ.--Returning to Fig. 136, 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 outer part of the cluster is _resolved_ 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 cases, however, this is not +possible, and we have an _irresolvable cluster_ which it is customary to +call a _nebula_ (Latin, _little cloud_). + +The most conspicuous example of this in the northern heavens is the +great nebula in Andromeda (R. A. 0^{h} 37^{m}, 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 Fig. +137, which is reproduced from a sketch. Fig. 138 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 nebulæ +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. Fig. 139 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 Fig. 140, which is from a +photograph made with a large reflecting telescope. + +[Illustration: FIG. 141.--Types of nebulæ.] + +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 nebulæ 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, +for half a century ago it was sketched much as shown in the latest of +them (Fig. 140). + +[Illustration: FIG. 142.--The Trifid nebula.--KEELER.] + +215. TYPICAL NEBULÆ.--Some of the fantastic forms which nebulæ present +in the telescope are shown on a small scale in Fig. 141, 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 nebula in +Sagittarius (Fig. 142). 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. + +[Illustration: FIG. 143.--A nebula in Cygnus.--KEELER.] + +Fig. 143 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. + +[Illustration: FIG. 144.--Spiral nebula in Canes Venatici.--KEELER.] + +A much smaller but equally striking nebula is that in the constellation +Canes Venatici (Fig. 144), 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 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 nebulæ, shows that they are really part and +parcel of the nebula and not merely on line with it. Fig. 145 shows how +a great nebula is associated with the star [r] Ophiuchi. + +[Illustration: FIG. 145.--Great nebula about the star [r] +Ophiuchi.--BARNARD.] + +Probably the most impressive of all nebulæ is the great one in Orion +(Fig. 146), whose position is shown on the star map between Rigel and +[z] Orionis. Look for it with an opera glass or even with the unaided +eye. This is sometimes called an _amorphous_--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 from the brighter parts of the central +region. This nebula, as shown in Fig. 146, 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. + +[Illustration: FIG. 146.--The Orion nebula.] + +The Pleiades (Plate IV) 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. + +[Illustration: THE PLEIADES (AFTER A PHOTOGRAPH)] + +Fig. 147 shows a series of so-called double nebulæ perhaps comparable +with double stars, although the most recent photographic work seems to +indicate that they are really faint spiral nebulæ in which only the +brightest parts are shown by the telescope. + +According to Keeler, the spiral is the prevailing type of nebulæ, and +while Fig. 144 presents the most perfect example of such a nebula, the +student should not fail to note that the Andromeda nebula (Fig. 140) +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. + +[Illustration: FIG. 147.--Double nebulæ. HERSCHEL.] + +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 _planetary nebulæ_. The comet in Fig. 138, if +smaller, would represent fairly well the nebulæ 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. + +216. SPECTRA OF NEBULÆ.--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 nebulæ 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 nebulæ all have spectra of this +kind and make up about half of all the known gaseous nebulæ. It is +worthy of note that a century ago Sir William Herschel had observed a +green shimmer in the light of certain nebulæ 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 +nebulæ. + +In faint nebulæ 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 nebulæ, and there are +indications of one or two other known substances. + +217. DENSITY OF NEBULÆ.--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 nebulæ. + +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^{10} 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. + +218. MOTION OF NEBULÆ.--The extreme minuteness of their proper motions +is a characteristic feature of all nebulæ. 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 nebulæ 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. + +[Illustration: FIG. 148.--A part of the Milky Way.] + +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 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 _vice +versa_; but, on the whole, even these changes are very small. + +[Illustration: FIG. 149.--The Milky Way near [th] Ophiuchi.--BARNARD.] + +219. THE MILKY WAY.--Closely related to nebulæ and star clusters is +another feature of the sky, the _galaxy_ or _Milky Way_, with whose +appearance to the unaided eye the student should become familiar by +direct study of the thing itself. Figs. 148 and 149 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 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. + +[Illustration: FIG. 150.--The Milky Way near [b] Cygni.--BARNARD.] + +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 [b] and [g] 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. Fig. 150 is a photograph 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 [a] Cygni, and between the extremes of +abundance and poverty here noted there may be found every gradation of +nebulous light. + +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 nebulæ 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 _construction of the heavens_. + +220. DISTRIBUTION OF THE STARS.--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. + +Parallaxes, proper motions, motions in the line of sight, while +pertinent to the problem of stellar distribution, are 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. + +The rate of increase in the number of stars from one magnitude to the +next, as shown in § 187, 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 § 187, 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. + +221. THE STELLAR SYSTEM.--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 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. + +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 nebulæ 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. + +On the other hand, nebulæ 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. + +222. RELATION OF THE SUN TO THE MILKY WAY.--The fact that the galaxy is +a _great circle_ of the sky, but only of moderate width, shows that it +is a widely extended and comparatively 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. + +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. 149 and 150 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. + +223. DIMENSIONS OF THE GALAXY.--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 +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 Fig. 140 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. + +224. BEYOND THE MILKY WAY.--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. + +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 nebulæ ... 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 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 nebulæ 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, nebulæ, and clusters, as is the Milky Way. + +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. + +225. ABSORPTION OF STARLIGHT.--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 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. + + + + +CHAPTER XV + +GROWTH AND DECAY + + +226. NATURE OF THE PROBLEM.--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. + +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, 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. + +227. LOGICAL BASES AND LIMITATIONS.--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. + +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 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." + +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. + +228. THE SUN'S DEVELOPMENT.--The first of these to claim our attention +is the shrinking of the sun's diameter which, as we have seen in Chapter +X, 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. + +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 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 nebulæ 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 § 126, 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. + +229. THE SUN'S FUTURE.--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 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. + +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 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. + +230. THE NEBULAR HYPOTHESIS.--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. + +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 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 § 228 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. + +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. + +[Illustration: PIERRE SIMON LAPLACE (1749-1827).] + +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 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." + +231. OBJECTIONS TO THE NEBULAR HYPOTHESIS.--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 +Chapter XI, 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 +(Chapter XI). Do these fortify or weaken his case? + +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. + +One proposed modification, much discussed in recent years, consists in +substituting for the primitive _gaseous_ 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. + +232. BODE'S LAW.--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 (§ 134). 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 _equal_ 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 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. + +233. TIDAL FRICTION BETWEEN EARTH AND MOON.--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 (§ 42) 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. + +Fig. 24 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 +(§ 36) 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_, therefore points a little _in advance_ 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 +_IŽŽ_ pulls back and tends to neutralize the effect of the wave at _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. + +234. CONSEQUENCES OF TIDAL FRICTION UPON THE EARTH.--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. + +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 _bodily tides_ of +semi-fluid matter not only higher, but with greater internal friction of +their molecules one upon another, and correspondingly greater effect in +checking the earth's rotation. + +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. + +235. CONSEQUENCES OF TIDAL FRICTION UPON THE MOON.--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 Chapter IX, +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. + +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 (§ 99), 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 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. + +236. THE EARTH-MOON SYSTEM.--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. + +337. TIDAL FRICTION UPON THE PLANETS.--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 Chapter +XI 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 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. + +238. THE SOLAR TIDE.--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 _from west +to east_, 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. + +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. + +239. ROCHE'S LIMIT.--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 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 _r_, and the +quotient obtained by dividing the density of the planet by the density +of the satellite by _q_, then + + Roche's limit = 2.44 × r × q^{1/3}. + +Thus in the case of earth and moon we find from the densities given in +§ 95, _q_ = 1.65, and with _r_ = 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. + +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. + +240. SATURN'S RINGS.--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 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. + +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. + +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. + +241. THE MOON'S DEVELOPMENT.--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 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. + +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. 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. + +242. STELLAR DEVELOPMENT.--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 Chapter XIII. The most +systematic development of this idea is due to Lockyer, who looks upon +all the celestial bodies--sun, moon and planets, stars, nebulæ, 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 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. + +[Illustration: FIG. 151.--Types of stellar spectra substantially +according to SECCHI.] + +243. STELLAR SPECTRA.--Thus the types of stellar spectra shown in Fig. +151 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. + +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 this idea, numerous subdivisions of the types of stellar +spectra shown in Fig. 151 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. + +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. + +We have noted in § 196 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. + +244. DOUBLE STARS.--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 Fig. 132, gravity must tend to make each +component of the double star shrink to 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 [b] Lyræ 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. + +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. + +245. NEBULÆ.--The nebular hypothesis of Laplace has inclined astronomers +to look upon nebulæ 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 nebulæ 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 nebulæ 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 _vice versa_. 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 Fig. 122. + +246. CLASSIFICATION.--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 nebulæ +of chaotic appearance such as that represented in Fig. 146. Above these +in point of development stand the spiral, ring, and planetary nebulæ, +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 Fig. 151, 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 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. + +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. + +247. STABILITY OF THE UNIVERSE.--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. + +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, 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." + +Compare with this the words of a great poet who in The Tempest puts into +the mouth of Prospero the lines: + + "The cloud-capp'd towers, the gorgeous palaces, + The solemn temples, the great globe itself, + Yea, all which it inherit, shall dissolve; + And, like this insubstantial pageant faded, + Leave not a rack behind." + +248. THE FUTURE.--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 _change_. 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 development. A universe +which is ever becoming something else and is never finished, as shadowed +forth by Goethe in the lines: + + "Thus work I at the roaring loom of Time, + And weave for Deity a living robe sublime." + + + + +APPENDIX + + +THE GREEK ALPHABET + +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: + + Greek. Name. English. + + [A] [a] Alpha a + + [B] [b] Beta b + + [G] [g] Gamma g + + [D] [d] Delta d + + [E] [e] or [e] Epsilon [)e] + + [Z] [z] Zeta z + + [Ê] [ê] Eta [=e] + + [Th] [th] or [th] Theta th + + [I] [i] Iota i + + [K] [k] Kappa k + + [L] [l] Lambda l + + [M] [m] Mu m + + [N] [n] Nu n + + [X] [x] Xi x + + [O] [o] Omicron [)o] + + [P] [p] Pi p + + [R] [r] Rho r + + [S] [s] or [s] Sigma s + + [T] [t] Tau t + + [Y] [y] Upsilon u + + [Ph] [ph] Phi ph + + [Ch] [ch] Chi ch + + [Ps] [ps] Psi ps + + [Ô] [ô] Omega [=o] + + +POPULAR LITERATURE OF ASTRONOMY + +The following brief bibliography, while making no pretense at +completeness, may serve as a useful guide to supplementary reading: + + +_General Treatises_ + +YOUNG. _General Astronomy._ An admirable general survey of the entire +field. + +NEWCOMB. _Popular Astronomy._ The second edition of a German translation +of this work by Engelmann and Vogel is especially valuable. + +BALL. _Story of the Heavens._ Somewhat easier reading than either of the +preceding. + +CHAMBERS. _Descriptive Astronomy._ An elaborate but elementary work in +three volumes. + +LANGLEY. _The New Astronomy._ Treats mainly of the physical condition of +the celestial bodies. + +PROCTOR and RANYARD. _Old and New Astronomy._ + + +_Special Treatises_ + +PROCTOR. _The Moon._ A general treatment of the subject. + +NASMYTH and CARPENTER. _The Moon._ 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. + +YOUNG. _The Sun._ International Scientific Series. The most recent and +authoritative treatise on this subject. + +PROCTOR. _Other Worlds than Ours._ An account of planets, comets, etc. + +NEWTON. _Meteor._ Encyclopædia Britannica. + +AIRY. _Gravitation._ A non-mathematical exposition of the laws of +planetary motion. + +STOKES. _On Light as a Means of Investigation._ Burnett Lectures. II. +The basis of spectrum analysis. + +SCHELLEN. _Spectrum Analysis._ + +THOMSON (Sir W., Lord KELVIN), _Popular Lectures, etc._ Lectures on the +Tides, The Sun's Heat, etc. + +BALL. _Time and Tide._ An exposition of the researches of G. H. Darwin +upon tidal friction. + +GORE. _The Visible Universe._ Deals with a class of problems +inadequately treated in most popular astronomies. + +DARWIN. _The Tides._ An admirable elementary exposition. + +CLERKE. _The System of the Stars._ Stellar astronomy. + +NEWCOMB. Chapters on the Stars, in _Popular Science Monthly_ for 1900. + +CLERKE. _History of Astronomy during the Nineteenth Century._ An +admirable work. + +WOLF. _Geschichte der Astronomie._ München, 1877. An excellent German +work. + + +A LIST OF STARS FOR TIME OBSERVATIONS + +See § 20. + + ------------------+---------------+------------------+-------------+ + NAME. | Magnitude. | Right Ascension. | Declination.| + ------------------+---------------+------------------+-------------+ + | | | | + | | h. m. | ° | + [b] Ceti | 2 | 0 38.6 | - 18.5 | + [ê] Ceti | 3 | 1 3.6 | - 10.7 | + [a] Ceti | 3 | 2 57.1 | + 3.7 | + [g] Eridani | 3 | 3 53.4 | - 13.8 | + _Aldebaran_ | 1 | 4 30.2 | + 16.3 | + | | | | + _Rigel_ | 0 | 5 9.7 | - 8.3 | + [k] Orionis | 2 | 5 43.0 | - 9.7 | + [b] Canis Majoris | 2 | 6 18.3 | - 17.9 | + _Sirius_ | -1 | 6 40.7 | - 16.6 | + _Procyon_ | 0 | 7 34.1 | + 5.5 | + | | | | + [a] Hydræ | 2 | 9 22.7 | - 8.2 | + _Regulus_ | 1 | 10 3.0 | + 12.5 | + [n] Hydræ | 3 | 10 44.7 | - 15.7 | + [e] Corvi | 3 | 12 5.0 | - 22.1 | + [g] Corvi | 3 | 12 10.7 | - 17.0 | + | | | | + _Spica_ | 1 | 13 19.9 | - 10.6 | + [z] Virginis | 3 | 13 29.6 | - 0.1 | + [a] Libræ | 3 | 14 45.3 | - 15.6 | + [b] Libræ | 3 | 15 11.6 | - 9.0 | + _Antares_ | 1 | 16 23.3 | - 26.2 | + | | | | + [a] Ophiuchi | 2 | 17 30.3 | + 12.6 | + [e] Sagittarii | 2 | 18 17.5 | - 34.4 | + [d] Aquilæ | 3 | 19 20.5 | + 2.9 | + _Altair_ | 1 | 19 45.9 | + 8.6 | + [b] Aquarii | 3 | 21 26.3 | - 6.0 | + | | | | + [a] Aquarii | 3 | 22 0.6 | - 0.8 | + _Fomalhaut_ | 1 | 22 52.1 | - 30.2 | + ------------------+---------------+------------------+-------------+ + + + + +INDEX + + +The references are to section numbers. + + + Absorption of starlight, 225. + + Absorption spectra, 87. + + Accelerating force, 35. + + Adjustment of observations, 2. + + Albedo of moon, 97. + of Venus, 148. + + Algol, 205. + + Altitudes, 4, 21. + + Andromeda nebula, 214. + + Angles, measurement of, 2. + + Angular diameter, 7. + + Annular eclipse, 64. + + Asteroids, 156. + + Atmosphere of the earth, 49. + of the moon, 103. + of Jupiter, 139. + of Mars, 153. + + Aurora, 51. + + Azimuth, 5, 21. + + + Biela's comet, 181. + + Bode's law, 134, 232. + + Bredichin's theory of comet tails, 180. + + + Calendar, O. S. and N. S., 61. + + Capture of comets and meteors, 176. + + Canals of Mars, 154. + + Celestial mechanics, 32. + + Changes upon the moon, 108. + + Chemical constitution of sun, 116. + of stars, 210. + + Chromosphere, the sun's, 124. + + Chronology, 59. + + Classification of stars, 212. + + Clocks and watches, 74. + sidereal clock, 12. + + Collisions with comets, 183. + + Colors of stars, 209. + + Comets, general characteristics, 158-164. + development of, 179, 181. + groups, 177. + orbits, 161. + periodic, 176. + spectra, 182. + tails, 180. + + Comets and meteors, relation of, 175. + + Conic sections, 38. + + Constellations, 184. + + Corona, the sun's, 123. + + Craters, lunar, 105. + + + Dark stars, 201. + + Day, 52, 62. + + Declination, 21. + + Development of comet, 179. + of moon, 241. + of nebulæ, 245. + of stars, 242, 244. + of sun, 228. + of universe, 226. + + Distribution of stars and nebulæ, 220. + + Diurnal motion, 10, 15. + + Doppler principle, 89. + + Double nebulæ, 215. + + Double stars, 198. + development of, 244. + + Driving clock, 80. + + + Earth, atmosphere, 48. + mass, 45. + size and shape, 44. + warming of the earth, 47. + + Eclipses, nature of, 63. + annular eclipse, 64. + eclipse limits, 68. + eclipse maps, 70, 71. + number of, in a year, 69. + partial eclipse, 64. + prediction of, 70, 71. + recurrence of, 72. + shadow cone, 64, 66. + total eclipse, 64. + uses of, 73. + + Eclipses of Jupiter's satellites, 141. + + Eclipse theory of variable stars, 205. + + Ecliptic, 26. + obliquity of, 25. + + Ellipse, 33. + + Epochs for planetary motion, 30. + + Energy, radiant, 75. + condensation of, 76. + + Epicycle, 32. + + Equation of time, 53. + + Equator, 16, 21. + + Equatorial mounting, 80. + + Equinoxes, 25. + + Ether, 75. + + Evening star, 31. + + + Faculæ, 122. + + Falling bodies, law of, 35. + + Finding the stars, 14. + + Fraunhofer lines, 87. + + + Galaxy, 219. + + Geography of the sky, 16. + + Graphical representation, 6. + + Grating, diffraction, 84. + + Gravitation, law of, 37. + + + Harvest moon, 93. + + Heat of the sun, 118, 126. + + Helmholtz, contraction theory of the sun, 126, 228. + + Horizon, 4, 21. + + Hour angle, 21. + + Hour circle, 21. + + Hyperbola, 38. + + + Japetus, satellite of Saturn, 145. + + Jupiter, 136. + atmosphere, 139. + belts, 137. + invisible from fixed stars, 197. + orbit of, 29. + physical condition, 139. + rotation and flattening, 138. + satellites, 140. + surface markings, 137. + + + Kepler's laws, 33, 111. + + + Latitude, determination of, 18. + + Leap year, 61. + + Lenses, 77. + + Leonid meteor shower, 172. + perturbations of, 174. + + Librations of moon, 98. + + Life upon the planets, 157. + + Light curves, 205. + + Light, nature of, 75. + + Light year, 190. + + Limits of eclipses, 68. + + Longitude, 56. + determination of, 58. + + Lunation, 60. + + + Magnifying power of telescope, 79. + + Magnitude, stellar, 9, 186. + + Mars, atmosphere, temperature, 150. + canals, 154. + orbit, 30. + polar caps, 152. + rotation, 151. + satellites, 155. + surface markings, 150. + + Mass, determination of, 37. + of comets, 164. + of double stars, 200. + of moon, 94. + of planets, 40, 133. + + Measurements, accurate, 1. + + Mercury, 149. + motion of its perihelion, 43. + orbit of, 30. + + Meridian, 19, 21. + + Meteors, nature of, 165, 169. + number of, 167. + velocity, 170. + + Meteors and comets, relation of, 175. + + Meteor showers, radiant, 171. + Leonids, capture of, 172, 173. + perturbations, 174. + + Milky Way, 219. + + Mira, [o] Ceti, 204. + + Mirrors, 77. + + Month, 60. + + Moon, 91. + albedo, 97. + atmosphere, 103. + changes in, 108. + density, surface gravity, 95. + development of, 241. + harvest moon, 93. + influence upon the earth, 109, 233. + librations, 98. + map of, 101. + mass and size, 94. + motion, 24, 92. + mountains and craters, 104. + phases, 91, 92. + physical condition, 100, 107. + + Month, 60. + + Morning star, 31. + + Motion in line of sight, 89, 193. + + Multiple stars, 202. + + + Names of stars, 8. + + Nebulæ, 214. + density, 217. + development of, 245. + motion, 218. + spectra, 216. + types and classes of, 215. + + Nebular hypothesis, 230. + objections to, 231. + + Neptune, 146. + discovery of, 41. + + Newton's laws of motion, 34. + law of gravitation, 37, 43. + + Nodes, 39. + relation to eclipses, 67, 71. + + Nucleus, of comet, 160. + + + Objective, of telescope, 78. + + Obliquity of ecliptic, 25. + + Observations, of stars, 10. + + Occultation of stars, 103. + + Orbits, of comets, 161. + of double stars, 199. + of moon, 92. + of planets, 28. + + Orion nebula, 215. + + + Parabola, 35, 38, 161. + + Parabolic velocity, 38. + + Parallax, 114, 188. + + Penumbra, 64, 121. + + Perihelion, 38. + + Periodic comets, 176. + + Personal equation, 82. + + Perturbations, 39. + of meteors, 174. + + Phases, of the moon, 91, 92. + + Photography, 81. + of stars, 13. + + Photosphere, of sun, 121. + + Planets, 26, 133. + distances from the sun, 134. + how to find, 29. + mass, density, size, 133. + motion of, 27, 38. + periodic times of, 30. + + Planetary nebulæ, 215. + + Pleiades, 16, 215. + + Plumb-line apparatus, 11, 18. + + Poles, 21. + + Precession, 46. + + Prisms, 84. + + Problem of three bodies, 39. + + Prominences, solar, 125. + + Proper motions, 191. + + Protractor, 2. + + Ptolemaic system, 32. + + + Radiant energy, 75. + + Radiant, of meteor shower, 171. + + Radius victor, 33. + + Reference lines and circles, 17. + + Refraction, 50. + + Right ascension, 16, 20, 21. + + Roche's limit, 239. + + Rotation, of earth, 55. + of Mars, 151. + of moon, 99. + of Jupiter, 138. + of Saturn, 144. + of sun, 120, 132. + + + Saros, 72. + + Satellites, of Jupiter, 136, 140. + of Mars, 155. + of Saturn, 145. + + Saturn, 142. + ball of, 144. + orbit, 29. + rings, 142. + rotation, 144. + satellites, 145. + + Seasons, on the earth, 47. + on Mars, 151. + + Shadow cone, 64, 66. + + Sidereal time, 20, 54. + + Shooting stars, 158. (See Meteor.) + + Spectroscope, 84. + + Spectroscopic binaries, 203. + + Spectrum, 84, 87. + of comets, 182. + of nebulæ, 216. + of stars, 211. + types of, 88. + + Spectrum analysis, 85. + + Spiral nebulæ, 215. + + Standard time, 57. + + Stars, 8, 184. + classes of, 212. + clusters, 213. + colors, 209. + dark stars, 201. + development of, 242. + distances from the sun, 188, 196. + distribution of, 220. + double stars, 198, 203. + drift, 194. + magnitudes, 9, 196. + number of, 185. + spectra, 211. + temporary, 208. + variable, 204. + + Starlight, absorption of, 225. + + Star maps, construction of, 23. + + Stellar system, extent of, 223. + + Sun's apparent motion, 25. + real motion, 195. + + Sun, 110. + chemical composition, 116. + chromosphere, 124. + corona, 123. + distance from the earth, 111. + faculæ, 119, 122. + gaseous constitution, 127. + heat of, 117. + mechanism of, 126. + physical properties, 115-120. + prominences, 125. + rotation, 120, 132. + surface of, 119. + temperature, 118. + + Sun spots, 119, 121. + period, 129, 131. + zones, 130. + + + Telescopes, 78. + equatorial mounting for, 80. + magnifying power of, 79. + + Temperature of Jupiter, 139. + of Mars, 152. + of Mercury, 149. + of moon, 107. + of sun, 118. + + Temporary stars, 208. + + Terminator, 91. + + Tenth meter, 75. + + Tidal friction, 233-238. + + Tides, 42. + + Time, sidereal, 20, 54. + solar, 52. + determination of, 20. + equation of, 53. + standard, 57. + + Triangulation, 3. + + Trifid nebula, 215. + + Twilight, 51. + + Twinkling, of stars, 48. + + + Universe, development of, 226. + stability of, 247. + + Uranus, 146. + + + Variable stars, 204. + + Velocity, its relation to orbital motion, 38. + + Venus, 148. + orbit of, 30. + + Vernal equinox, 21, 25. + + Vertical circle, 21. + + + Wave front, 76. + + Wave lengths, 75, 86. + + + Year, 25. + leap year, 61. + sidereal year, 59. + tropical year, 60. + + + Zenith, 21. + + Zodiac, 26. + + Zodiacal light, 168. + + + + +THE END + + + + + + + +End of Project Gutenberg's A Text-Book of Astronomy, by George C. Comstock + +*** END OF THIS PROJECT GUTENBERG EBOOK A TEXT-BOOK OF ASTRONOMY *** + +***** This file should be named 34834.txt or 34834.zip ***** +This and all associated files of various formats will be found in: + http://www.gutenberg.org/3/4/8/3/34834/ + +Produced by Chris Curnow, Iris Schimandle, Lindy Walsh and +the Online Distributed Proofreading Team at +http://www.pgdp.net + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. Special rules, +set forth in the General Terms of Use part of this license, apply to +copying and distributing Project Gutenberg-tm electronic works to +protect the PROJECT GUTENBERG-tm concept and trademark. Project +Gutenberg is a registered trademark, and may not be used if you +charge for the eBooks, unless you receive specific permission. If you +do not charge anything for copies of this eBook, complying with the +rules is very easy. You may use this eBook for nearly any purpose +such as creation of derivative works, reports, performances and +research. They may be modified and printed and given away--you may do +practically ANYTHING with public domain eBooks. Redistribution is +subject to the trademark license, especially commercial +redistribution. + + + +*** START: FULL LICENSE *** + +THE FULL PROJECT GUTENBERG LICENSE +PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK + +To protect the Project Gutenberg-tm mission of promoting the free +distribution of electronic works, by using or distributing this work +(or any other work associated in any way with the phrase "Project +Gutenberg"), you agree to comply with all the terms of the Full Project +Gutenberg-tm License (available with this file or online at +http://gutenberg.org/license). + + +Section 1. General Terms of Use and Redistributing Project Gutenberg-tm +electronic works + +1.A. By reading or using any part of this Project Gutenberg-tm +electronic work, you indicate that you have read, understand, agree to +and accept all the terms of this license and intellectual property +(trademark/copyright) agreement. If you do not agree to abide by all +the terms of this agreement, you must cease using and return or destroy +all copies of Project Gutenberg-tm electronic works in your possession. +If you paid a fee for obtaining a copy of or access to a Project +Gutenberg-tm electronic work and you do not agree to be bound by the +terms of this agreement, you may obtain a refund from the person or +entity to whom you paid the fee as set forth in paragraph 1.E.8. + +1.B. "Project Gutenberg" is a registered trademark. It may only be +used on or associated in any way with an electronic work by people who +agree to be bound by the terms of this agreement. There are a few +things that you can do with most Project Gutenberg-tm electronic works +even without complying with the full terms of this agreement. See +paragraph 1.C below. There are a lot of things you can do with Project +Gutenberg-tm electronic works if you follow the terms of this agreement +and help preserve free future access to Project Gutenberg-tm electronic +works. See paragraph 1.E below. + +1.C. The Project Gutenberg Literary Archive Foundation ("the Foundation" +or PGLAF), owns a compilation copyright in the collection of Project +Gutenberg-tm electronic works. Nearly all the individual works in the +collection are in the public domain in the United States. If an +individual work is in the public domain in the United States and you are +located in the United States, we do not claim a right to prevent you from +copying, distributing, performing, displaying or creating derivative +works based on the work as long as all references to Project Gutenberg +are removed. Of course, we hope that you will support the Project +Gutenberg-tm mission of promoting free access to electronic works by +freely sharing Project Gutenberg-tm works in compliance with the terms of +this agreement for keeping the Project Gutenberg-tm name associated with +the work. You can easily comply with the terms of this agreement by +keeping this work in the same format with its attached full Project +Gutenberg-tm License when you share it without charge with others. + +1.D. The copyright laws of the place where you are located also govern +what you can do with this work. Copyright laws in most countries are in +a constant state of change. If you are outside the United States, check +the laws of your country in addition to the terms of this agreement +before downloading, copying, displaying, performing, distributing or +creating derivative works based on this work or any other Project +Gutenberg-tm work. The Foundation makes no representations concerning +the copyright status of any work in any country outside the United +States. + +1.E. Unless you have removed all references to Project Gutenberg: + +1.E.1. The following sentence, with active links to, or other immediate +access to, the full Project Gutenberg-tm License must appear prominently +whenever any copy of a Project Gutenberg-tm work (any work on which the +phrase "Project Gutenberg" appears, or with which the phrase "Project +Gutenberg" is associated) is accessed, displayed, performed, viewed, +copied or distributed: + +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 + +1.E.2. If an individual Project Gutenberg-tm electronic work is derived +from the public domain (does not contain a notice indicating that it is +posted with permission of the copyright holder), the work can be copied +and distributed to anyone in the United States without paying any fees +or charges. If you are redistributing or providing access to a work +with the phrase "Project Gutenberg" associated with or appearing on the +work, you must comply either with the requirements of paragraphs 1.E.1 +through 1.E.7 or obtain permission for the use of the work and the +Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or +1.E.9. + +1.E.3. If an individual Project Gutenberg-tm electronic work is posted +with the permission of the copyright holder, your use and distribution +must comply with both paragraphs 1.E.1 through 1.E.7 and any additional +terms imposed by the copyright holder. Additional terms will be linked +to the Project Gutenberg-tm License for all works posted with the +permission of the copyright holder found at the beginning of this work. + +1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm +License terms from this work, or any files containing a part of this +work or any other work associated with Project Gutenberg-tm. + +1.E.5. Do not copy, display, perform, distribute or redistribute this +electronic work, or any part of this electronic work, without +prominently displaying the sentence set forth in paragraph 1.E.1 with +active links or immediate access to the full terms of the Project +Gutenberg-tm License. + +1.E.6. You may convert to and distribute this work in any binary, +compressed, marked up, nonproprietary or proprietary form, including any +word processing or hypertext form. However, if you provide access to or +distribute copies of a Project Gutenberg-tm work in a format other than +"Plain Vanilla ASCII" or other format used in the official version +posted on the official Project Gutenberg-tm web site (www.gutenberg.org), +you must, at no additional cost, fee or expense to the user, provide a +copy, a means of exporting a copy, or a means of obtaining a copy upon +request, of the work in its original "Plain Vanilla ASCII" or other +form. Any alternate format must include the full Project Gutenberg-tm +License as specified in paragraph 1.E.1. + +1.E.7. Do not charge a fee for access to, viewing, displaying, +performing, copying or distributing any Project Gutenberg-tm works +unless you comply with paragraph 1.E.8 or 1.E.9. + +1.E.8. You may charge a reasonable fee for copies of or providing +access to or distributing Project Gutenberg-tm electronic works provided +that + +- You pay a royalty fee of 20% of the gross profits you derive from + the use of Project Gutenberg-tm works calculated using the method + you already use to calculate your applicable taxes. The fee is + owed to the owner of the Project Gutenberg-tm trademark, but he + has agreed to donate royalties under this paragraph to the + Project Gutenberg Literary Archive Foundation. Royalty payments + must be paid within 60 days following each date on which you + prepare (or are legally required to prepare) your periodic tax + returns. Royalty payments should be clearly marked as such and + sent to the Project Gutenberg Literary Archive Foundation at the + address specified in Section 4, "Information about donations to + the Project Gutenberg Literary Archive Foundation." + +- You provide a full refund of any money paid by a user who notifies + you in writing (or by e-mail) within 30 days of receipt that s/he + does not agree to the terms of the full Project Gutenberg-tm + License. You must require such a user to return or + destroy all copies of the works possessed in a physical medium + and discontinue all use of and all access to other copies of + Project Gutenberg-tm works. + +- You provide, in accordance with paragraph 1.F.3, a full refund of any + money paid for a work or a replacement copy, if a defect in the + electronic work is discovered and reported to you within 90 days + of receipt of the work. + +- You comply with all other terms of this agreement for free + distribution of Project Gutenberg-tm works. + +1.E.9. If you wish to charge a fee or distribute a Project Gutenberg-tm +electronic work or group of works on different terms than are set +forth in this agreement, you must obtain permission in writing from +both the Project Gutenberg Literary Archive Foundation and Michael +Hart, the owner of the Project Gutenberg-tm trademark. Contact the +Foundation as set forth in Section 3 below. + +1.F. + +1.F.1. Project Gutenberg volunteers and employees expend considerable +effort to identify, do copyright research on, transcribe and proofread +public domain works in creating the Project Gutenberg-tm +collection. Despite these efforts, Project Gutenberg-tm electronic +works, and the medium on which they may be stored, may contain +"Defects," such as, but not limited to, incomplete, inaccurate or +corrupt data, transcription errors, a copyright or other intellectual +property infringement, a defective or damaged disk or other medium, a +computer virus, or computer codes that damage or cannot be read by +your equipment. + +1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right +of Replacement or Refund" described in paragraph 1.F.3, the Project +Gutenberg Literary Archive Foundation, the owner of the Project +Gutenberg-tm trademark, and any other party distributing a Project +Gutenberg-tm electronic work under this agreement, disclaim all +liability to you for damages, costs and expenses, including legal +fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT +LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE +PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE +TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE +LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR +INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH +DAMAGE. + +1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a +defect in this electronic work within 90 days of receiving it, you can +receive a refund of the money (if any) you paid for it by sending a +written explanation to the person you received the work from. If you +received the work on a physical medium, you must return the medium with +your written explanation. The person or entity that provided you with +the defective work may elect to provide a replacement copy in lieu of a +refund. If you received the work electronically, the person or entity +providing it to you may choose to give you a second opportunity to +receive the work electronically in lieu of a refund. If the second copy +is also defective, you may demand a refund in writing without further +opportunities to fix the problem. + +1.F.4. Except for the limited right of replacement or refund set forth +in paragraph 1.F.3, this work is provided to you 'AS-IS' WITH NO OTHER +WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO +WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE. + +1.F.5. Some states do not allow disclaimers of certain implied +warranties or the exclusion or limitation of certain types of damages. +If any disclaimer or limitation set forth in this agreement violates the +law of the state applicable to this agreement, the agreement shall be +interpreted to make the maximum disclaimer or limitation permitted by +the applicable state law. The invalidity or unenforceability of any +provision of this agreement shall not void the remaining provisions. + +1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the +trademark owner, any agent or employee of the Foundation, anyone +providing copies of Project Gutenberg-tm electronic works in accordance +with this agreement, and any volunteers associated with the production, +promotion and distribution of Project Gutenberg-tm electronic works, +harmless from all liability, costs and expenses, including legal fees, +that arise directly or indirectly from any of the following which you do +or cause to occur: (a) distribution of this or any Project Gutenberg-tm +work, (b) alteration, modification, or additions or deletions to any +Project Gutenberg-tm work, and (c) any Defect you cause. + + +Section 2. Information about the Mission of Project Gutenberg-tm + +Project Gutenberg-tm is synonymous with the free distribution of +electronic works in formats readable by the widest variety of computers +including obsolete, old, middle-aged and new computers. It exists +because of the efforts of hundreds of volunteers and donations from +people in all walks of life. + +Volunteers and financial support to provide volunteers with the +assistance they need, are critical to reaching Project Gutenberg-tm's +goals and ensuring that the Project Gutenberg-tm collection will +remain freely available for generations to come. In 2001, the Project +Gutenberg Literary Archive Foundation was created to provide a secure +and permanent future for Project Gutenberg-tm and future generations. +To learn more about the Project Gutenberg Literary Archive Foundation +and how your efforts and donations can help, see Sections 3 and 4 +and the Foundation web page at http://www.pglaf.org. + + +Section 3. Information about the Project Gutenberg Literary Archive +Foundation + +The Project Gutenberg Literary Archive Foundation is a non profit +501(c)(3) educational corporation organized under the laws of the +state of Mississippi and granted tax exempt status by the Internal +Revenue Service. The Foundation's EIN or federal tax identification +number is 64-6221541. Its 501(c)(3) letter is posted at +http://pglaf.org/fundraising. Contributions to the Project Gutenberg +Literary Archive Foundation are tax deductible to the full extent +permitted by U.S. federal laws and your state's laws. + +The Foundation's principal office is located at 4557 Melan Dr. S. +Fairbanks, AK, 99712., but its volunteers and employees are scattered +throughout numerous locations. Its business office is located at +809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email +business@pglaf.org. Email contact links and up to date contact +information can be found at the Foundation's web site and official +page at http://pglaf.org + +For additional contact information: + Dr. Gregory B. Newby + Chief Executive and Director + gbnewby@pglaf.org + + +Section 4. Information about Donations to the Project Gutenberg +Literary Archive Foundation + +Project Gutenberg-tm depends upon and cannot survive without wide +spread public support and donations to carry out its mission of +increasing the number of public domain and licensed works that can be +freely distributed in machine readable form accessible by the widest +array of equipment including outdated equipment. Many small donations +($1 to $5,000) are particularly important to maintaining tax exempt +status with the IRS. + +The Foundation is committed to complying with the laws regulating +charities and charitable donations in all 50 states of the United +States. Compliance requirements are not uniform and it takes a +considerable effort, much paperwork and many fees to meet and keep up +with these requirements. We do not solicit donations in locations +where we have not received written confirmation of compliance. To +SEND DONATIONS or determine the status of compliance for any +particular state visit http://pglaf.org + +While we cannot and do not solicit contributions from states where we +have not met the solicitation requirements, we know of no prohibition +against accepting unsolicited donations from donors in such states who +approach us with offers to donate. + +International donations are gratefully accepted, but we cannot make +any statements concerning tax treatment of donations received from +outside the United States. U.S. laws alone swamp our small staff. + +Please check the Project Gutenberg Web pages for current donation +methods and addresses. Donations are accepted in a number of other +ways including checks, online payments and credit card donations. +To donate, please visit: http://pglaf.org/donate + + +Section 5. General Information About Project Gutenberg-tm electronic +works. + +Professor Michael S. Hart is the originator of the Project Gutenberg-tm +concept of a library of electronic works that could be freely shared +with anyone. For thirty years, he produced and distributed Project +Gutenberg-tm eBooks with only a loose network of volunteer support. + + +Project Gutenberg-tm eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the U.S. +unless a copyright notice is included. Thus, we do not necessarily +keep eBooks in compliance with any particular paper edition. + + +Most people start at our Web site which has the main PG search facility: + + http://www.gutenberg.org + +This Web site includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. |