,transcriber's ,note3 ,the angle symbol has been replaced with angle4 ,greek letters have been replaced with their transliterations in brackets1 e4 g4 a for alpha4 ,the upside-down ,omega symbol has been replaced with mho4 ,,twentieth ,,century ,,text-,,books ,,edited ,,by ,a4 ,f4 ,,nightingale1 ,,ph4,d41 ,,ll4,d4 ,,formerly ,,superintendent ,,of ,,high ,,schools1 ,,chicago ,illustration3 ,a ,,total ,,solar ,,eclipse4 ,after ,burckhalter's photographs of the eclipse of ,may #bh1 #aijj4 ,,twentieth ,,century ,,text-,,books ,a ,,text-,,book ,,of ,,astronomy ,,by ,,george ,c4 ,,comstock ,,director ,,of ,,the ,,washburn ,,observatory ,,and ,,professor ,,of ,,astronomy ,,in ,,the ,,university ,,of ,,wisconsin ,illustration ,,new ,,york ,d4 ,,appleton ,,and ,,company #aijc ,,copyright1 #aija ,,by ,d4 ,,appleton ,,and ,,company ,,preface ,the present work is not a compendium of astronomy or an outline course of popular reading in that science4 ,it has been prepared as a text-book1 and the author has purposely omitted from it much matter interesting as well as important to a complete view of the science1 and has endeavored to concentrate attention upon those parts of the subject that possess special educational value4 ,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 astronomy1 while topics1 such as the results of spectrum analysis1 which depend upon elaborate apparatus1 are in the experimental part of the work accorded much less space than their intrinsic importance would justify4 ,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 capable4 ,the instruments required are few and easily obtained4 ,with exception of a watch and a protractor1 all of the apparatus needed may be built by any one of fair mechanical talent who will follow the illustrations and descriptions of the text4 ,in order that proper opportunity for observations may be had1 the study should be pursued during the milder portion of the year1 between ,april and ,november in northern latitudes1 using clear weather for a direct study of the sky and cloudy days for book work4 ,the illustrations contained in the present work are worthy of as careful study as is the text1 and many of them are intended as an aid to experimental work and accurate measurement1 e4 g41 the star maps1 the diagrams of the planetary orbits1 pictures of the moon1 sun1 etc4 ,if the school possesses a projection lantern1 a set of astronomical slides to be used in connection with it may be made of great advantage1 if the pictures are studied as an auxiliary to ,nature4 ,mere display and scenic effect are of little value4 ,a brief bibliography of popular literature upon astronomy may be found at the end of this book1 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 reading4 ,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 students4 ,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 essay4 ,the author is under obligations to many of his professional friends who have contributed illustrative matter for his text1 and his thanks are in an especial manner due to the editors of the ,astrophysical ,journal1 ,astronomy and ,astrophysics1 and ,popular ,astronomy for permission to reproduce here plates which have appeared in those periodicals1 and to ,dr4 ,charles ,boynton1 who has kindly read and criticised the proofs4 ,,george ,c4 ,,comstock4 ,,university ,,of ,,wisconsin1 ,february1 #aija4 ,,contents ,,chapter ,,page ,i4--,,different ,,kinds ,,of ,,measurement #a ,the measurement of angles and time4 ,,ii4--,,the ,,stars ,,and ,,their ,,diurnal ,,motion #aj ,finding the stars--,their apparent motion-- ,latitude--,direction of the meridian--,sidereal time--,definitions4 ,,iii4--,,fixed ,,and ,,wandering ,,stars #bi ,apparent motion of the sun1 moon1 and planets--,orbits of the planets--,how to find the planets4 ,,iv4--,,celestial ,,mechanics #df ,kepler's laws--,newton's laws of motion--,the law of gravitation--,orbital motion--,perturbations-- ,masses of the planets--,discovery of ,neptune-- ,the tides4 ,v4--,,the ,,earth ,,as ,a ,,planet #gj ,size--,mass--,precession--,the warming of the earth--,the atmosphere--,twilight4 ,,vi4--,,the ,,measurement ,,of ,,time #hf ,solar and sidereal time--,longitude--,the calendar--,chronology4 ,,vii4--,,eclipses #aja ,their cause and nature--,eclipse limits--,eclipse maps--,recurrence and prediction of eclipses4 ,,viii4--,,instruments ,,and ,,the ,,principles ,,involved ,,in ,,their ,,use #aba ,the clock--,radiant energy--,mirrors and lenses-- ,the telescope--,camera--,spectroscope--,prin ciples of spectrum analysis4 ,,ix4--,,the ,,moon #aej ,numerical data--,phases--,motion--,librations--,lu nar topography--,physical condition4 ,x4--,,the ,,sun #agh ,numerical data--,chemical nature--,temperature-- ,visible and invisible parts--,photosphere--,spots-- ,facul--,chromosphere--,prominences--,co rona--,the sun-spot period--,the sun's rotation--,mechanical theory of the sun4 ,,xi4--,,the ,,planets #bab ,arrangement of the solar system--,bode's law-- ,physical condition of the planets--,jupiter-- ,saturn--,uranus and ,neptune--,venus--,mercury-- ,mars--,the asteroids4 ,,xii4--,,comets ,,and ,,meteors #bea ,motion1 size1 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--,collisions4 ,,xiii4--,,the ,,fixed ,,stars #bia ,number of the stars--,brightness--,distance--,proper motion--,motion in line of sight--,double stars-- ,variable stars--,new stars4 ,,xiv4--,,stars ,,and ,,nebul #ccj ,stellar colors and spectra--,classes of stars-- ,clusters--,nebul--,their spectra and physical condition--,the ,milky ,way--,construction of the heavens--,extent of the stellar system4 ,,xv4--,,growth ,,and ,,decay #ceh ,logical bases and limitations--,development of the sun--,the nebular hypothesis--,tidal friction--,roche's limit--,development of the moon--,development of stars and nebul--,the future4 ,,appendix #chc ,,index #chg ,,list ,,of ,,lithographic ,,plates ,,facing ,,page ,i4--,northern ,constellations #abd ,,ii4--,equatorial ,constellations #aij ,,iii4--,map of ,mars #bdf ,,iv4--,the ,pleiades #cdd ,protractor ,in pocket at back of book ,,list ,,of ,,full-,,page ,,illustrations ,,facing ,,page ,a ,total ,solar ,eclipse ,frontispiece ,the ,harvard ,college ,observatory1 ,cambridge1 ,mass4 #bd ,isaac ,newton #df ,galileo ,galilei #eb ,the ,lick ,observatory1 ,mount ,hamilton1 ,cal4 #fj ,the ,yerkes ,observatory1 ,williams ,bay1 ,wis4 #ajj ,the ,moon1 one day after ,first ,quarter #aej ,william ,herschel #bcd ,pierre ,simon ,laplace #cfd ,,astronomy ,,chapter ,i ,,different ,,kinds ,,of ,,measurement #a4 ,,accurate ,,measurement4--,accurate measurement is the foundation of exact science1 and at the very beginning of his study in astronomy the student should learn something of the astronomer's kind of measurement4 ,he should practice measuring the stars with all possible care1 and should seek to attain the most accurate results of which his instruments and apparatus are capable4 ,the ordinary affairs of life furnish abundant illustration of some of these measurements1 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 astronomy1 but of far greater astronomical importance than these are the measurement of angles and the measurement of time4 ,a kitchen clock or a cheap watch is usually thought of as a machine to tell the time of day1 but it may be used to time a horse or a bicycler upon a race course1 and then it becomes an instrument to measure the amount of time required for covering the length of the course4 ,astronomers use a clock in both of these ways--to tell the time at which something happens or is done1 and to measure the amount of time required for something2 and in using a clock for either purpose the student should learn to take the time from it to the nearest second or better1 if it has a seconds hand1 or to a small fraction of a minute1 by estimating the position of the minute hand between the minute marks on the dial4 ,estimate the fraction in tenths of a minute1 not in halves or quarters4 ,,exercise #a4--;,if several watches are available1 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 follows3 #b;h4 #dd4em4 ,first tap4 #b;h4 #df4dm4 #a4im4 #b;h4 #dd4im4 ,second tap4 #b;h4 #df4gm4 #a4hm4 #b;h4 #df4fm4 ,third tap4 #b;h4 #dh4fm4 #b4jm4 ,the letters h and m are used as abbreviations for hour and minute4 ,the first and second columns of the table are the record made by one student1 and second and third the record made by another4 ,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 tap1 as is shown in the last column4 ,this difference shows how much faster one watch is than the other1 and the agreement or disagreement of these differences shows the degree of accuracy of the observations4 ,keep up this practice until tenths of a minute can be estimated with fair precision4 #b4 ,,angles ,,and ,,their ,,use4--,an angle is the amount of opening or difference of direction between two lines that cross each other4 ,at twelve o'clock the hour and minute hand of a watch point in the same direction and the angle between them is zero4 ,at one o'clock the minute hand is again at ,,xii1 but the hour hand has moved to ,i1 one twelfth part of the circumference of the dial1 and the angle between the hands is one twelfth of a circumference4 ,it is customary to imagine the circumference of a dial to be cut up into #cfj equal parts--i4 e41 each minute space of an ordinary dial to be subdivided into six equal parts1 each of which is called a degree1 and the measurement of an angle consists in finding how many of these degrees are included in the opening between its sides4 ,at one o'clock the angle between the hands of a watch is thirty degrees1 which is usually written #cj1 at three o'clock it is #ij1 at six o'clock #ahj1 etc4 ,a watch may be used to measure angles4 ,how8 ,but a more convenient instrument is the protractor1 which is shown in ,fig4 #a1 applied to the angle ,a ,b ,c and showing that ,a ,b ,c #he as nearly as the protractor scale can be read4 ,the student should have and use a protractor1 such as is furnished with this book1 for the numerous exercises which are to follow4 ,illustration3 ,,fig4 #a4--;,a protractor4 ,,exercise #b4--;,draw neatly a triangle with sides about #ajj millimeters long1 measure each of its angles and take their sum4 ,no matter what may be the shape of the triangle1 this sum should be very nearly #ahj--;exactly #ahj 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 is1 that however careful we may be in our work some minute error will cling to it and our results can be only approximately correct4 ,this1 however1 should not be taken as an excuse for careless work1 but rather as a stimulus to extra effort in order that the unavoidable errors may be made as small as possible4 ,in the present case the measured angles may be improved a little by adding 7algebraically7 to each of them one third of the amount by which their sum falls short of #ahj1 as in the following example3 ,measured angles4 ,correction4 ,corrected angles4 ,a #gc4d #j4a #gc4e ,b #di4c #j4a #di4d ,c #eg4j #j4a #eg4a ----- ----- ,sum #agi4g #ahj4j ,defect #j4c ,this process is in very common use among astronomers1 and is called adjusting the observations4 ,illustration3 ,,fig4 #b4--,triangulation4 #c4 ,,triangles4--,the instruments used by astronomers for the measurement of angles are usually provided with a telescope1 which may be pointed at different objects1 and with a scale1 like that of the protractor1 to measure the angle through which the telescope is turned in passing from one object to another4 ,in this way it is possible to measure the angle between lines drawn from the instrument to two distant objects1 such as two church steeples or the sun and moon1 and this is usually called the angle between the objects4 ,by measuring angles in this way it is possible to determine the distance to an inaccessible point1 as shown in ,fig4 #b4 ,a surveyor at ,a desires to know the distance to ,c1 on the opposite side of a river which he can not cross4 ,he measures with a tape line along his own side of the stream the distance ,a ,b #ajj yards and then1 with a suitable instrument1 measures the angle at ,a between the points ,c and ,b1 and the angle at ,b between ,c and ,a1 finding ,b ,a ,c #gc4d1 ,a ,b ,c #di4c4 ,to determine the distance ,a ,c he draws upon paper a line #ajj millimeters long1 and marks the ends a and b2 with a protractor he constructs at a the angle b a c #gc4d1 and at b the angle a b c #di4c1 and marks by c the point where the two lines thus drawn meet4 ,with the millimeter scale he now measures the distance a c #ij4b millimeters1 which determines the distance ,a ,c across the river to be #ij4b yards1 since the triangle on paper has been made similar to the one across the river1 and millimeters on the one correspond to yards on the other4 ,what is the proposition of geometry upon which this depends8 ,the measured distance ,a ,b in the surveyor's problem is called a base line4 ,,exercise #c4--,with a foot rule and a protractor measure a base line and the angles necessary to determine the length of the schoolroom4 ,after the length has been thus found1 measure it directly with the foot rule and compare the measured length with the one found from the angles4 ,if any part of the work has been carelessly done1 the student need not expect the results to agree4 ,illustration3 ,,fig4 #c4--;,finding the moon's distance from the earth4 ,in the same manner1 by sighting at the moon from widely different parts of the earth1 as in ,fig4 #c1 the moon's distance from us is found to be about a quarter of a million miles4 ,what is the base line in this case8 #d4 ,,the ,,horizon--,,altitudes4--,in their observations astronomers and sailors make much use of the plane of the horizon1 and practically any flat and level surface1 such as that of a smooth pond1 may be regarded as a part of this plane and used as such4 ,a very common observation relating to the plane of the horizon is called taking the sun's altitude1 and consists in measuring the angle between the sun's rays and the plane of the horizon upon which they fall4 ,this angle between a line and a plane appears slightly different from the angle between two lines1 but is really the same thing1 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 sun4 ,compare this with the definition given in the geographies1 ,the latitude of a point on the earth's surface is its angular distance north or south of the equator1 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 surface4 ,a convenient method of obtaining a part of the plane of the horizon for use in observation is as follows3 ,place a slate or a pane of glass upon a table in the sunshine4 ,slightly moisten its whole surface and then pour a little more water upon it near the center4 ,if the water runs toward one side1 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 another2 it is then level and a part of the plane of the horizon4 ,get several wedges ready before commencing the experiment4 ,after they have been properly placed1 drive a pin or tack behind each one so that it may not slip4 #e4 ,,taking ,,the ,,sun',s ,,altitude4 ,,exercise #d4--,prepare a piece of board #bj centimeters1 or more1 square1 planed smooth on one face and one edge4 ,drive a pin perpendicularly into the face of the board1 near the middle of the planed edge4 ,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 plane4 ,stick another pin into the board1 near its upper edge1 so that its shadow shall fall exactly upon the shadow of the first pin1 and with a watch or clock observe the time at which the two shadows coincide4 ,without lifting the board from the plane1 turn it around so that the opposite edge is directed toward the sun and set a third pin just as the second one was placed1 and again take the time4 ,remove the pins and draw fine pencil lines1 connecting the holes1 as shown in ,fig4 #d1 and with the protractor measure the angle thus marked4 ,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 figure4 ,illustration3 ,,fig4 #d4--,taking the sun's altitude4 ,when the board is turned edgewise toward the sun so that its shadow is as thin as possible1 rule a pencil line alongside it on the horizon plane4 ,the angle which this line makes with a line pointing due south is called the sun's azimuth4 ,when the sun is south1 its azimuth is zero2 when west1 it is #ij2 when east1 #bgj1 etc4 ,,exercise #e4--,let a number of different students take the sun's altitude during both the morning and afternoon session and note the time of each observation1 to the nearest minute4 ,verify the setting of the plane of the horizon from time to time1 to make sure that no change has occurred in it4 #f4 ,,graphical ,,representations4--,make a graph 7drawing7 of all the observations1 similar to ,fig4 #e1 and find by bisecting a set of chords g to g1 e to e1 d to d1 drawn parallel to ,b ,b1 the time at which the sun's altitude was greatest4 ,in ,fig4 #e we see from the intersection of ,m ,m with ,b ,b that this time was #aa;h4 #ejm4 ,the method of graphs which is here introduced is of great importance in physical science1 and the student should carefully observe in ,fig4 #e that the line ,b ,b is a scale of times1 which may be made long or short1 provided only the intervals between consecutive hours #i to #aj1 #aj to #aa1 #aa to #ab1 etc41 are equal4 ,the distance of each little circle from ,b ,b is taken proportional to the sun's altitude1 and may be upon any desired scale--e4 g41 a millimeter to a degree--provided the same scale is used for all observations4 ,each circle is placed accurately over that part of the base line which corresponds to the time at which the altitude was taken4 ,square ruled paper is very convenient1 although not necessary1 for such diagrams4 ,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 altitude1 and this curve shows the altitude of the sun at every moment between #i ,a4 ,m4 and #c ,p4 ,m4 ,in ,fig4 #e the sun's altitude at noon was #eg4 ,what was it at half past two8 ,illustration3 ,,fig4 #e4--;,a graph of the sun's altitude4 #g4 ,,diameter ,,of ,a ,,distant ,,object4--,by sighting over a protractor1 measure the angle between imaginary lines drawn from it to the opposite sides of a window4 ,carry the protractor farther away from the window and repeat the experiment1 to see how much the angle changes4 ,the angle thus measured is called the angle subtended by the window at the place where the measurement was made4 ,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--e4 g41 a millimeter for each centimeter of real distance4 ,if a cross line be now drawn connecting the points thus found1 its length will be proportional to the width of the window1 and the width may be read off to scale1 a centimeter for every millimeter in the length of the cross line4 ,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 has1 in fact1 found it to be #b1afc miles4 ,can the same method be used to find the diameter of the sun8 ,a planet8 ,the earth8 ,,chapter ,,ii ,,the ,,stars ,,and ,,their ,,diurnal ,,motion #h4 ,,the ,,stars4--,from the very beginning of his study in astronomy1 and as frequently as possible1 the student should practice watching the stars by night1 to become acquainted with the constellations and their movements4 ,as an introduction to this study he may face toward the north1 and compare the stars which he sees in that part of the sky with the map of the northern heavens1 given on ,plate ,i1 opposite page #abd4 ,turn the map around1 upside down if necessary1 until the stars upon it match the brighter ones in the sky4 ,note how the stars are grouped in such conspicuous constellations as the ,big ,dipper 7,ursa ,major71 the ,little ,dipper 7,ursa ,minor71 and ,cassiopeia4 ,these three constellations should be learned so that they can be recognized at any time4 ,the names of the stars4--,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 constellations4 ,these names are for the most part a ,greek letter prefixed to the genitive case of the ,latin name of the constellation4 7,see the ,greek alphabet printed at the end of the book47 #i4 ,,magnitudes ,,of ,,the ,,stars4--,nearly nineteen centuries ago ,st4 ,paul noted that one star differeth from another star in glory1 and no more apt words can be found to mark the difference of brightness which the stars present4 ,even prior to ,st4 ,paul's day the ancient ,greek astronomers had divided the stars in respect of brightness into six groups1 which the modern astronomers still use1 calling each group a magnitude4 ,thus a few of the brightest stars are said to be of the first magnitude1 the great mass of faint ones which are just visible to the unaided eye are said to be of the sixth magnitude1 and intermediate degrees of brilliancy are represented by the intermediate magnitudes1 second1 third1 fourth1 and fifth4 ,the student must not be misled by the word magnitude4 ,it has no reference to the size of the stars1 but only to their brightness1 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 magnitudes4 ,following the indications of these maps1 the student should1 in learning the principal stars and constellations1 learn also to recognize how bright is a star of the second1 fourth1 or other magnitude4 #aj4 ,,observing ,,the ,,stars4--,find on the map and in the sky the stars a ,urs ,minoris1 a ,urs ,majoris1 b ,urs ,majoris4 ,what geometrical figure will fit on to these stars8 ,in addition to its regular name1 a ,urs ,minoris is frequently called by the special name ,polaris1 or the pole star4 ,why are the other two stars called the ,pointers8 ,what letter of the alphabet do the five bright stars in ,cassiopeia suggest8 ,,exercise #f4--,stand in such a position that ,polaris is just hidden behind the corner of a building or some other vertical line1 and mark upon the key map as accurately as possible the position of this line with respect to the other stars1 showing which stars are to the right and which are to the left of it4 ,record the time 7date1 hour1 and minute7 at which this observation was made4 ,an hour or two later repeat the observation at the same place1 draw the line and note the time1 and you will find that the line last drawn upon the map does not agree with the first one4 ,the stars have changed their positions1 and with respect to the vertical line the ,pointers are now in a different direction from ,polaris4 ,measure with a protractor the angle between the two lines drawn in the map1 and use this angle and the recorded times of the observation to find how many degrees per hour this direction is changing4 ,it should be about #ae per hour4 ,if the observation were repeated #ab hours after the first recorded time1 what would be the position of the vertical line among the stars8 ,what would it be #bd hours later8 ,a week later8 ,repeat the observation on the next clear night1 and allowing for the number of whole revolutions made by the stars between the two dates1 again determine from the time interval a more accurate value of the rate at which the stars move4 ,the motion of the stars which the student has here detected is called their diurnal motion4 ,what is the significance of the word diurnal8 ,in the preceding paragraph there is introduced a method of great importance in astronomical practice--i4 e41 determining something--in this case the rate per hour1 from observations separated by a long interval of time1 in order to get a more accurate value than could be found from a short interval4 ,why is it more accurate8 ,to determine the rate at which the planet ,mars rotates about its axis1 astronomers use observations separated by an interval of more than #bjj years1 during which the planet made more than #ge1jjj revolutions upon its axis4 ,if we were to write out in algebraic form an equation for determining the length of one revolution of ,mars about its axis1 the large number1 #ge1jjj1 would appear in the equation as a divisor1 and in the final result would greatly reduce whatever errors existed in the observations employed4 ,repeat ,exercise #f night after night1 and note whether the stars come back to the same position at the same hour and minute every night4 ,illustration3 ,,fig4 #f4 ,the plumb-line apparatus4 ,illustration3 ,,fig4 #g4 ,the plumb-line apparatus4 #aa4 ,,the ,,plumb-,,line ,,apparatus4--,this experiment1 and many others1 may be conveniently and accurately made with no other apparatus than a plumb line1 and a device for sighting past it4 ,in ,figs4 #f and #g there is shown a simple form of such apparatus1 consisting essentially of a board which rests in a horizontal position upon the points of three screws that pass through it4 ,this board carries a small box1 to one side of which is nailed in vertical position another board #e or #f feet long to carry the plumb line4 ,this consists of a wire or fish line with any heavy weight--e4 g41 a brick or flatiron--tied to its lower end and immersed in a vessel of water placed inside the box1 so as to check any swinging motion of the weight4 ,in the cover of the box is a small hole through which the wire passes1 and by turning the screws in the baseboard the apparatus may be readily leveled1 so that the wire shall swing freely in the center of the hole without touching the cover of the box4 ,guy wires1 shown in the figure1 are applied so as to stiffen the whole apparatus4 ,a board with a screw eye at each end may be pivoted to the upright1 as in ,fig4 #f1 for measuring altitudes2 or to the box1 as in ,fig4 #g1 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 looks4 ,the whole apparatus may be constructed by any person of ordinary mechanical skill at a very small cost1 and it or something equivalent should be provided for every class beginning observational astronomy4 ,to use the apparatus for the experiment of #aj1 it should be leveled1 and the board with the screw eyes1 attached as in ,fig4 #g1 should be turned until the observer1 looking through the screw eye1 sees ,polaris exactly behind the wire4 ,use a bicycle lamp to illumine the wire by night4 ,the apparatus is now adjusted1 and the observer has only to wait for the stars which he desires to observe1 and to note by his watch the time at which they pass behind the wire4 ,it will be seen that the wire takes the place of the vertical edge of the building1 and that the board with the screw eyes is introduced solely to keep the observer in the right place relative to the wire4 #ab4 ,a ,,sidereal ,,clock4--,clocks are sometimes so made and regulated that they show always the same hour and minute when the stars come back to the same place1 and such a timepiece is called a sidereal clock--i4 e41 a star-time clock4 ,would such a clock gain or lose in comparison with an ordinary watch8 ,could an ordinary watch be turned into a sidereal watch by moving the regulator8 ,illustration3 ,,fig4 #h4--,photographing the circumpolar stars4--,,barnard4 #ac4 ,,photographing ,,the ,,stars4--,,exercise #g4--;,for any student who uses a camera4 ,upon some clear and moonless night point the camera1 properly focused1 at ,polaris1 and expose a plate for three or four hours4 ,upon developing the plate you should find a series of circular trails such as are shown in ,fig4 #h1 only longer4 ,each one of these is produced by a star moving slowly over the plate1 in consequence of its changing position in the sky4 ,the center indicated by these curved trails is called the pole of the heavens4 ,it is that part of the sky toward which is pointed the axis about which the earth rotates1 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 still1 just as trees and fences and telegraph poles stand still1 although to the passenger upon a railway train they appear to be in rapid motion4 ,so far as simple observations are concerned1 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 one1 and1 following the custom of astronomers1 we shall habitually speak as if it were a real movement of the stars4 ,how long was the plate exposed in photographing ,fig4 #h8 #ad4 ,,finding ,,the ,,stars4--,on ,plate ,i1 opposite page #abd1 the pole of the heavens is at the center of the map1 near ,polaris1 and the heavy trail near the center of ,fig4 #h is made by ,polaris4 ,see if you can identify from the map any of the stars whose trails show in the photograph4 ,the brighter the star the bolder and heavier its trail4 ,find from the map and locate in the sky the two bright stars ,capella and ,vega1 which are on opposite sides of ,polaris and nearly equidistant from it4 ,do these stars share in the motion around the pole8 ,are they visible on every clear night1 and all night8 ,observe other bright stars farther from ,polaris than are ,vega and ,capella and note their movement4 ,do they move like the sun and moon8 ,do they rise and set8 ,in what part of the sky do the stars move most rapidly1 near the pole or far from it8 ,how long does it take the fastest moving stars to make the circuit of the sky and come back to the same place8 ,how long does it take the slow stars8 #ae4 ,,rising ,,and ,,setting ,,of ,,the ,,stars4--,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 night4 ,the same star is sometimes high in the sky1 sometimes low1 sometimes to the east of the pole and at other times west of it1 but is always above the horizon4 ,such stars are said to be circumpolar4 ,a little farther from the pole each star1 when at the lowest point of its circular path1 dips for a time below the horizon and is lost to view1 and the farther it is away from the pole the longer does it remain invisible1 until1 in the case of stars #ij away from the pole1 we find them hidden below the horizon for twelve hours out of every twenty-four 7see ,fig4 #i74 ,the sun is such a star1 and in its rising and setting acts precisely as does every other star at a similar distance from the pole--only1 as we shall find later1 each star keeps always at 7nearly7 the same distance from the pole1 while the sun in the course of a year changes its distance from the pole very greatly1 and thus changes the amount of time it spends above and below the horizon1 producing in this way the long days of summer and the short ones of winter4 ,illustration3 ,,fig4 #i4--;,diurnal motion of the northern constellations4 ,how much time do stars which are more than #ij from the pole spend above the horizon8 ,we say in common speech that the sun rises in the east1 but this is strictly true only at the time when it is #ij distant from the pole--i4 e41 in ,march and ,september4 ,at other seasons it rises north or south of east according as its distance from the pole is less or greater than #ij1 and the same is true for the stars4 #af4 ,,the ,,geography ,,of ,,the ,,sky4--,find from a map the latitude and longitude of your schoolhouse4 ,find on the map the place whose latitude is #ci and longitude #gg west of the meridian of ,greenwich4 ,is there any other place in the world which has the same latitude and longitude as your schoolhouse8 ,the places of the stars in the sky are located in exactly the manner which is illustrated by these geographical questions1 only different names are used4 ,instead of latitude the astronomer says declination1 in place of longitude he says right ascension1 in place of meridian he says hour circle1 but he means by these new names the same ideas that the geographer expresses by the old ones4 ,imagine the earth swollen up until it fills the whole sky2 the earth's equator would meet the sky along a line 7a great circle7 everywhere #ij distant from the pole1 and this line is called the celestial equator4 ,trace its position along the middle of the map opposite page #aij and notice near what stars it runs4 ,every meridian of the swollen earth would touch the sky along an hour circle--i4 e41 a great circle passing through the pole and therefore perpendicular to the equator4 ,note that in the map one of these hour circles is marked #j4 ,it plays the same part in measuring right ascensions as does the meridian of ,greenwich in measuring longitudes2 it is the beginning1 from which they are reckoned4 ,note also1 at the extreme left end of the map1 the four bright stars in the form of a square1 one side of which is parallel and close to the hour circle1 which is marked #j4 ,this is familiarly called the ,great ,square in ,pegasus1 and may be found high up in the southern sky whenever the ,big ,dipper lies below the pole4 ,why can it not be seen when ,ursa ,major is above the pole8 ,astronomers use the right ascensions of the stars not only to tell in what part of the sky the star is placed1 but also in time reckonings1 to regulate their sidereal clocks1 and with regard to this use they find it convenient to express right ascension not in degrees but in hours1 #bd of which fill up the circuit of the sky and each of which is equal to #ae of arc1 #bd #ae #cfj4 ,the right ascension of ,capella is #e;h4 #im4 #gg4b1 but the student should accustom himself to using it in hours and minutes as given and not to change it into degrees4 ,he should also note that some stars lie on the side of the celestial equator toward ,polaris1 and others are on the opposite side1 so that the astronomer has to distinguish between north declinations and south declinations1 just as the geographer distinguishes between north latitudes and south latitudes4 ,this is done by the use of the and - signs1 a denoting that the star lies north of the celestial equator1 i4 e41 toward ,polaris4 ,illustration3 ,,fig4 #aj4--;,from a photograph of the ,pleiades4 ,find on ,plate ,,ii1 opposite page #aij1 the ,pleiades 7,pleades71 ,r4 ,a4 #c;h4 #dbm41 ,dec4 #bc4h4 ,why do they not show on ,plate ,i1 opposite page #abd8 ,in what direction are they from ,polaris8 ,this is one of the finest star clusters in the sky1 but it needs a telescope to bring out its richness4 ,see how many stars you can count in it with the naked eye1 and afterward examine it with an opera glass4 ,compare what you see with ,fig4 #aj4 ,find ,antares1 ,r4 ,a4 #af;h4 #bcm4 ,dec4 -#bf4b4 ,how far is it1 in degrees1 from the pole8 ,is it visible in your sky8 ,if so1 what is its color8 ,find the ,r4 ,a4 and ,dec4 of a ,urs ,majoris2 of b ,urs ,majoris2 of ,polaris4 ,find the ,northern ,crown1 ,corona ,borealis1 ,r4 ,a4 #ae;h4 #cjm41 ,dec4 #bg4j2 the ,beehive1 ,prsepe1 ,r4 ,a4 #h;h4 #ccm41 ,dec4 #bj4d4 ,these should be looked up1 not only on the map1 but also in the sky4 #ag4 ,,reference ,,lines ,,and ,,circles4--,as the stars move across the sky in their diurnal motion1 they carry the framework of hour circles and equator with them1 so that the right ascension and declination of each star remain unchanged by this motion1 just as longitudes and latitudes remain unchanged by the earth's rotation4 ,they are the same when a star is rising and when it is setting2 when it is above the pole and when it is below it4 ,during each day the hour circle of every star in the heavens passes overhead1 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--i4 e41 at that particular moment they stand directly over the observer's geographical meridian and upon the corresponding celestial meridian4 ,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 pole4 ,in ,fig4 #aa the inner circle represents the terrestrial meridian of a certain place1 ,o1 as seen from the center of the earth1 ,c1 and the outer circle represents the celestial meridian of ,o as seen from ,c1 only we must imagine1 what can not be shown on the figure1 that the outer circle is so large that the inner one shrinks to a mere point in comparison with it4 ,if ,c ,p represents the direction in which the earth's axis passes through the center1 then ,c ,e at right angles to it must be the direction of the equator which we suppose to be turned edgewise toward us2 and if ,c ,o is the direction of some particular point on the earth's surface1 then ,z directly overhead is called the zenith of that point1 upon the celestial sphere4 ,the line ,c ,h represents a direction parallel to the horizon plane at ,o1 and ,h ,c ,p is the angle which the axis of the earth makes with this horizon plane4 ,the arc ,o ,e measures the latitude of ,o1 and the arc ,z ,e measures the declination of ,z1 and since by elementary geometry each of these arcs contains the same number of degrees as the angle ,e ,c ,z1 we have the ,theorem4--,the latitude of any place is equal to the declination of its zenith4 ,corollary4--,any star whose declination is equal to your latitude will once in each day pass through your zenith4 ,illustration3 ,,fig4 #aa4--,reference lines and circles4 #ah4 ,,latitude4--,from the construction of the figure angle ,e ,c ,z angle ,z ,c ,p #ij angle ,h ,c ,p angle ,z ,c ,p #ij from which we find by subtraction and transposition angle ,e ,c ,z angle ,h ,c ,p and this gives the further ,theorem4--,the latitude of any place is equal to the elevation of the pole above its horizon plane4 ,an observer who travels north or south over the earth changes his latitude1 and therefore changes the angle between his horizon plane and the axis of the earth4 ,what effect will this have upon the position of stars in his sky8 ,if you were to go to the earth's equator1 in what part of the sky would you look for ,polaris8 ,can ,polaris be seen from ,australia8 ,from ,south ,america8 ,if you were to go from ,minnesota to ,texas1 in what respect would the appearance of stars in the northern sky be changed8 ,how would the appearance of stars in the southern sky be changed8 ,illustration3 ,,fig4 #ab4--;,diurnal path of ,polaris4 ,,exercise #h4--;,determine your latitude by taking the altitude of ,polaris when it is at some one of the four points of its diurnal path1 shown in ,fig4 #ab4 ,when it is at #a it is said to be at upper culmination1 and the star z ,urs ,majoris in the handle of the ,big ,dipper will be directly below it4 ,when at #b it is at western elongation1 and the star ,castor is near the meridian4 ,when it is at #c it is at lower culmination1 and the star ,spica is on the meridian4 ,when it is at #d it is at eastern elongation1 and ,altair is near the meridian4 ,all of these stars are conspicuous ones1 which the student should find upon the map and learn to recognize in the sky4 ,the altitude observed at either #b or #d may be considered equal to the latitude of the place1 but the altitude observed when ,polaris is at the positions marked #a and #c must be corrected for the star's distance from the pole1 which may be assumed equal to #a4c4 ,the plumb-line apparatus described at page #ab is shown in ,fig4 #f slightly modified1 so as to adapt it to measuring the altitudes of stars4 ,note that the board with the screw eye at one end has been transferred from the box to the vertical standard1 and has a screw eye at each end4 ,when the apparatus has been properly leveled1 so that the plumb line hangs at the middle of the hole in the box cover1 the board is to be pointed at the star by sighting through the centers of the two screw eyes1 and a pencil line is to be ruled along its edge upon the face of the vertical standard4 ,after this has been done turn the apparatus halfway around so that what was the north side now points south1 level it again and revolve the board about the screw which holds it to the vertical standard1 until the screw eyes again point to the star4 ,rule another line along the same edge of the board as before and with a protractor measure the angle between these lines4 ,use a bicycle lamp if you need artificial light for your work4 ,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 star4 ,after you have determined your latitude from ,polaris1 compare the result with your position as shown upon the best map available4 ,with a little practice and considerable care the latitude may be thus determined within one tenth of a degree1 which is equivalent to about #g miles4 ,if you go #aj 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 apparatus4 #ai4 ,,the ,,meridian ,,line4--,to establish a true north and south line upon the ground1 use the apparatus as described at page #ac1 and when ,polaris is at upper or lower culmination drive into the ground two stakes in line with the star and the plumb line4 ,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 which1 if possible1 all parts of the sky are visible4 ,june and ,november are convenient months for this exercise1 since ,polaris then comes to culmination early in the evening4 #bj4 ,,time4--,what is the time at which school begins in the morning8 ,what do you mean by the time8 ,the sidereal time at any moment is the right ascension of the hour circle which at that moment coincides with the meridian4 ,when the hour circle passing through ,sirius coincides with the meridian1 the sidereal time is #f;h4 #djm41 since that is the right ascension of ,sirius1 and in astronomical language ,sirius is on the meridian at #f;h4 #djm4 sidereal time4 ,as may be seen from the map1 this #f;h4 #djm4 is the right ascension of ,sirius1 and if a clock be set to indicate #f;h4 #djm4 when ,sirius crosses the meridian1 it will show sidereal time4 ,if the clock is properly regulated1 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 star4 ,a clock properly regulated for this purpose will gain about four minutes per day in comparison with ordinary clocks1 and when so regulated it is called a sidereal clock4 ,the student should be provided with such a clock for his future work1 but one such clock will serve for several persons1 and a nutmeg clock or a watch of the cheapest kind is quite sufficient4 ,illustration3 ,,the ,,harvard ,,college ,,observatory1 ,,cambridge1 ,,mass4 ,,exercise #i4--,set such a clock to sidereal time by means of the transit of a star over your meridian4 ,for this experiment it is presupposed that a meridian line has been marked out on the ground as in #ai1 and the simplest mode of performing the experiment required is for the observer1 having chosen a suitable star in the southern part of the sky1 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 line4 ,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 star4 ,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 time4 ,a more accurate mode of performing the experiment consists in using the plumb-line apparatus carefully adjusted1 as in ,fig4 #g1 so that the line joining the wire to the center of the screw eye shall be parallel to the meridian line4 ,observe the time by the clock at which the star disappears behind the wire as seen through the center of the screw eye4 ,if the star is too high up in the sky for convenient observation1 place a mirror1 face up1 just north of the screw eye and observe star1 wire and screw eye by reflection in it4 ,the numerical right ascension of the observed star is needed for this experiment1 and it may be measured from the star map1 but it will usually be best to observe one of the stars of the table at the end of the book1 and to obtain its right ascension as follows3 ,the table gives the right ascension and declination of each star as they were at the beginning of the year #aijj1 but on account of the precession 7see ,chapter ,v71 these numbers all change slowly with the lapse of time1 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 #aijj--;i4 e41 in #aiaj the right ascension of the first star of the table will be #j;h4 #ch4fm4 7#aj_/bj7m4 #j;h4 #ci4am4 ,the declinations also change slightly1 but as they are only intended to help in finding the star on the star maps1 their change may be ignored4 ,having set the clock approximately to sidereal time1 observe one or two more stars in the same way as above4 ,the difference between the observed time and the right ascension1 if any is found1 is the correction of the clock4 ,this correction ought not to exceed a minute if due care has been taken in the several operations prescribed4 ,the relation of the clock to the right ascension of the stars is expressed in the following equation1 with which the student should become thoroughly familiar3 ,a ,t ,u ,t stands for the time by the clock at which the star crossed the meridian4 ,a is the right ascension of the star1 and ,u is the correction of the clock4 ,use the sign in the equation whenever the clock is too slow1 and the - sign when it is too fast4 ,u may be found from this equation when ,a and ,t are given1 or ,a may be found when ,t and ,u are given4 ,it is in this way that astronomers measure the right ascensions of the stars and planets4 ,determine ,u from each star you have observed1 and note how the several results agree one with another4 #ba4 ,,definitions4--,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 idea4 ,if a definition does not come up to this standard it is insufficient4 ,anything beyond this requirement is certainly useless and probably mischievous4 ,let the student define the following geographical terms1 and let him also criticise the definitions offered by his fellow-students3 ,equator1 poles1 meridian1 latitude1 longitude1 north1 south1 east1 west4 ,compare the following astronomical definitions with your geographical definitions1 and criticise them in the same way4 ,if you are not able to improve upon them1 commit them to memory3 ,the ,poles of the heavens are those points in the sky toward which the earth's axis points4 ,how many are there8 ,the one near ,polaris is called the north pole4 ,the ,celestial ,equator is a great circle of the sky distant #ij from the poles4 ,the ,zenith is that point of the sky1 overhead1 toward which a plumb line points4 ,why is the word overhead placed in the definition8 ,is there more than one zenith8 ,the ,horizon is a great circle of the sky #ij distant from the zenith4 ,an ,hour ,circle is any great circle of the sky which passes through the poles4 ,every star has its own hour circle4 ,the ,meridian is that hour circle which passes through the zenith4 ,a ,vertical ,circle is any great circle that passes through the zenith4 ,is the meridian a vertical circle8 ,the ,declination of a star is its angular distance north or south of the celestial equator4 ,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 ,equinox4 ,from spherical geometry we learn that this angle is to be measured either at the pole where the two hour circles intersect1 as is done in the star map opposite page #abd1 or along the equator1 as is done in the map opposite page #aij4 ,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--i4 e41 from west toward east4 ,the ,altitude of a star is its angular distance above the horizon4 ,the ,azimuth of a star is the angle between the meridian and the vertical circle passing through the star4 ,a star due south has an azimuth of #j4 ,due west1 #ij4 ,due north1 #ahj4 ,due east1 #bgj4 ,what is the azimuth of ,polaris in degrees8 ,what is the azimuth of the sun at sunrise8 ,at sunset8 ,at noon8 ,are these azimuths the same on different days8 ,the ,hour ,angle of a star is the angle between its hour circle and the meridian4 ,it is measured from the meridian in the direction in which the stars appear to travel in their diurnal motion--i4 e41 from east toward west4 ,what is the hour angle of the sun at noon8 ,what is the hour angle of ,polaris when it is at the lowest point in its daily motion8 #bb4 ,,exercises4--,the student must not be satisfied with merely learning these definitions4 ,he must learn to see these points and lines in his mind as if they were visibly painted upon the sky4 ,to this end it will help him to note that the poles1 the zenith1 the meridian1 the horizon1 and the equator seem to stand still in the sky1 always in the same place with respect to the observer1 while the hour circles and the vernal equinox move with the stars and keep the same place among them4 ,does the apparent motion of a star change its declination or right ascension8 ,what is the hour angle of the sun when it has the greatest altitude8 ,will your answer to the preceding question be true for a star8 ,what is the altitude of the sun after sunset8 ,in what direction is the north pole from the zenith8 ,from the vernal equinox8 ,where are the points in which the meridian and equator respectively intersect the horizon8 ,,chapter ,,iii ,,fixed ,,and ,,wandering ,,stars #bc4 ,,star ,,maps4--,select from the map some conspicuous constellation that will be conveniently placed for observation in the evening1 and make on a large scale a copy of all the stars of the constellation that are shown upon the map4 ,at night compare this copy with the sky1 and mark in upon your paper all the stars of the constellation which are not already there4 ,both the original drawing and the additions made to it by night should be carefully done1 and for the latter purpose what is called the method of allineations may be used with advantage--i4 e41 the new star is in line with two already on the drawing and is midway between them1 or it makes an equilateral triangle with two others1 or a square with three others1 etc4 ,a series of maps of the more prominent constellations1 such as ,ursa ,major1 ,cassiopea1 ,pegasus1 ,taurus1 ,orion1 ,gemini1 ,canis ,major1 ,leo1 ,corvus1 ,bootes1 ,virgo1 ,hercules1 ,lyra1 ,aquila1 ,scorpius1 should be constructed in this manner upon a uniform scale and preserved as a part of the student's work4 ,let the magnitude of the stars be represented on the maps as accurately as may be1 and note the peculiarity of color which some stars present4 ,for the most part their color is a very pale yellow1 but occasionally one may be found of a decidedly ruddy hue--e4 g41 ,aldebaran or ,antares4 ,such a star map1 not quite complete1 is shown in ,fig4 #ac4 ,so1 too1 a sharp eye may detect that some stars do not remain always of the same magnitude1 but change their brightness from night to night1 and this not on account of cloud or mist in the atmosphere1 but from something in the star itself4 ,algol is one of the most conspicuous of these variable stars1 as they are called4 ,illustration3 ,,fig4 #ac4--,star map of the region about ,orion4 #bd4 ,,the ,,moon',s ,,motion ,,among ,,the ,,stars4--,whenever the moon is visible note its position among the stars by allineations1 and plot it on the key map opposite page #aij4 ,keep a record of the day and hour corresponding to each such observation4 ,you will find1 if the work is correctly done1 that the positions of the moon all fall near the curved line shown on the map4 ,this line is called the ecliptic4 ,after several such observations have been made and plotted1 find by measurement from the map how many degrees per day the moon moves4 ,how long would it require to make the circuit of the heavens and come back to the starting point8 ,on each night when you observe the moon1 make on a separate piece of paper a drawing of it about #aj centimeters in diameter and show in the drawing every feature of the moon's face which you can see--e4 g41 the shape of the illuminated surface 7phase72 the direction among the stars of the line joining the horns2 any spots which you can see upon the moon's face1 etc4 ,an opera glass will prove of great assistance in this work4 ,use your drawings and the positions of the moon plotted upon the map to answer the following questions3 ,does the direction of the line joining the horns have any special relation to the ecliptic8 ,does the amount of illuminated surface of the moon have any relation to the moon's angular distance from the sun8 ,does it have any relation to the time at which the moon sets8 ,do the spots on the moon when visible remain always in the same place8 ,do they come and go8 ,do they change their position with relation to each other8 ,can you determine from these spots that the moon rotates about an axis1 as the earth does8 ,in what direction does its axis point8 ,how long does it take to make one revolution about the axis8 ,is there any day and night upon the moon8 ,each of these questions can be correctly answered from the student's own observations without recourse to any book4 #be4 ,,the ,,sun ,,and ,,its ,,motion4--,examine the face of the sun through a smoked glass to see if there is anything there that you can sketch4 ,by day as well as by night the sky is studded with stars1 only they can not be seen by day on account of the overwhelming glare of sunlight1 but the position of the sun among the stars may be found quite as accurately as was that of the moon1 by observing from day to day its right ascension and declination1 and this should be practiced at noon on clear days by different members of the class4 ,,exercise #aj4--,the right ascension of the sun may be found by observing with the sidereal clock the time of its transit over the meridian4 ,use the equation in #bj1 and substitute in place of ,u the value of the clock correction found from observations of stars on a preceding or following night4 ,if the clock gains or loses with respect to sidereal time1 take this into account in the value of ,u4 ,,exercise #aa4--,to determine the sun's declination1 measure its altitude at the time it crosses the meridian4 ,use either the method of ,exercise #d1 or that used with ,polaris in ,exercise #h4 ,the student should be able to show from ,fig4 #aa that the declination is equal to the sum of the altitude and the latitude of the place diminished by #ij1 or in an equation ,declination ,altitude ,latitude - #ij4 ,if the declination as found from this equation is a negative number it indicates that the sun is on the south side of the equator4 ,the right ascension and declination of the sun as observed on each day should be plotted on the map and the date1 written opposite it4 ,if the work has been correctly done1 the plotted points should fall upon the curved line 7ecliptic7 which runs lengthwise of the map4 ,this line1 in fact1 represents the sun's path among the stars4 ,note that the hours of right ascension increase from #j up to #bd1 while the numbers on the clock dial go only from #j to #ab1 and then repeat #j to #ab again during the same day4 ,when the sidereal time is #ac hours1 #ad hours1 etc41 the clock will indicate #a hour1 #b hours1 etc41 and #ab hours must then be added to the time shown on the dial4 ,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 times1 and he should determine from his observations1 as accurately as possible1 the date and hour of this crossing and the point on the equator at which the sun crosses it4 ,these points are called the equinoxes1 ,vernal ,equinox and ,autumnal ,equinox for the spring and autumn crossings respectively1 and the student will recall that the vernal equinox is the point from which right ascensions are measured4 ,its position among the stars is found by astronomers from observations like those above described1 only made with much more elaborate apparatus4 ,similar observations made in ,june and ,december show that the sun's midday altitude is about #dg greater in summer than in winter4 ,they show also that the sun is as far north of the equator in ,june as he is south of it in ,december1 from which it is easily inferred that his path1 the ecliptic1 is inclined to the equator at an angle of #bc4e1 one half of #dg4 ,this angle is called the obliquity of the ecliptic4 ,the student may recall that in the geographies the torrid zone is said to extend #bc4e on either side of the earth's equator4 ,is there any connection between these limits and the obliquity of the ecliptic8 ,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 zenith8 ,,exercise #ab4--;,after a half dozen observations of the sun have been plotted upon the map1 find by measurement the rate1 in degrees per day1 at which the sun moves along the ecliptic4 ,how many days will be required for it to move completely around the ecliptic from vernal equinox back to vernal equinox again8 ,accurate observations with the elaborate apparatus used by professional astronomers show that this period1 which is called a tropical year1 is #cfe days #e hours #dh minutes #df seconds4 ,is this the same as the ordinary year of our calendars8 #bf4 ,,the ,,planets4--,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 maps1 and to have found also that these stars do not remain fixed in position among their fellows1 but wander about from one constellation to another4 ,observe the motion of one of these planets from night to night and plot its positions on the star map1 precisely as was done for the moon4 ,what kind of path does it follow8 ,both the ancient ,greeks and the modern ,germans have called these bodies wandering stars1 and in ,english we name them planets1 which is simply the ,greek word for wanderer1 bent to our use4 ,besides the sun and moon there are in the heavens five planets easily visible to the naked eye and1 as we shall see later1 a great number of smaller ones visible only in the telescope4 ,more than #b1jjj years ago astronomers began observing the motion of sun1 moon1 and planets among the stars1 and endeavored to account for these motions by the theory that each wandering star moved in an orbit about the earth4 ,classical and medival literature are permeated with this idea1 which was displaced only after a long struggle begun by ,copernicus 7#aedc ,a4 ,d471 who taught that the moon alone of these bodies revolves about the earth1 while the earth and the other planets revolve around the sun4 ,the ecliptic is the intersection of the plane of the earth's orbit with the sky1 and the sun appears to move along the ecliptic because1 as the earth moves around its orbit1 the sun is always seen projected against the opposite side of it4 ,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 orbit1 and a narrow strip on either side of the ecliptic1 following its course completely around the sky1 is called the zodiac1 a word which may be regarded as the name of a narrow street 7#af wide7 within which all the wanderings of the visible planets are confined and outside of which they never venture4 ,indeed1 ,mars is the only planet which ever approaches the edge of the street1 the others traveling near the middle of the road4 ,illustration3 ,,fig4 #ad4--,the apparent motion of a planet4 #bg4 ,a ,,typical ,,case ,,of ,,planetary ,,motion4--,the ,copernican theory1 enormously extended and developed through the ,newtonian law of gravitation 7see ,chapter ,,iv71 has completely supplanted the older ,ptolemaic doctrine1 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 ,figs4 #ad and #ae1 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 #ahid1 while the second shows the true motions of ,mars and the earth in their orbits about the sun during the same period4 ,the straight line in ,fig4 #ad1 with cross ruling upon it1 is a part of the ecliptic1 and the numbers placed opposite it represent the distance1 in degrees1 from the vernal equinox4 ,in ,fig4 #ae the straight line represents the direction from the sun toward the vernal equinox1 and the angle which this line makes with the line joining earth and sun is called the earth's longitude4 ,the imaginary line joining the earth and sun is called the earth's radius vector1 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--i4 e41 they fix the relative positions of the two bodies4 ,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 earth4 ,how does ,fig4 #ad show that the orbit of ,mars does not lie exactly in the same plane with the orbit of the earth8 ,,exercise #ac4--;,find from ,fig4 #ae what ought to have been the apparent course of ,mars among the stars during the period shown in the two figures1 and compare what you find with ,fig4 #ad4 ,the apparent position of ,mars among the stars is merely its direction from the earth1 and this direction is represented in ,fig4 #ad by the distance of the planet from the ecliptic and by its longitude4 ,illustration3 ,,fig4 #ae4--,the real motion of a planet4 ,the longitude of ,mars for each date can be found from ,fig4 #ae by measuring the angle between the straight line ,s ,v and the line drawn from the earth to ,mars4 ,thus for ,october #abth 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 #cj1 and in ,fig4 #ad the position of ,mars for this date is shown nearly opposite the cross line corresponding to #cj on the ecliptic4 ,just how far below the ecliptic this position of ,mars should fall can not be told from ,fig4 #ae1 which from necessity is constructed as if the orbits of ,mars and the earth lay in the same plane1 and ,mars in this case would always appear to stand exactly on the ecliptic and to oscillate back and forth as shown in ,fig4 #ad1 but without the up-and-down motion there shown4 ,in this way plot in ,fig4 #ad 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 stars4 ,illustration3 ,,fig4 #af4--,the orbits of ,jupiter and ,saturn4 #bh4 ,,the ,,orbits ,,of ,,the ,,planets4--,each planet1 great or small1 moves in its own appropriate orbit about the sun1 and the exact determination of these orbits1 their sizes1 shapes1 positions1 etc41 has been one of the great problems of astronomy for more than #b1jjj years1 in which successive generations of astronomers have striven to push to a still higher degree of accuracy the knowledge attained by their predecessors4 ,without attempting to enter into the details of this problem we may say1 generally1 that every planet moves in a plane passing through the sun1 and for the six planets visible to the naked eye these planes nearly coincide1 so that the six orbits may all be shown without much error as lying in the flat surface of one map4 ,it is1 however1 more convenient to use two maps1 such as ,figs4 #af and #ag1 one of which shows the group of planets1 ,mercury1 ,venus1 the earth1 and ,mars1 which are near the sun1 and on this account are sometimes called the inner planets1 while the other shows the more distant planets1 ,jupiter and ,saturn1 together with the earth1 whose orbit is thus made to serve as a connecting link between the two diagrams4 ,these diagrams are accurately drawn to scale1 and are intended to be used by the student for accurate measurement in connection with the exercises and problems which follow4 ,in addition to the six planets shown in the figures the solar system contains two large planets and several hundred small ones1 for the most part invisible to the naked eye1 which are omitted in order to avoid confusing the diagrams4 #bi4 ,,jupiter ,,and ,,saturn4--,in ,fig4 #af the sun at the center is encircled by the orbits of the three planets1 and inclosing all of these is a circular border showing the directions from the sun of the constellations which lie along the zodiac4 ,the student must note carefully that it is only the directions of these constellations that are correctly shown1 and that in order to show them at all they have been placed very much too close to the sun4 ,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 7,i71 first day of ,february 7,,ii71 etc41 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 indicated1 so that the figure serves to show not only the orbits of the planets1 but their actual positions in their orbits for something more than the first decade of the twentieth century4 ,the line drawn from the sun toward the right of the figure shows the direction to the vernal equinox4 ,it forms one side of the angle which measures a planet's longitude4 ,illustration3 ,,fig4 #ag4--,the orbits of the inner planets4 ,,exercise #ad4--,measure with your protractor the longitude of the earth on ,january #ast4 ,is this longitude the same in all years8 ,measure the longitude of ,jupiter on ,january #a1 #aijj2 on ,july #a1 #aijj2 on ,september #be1 #aijf4 ,draw neatly on the map a pencil line connecting the position of the earth for ,january #a1 #aijj1 with the position of ,jupiter for the same date1 and produce the line beyond ,jupiter until it meets the circle of the constellations4 ,this line represents the direction of ,jupiter from the earth1 and points toward the constellation in which the planet appears at that date4 ,but this representation of the place of ,jupiter in the sky is not a very accurate one1 since on the scale of the diagram the stars are in fact more than #ajj1jjj times as far off as they are shown in the figure1 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 position4 ,to remedy this defect we must draw another line from the sun parallel to the one first drawn1 and its intersection with the constellations will give very approximately the true position of ,jupiter in the sky4 ,,exercise #ae4--;,find the present positions of ,jupiter and ,saturn1 and look them up in the sky by means of your star maps4 ,the planets will appear in the indicated constellations as very bright stars not shown on the map4 ,which of the planets1 ,jupiter and ,saturn1 changes its direction from the sun more rapidly8 ,which travels the greater number of miles per day8 ,when will ,jupiter and ,saturn be in the same constellation8 ,does the earth move faster or slower than ,jupiter8 ,the distance of ,jupiter or ,saturn from the earth at any time may be readily obtained from the figure4 ,thus1 by direct measurement with the millimeter scale we find for ,january #a1 #aijj1 the distance of ,jupiter from the earth is #f4a times the distance of the sun from the earth1 and this may be turned into miles by multiplying it by #ic1jjj1jjj1 which is approximately the distance of the sun from the earth4 ,for most purposes it is quite as well to dispense with this multiplication and call the distance #f4a astronomical units1 remembering that the astronomical unit is the distance of the sun from the earth4 ,,exercise #af4--,what is ,jupiter's distance from the earth at its nearest approach8 ,what is the greatest distance it ever attains8 ,is ,jupiter's least distance from the earth greater or less than its least distance from ,saturn8 ,on what day in the year #aijf will the earth be on line between ,jupiter and the sun8 ,on this day ,jupiter is said to be in opposition--i4 e41 the planet and the sun are on opposite sides of the earth1 and ,jupiter then comes to the meridian of any and every place at midnight4 ,when the sun is between the earth and ,jupiter 7at what date in #aijf87 the planet is said to be in conjunction with the sun1 and of course passes the meridian with the sun at noon4 ,can you determine from the figure the time at which ,jupiter comes to the meridian at other dates than opposition and conjunction8 ,can you determine when it is visible in the evening hours8 ,tell from the figure what constellation is on the meridian at midnight on ,january #ast4 ,will it be the same constellation in every year8 #cj4 ,,mercury1 ,,venus1 ,,and ,,mars4--,fig4 #ag1 which represents the orbits of the inner planets1 differs from ,fig4 #af only in the method of fixing the positions of the planets in their orbits at any given date4 ,the motion of these planets is so rapid1 on account of their proximity to the sun1 that it would not do to mark their positions as was done for ,jupiter and ,saturn1 and with the exception of the earth they do not always return to the same place on the same day in each year4 ,it is therefore necessary to adopt a slightly different method1 as follows3 ,the straight line extending from the sun toward the vernal equinox1 ,v1 is called the prime radius1 and we know from past observations that the earth in its motion around the sun crosses this line on ,september #bc;d in each year1 and to fix the earth's position for ,september #bc;d in the diagram we have only to take the point at which the prime radius intersects the earth's orbit4 ,a month later1 on ,october #bc;d1 the earth will no longer be at this point1 but will have moved on along its orbit to the point marked #cj 7thirty days after ,september #bc;d74 ,sixty days after ,september #bc;d it will be at the point marked #fj1 etc41 and for any date we have only to find the number of days intervening between it and the preceding ,september #bc;d1 and this number will show at once the position of the earth in its orbit4 ,thus for the date ,july #d1 #aijj1 we find #aijj1 ,july #d - #ahii1 ,september #bc #bhd days1 and the little circle marked upon the earth's orbit between the numbers #bgj and #cjj shows the position of the earth on that date4 ,in what constellation was the sun on ,july #d1 #aijj8 ,what zodiacal constellation came to the meridian at midnight on that date8 ,what other constellations came to the meridian at the same time8 ,the positions of the other planets in their orbits are found in the same manner1 save that they do not cross the prime radius on the same date in each year1 and the times at which they do cross it must be taken from the following table3 ,,table ,,of ,,epochs ---------------------------------------- ------------------- ,a4 ,d4 ,mercury4 ,venus4 ,earth4 ,mars4 ---------------------------------------- --------------- ,period #hh4j days4 #bbd4g days4#cfe4be days4 #fhg4a days4 #aijj ,feb4 #ahth4 ,jan4 #aath4 ,sept4 #bc;d4 ,april #bhth4 #aija ,feb4 #eth4 ,april #eth4 ,sept4 #bc;d4 444 #aijb ,jan4 #bc;d4 ,june #bith4 ,sept4 #bc;d4 ,march #afth4 #aijc ,april #hth4 ,feb4 #hth4 ,sept4 #bc;d4 444 #aijd ,march #beth4 ,may #c;d4 ,sept4 #bc;d4 ,feb4 #ast4 #aije ,march #abth4 ,july #bfth4 ,sept4 #bc;d4 ,dec4 #aith4 #aijf ,feb4 #bgth4 ,march #hth4 ,sept4 #bc;d4 444 #aijg ,feb4 #adth4 ,may #cast4 ,sept4 #bc;d4 ,nov4 #fth4 #aijh ,feb4 #ast4 ,jan4 #aath4 ,sept4 #bc;d4 444 #aiji ,jan4 #ahth4 ,april #dth4 ,sept4 #bc;d4 ,sept4 #bc;d4 #aiaj ,jan4 #eth4 ,june #bhth4 ,sept4 #bc;d4 444 ---------------------------------------- ------------------- ,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 sun1 and it appears from these numbers that ,mercury makes about four revolutions in its orbit per year1 and therefore crosses the prime radius four times in each year1 while the other planets are decidedly slower in their movements4 ,the following lines of the table show for each year the date at which each planet first crossed the prime radius in that year2 the dates of subsequent crossings in any year can be found by adding once1 twice1 or three times the period to the given date1 and the table may be extended to later years1 if need be1 by continuously adding multiples of the period4 ,in the case of ,mars it appears that there is only about one year out of two in which this planet crosses the prime radius4 ,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 earth1 and the constellation in which the planet will appear from the earth is found as explained above in connection with ,jupiter and ,saturn4 ,the broken lines in the figure represent the construction for finding the places in the sky occupied by ,mercury1 ,venus1 and ,mars on ,july #d1 #aijj4 ,let the student make a similar construction and find the positions of these planets at the present time4 ,look them up in the sky and see if they are where your work puts them4 #ca4 ,,exercises4--,the evening star is a term loosely applied to any planet which is visible in the western sky soon after sunset4 ,it is easy to see that such a planet must be farther toward the east in the sky than is the sun1 and in either ,fig4 #af or ,fig4 #ag any planet which viewed from the position of the earth lies to the left of the sun and not more than #ej away from it will be an evening star4 ,if to the right of the sun it is a morning star1 and may be seen in the eastern sky shortly before sunrise4 ,what planet is the evening star now8 ,is there more than one evening star at a time8 ,what is the morning star now8 ,do ,mercury1 ,venus1 or ,mars ever appear in opposition8 ,what is the maximum angular distance from the sun at which ,venus can ever be seen8 ,why is ,mercury a more difficult planet to see than ,venus8 ,in what month of the year does ,mars come nearest to the earth8 ,will it always be brighter in this month than in any other8 ,which of all the planets comes nearest to the earth8 ,the earth always comes to the same longitude on the same day of each year4 ,why is not this true of the other planets8 ,the student should remember that in one respect ,figs4 #af and #ag are not altogether correct representations1 since they show the orbits as all lying in the same plane4 ,if this were strictly true1 every planet would move1 like the sun1 always along the ecliptic2 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 ecliptic1 first to one side then to the other2 but not even ,mars1 which is the most erratic in this respect1 ever gets more than eight degrees away from the ecliptic1 and for the most part all of them are much closer to the ecliptic than this limit4 ,,chapter ,,iv ,,celestial ,,mechanics #cb4 ,,the ,,beginnings ,,of ,,celestial ,,mechanics4--,from the earliest dawn of civilization1 long before the beginnings of written history1 the motions of sun and moon and planets among the stars from constellation to constellation had commanded the attention of thinking men1 particularly of the class of priests4 ,the religions of which they were the guardians and teachers stood in closest relations with the movements of the stars1 and their own power and influence were increased by a knowledge of them4 ,illustration3 ,,isaac ,,newton 7#afdc-agbg74 ,out of these professional needs1 as well as from a spirit of scientific research1 there grew up and flourished for many centuries a study of the motions of the planets1 simple and crude at first1 because the observations that could then be made were at best but rough ones1 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 bodies4 ,it was early seen that while for the most part the planets1 including the sun and moon1 traveled through the constellations from west to east1 some of them sometimes reversed their motion and for a time traveled in the opposite way4 ,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 center1 and so it was said to move around in a small circular orbit1 called an epicycle1 whose center was situated upon and moved along a circular orbit1 called the deferent1 within which the earth was placed1 as is shown in ,fig4 #ah1 where the small circle is the epicycle1 the large circle is the deferent1 ,p is the planet1 and ,e the earth4 ,when this proved inadequate to account for the really complicated movements of the planets1 another epicycle was put on top of the first one1 and then another and another1 until the supposed system became so complicated that ,copernicus1 a ,polish astronomer1 repudiated its fundamental theorem and taught that the motions of the planets take place in circles around the sun instead of about the earth1 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 planets1 since from day to day we see them and observe their positions from different points of view4 ,illustration3 ,,fig4 #ah4--;,epicycle and deferent4 #cc4 ,,kepler',s ,,laws4--,two generations later came ,kepler with his three famous laws of planetary motion3 ,i4 ,every planet moves in an ellipse which has the sun at one of its foci4 ,,ii4 ,the radius vector of each planet moves over equal areas in equal times4 ,,iii4 ,the squares of the periodic times of the planets are proportional to the cubes of their mean distances from the sun4 ,these laws are the crowning glory1 not only of ,kepler's career1 but of all astronomical discovery from the beginning up to his time1 and they well deserve careful study and explanation1 although more modern progress has shown that they are only approximately true4 ,,exercise #ag4--;,drive two pins into a smooth board an inch apart and fasten to them the ends of a string a foot long4 ,take up the slack of the string with the point of a lead pencil and1 keeping the string drawn taut1 move the pencil point over the board into every possible position4 ,the curve thus traced will be an ellipse having the pins at the two points which are called its foci4 ,in the case of the planetary orbits one focus of the ellipse is vacant1 and1 in accordance with the first law1 the center of the sun is at the other focus4 ,in ,fig4 #ag the dot1 inside the orbit of ,mercury1 which is marked a1 shows the position of the vacant focus of the orbit of ,mars1 and the dot b is the vacant focus of ,mercury's orbit4 ,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 figure4 ,the line drawn from the sun to any point of the orbit 7the string from pin to pencil point7 is a radius vector4 ,the point midway between the pins is the center of the ellipse1 and the distance of either pin from the center measures the eccentricity of the ellipse4 ,draw several ellipses with the same length of string1 but with the pins at different distances apart1 and note that the greater the eccentricity the flatter is the ellipse1 but that all of them have the same length4 ,if both pins were driven into the same hole1 what kind of an ellipse would you get8 ,the ,second ,law was worked out by ,kepler as his answer to a problem suggested by the first law4 ,in ,fig4 #ag 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 other1 the distance covered in ten days between the numbers #aj and #bj being more than fifty per cent greater than that between #ej and #fj4 ,the same difference is found1 though usually in less degree1 for every other planet1 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 time4 ,his solution of this problem1 contained in the second law1 asserts that if we draw radii vectors from the sun to each of the marked points taken at equal time intervals around the orbit1 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 sector1 the short radii vectores being spread apart so as to include a long arc between them while the long radii vectores have a short arc4 ,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 orbit4 ,the spacing of the numbers in ,fig4 #ag was done by means of this law4 ,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 orbit4 ,representing the first of these by a and the second by ,t1 we have1 as the mathematical equivalent of the law1 a#c ,t#b ,c where the quotient1 ,c1 is a number which1 as ,kepler found1 is the same for every planet of the solar system4 ,if we take the mean distance of the earth from the sun as the unit of distance1 and the year as the unit of time1 we shall find by applying the equation to the earth's motion1 ,c #a4 ,applying this value to any other planet we shall find in the same units1 a ,t#b_/c1 by means of which we may determine the distance of any planet from the sun when its periodic time1 ,t1 has been learned from observation4 ,,exercise #ah4--,uranus requires #hd years to make a revolution in its orbit4 ,what is its mean distance from the sun8 ,what are the mean distances of ,mercury1 ,venus1 and ,mars8 7,see ,chapter ,,iii for their periodic times47 ,would it be possible for two planets at different distances from the sun to move around their orbits in the same time8 ,a circle is an ellipse in which the two foci have been brought together4 ,would ,kepler's laws hold true for such an orbit8 #cd4 ,,newton',s ,,laws ,,of ,,motion4--,kepler studied and described the motion of the planets4 ,newton1 three generations later 7#agbg ,a4 ,d471 studied and described the mechanism which controls that motion4 ,to ,kepler and his age the heavens were supernatural1 while to ,newton and his successors they are a part of ,nature1 governed by the same laws which obtain upon the earth1 and we turn to the ordinary things of everyday life as the foundation of celestial mechanics4 ,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 rough2 but however smooth and hard the road may be and however fast the wheel may have been started1 it is sooner or later stopped by the resistance which the road and the air offer to its motion1 and when once stopped or checked it can be started again only by applying fresh power4 ,we have here a familiar illustration of what is called ,,the ,,first ,,law ,,of ,,motion4--,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 state4 ,a gust of wind1 a stone1 a careless movement of the rider may turn the bicycle to the right or the left1 but unless some disturbing force is applied it will go straight ahead1 and if all resistance to its motion could be removed it would go always at the speed given it by the last power applied1 swerving neither to the one hand nor the other4 ,when a slow rider increases his speed we recognize at once that he has applied additional power to the wheel1 and when this speed is slackened it equally shows that force has been applied against the motion4 ,it is force alone which can produce a change in either velocity or direction of motion2 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 above4 #ce4 ,,the ,,second ,,law ,,of ,,motion1 which is also due to ,galileo and ,newton1 is3 ,change of motion is proportional to force applied and takes place in the direction of the straight line in which the force acts4 ,suppose a man to fall from a balloon at some great elevation in the air2 his own weight is the force which pulls him down1 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 #cb feet per second--i4 e41 it has changed his state from rest1 to motion at this rate1 and the motion is toward the earth because the force acts in that direction4 ,during the next second the ceaseless operation of this force will have the same effect as in the first second and will add another #cb feet to his velocity1 so that two seconds from the time he commenced to fall he will be moving at the rate of #fd feet per second1 etc4 ,the column of figures marked v in the table below shows what his velocity will be at the end of subsequent seconds4 ,the changing velocity here shown is the change of motion to which the law refers1 and the velocity is proportional to the time shown in the first column of the table1 because the amount of force exerted in this case is proportional to the time during which it operated4 ,the distance through which the man will fall in each second is shown in the column marked d1 and is found by taking the average of his velocity at the beginning and end of this second1 and the total distance through which he has fallen at the end of each second1 marked s in the table1 is found by taking the sum of all the preceding values of d4 ,the velocity1 #cb feet per second1 which measures the change of motion in each second1 also measures the accelerating force which produces this motion1 and it is usually represented in formul by the letter g4 ,let the student show from the numbers in the table that the accelerating force1 the time1 t1 during which it operates1 and the space1 s1 fallen through1 satisfy the relation s #a_/b gt#b1 which is usually called the law of falling bodies4 ,how does the table show that g is equal to #cb8 ,,table t v d s #j #j #j #j #a #cb #af #af #b #fd #dh #fd #c #if #hj #add #d #abh #aab #bef #e #afj #add #djj etc4 etc4 etc4 etc4 ,if the balloon were half a mile high how long would it take to fall to the ground8 ,what would be the velocity just before reaching the ground8 ,illustration3 ,,galileo ,,galilei 7#aefd-afdb74 ,fig4 #ai shows the path through the air of a ball which has been struck by a bat at the point ,a1 and started off in the direction ,a ,b with a velocity of #bjj feet per second4 ,in accordance with the first law of motion1 if it were acted upon by no other force than the impulse given by the bat1 it should travel along the straight line ,a ,b at the uniform rate of #bjj feet per second1 and at the end of the fourth second it should be #hjj feet from ,a1 at the point marked #d1 but during these four seconds its weight has caused it to fall #bef feet1 and its actual position1 #d'1 is #bef feet below the point #d4 ,in this way we find its position at the end of each second1 #a'1 #b'1 #c'1 #d'1 etc41 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 ,c4 ,no matter how far the ball may go before striking the ground1 it can not get back to the point ,a1 and the curve ,a ,c therefore can not be a part of a circle1 since that curve returns into itself4 ,it is1 in fact1 a part of a parabola1 which1 as we shall see later1 is a kind of orbit in which comets and some other heavenly bodies move4 ,a skyrocket moves in the same kind of a path1 and so does a stone1 a bullet1 or any other object hurled through the air4 ,illustration3 ,,fig4 #ai4--,the path of a ball4 #cf4 ,,the ,,third ,,law ,,of ,,motion4--,to every action there is always an equal and contrary reaction2 or the mutual actions of any two bodies are always equal and oppositely directed4 ,this is well illustrated in the case of a man climbing a rope hand over hand4 ,the direct force or action which he exerts is a downward pull upon the rope1 and it is the reaction of the rope to this pull which lifts him along it4 ,we shall find in a later chapter a curious application of this law to the history of the earth and moon4 ,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 earth2 that the complicated motion of a planet1 a comet1 or a star is determined in accordance with these laws by the forces which act upon the bodies1 and that these forces are essentially the same as that which we call weight4 ,the formal statement of the principle last named is included in-- #cg4 ,,newton',s ,,law ,,of ,,gravitation4--,every particle of matter in the universe attracts every other particle with a force whose direction is that of a line joining the two1 and whose magnitude is directly as the product of their masses1 and inversely as the square of their distance from each other4 ,we know that we ourselves and the things about us are pulled toward the earth by a force 7weight7 which is called1 in the ,latin that ,newton wrote1 gravitas1 and the word marks well the true significance of the law of gravitation4 ,newton did not discover a new force in the heavens1 but he extended an old and familiar one from a limited terrestrial sphere of action to an unlimited and celestial one1 and furnished a precise statement of the way in which the force operates4 ,whether a body be hot or cold1 wet or dry1 solid1 liquid1 or gaseous1 is of no account in determining the force which it exerts1 since this depends solely upon mass and distance4 ,the student should perhaps be warned against straining too far the language which it is customary to employ in this connection4 ,the law of gravitation is certainly a far-reaching one1 and it may operate in every remotest corner of the universe precisely as stated above1 but additional information about those corners would be welcome to supplement our rather scanty stock of knowledge concerning what happens there4 ,we may not controvert the words of a popular preacher who says1 ,when ,i lift my hand ,i move the stars in ,ursa ,major1 but we should not wish to stand sponsor for them1 even though they are justified by a rigorous interpretation of the ,newtonian law4 ,the word mass1 in the statement of the law of gravitation1 means the quantity of matter contained in the body1 and if we represent by the letters m and m the respective quantities of matter contained in the two bodies whose distance from each other is r1 we shall have1 in accordance with the law of gravitation1 the following mathematical expression for the force1 ,f1 which acts between them3 ,f k mm_/r#b4 ,this equation1 which is the general mathematical expression for the law of gravitation1 may be made to yield some curious results4 ,thus1 if we select two bullets1 each having a mass of #a gram1 and place them so that their centers are #a centimeter apart1 the above expression for the force exerted between them becomes ,f k 7#a #a7_/ab k1 from which it appears that the coefficient k is the force exerted between these bodies4 ,this is called the gravitation constant1 and it evidently furnishes a measure of the specific intensity with which one particle of matter attracts another4 ,elaborate experiments which have been made to determine the amount of this force show that it is surprisingly small1 for in the case of the two bullets whose mass of #a gram each is supposed to be concentrated into an indefinitely small space1 gravity would have to operate between them continuously for more than forty minutes in order to pull them together1 although they were separated by only #a centimeter to start with1 and nothing save their own inertia opposed their movements4 ,it is only when one or both of the masses m1 m are very great that the force of gravity becomes large1 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 earth4 ,many of the heavenly bodies are much more massive than the earth1 as the mathematical astronomers have found by applying the law of gravitation to determine numerically their masses1 or1 in more popular language1 to weigh them4 ,the student should observe that the two terms mass and weight are not synonymous2 mass is defined above as the quantity of matter contained in a body1 while weight is the force with which the earth attracts that body1 and in accordance with the law of gravitation its weight depends upon its distance from the center of the earth1 while its mass is quite independent of its position with respect to the earth4 ,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--i4 e41 by a force equal to the weight of the body4 ,how much does the earth rise toward the body8 #ch4 ,,the ,,motion ,,of ,a ,,planet4--,in ,fig4 #bj ,s represents the sun and ,p a planet or other celestial body1 which for the moment is moving along the straight line ,p #a4 ,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 it2 but such a force1 the sun's attraction1 is acting1 and by virtue of this attraction the body is pulled aside from the line ,p #a4 ,knowing the velocity and direction of the body's motion and the force with which the sun attracts it1 the mathematician is able to apply ,newton's laws of motion so as to determine the path of the body1 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 sun4 ,this point is called the perihelion4 ,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 range1 and therefore the force exerted by the sun1 and the resulting change of motion1 will be small1 as in the orbits ,p #a and ,p #b4 ,on the other hand1 ,p #e and ,p #f represent orbits in which the velocity at ,p was comparatively small1 and the resulting change of motion greater than would be possible for a more swiftly moving body4 ,what would be the orbit if the velocity at ,p were reduced to nothing at all8 ,what would be the effect if the body starting at ,p moved directly away from #a8 ,illustration3 ,,fig4 #bj4--;,different kinds of orbits4 ,the student should not fail to observe that the sun's attraction tends to pull the body at ,p forward along its path1 and therefore increases its velocity1 and that this influence continues until the planet reaches perihelion1 at which point it attains its greatest velocity1 and the force of the sun's attraction is wholly expended in changing the direction of its motion4 ,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 it1 so that the two halves of the orbit on opposite sides of a line drawn from the perihelion through the sun are exactly alike4 ,we may here note the explanation of ,kepler's second law3 when the planet is near the sun it moves faster1 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 attracted1 and the exact relation between the rates at which the radius vector turns in different parts of the orbit1 as given by the second law1 depends upon the changes in this force4 ,when the velocity is not too great1 the sun's backward pull1 after a planet has passed perihelion1 finally overcomes it and turns the planet toward the sun again1 in such a way that it comes back to the point ,p1 moving in the same direction and with the same speed as before--i4 e41 it has gone around the sun in an orbit like ,p #f or ,p #d1 an ellipse1 along which it will continue to move ever after4 ,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 7p4 #ed71 and that1 if the magnitude of this force were inversely as the cube of the distance or any other proportion than the square1 the orbit would be something very different4 ,if the velocity is too great for the sun's attraction to overcome1 the orbit will be a hyperbola1 like ,p #b1 along which the body will move away never to return1 while a velocity just at the limit of what the sun can control gives an orbit like ,p #c1 a parabola1 along which the body moves with parabolic velocity1 which is ever diminishing as the body gets farther from the sun1 but is always just sufficient to keep it from returning4 ,if the earth's velocity could be increased #da per cent1 from #ai up to #bg miles per second1 it would have parabolic velocity1 and would quit the sun's company4 ,the summation of the whole matter is that the orbit in which a body moves around the sun1 or past the sun1 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 them1 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 laws2 and the same is true for any other heavenly body--moon1 comet1 meteor1 etc4 ,it is in this way that astronomers are able to predict1 years in advance1 in what particular part of the sky a given planet will appear at a given time4 ,it is sometimes a source of wonder that the planets move in ellipses instead of circles1 but it is easily seen from ,fig4 #bj that the planet1 ,p1 could not by any possibility move in a circle1 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 orbit1 and even if it were perpendicular to the radius vector the planet must needs have exactly the right velocity given to it at this point1 since either more or less speed would change the circle into an ellipse4 ,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 point1 and the really surprising thing is that the orbits of the planets should be so nearly circular as they are4 ,if the orbit of the earth were drawn accurately to scale1 the untrained eye would not detect the slightest deviation from a true circle1 and even the orbit of ,mercury 7,fig4 #ag71 which is much more eccentric than that of the earth1 might almost pass for a circle4 ,illustration3 ,,fig4 #ba4 ,an impossible orbit4 ,the orbit ,p #b1 which lies between the parabola and the straight line1 is called in geometry a hyperbola1 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 ellipse2 but it must move in some one of these curves2 no other orbit is possible4#a ,thus it would not be possible for a body moving under the law of gravitation to describe about the sun any such orbit as is shown in ,fig4 #ba4 ,if the body passes a second time through any point of its orbit1 such as ,p in the figure1 then it must retrace1 time after time1 the whole path that it first traversed in getting from ,p around to ,p again--i4 e41 the orbit must be an ellipse4 #a ,the circle and straight line are considered to be special cases of these curves1 which1 taken collectively1 are called the conic sections4 ,newton also proved that ,kepler's three laws are mere corollaries from the law of gravitation1 and that to be strictly correct the third law must be slightly altered so as to take into account the masses of the planets4 ,these are1 however1 so small in comparison with that of the sun1 that the correction is of comparatively little moment4 #ci4 ,,perturbations4--,in what precedes we have considered the motion of a planet under the influence of no other force than the sun's attraction1 while in fact1 as the law of gravitation asserts1 every other body in the universe is in some measure attracting it and changing its motion4 ,the resulting disturbances in the motion of the attracted body are called perturbations1 but for the most part these are insignificant1 because the bodies by whose disturbing attractions they are caused are either very small or very remote1 and it is only when our moving planet1 ,p1 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 account4 ,the problem of the motion of three bodies--sun1 ,jupiter1 planet--which must then be dealt with is vastly more complicated than that which we have considered1 and the ablest mathematicians and astronomers have not been able to furnish a complete solution for it1 although they have worked upon the problem for two centuries1 and have developed an immense amount of detailed information concerning it4 ,illustration3 ,,the ,,lick ,,observatory1 ,,mount ,,hamilton1 ,,cal4 ,in general each planet works ceaselessly upon the orbit of every other1 changing its size and shape and position1 backward and forward in accordance with the law of gravitation1 and it is a question of serious moment how far this process may extend4 ,if the diameter of the earth's orbit were very much increased or diminished by the perturbing action of the other planets1 the amount of heat received from the sun would be correspondingly changed1 and the earth1 perhaps1 be rendered unfit for the support of life4 ,the tipping of the plane of the earth's orbit into a new position might also produce serious consequences2 but the great ,french mathematician of a century ago1 ,laplace1 succeeded in proving from the law of gravitation that although both of these changes are actually in progress they can not1 at least for millions of years1 go far enough to prove of serious consequence1 and the same is true for all the other planets1 unless here and there an asteroid may prove an exception to the rule4 ,the precession 7,chapter ,v7 is a striking illustration of a perturbation of slightly different character from the above1 and another is found in connection with the plane of the moon's orbit4 ,it will be remembered that the moon in its motion among the stars never goes far from the ecliptic1 but in a complete circuit of the heavens crosses it twice1 once in going from south to north and once in the opposite direction4 ,the points at which it crosses the ecliptic are called the nodes1 and under the perturbing influence of the sun these nodes move westward along the ecliptic about twenty degrees per year1 an extraordinarily rapid perturbation1 and one of great consequence in the theory of eclipses4 ,illustration3 ,,fig4 #bb4--;,a planet subject to great perturbations by ,jupiter4 #dj4 ,,weighing ,,the ,,planets4--,although these perturbations can not be considered dangerous1 they are interesting since they furnish a method for weighing the planets which produce them4 ,from the law of gravitation we learn that the ability of a planet to produce perturbations depends directly upon its mass1 since the force ,f which it exerts contains this mass1 m1 as a factor4 ,so1 too1 the divisor r#b in the expression for the force shows that the distance between the disturbing and disturbed bodies is a matter of great consequence1 for the smaller the distance the greater the force4 ,when1 therefore1 the mass of a planet such as ,jupiter is to be determined from the perturbations it produces1 it is customary to select some such opportunity as is presented in ,fig4 #bb1 where one of the small planets1 called asteroids1 is represented as moving in a very eccentric orbit1 which at one point approaches close to the orbit of ,jupiter1 and at another place comes near to the orbit of the earth4 ,for the most part ,jupiter will not exert any very great disturbing influence upon a planet moving in such an orbit as this1 since it is only at rare intervals that the asteroid and ,jupiter approach so close to each other1 as is shown in the figure4 ,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 is1 to determine carefully the undisturbed orbit in which it moves2 but there comes a time at which the asteroid passes close to ,jupiter1 as shown in the figure1 and the orbital motion which the sun imparts to it will then be greatly disturbed1 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 earth4 ,if now the astronomer observes the actual position of the asteroid in the sky1 its right ascension and declination1 and compares these with the position assigned to the planet by the law of gravitation when the attraction of ,jupiter is ignored1 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 asteroid1 and the amount by which ,jupiter has shifted it1 compared with the amount by which the sun has moved it--that is1 with the motion in its orbit--furnishes the mass of ,jupiter expressed as a fractional part of the mass of the sun4 ,there has been determined in this manner the mass of every planet in the solar system which is large enough to produce any appreciable perturbation1 and all these masses prove to be exceedingly small fractions of the mass of the sun1 as may be seen from the following table1 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 planet3 ,mercury #g1jjj1jjj 787 ,venus #djh1jjj ,earth #cbi1jjj ,mars #c1jic1ejj ,jupiter #a1jdg4d ,saturn #c1ejb ,uranus #bb1hjj ,neptune #ai1gjj ,it is to be especially noted that the mass given for each planet includes the mass of all the satellites which attend it1 since their influence was felt in the perturbations from which the mass was derived4 ,thus the mass assigned to the earth is the combined mass of earth and moon4 #da4 ,,discovery ,,of ,,neptune4--,the most famous example of perturbations is found in connection with the discovery1 in the year #ahdf1 of ,neptune1 the outermost planet of the solar system4 ,for many years the motion of ,uranus1 his next neighbor1 had proved a puzzle to astronomers4 ,in accordance with ,kepler's first law this planet should move in an ellipse having the sun at one of its foci1 but no ellipse could be found which exactly fitted its observed path among the stars1 although1 to be sure1 the misfit was not very pronounced4 ,astronomers surmised that the small deviations of ,uranus from the best path which theory combined with observation could assign1 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 prove1 and harder still to find the unknown disturber4 ,but almost simultaneously two young men1 ,adams in ,england and ,le ,verrier in ,france1 attacked the problem quite independently of each other1 and carried it to a successful solution1 showing that if the irregularities in the motion of ,uranus were indeed caused by an unknown planet1 then that planet must1 in ,september1 #ahdf1 be in the direction of the constellation ,aquarius2 and there it was found on ,september #bc;d by the astronomers of the ,berlin ,observatory whom ,le ,verrier had invited to search for it1 and found within a degree of the exact point which the law of gravitation in his hands had assigned to it4 ,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 intellect1 and it is worthy of note that we are approaching the time at which it may be repeated1 for ,neptune now behaves much as did ,uranus three quarters of a century ago1 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 planet4 #db4 ,,the ,,shape ,,of ,a ,,planet4--,there is an effect of gravitation not yet touched upon1 which is of considerable interest and wide application in astronomy--viz41 its influence in determining the shape of the heavenly bodies4 ,the earth is a globe because every part of it is drawn toward the center by the attraction of the other parts1 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 form1 no matter what may have been the shape in which it was originally made4 ,but such is not the real condition of the earth1 for its diurnal rotation develops in every particle of its body a force which is sometimes called centrifugal1 but which is really nothing more than the inertia of its particles1 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 rotation1 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 circle4 ,a few experiments with such a stone will show that the faster it goes the harder does it pull upon the string1 and the same is true of each particle of the earth1 the swiftly moving ones near the equator having a greater centrifugal force than the slow ones near the poles4 ,at the equator the centrifugal force is directly opposed to the force of gravity1 and in effect diminishes it1 so that1 comparatively1 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 restored4 ,as we have learned from the study of geography1 in the case of the earth1 this compression amounts to about #bg miles1 but in the larger planets1 ,jupiter and ,saturn1 it is much greater1 amounting to several thousand miles4 ,but rotation is not the only influence that tends to pull a planet out of shape4 ,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 center1 and this difference of attraction tends to warp the moon1 as is illustrated in ,fig4 #bc where #a1 #b1 and #c represent pieces of iron of equal mass placed in line on a table near a horseshoe magnet1 ,h4 ,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 pulley1 ,p1 at the edge of the table4 ,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 piece1 ,no4 #b4 ,it is clear that under this arrangement ,no4 #b will move neither to the right nor to the left1 since the forces exerted upon it by the magnet and the weight just balance each other4 ,upon ,no4 #a1 however1 the magnet pulls harder than upon ,no4 #b1 because it is nearer and its pull therefore more than balances the force exerted by the weight1 so that ,no4 #a will be pulled away from ,no4 #b and will stretch the elastic cords1 which are represented by the lines joining #a and #b1 until their tension1 together with the force exerted by the weight1 just balances the attraction of the magnet4 ,for ,no4 #c1 the force exerted by the magnet is less than that of the weight1 and it will also be pulled away from ,no4 #b until its elastic cords are stretched to the proper tension4 ,the net result is that the three blocks which1 without the magnet's influence1 would be held close together by the elastic cords1 are pulled apart by this outside force as far as the resistance of the cords will permit4 ,illustration3 ,,fig4 #bc4--,tide-raising forces4 ,an entirely analogous set of forces produces a similar effect upon the shape of the moon4 ,the elastic cords of ,fig4 #bc stand for the attraction of gravitation by which all the parts of the moon are bound together4 ,the magnet represents the earth pulling with unequal force upon different parts of the moon4 ,the weights are the inertia of the moon in its orbital motion which1 as we have seen in a previous section1 upon the whole just balances the earth's attraction and keeps the moon from falling into it4 ,the effect of these forces is to stretch out the moon along a line pointing toward the earth1 just as the blocks were stretched out along the line of the magnet1 and to make this diameter of the moon slightly but permanently longer than the others4 ,illustration3 ,,fig4 #bd4--,the tides4 ,,the ,,tides4--,similarly the moon and the sun attract opposite sides of the earth with different forces and feebly tend to pull it out of shape4 ,but here a new element comes into play3 the earth turns so rapidly upon its axis that its solid parts have no time in which to yield sensibly to the strains1 which shift rapidly from one diameter to another as different parts of the earth are turned toward the moon1 and it is chiefly the waters of the sea which respond to the distorting effect of the sun's and moon's attraction4 ,these are heaped up on opposite sides of the earth so as to produce a slight elongation of its diameter1 and ,fig4 #bd 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 moon4 ,this heaping up of the waters is called a tide4 ,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 axis1 but whenever the island comes back to the position ,i1 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 tide4 ,so too when they reach ,i1 half a day later1 they will again rise in flood tide1 and midway between these points1 at ,i1 the waters must subside1 giving low or ebb tide4 ,the height of the tide raised by the moon in the open sea is only a very few feet1 and the tide raised by the sun is even less1 but along the coast of a continent1 in bays and angles of the shore1 it often happens that a broad but low tidal wave is forced into a narrow corner1 and then the rise of the water may be many feet1 especially when the solar tide and the lunar tide come in together1 as they do twice in every month1 at new and full moon4 ,why do they come together at these times instead of some other8 ,small as are these tidal effects1 it is worth noting that they may in certain cases be very much greater--e4 g41 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 fragments4 ,although the earth escapes this fate1 some other bodies are not so fortunate1 and we shall see in later chapters some evidence of their disintegration4 #dc4 ,,the ,,scope ,,of ,,the ,,law ,,of ,,gravitation4--,in all the domain of physical science there is no other law so famous as the ,newtonian law of gravitation2 none other that has been so dwelt upon1 studied1 and elaborated by astronomers and mathematicians1 and perhaps none that can be considered so indisputably proved4 ,over and over again mathematical analysis1 based upon this law1 has pointed out conclusions which1 though hitherto unsuspected1 have afterward been found true1 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 time1 and not proved by actual measurement until long afterward4 ,it is1 in fact1 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 gravitation1 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 observed4 ,chief among these is the case of the planet ,mercury1 the long diameter of whose orbit is slowly turning around in a way for which the law of gravitation as yet furnishes no explanation4 ,whether this is because the law itself is inaccurate or incomplete1 or whether it only marks a case in which astronomers have not yet properly applied the law and traced out its consequences1 we do not know2 but whether it be the one or the other1 this and other similar cases show that even here1 in its most perfect chapter1 astronomy still remains an incomplete science4 ,,chapter ,v ,,the ,,earth ,,as ,a ,,planet #dd4 ,,the ,,size ,,of ,,the ,,earth4--,the student is presumed to have learned1 in his study of geography1 that the earth is a globe about #h1jjj miles in diameter and1 without dwelling upon the proofs which are commonly given for these statements1 we proceed to consider the principles upon which the measurement of the earth's size and shape are based4 ,illustration3 ,,fig4 #be4--,measuring the size of the earth4 ,in ,fig4 #be the circle represents a meridian section of the earth2 ,p ,p is the axis about which it rotates1 and the dotted lines represent a beam of light coming from a star in the plane of the meridian1 and so distant that the dotted lines are all practically parallel to each other4 ,the several radii drawn through the points #a1 #b1 #c1 represent the direction of the vertical at these points1 and the angles which these radii produced1 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 meridian4 ,we have already seen1 in ,chapter ,,ii1 how these angles may be measured1 and it is apparent from the figure that the difference between any two of these angles--e4 g41 the angles at #a and #b--;is equal to the angle at the center1 ,o1 between the points #a and #b4 ,by measuring these angular distances of the star from the zenith1 the astronomer finds the angles at the center of the earth between the stations #a1 #b1 #c1 etc41 at which his observations are made4 ,if the meridian were a perfect circle the change of zenith distance of the star1 as one traveled along a meridian from the equator to the pole1 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 true1 but that1 on the whole1 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 equator4 ,the earth is1 in fact1 flattened at the poles to the amount of about #bg miles in the length of its diameter1 and by this amount1 as well as by smaller variations due to mountains and valleys1 the shape of the earth differs from a perfect sphere4 ,these astronomical measurements of the curvature of the earth's surface furnish by far the most satisfactory proof that it is very approximately a sphere1 and furnish as its equatorial diameter #g1ibf miles4 ,neglecting the compression1 as it is called1 i4 e41 the #bg miles by which the equatorial diameter exceeds the polar1 the size of the earth may easily be found by measuring the distance #a--b along the surface and by combining with this the angle #a ,o #b obtained through measuring the meridian altitudes of any star as seen from #a and #b4 ,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 sides1 measured along an arc of a circle1 equal to the measured distance between #a and #b4 ,this distance from the vertex will be the earth's radius4 ,,exercise #ai4--,measure the diameter of the earth by the method given above4 ,in order that this may be done satisfactorily1 the two stations at which observations are made must be separated by a considerable distance--i4 e41 #bjj miles4 ,they need not be on the same meridian1 but if they are on different meridians in place of the actual distance between them1 there must be used the projection of that distance upon the meridian--i4 e41 the north and south part of the distance4 ,by co-operation between schools in the ,northern and ,southern ,states1 using a good map to obtain the required distances1 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 value4 #de4 ,,the ,,mass ,,of ,,the ,,earth4--,we have seen in ,chapter ,,iv the possibility of determining the masses of the planets as fractional parts of the sun's mass1 but nothing was there shown1 or could be shown1 about measuring these masses after the common fashion in kilogrammes or tons4 ,to do this we must first get the mass of the earth in tons or kilogrammes1 and while the principles involved in this determination are simple enough1 their actual application is delicate and difficult4 ,illustration3 ,,fig4 #bf4--;,illustrating the principles involved in weighing the earth4 ,in ,fig4 #bf we suppose a long plumb line to be suspended above the surface of the earth and to be attracted toward the center of the earth1 ,c1 by a force whose intensity is 7,chapter ,,iv7 ,f k m,e_/,r#b1 where ,e denotes the mass of the earth1 which is to be determined by experiment1 and ,r is the radius of the earth1 #c1ifc miles4 ,if there is no disturbing influence present1 the plumb line will point directly downward1 but if a massive ball of lead or other heavy substance is placed at one side1 #a1 it will attract the plumb line with a force equal to f k m,b_/r#b1 where r is the distance of its center from the plumb bob and ,b is its mass which we may suppose1 for illustration1 to be a ton4 ,in consequence of this attraction the plumb line will be pulled a little to one side1 as shown by the dotted line1 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 3 f 33 l 3 d2 and introducing the values of ,f and f given above1 and solving for ,e the proportion thus transformed1 we find ,e ,b l_/d 7,r_/r7#b4 ,in this equation the mass of the ball1 ,b1 the length of the plumb line1 l1 the distance between the center of the ball and the center of the plumb bob1 r1 and the radius of the earth1 ,r1 can all be measured directly1 and d1 the amount by which the plumb bob is pulled to one side by the ball1 is readily found by shifting the ball over to the other side1 at #b1 and measuring with a microscope how far the plumb bob moves4 ,this distance will1 of course1 be equal to #b d4 ,by methods involving these principles1 but applied in a manner more complicated as well as more precise1 the mass of the earth is found to be1 in tons1 #f1fdb #ajah--;i4 e41 #f1fdb followed by #ah ciphers1 or in kilogrammes #fj1beh #ajbj4 ,the earth's atmosphere makes up about a millionth part of this mass4 ,if the length of the plumb line were #ajj feet1 the weight of the ball a ton1 and the distance between the two positions of the ball1 #a and #b1 six feet1 how many inches1 d1 would the plumb bob be pulled out of place8 ,find from the mass of the earth and the data of #dj the mass of the sun in tons4 ,find also the mass of ,mars4 ,the computation can be very greatly abridged by the use of logarithms4 #df4 ,,precession4--,that the earth is isolated in space and has no support upon which to rest1 is sufficiently shown by the fact that the stars are visible upon every side of it1 and no support can be seen stretching out toward them4 ,we must then consider the earth to be a globe traveling freely about the sun in a circuit which it completes once every year1 and rotating once in every twenty-four hours about an axis which remains at all seasons directed very nearly toward the star ,polaris4 ,the student should be able to show from his own observations of the sun that1 with reference to the stars1 the direction of the sun from the earth changes about a degree a day4 ,does this prove that the earth revolves about the sun8 ,but it is only in appearance that the pole maintains its fixed position among the stars4 ,if photographs are taken year after year1 after the manner of ,exercise #g1 it will be found that slowly the pole is moving 7nearly7 toward ,polaris1 and making this star describe a smaller and smaller circle in its diurnal path1 while stars on the other side of the pole 7in right ascension #ab;h47 become more distant from it and describe larger circles in their diurnal motion2 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 moon4 ,spin a top and note how its rapid whirl about its axis corresponds to the earth's diurnal rotation4 ,when the axis about which the top spins is truly vertical the top sleeps2 but if the axis is tipped ever so little away from the vertical it begins to wobble1 so that if we imagine the axis prolonged out to the sky and provided with a pencil point as a marker1 this would trace a circle around the zenith1 along which the pole of the top would move1 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 place4 ,were it not for the spinning of the top about its axis1 it would promptly fall over when tipped from the vertical position1 but the spin combines with the force which pulls the top over and produces the wobbling motion4 ,spin the top in opposite directions1 with the hands of a watch and contrary to the hands of a watch1 and note the effect which is produced upon the wobbling4 ,the earth presents many points of resemblance to the top4 ,its diurnal rotation is the spin about the axis4 ,this axis is tipped #bc4e away from the perpendicular to its orbit 7obliquity of the ecliptic7 just as the axis of the top is tipped away from the vertical line4 ,in consequence of its rapid spin1 the body of the earth bulges out at the equator 7#bg miles71 and the sun and moon1 by virtue of their attraction 7see ,chapter ,,iv71 lay hold of this protuberance and pull it down toward the plane of the earth's orbit1 so that if it were not for the spin this force would straighten the axis up and set it perpendicular to the orbit plane4 ,but here1 as in the case of the top1 the spin and the tipping force combine to produce a wobble which is called precession1 and whose effect we recognize in the shifting position of the pole among the stars4 ,the motion of precession is very much slower than the wobbling of the top1 since the tipping force for the earth is relatively very small1 and a period of nearly #bf1jjj years is required for a complete circuit of the pole about its center of motion4 ,friction ultimately stops both the spin and the wobble of the top1 but this influence seems wholly absent in the case of the earth1 and both rotation and precession go on unchanged from century to century1 save for certain minor forces which for a time change the direction or rate of the precessional motion1 first in one way and then in another1 without in the long run producing any results of consequence4 ,the center of motion1 about which the pole travels in a small circle having an angular radius of #bc4e1 is at that point of the heavens toward which a perpendicular to the plane of the earth's orbit points1 and may be found on the star map in right ascension #ah;h4 #jm4 and declination #ff4e4 ,,exercise #bj4--;,find this point on the map1 and draw as well as you can the path of the pole about it4 ,the motion of the pole along its path is toward the constellation ,cepheus4 ,mark the position of the pole along this path at intervals of #a1jjj years1 and refer to these positions in dealing with some of the following questions3 ,does the wobbling of the top occur in the same direction as the motion of precession8 ,do the tipping forces applied to the earth and top act in the same direction8 ,what will be the polar star #ab1jjj years hence8 ,the ,great ,pyramid of ,egypt is thought to have been used as an observatory when ,alpha ,draconis was the bright star nearest the pole4 ,how long ago was that8 ,the motion of the pole of course carries the equator and the equinoxes with it1 and thus slowly changes the right ascensions and declinations of all the stars4 ,on this account it is frequently called the precession of the equinoxes1 and this motion of the equinox1 slow though it is1 is a matter of some consequence in connection with chronology and the length of the year4 ,will the precession ever bring back the right ascensions and declinations to be again what they now are8 ,in what direction is the pole moving with respect to the ,big ,dipper8 ,will its motion ever bring it exactly to ,polaris8 ,how far away from ,polaris will the precession carry the pole8 ,what other bright stars will be brought near the pole by the precession8 #dg4 ,,the ,,warming ,,of ,,the ,,earth4--,winter and summer alike the day is on the average warmer than the night1 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 earth2 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 surroundings4 ,the earth's loss of heat by radiation goes on ceaselessly day and night1 and were it not for the influx of solar heat this radiation would steadily diminish the temperature toward what is called the absolute zero--i4 e41 a state in which all heat has been taken away and beyond which there can be no greater degree of cold4 ,this must not be confounded with the zero temperatures shown by our thermometers1 since it lies nearly #ejj below the zero of the ,fahrenheit scale 7-#bgc ,centigrade71 a temperature which by comparison makes the coldest winter weather seem warm1 although the ordinary thermometer may register many degrees below its zero4 ,the heat radiated by the sun into the surrounding space on every side of it is another example of the same cooling process1 a hot body giving up its heat to the colder space about it1 and it is the minute fraction of this heat poured out by the sun1 and in small part intercepted by the earth1 which warms the latter and produces what we call weather1 climate1 the seasons1 etc4 ,observe the fluctuations1 the ebb and flow1 which are inherent in this process4 ,from sunset to sunrise there is nothing to compensate the steady outflow of heat1 and air and ground grow steadily colder1 but with the sunrise there comes an influx of solar heat1 feeble at first because it strikes the earth's surface very obliquely1 but becoming more and more efficient as the sun rises higher in the sky4 ,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 heat1 just as a steam pipe or a cup of coffee radiates heat more rapidly when very hot4 ,the warmest hour of the day is reached when these opposing tendencies of income and expenditure of heat are just balanced2 and barring such disturbing factors as wind and clouds1 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 efficient1 when radiation gains the upper hand and the temperature becomes for a short time stationary1 and then commences to fall steadily until the next sunrise4 ,we have here an example of what is called a periodic change--i4 e41 one which1 within a definite and uniform period 7#bd hours71 oscillates from a minimum up to a maximum temperature and then back again to a minimum1 repeating substantially the same variation day after day4 ,but it must be understood that minor causes not taken into account above1 such as winds1 water1 etc41 produce other fluctuations from day to day which sometimes obscure or even obliterate the diurnal variation of temperature caused by the sun4 ,expose the back of your hand to the sun1 holding the hand in such a position that the sunlight strikes perpendicularly upon it2 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 second4 ,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 horizon1 and more effective in summer than in winter4 ,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 #bc4e1 and the stars show by their earlier risings and later settings1 as we pass from the equator toward the north pole of the heavens1 that as the sun moves northward from the equator1 each day in the northern hemisphere will become a little longer1 each night a little shorter1 and every day the sun will rise higher toward the zenith until this process culminates toward the end of ,june1 when the sun begins to move southward1 bringing shorter days and smaller altitudes until the ,christmas season1 when again it is reversed and the sun moves northward4 ,we have here another periodic variation1 which runs its complete course in a period of a year1 and it is easy to see that this variation must have a marked effect on the warming of the earth1 the long days and great altitudes of summer producing the greater warmth of that season1 while the shorter days and lower altitudes of ,december1 by diminishing the daily supply of solar heat1 bring on the winter's cold4 ,the succession of the seasons1 winter following summer and summer winter1 is caused by the varying altitude of the sun1 and this in turn is due to the obliquity of the ecliptic1 or1 what is the same thing1 the amount by which the axis of the earth is tipped from being perpendicular to the plane of its orbit1 and the seasons are simply a periodic change in the warming of the earth1 quite comparable with the diurnal change but of longer period4 ,it is evident that the period within which the succession of winter and summer is completed1 the year1 as we commonly call it1 must equal the time required by the sun to go from the vernal equinox around to the vernal equinox again1 since this furnishes a complete cycle of the sun's motions north and south from the equator4 ,on account of the westward motion of the equinox 7precession7 this is not quite the same as the time required for a complete revolution of the earth in its orbit1 but is a little shorter 7#bjm4 #bcs471 since the equinox moves back to meet the sun4 #dh4 ,,relation ,,of ,,the ,,sun ,,to ,,climate4--,it is clear that both the northern and southern hemispheres of the earth must have substantially the same kind of seasons1 since the motion of the sun north and south affects both alike2 but when the sun is north of the equator and warming our hemisphere most effectively1 his light falls more obliquely upon the other hemisphere1 the days there are short and winter reigns at the time we are enjoying summer1 while six months later the conditions are reversed4 ,in those parts of the earth near the equator--the torrid zone--there is no such marked change from cold to warm as we experience1 because1 as the sun never gets more than #bc4e away from the celestial equator1 on every day of the year he mounts high in the tropic skies1 always coming within #bc4e of the zenith1 and usually closer than this1 so that there is no such periodic change in the heat supply as is experienced in higher latitudes1 and within the tropics the temperature is therefore both higher and more uniform than in our latitude4 ,in the frigid zones1 on the contrary1 the sun never rises high in the sky2 at the poles his greatest altitude is only #bc4e1 and during the winter season he does not rise at all1 so that the temperature is here low the whole year round1 and during the winter season1 when for weeks or months at a time the supply of solar light is entirely cut off1 the temperature falls to a degree unknown in more favored climes4 ,if the obliquity of the ecliptic were made #aj greater1 what would be the effect upon the seasons in the temperate zones8 ,what if it were made #aj less8 ,does the precession of the equinoxes have any effect upon the seasons or upon the climate of different parts of the earth8 ,if the axis of the earth pointed toward ,arcturus instead of ,polaris1 would the seasons be any different from what they are now8 #di4 ,,the ,,atmosphere4--,although we live upon its surface1 we are not outside the earth1 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 miles4 ,the study of most of the phenomena of the atmosphere belongs to that branch of physics called meteorology1 but there are a few matters which fairly come within our consideration of the earth as a planet4 ,we can not see the stars save as we look through this atmosphere1 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 bodies4 ,frequently this disturbance is visible to the naked eye1 and the stars are said to twinkle--i4 e41 to quiver and change color many times per second1 solely in consequence of a disturbed condition of the air and not from anything which goes on in the star4 ,this effect is more marked low down in the sky than near the zenith1 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 area1 while a star1 being much smaller and farther from the earth1 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' disk4 #ej4 ,,refraction4--,at all times1 whether the stars twinkle or not1 their light is bent in its passage through the atmosphere1 so that the stars appear to stand higher up in the sky than their true positions4 ,this effect1 which the astronomer calls refraction1 must be allowed for in observations of the more precise class1 although save at low altitudes its amount is a very small fraction of a degree1 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 horizontal4 ,the refraction lifts both upper and lower edge of the sun1 but lifts the lower edge more than the upper1 thus shortening the vertical diameter4 ,see ,fig4 #bg1 which shows not only this effect1 but also the reflection of the sun from the curved surface of the sea1 still further flattening the image4 ,if the surface of the water were flat1 the reflected image would have the same shape as the sun's disk1 and its altered appearance is sometimes cited as a proof that the earth's surface is curved4 ,the total amount of the refraction at the horizon is a little more than half a degree1 and since the diameters of the sun and moon subtend an angle of about half a degree1 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 begins4 ,the same effect exists at sunrise1 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 refraction4 ,a partial offset to this benefit is found in the fact that the atmosphere absorbs the light of the heavenly bodies1 so that stars appear much less bright when near the horizon than when they are higher up in the sky1 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 noon4 ,illustration3 ,,fig4 #bg4--;,flattening of the sun's disk by refraction and by reflection from the surface of the sea4 #ea4 ,,the ,,twilight4--,another effect of the atmosphere1 even more marked than the preceding1 is the twilight4 ,as at sunrise the mountain top catches the rays of the coming sun before they reach the lowland1 and at sunset it keeps them after they have faded from the regions below1 so the particles of dust and vapor1 which always float in the atmosphere1 catch the sunlight and reflect it to the surface of the earth while the sun is still below the horizon1 giving at the beginning and end of day that vague and diffuse light which we call twilight4 ,illustration3 ,,fig4 #bh4--,twilight phenomena4 ,fig4 #bh shows a part of the earth surrounded by such a dust-laden atmosphere1 which is illuminated on the left by the rays of the sun1 but which1 on the right of the figure1 lies in the shadow cast by the earth4 ,to an observer placed at #a the sun is just setting1 and all the atmosphere above him is illumined with its rays1 which furnish a bright twilight4 ,when1 by the earth's rotation1 this observer has been carried to #b1 all the region to the east of his zenith lies in the shadow1 while to the west there is a part of the atmosphere from which there still comes a twilight1 but now comparatively faint1 because the lower part of the atmosphere about our observer lies in the shadow1 and it is mainly its upper regions from which the light comes1 and here the dust and moisture are much less abundant than in the lower strata4 ,still later1 when the observer has been carried by the earth's rotation to the point #c1 every vestige of twilight will have vanished from his sky1 because all of the illuminated part of the atmosphere is now below his horizon1 which is represented by the line #c ,l4 ,in the figure the sun is represented to be #gh below this horizon line at the end of twilight1 but this is a gross exaggeration1 made for the sake of clearness in the drawing--in fact1 twilight is usually said to end when the sun is #ah below the horizon4 ,let the student redraw ,fig4 #bh on a large scale1 so that the points #a and #c shall be only #ah apart1 as seen from the earth's center4 ,he will find that the point ,l is brought down much closer to the surface of the earth1 and measuring the length of the line #b ,l1 he should find for the height of the atmosphere about one-eightieth part of the radius of the earth--i4 e41 a little less than #ej miles4 ,this1 however1 is not the true height of the atmosphere4 ,the air extends far beyond this1 but the particles of dust and vapor which are capable of sending sunlight down to the earth seem all to lie below this limit4 ,the student should not fail to watch the eastern sky after sunset1 and see the shadow of the earth rise up and fill it while the twilight arch retreats steadily toward the west4 ,illustration3 ,,fig4 #bi4--,the cause of long and short twilights4 ,duration of twilight4--,since twilight ends when the sun is #ah below the horizon1 any circumstance which makes the sun go down rapidly will shorten the duration of twilight1 and anything which retards the downward motion of the sun will correspondingly prolong it4 ,chief among influences of this kind is the angle which the sun's course makes with the horizon4 ,if it goes straight down1 as at a1 ,fig4 #bi1 a much shorter time will suffice to carry it to a depression of #ah than is needed in the case shown at b in the same figure1 where the motion is very oblique to the horizon4 ,if we consider different latitudes and different seasons of the year1 we shall find every possible variety of circumstance from a to b1 and corresponding to these1 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 ,peru4 ,for the sake of graphical effect1 the shortness of tropical twilight is somewhat exaggerated by ,coleridge in the lines1 ,the sun's rim dips2 the stars rush out3 ,at one stride comes the dark4 ,the ,ancient ,mariner4 ,in the ,united ,states the longest twilights come at the end of ,june1 and last for a little more than two hours1 while the shortest ones are in ,march and ,september1 amounting to a little more than an hour and a half2 but at all times the last half hour of twilight is hardly to be distinguished from night1 so small is the quantity of reflecting matter in the upper regions of the atmosphere4 ,for practical convenience it is customary to assume in the courts of law that twilight ends an hour after sunset4 ,how long does twilight last at the north pole8 ,the ,aurora4--,one other phenomenon of the atmosphere may be mentioned1 only to point out that it is not of an astronomical character4 ,the ,aurora1 or northern lights1 is as purely an affair of the earth as is a thunderstorm1 and its explanation belongs to the subject of terrestrial magnetism4 ,,chapter ,,vi ,,the ,,measurement ,,of ,,time #eb4 ,,solar ,,time4--,to measure any quantity we need a unit in terms of which it must be expressed4 ,angles are measured in degrees1 and the degree is the unit for angular measurement4 ,for most scientific purposes the centimeter is adopted as the unit with which to measure distances1 and similarly a day is the fundamental unit for the measurement of time4 ,hours1 minutes1 and seconds are aliquot parts of this unit convenient for use in dealing with shorter periods than a day1 and the week1 month1 and year which we use in our calendars are multiples of the day4 ,strictly speaking1 a day is not the time required by the earth to make one revolution upon its axis1 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 again4 ,the day begins at the moment when this specified part of the sky is on the meridian1 and the time at any moment is the hour angle of this particular part of the sky--i4 e41 the number of hours1 minutes1 etc41 that have elapsed since it was on the meridian4 ,the student has already become familiar with the kind of day which is based upon the motion of the vernal equinox1 and which furnishes sidereal time1 and he has seen that sidereal time1 while very convenient in dealing with the motions of the stars1 is decidedly inconvenient for the ordinary affairs of life since in the reckoning of the hours it takes no account of daylight and darkness4 ,one can not tell off-hand whether #aj hours1 sidereal time1 falls in the day or in the night4 ,we must in some way obtain a day and a system of time reckoning based upon the apparent diurnal motion of the sun1 and we may1 if we choose1 take the sun itself as the point in the heavens whose transit over the meridian shall mark the beginning and the end of the day4 ,in this system the time is the number of hours1 minutes1 etc41 which have elapsed since the sun was on the meridian1 and this is the kind of time which is shown by a sun dial1 and which was in general use1 years ago1 before clocks and watches became common4 ,since the sun moves among the stars about a degree per day1 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 again1 than to carry it from a star around to the same star1 or from the vernal equinox around to the vernal equinox again2 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 ,,xii4 ,these solar days and hours and minutes are therefore a little longer than the corresponding sidereal ones1 and this furnishes the explanation why the stars come to the meridian a little earlier1 by solar time1 every night than on the night before1 and why sidereal time gains steadily upon solar time1 this gain amounting to approximately #cm4 #ef4es4 per day1 or exactly one day per year1 since the sun makes the complete circuit of the constellations once in a year4 ,with the general introduction of clocks and watches into use about a century ago this kind of solar time went out of common use1 since no well-regulated clock could keep the time correctly4 ,the earth in its orbital motion around the sun goes faster in some parts of its orbit than in others1 and in consequence the sun appears to move more rapidly among the stars in winter than in summer2 moreover1 on account of the convergence of hour circles as we go away from the equator1 the same amount of motion along the ecliptic produces more effect in winter and summer when the sun is north or south1 than it does in the spring and autumn when the sun is near the equator1 and as a combined result of these causes and other minor ones true solar time1 as it is called1 is itself not uniform1 but falls behind the uniform lapse of sidereal time at a variable rate1 sometimes quicker1 sometimes slower4 ,a true solar day1 from noon to noon1 is #ea seconds shorter in ,september than in ,december4 ,illustration3 ,,fig4 #cj4--,the equation of time4 #ec4 ,,mean ,,solar ,,time4--,to remedy these inconveniences there has been invented and brought into common use what is called mean solar time1 which is perfectly uniform in its lapse and which1 by comparison with sidereal time1 loses exactly one day per year4 ,the time in this system never differs much from true solar time1 and the difference between the two for any particular day may be found in any good almanac1 or may be read from the curve in ,fig4 #cj1 in which the part of the curve above the line marked #jm shows how many minutes mean solar time is faster than true solar time4 ,the correct name for this difference between the two kinds of solar time is the equation of time1 but in the almanacs it is frequently marked sun fast or sun slow4 ,in sidereal time and true solar time the distinction between ,a4 ,m4 hours 7ante meridiem before the sun reaches the meridian7 and ,p4 ,m4 hours 7post meridiem after the sun has passed the meridian7 is not observed1 the time being counted from #j hours to #bd hours1 commencing when the sun or vernal equinox is on the meridian4 ,occasionally the attempt is made to introduce into common use this mode of reckoning the hours1 beginning the day 7date7 at midnight and counting the hours consecutively up to #bd1 when the next date is reached and a new start made4 ,such a system would simplify railway time tables and similar publications2 but the ,american public is slow to adopt it1 although the system has come into practical use in ,canada and ,spain4 #ed4 ,,to ,,find 7,,approximately7 ,,the ,,sidereal ,,time ,,at ,,any ,,moment4--,,rule ,i4 ,when the mean solar time is known4 ,let ,w represent the time shown by an ordinary watch1 and represent by ,s the corresponding sidereal time and by ,d the number of days that have elapsed from ,march #bc;d to the date in question4 ,then ,s ,w #fi_/gj ,d #d4 ,the last term is expressed in minutes1 and should be reduced to hours and minutes4 ,thus at #d ,p4 ,m4 on ,july #dth-- ,d #ajc days4 #fi_/gj ,d #d #djfm4 #f;h4 #dfm4 ,w #d;h4 #jm4 ,s #aj;h4 #dfm4 ,the daily gain of sidereal upon mean solar time is #fi_/gj of #d minutes1 and ,march #bc;d is the date on which sidereal and mean solar time are together1 taking the average of one year with another1 but it varies a little from year to year on account of the extra day introduced in leap years4 ,,rule ,,ii4 ,when the stars in the northern sky can be seen4 ,find b ,cassiopei1 and imagine a line drawn from it to ,polaris1 and another line from ,polaris to the zenith4 ,the sidereal time is equal to the angle between these lines1 provided that that angle must be measured from the zenith toward the west4 ,turn the angle from degrees into hours by dividing by #ae4 #ee4 ,,the ,,earth',s ,,rotation4--,we are familiar with the fact that a watch may run faster at one time than at another1 and it is worth while to inquire if the same is not true of our chief timepiece--the earth4 ,it is assumed in the sections upon the measurement of time that the earth turns about its axis with absolute uniformity1 so that mean solar time never gains or loses even the smallest fraction of a second4 ,whether this be absolutely true or not1 no one has ever succeeded in finding convincing proof of a variation large enough to be measured1 although it has recently been shown that the axis about which it rotates is not perfectly fixed within the body of the earth4 ,the solid body of the earth wriggles about this axis like a fish upon a hook1 so that the position of the north pole upon the earth's surface changes within a year to the extent of #dj or #ej feet 7#ae meters7 without ever getting more than this distance away from its average position4 ,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 change1 and it seems probable that these changes will produce some small effect upon the rotation of the earth4 ,but in spite of these1 for any such moderate interval of time as a year or a century1 so far as present knowledge goes1 we may regard the earth's rotation as uniform and undisturbed4 ,for longer intervals--e4 g41 #a1jjj1jjj or #aj1jjj1jjj years--the question is a very different one1 and we shall have to meet it again in another connection4 #ef4 ,,longitude ,,and ,,time4--,in what precedes there has been constant reference to the meridian4 ,the day begins when the sun is on the meridian4 ,solar time is the angular distance of the sun past the meridian4 ,sidereal time was determined by observing transits of stars over a meridian line actually laid out upon the ground1 etc4 ,but every place upon the earth has its own meridian from which the time may be reckoned1 and in ,fig4 #ca1 where the rays of sunlight are represented as falling upon a part of the earth's equator through which the meridians of ,new ,york1 ,chicago1 and ,san ,francisco pass1 it is evident that these rays make different angles with the meridians1 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 meridians4 ,this angle is called by geographers the difference of longitude between the two places1 and the student should note that the word longitude is here used in a different sense from that on page #cf4 ,from ,fig4 #ca we obtain the ,theorem4--,the difference between the times at any two meridians is equal to their difference of longitude1 and the time at the eastern meridian is greater than at the western meridian4 ,astronomers usually express differences of longitude in hours instead of degrees4 #a;h4 #ae4 ,the name given to any kind of time should distinguish all the elements which enter into it--e4 g41 ,new ,york sidereal time means the hour angle of the vernal equinox measured from the meridian of ,new ,york1 ,chicago true solar time is the hour angle of the sun reckoned from the meridian of ,chicago1 etc4 ,illustration3 ,,fig4 #ca4--,longitude and time ,illustration3 ,,fig4 #cb4--,standard time4 #eg4 ,,standard ,,time4--,the requirements of railroad traffic have led to the use throughout the ,united ,states and ,canada of four standard times1 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 ,greenwich1 ,england4 ,eastern time is #e hours slower than that of ,greenwich4 ,central #f ,mountain #g ,pacific #h ,in ,fig4 #cb the broken lines indicate roughly the parts of the ,united ,states and ,canada in which these several kinds of time are used1 and illustrate how irregular are the boundaries of these parts4 ,standard time is sent daily into all of the more important telegraph offices of the ,united ,states1 and serves to regulate watches and clocks1 to the almost complete exclusion of local time4 #eh4 ,,to ,,determine ,,the ,,longitude4--,with an ordinary watch observe the time of the sun's transit over your local meridian1 and correct the observed time for the equation of time by means of the curve in ,fig4 #cj4 ,the difference between the corrected time and #ab o'clock will be the correction of your watch referred to local mean solar time4 ,compare your watch with the time signals in the nearest telegraph office and find its correction referred to standard time4 ,the difference between the two corrections is the difference between your longitude and that of the standard meridian4 ,n4 ,b4--,don't tamper with the watch by trying to set it right4 ,no harm will be done if it is wrong1 provided you take due account of the correction as indicated above4 ,if the correction of the watch changed between your observation and the comparison in the telegraph office1 what effect would it have upon the longitude determination8 ,how can you avoid this effect8 #ei4 ,,chronology4--,the ,century ,dictionary defines chronology as the science of time--that is1 the method of measuring or computing time by regular divisions or periods according to the revolutions of the sun or moon4 ,we have already seen that for the measurement of short intervals of time the day and its subdivisions--hours1 minutes1 seconds--furnish a very complete and convenient system4 ,but for longer periods1 extending to hundreds and thousands of days1 a larger unit of time is required1 and for the most part these longer units have in all ages and among all peoples been based upon astronomical considerations4 ,but to this there is one marked exception4 ,the week is a simple multiple of the day1 as the dime is a multiple of the cent1 and while it may have had its origin in the changing phases of the moon this is at best doubtful1 since it does not follow these with any considerable accuracy4 ,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 avoided1 and the annals of ancient times would have presented fewer pitfalls to the historian than is now the case4 ,the month is plainly connected with the motion of the moon among the stars4 ,the year is1 of course1 based upon the motion of the sun through the heavens and the change of seasons which is thus produced2 although1 as commonly employed1 it is not quite the same as the time required by the earth to make one complete revolution in its orbit4 ,this time of one revolution is called a sidereal year1 while1 as we have already seen in ,chapter ,v1 the year which measures the course of the seasons is shorter than this on account of the precession of the equinoxes4 ,it is called a tropical year with reference to the circuit which the sun makes from one tropic to the other and back again4 ,we can readily understand why primitive peoples should adopt as units of time these natural periods1 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 life4 ,how many dollars make a pound sterling8 ,how shall we make change with ,english shillings and ,american dimes1 etc48 ,how much is one unit worth in terms of the other8 ,one of the ,greek poets#b 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 calendar3 ,the moon by us to you her greeting sends1 ,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-turvy1 ,so that when gods1 who know their feast days well1 ,by your false count are sent home supperless1 ,they scold and storm at her for your neglect4 #b ,aristophanes1 ,the ,clouds1 ,whewell's translation4 #fj4 ,,day1 ,,month1 ,,and ,,year4--,if the day1 the month1 and the year are to be used concurrently1 it is necessary to determine how many days are contained in the month and year1 and when this has been done by the astronomer the numbers are found to be very awkward and inconvenient for daily use2 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 follow4 ,according to ,professor ,harkness1 for the epoch #aijj ,a4 ,d4-- ,one tropical year #cfe4bdbaig mean solar days4 #cfe;d4 #e;h4 #dhm4 #de4hs4 ,one lunation #bi4ecjehh mean solar days4 #bi;d4 #ab;h4 #ddm4 #b4hs4 ,the word lunation means the average interval from one new moon to the next one--i4 e41 the time required by the moon to go from conjunction with the sun round to conjunction again4 ,a very ancient device was to call a year equal to #cfe days1 and to have months alternately of #bi and #cj days in length1 but this was unsatisfactory in more than one way4 ,at the end of four years this artificial calendar would be about one day ahead of the true one1 at the end of forty years ten days in error1 and within a single lifetime the seasons would have appreciably changed their position in the year1 ,april weather being due in ,march1 according to the calendar4 ,so1 too1 the year under this arrangement did not consist of any integral number of months1 #ab months of the average length of #bi4e days being #ced days1 and #ac months #chc4e days1 thus making any particular month change its position from the beginning to the middle and the end of the year within a comparatively short time4 ,some peoples gave up the astronomical year as an independent unit and adopted a conventional year of #ab lunar months1 #ced days1 which is now in use in certain ,mohammedan countries1 where it is known as the wandering year1 with reference to the changing positions of the seasons in such a year4 ,others held to the astronomical year and adopted a system of conventional months1 such that twelve of them would just make up a year1 as is done to this day in our own calendar1 whose months of arbitrary length we are compelled to remember by some such jingle as the following3 ,thirty days hath ,september1 ,april1 ,june1 and ,november2 ,all the rest have thirty-one ,save ,february1 ,which alone hath twenty-eight1 ,till leap year gives it twenty-nine4 #fa4 ,,the ,,calendar4--,the foundations of our calendar may fairly be ascribed to ,julius ,csar1 who1 under the advice of the ,egyptian astronomer ,sosigines1 adopted the old ,egyptian device of a leap year1 whereby every fourth year was to consist of #cff days1 while ordinary years were only #cfe days long4 ,he also placed the beginning of the year at the first of ,january1 instead of in ,march1 where it had formerly been1 and gave his own name1 ,julius1 to the month which we now call ,july4 ,august was afterward named in honor of his successor1 ,augustus4 ,the names of the earlier months of the year are drawn from ,roman mythology2 those of the later months1 ,september1 ,october1 etc41 meaning seventh month1 eighth month1 represent the places of these months in the year1 before ,csar's reformation1 and also their places in some of the subsequent calendars1 for the widest diversity of practice existed during medival times with regard to the day on which the new year should begin1 ,christmas1 ,easter1 ,march #beth1 and others having been employed at different times and places4 ,the system of leap years introduced by ,csar makes the average length of a year #cfe4be days1 which differs by about eleven minutes from the true length of the tropical year1 a difference so small that for ordinary purposes no better approximation to the true length of the year need be desired4 ,but any deviation from the true length1 however small1 must in the course of time shift the seasons1 the vernal and autumnal equinox1 to another part of the year1 and the ecclesiastical authorities of medival ,europe found here ground for objection to ,csar's calendar1 since the great ,church festival of ,easter has its date determined with reference to the vernal equinox1 and with the lapse of centuries ,easter became more and more displaced in the calendar1 until ,pope ,gregory ,,xiii1 late in the sixteenth century1 decreed another reformation1 whereby ten days were dropped from the calendar1 the day after ,march #aath being called ,march #bast1 to bring back the vernal equinox to the date on which it fell in ,a4 ,d4 #cbe1 the time of the ,council of ,nica1 which ,gregory adopted as the fundamental epoch of his calendar4 ,the calendar having thus been brought back into agreement with that of old time1 ,gregory purposed to keep it in such agreement for the future by modifying ,csar's leap-year rule so that it should run3 ,every year whose number is divisible by #d shall be a leap year except those years whose numbers are divisible by #ajj but not divisible by #djj4 ,these latter years--e4 g41 #aijj--;are counted as common years4 ,the calendar thus altered is called ,gregorian to distinguish it from the older1 ,julian calendar1 and it found speedy acceptance in those civilized countries whose ,church adhered to ,rome2 but the ,protestant powers were slow to adopt it1 and it was introduced into ,england and her ,american colonies by act of ,parliament in the year #ageb1 nearly two centuries after ,gregory's time4 ,in ,russia the ,julian calendar has remained in common use to our own day1 but in commercial affairs it is there customary to write the date according to both calendars--e4 g41 ,july #d_/af1 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 one4 ,the ,julian and ,gregorian calendars are frequently represented by the abbreviations ,o4 ,s4 and ,n4 ,s41 old style1 new style1 and as the older historical dates are usually expressed in ,o4 ,s41 it is sometimes convenient to transform a date from the one calendar to the other4 ,this is readily done by the formula ,g ,j 7,n - #b7 - ,n_/#d1 where ,g and ,j are the respective dates1 ,n is the number of the century1 and the remainder is to be neglected in the division by #d4 ,for ,september #c1 #ageb1 ,o4 ,s41 we have ,j ,sept4 #c ,n - #b #ae - ,n_/#d - #d ------------------ ,g ,sept4 #ad and ,september #ad is the date fixed by act of ,parliament to correspond to ,september #c1 #ageb1 ,o4 ,s4 ,columbus discovered ,america on ,october #ab1 #adib1 ,o4 ,s4 ,what is the corresponding date in the ,gregorian calendar8 #fb4 ,,the ,,day ,,of ,,the ,,week4--,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--e4 g41 ,october #ba1 #adib4 ,the formula for this case is #gq r ,y ,d 7,y - #a7_/d - 7,y - #a7_/ajj 7,y - #a7_/djj where ,y denotes the given year1 ,d the number of the day 7date7 in that year1 and q and r are respectively the quotient and the remainder obtained by dividing the second member of the equation by #g4 ,if r #a the date falls on ,sunday1 etc41 and if r #j the day is ,saturday4 ,for the example suggested above we have ,jan4 #ca ,feb4 #bi ,mch4 #ca ,april #cj ,may #ca ,june #cj ,july #ca ,aug4 #ca ,sept4 #cj ,oct4 #ba --- ,d #bie ,y #adib ,d #bie 7,y - #a7 #d #cgb - 7,y - #a7 #ajj - #ad 7,y - #a7 #djj #c ------- #g7 #badh q #cjf r #f ,friday4 ,find from some history the day of the week on which ,columbus first saw ,america1 and compare this with the above4 ,on what day of the week did last ,christmas fall8 ,on what day of the week were you born8 ,in the formula for the day of the week why does q have the coefficient #g8 ,what principles in the calendar give rise to the divisors #d1 #ajj1 #djj8 ,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 encyclopdia4 ,illustration3 ,,the ,,yerkes ,,observatory1 ,,williams ,,bay1 ,,wis4 ,,chapter ,,vii ,,eclipses #fc4 ,,the ,,nature ,,of ,,eclipses4--,every planet has a shadow which travels with the planet along its orbit1 always pointing directly away from the sun1 and cutting off from a certain region of space the sunlight which otherwise would fill it4 ,for the most part these shadows are invisible1 but occasionally one of them falls upon a planet or some other body which shines by reflected sunlight1 and1 cutting off its supply of light1 produces the striking phenomenon which we call an eclipse4 ,the satellites of ,jupiter1 ,saturn1 and ,mars are eclipsed whenever they plunge into the shadows cast by their respective planets1 and ,jupiter himself is partially eclipsed when one of his own satellites passes between him and the sun1 and casts upon his broad surface a shadow too small to cover more than a fraction of it4 ,but the eclipses of most interest to us are those of the sun and moon1 called respectively solar and lunar eclipses4 ,in ,fig4 #cc the full moon1 ,m1 is shown immersed in the shadow cast by the earth1 and therefore eclipsed1 and in the same figure the new moon1 ,m1 is shown as casting its shadow upon the earth and producing an eclipse of the sun4 ,from a mere inspection of the figure we may learn that an eclipse of the sun can occur only at new moon--i4 e41 when the moon is on line between the earth and sun--and an eclipse of the moon can occur only at full moon4 ,why8 ,also1 the eclipsed moon1 ,m1 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 earth4 ,thus1 at ,l1 within the moon's shadow1 the sunlight will be entirely cut off1 producing what is called a total eclipse4 ,at points of the earth's surface near ,j and ,k there will be no interference whatever with the sunlight1 and no eclipse1 since the moon is quite off the line joining these regions to any part of the sun4 ,at places between ,j and ,l or ,k and ,l the moon will cut off a part of the sun's light1 but not all of it1 and will produce what is called a partial eclipse1 which1 as seen from the northern parts of the earth1 will be an eclipse of the lower 7southern7 part of the sun1 and as seen from the southern hemisphere will be an eclipse of the northern part of the sun4 ,illustration3 ,,fig4 #cc4--;,different kinds of eclipse4 ,the moon revolves around the earth in a plane1 which1 in the figure1 we suppose to be perpendicular to the surface of the paper1 and to pass through the sun along the line ,m ,m produced4 ,but it frequently happens that this plane is turned to one side of the sun1 along some such line as ,p ,q1 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 it1 giving a partial eclipse of the moon1 as is shown in the figure4 ,in what parts of the earth would this eclipse be visible8 ,what kinds of solar eclipse would be produced by the new moon at ,q8 ,in what parts of the earth would they be visible8 #fd4 ,,the ,,shadow ,,cone4--,the shape and position of the earth's shadow are indicated in ,fig4 #cc by the lines drawn tangent to the circles which represent the sun and earth1 since it is only between these lines that the earth interferes with the free radiation of sunlight1 and since both sun and earth are spheres1 and the earth is much the smaller of the two1 it is evident that the earth's shadow must be1 in geometrical language1 a cone whose base is at the earth1 and whose vertex lies far to the right of the figure--in other words1 the earth's shadow1 although very long1 tapers off finally to a point and ends4 ,so1 too1 the shadow of the moon is a cone1 having its base at the moon and its vertex turned away from the sun1 and1 as shown in the figure1 just about long enough to reach the earth4 ,it is easily shown1 by the theorem of similar triangles in connection with the known size of the earth and sun1 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 #ajh1 and1 similarly1 that the length of the moon's shadow is equal to the distance of the moon from the sun divided by #djj1 the moon's shadow being the smaller and shorter of the two1 because the moon is smaller than the earth4 ,the radius of the moon's orbit is just about #a_/djjth part of the radius of the earth's orbit--i4 e41 the distance of the moon from the earth is #a_/djjth part of the distance of the earth from the sun1 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 eclipses4 ,indeed1 the elliptical shape of the moon's orbit produces considerable variations in the distance of the moon from the earth1 and in consequence of these variations the vertex of the shadow sometimes falls short of reaching the earth1 and sometimes even projects considerably beyond its farther side4 ,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 sun1 for there is no shadow which can fall upon the earth1 even though the moon does come directly between earth and sun4 ,but there is then produced a peculiar kind of partial eclipse called annular1 or ring-shaped1 because the moon1 although eclipsing the central parts of the sun1 is not large enough to cover the whole of it1 but leaves the sun's edge visible as a ring of light1 which completely surrounds the moon4 ,although1 strictly speaking1 this is only a partial eclipse1 it is customary to put total and annular eclipses together in one class1 which is called central eclipses1 since in these eclipses the line of centers of sun and moon strikes the earth1 while in ordinary partial eclipses it passes to one side of the earth without striking it4 ,in this latter case we have to consider another cone called the penumbra--i4 e41 partial shadow--which is shown in ,fig4 #cc by the broken lines tangent to the sun and moon1 and crossing at the point ,v1 which is the vertex of this cone4 ,this penumbral cone includes within its surface all that region of space within which the moon cuts off any of the sunlight1 and of course it includes the shadow cone which produces total eclipses4 ,wherever the penumbra falls there will be a solar eclipse of some kind1 and the nearer the place is to the axis of the penumbra1 the more nearly total will be the eclipse4 ,since the moon stands about midway between the earth and the vertex of the penumbra1 the diameter of the penumbra where it strikes the earth will be about twice as great as the diameter of the moon1 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 #b1ajj miles on either side of the region where the eclipse is total4 ,measured along the curved surface of the earth1 this distance is frequently much greater4 ,is it true that if at any time the axis of the shadow cone comes within #b1ajj miles of the earth's surface a partial eclipse will be visible in those parts of the earth nearest the axis of the shadow8 #fe4 ,,different ,,characteristics ,,of ,,lunar ,,and ,,solar ,,eclipses4--,one marked difference between lunar and solar eclipses which has been already suggested1 may be learned from ,fig4 #cc4 ,the full moon1 ,m1 will be seen eclipsed from every part of the earth where it is visible at all at the time of the eclipse--that is1 from the whole night side of the earth2 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 falls4 ,since the point of the shadow at best but little more than reaches to the earth1 the amount of space upon the earth which it can cover at any one moment is very small1 seldom more than #ajj to #bjj miles in length1 and it is only within the space thus actually covered by the shadow that the sun is at any given moment totally eclipsed1 but within this region the sun disappears1 absolutely1 behind the solid body of the moon1 leaving to view only such outlying parts and appendages as are too large for the moon to cover4 ,at a lunar eclipse1 on the other hand1 the earth coming between sun and moon cuts off the light from the latter1 but1 curiously enough1 does not cut it off so completely that the moon disappears altogether from sight even in mid-eclipse4 ,the explanation of this continued visibility is furnished by the broken lines extending1 in ,fig4 #cc1 from the earth through the moon4 ,these represent sunlight1 which1 entering the earth's atmosphere near the edge of the earth 7edge as seen from sun and moon71 passes through it and emerges in a changed direction1 refracted1 into the shadow cone and feebly illumines the moon's surface with a ruddy light like that often shown in our red sunsets4 ,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 freely1 and the attentive observer may often see at a clear sunset something which corresponds exactly to the bending of the sunlight into the shadow cone2 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 7see #ej74 ,,query4--,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 clouds8 #ff4 ,,the ,,track ,,of ,,the ,,shadow4--,we may regard the moon's shadow cone as a huge pencil attached to the moon1 moving with it along its orbit in the direction of the arrowhead 7,fig4 #cd71 and as it moves drawing a black line across the face of the earth at the time of total eclipse4 ,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 progress4 ,if the point of the shadow just reaches the earth its trace will have no sensible width1 while1 if the moon is nearer1 the point of the cone will be broken off1 and1 like a blunt pencil1 it will draw a broad streak across the earth1 and this under the most favorable circumstances may have a breadth of a little more than #afj miles and a length of #aj1jjj or #ab1jjj miles4 ,the student should be able to show from the known distance of the moon 7#bdj1jjj miles7 and the known interval between consecutive new moons 7#bi4e days7 that on the average the moon's shadow sweeps past the earth at the rate of #b1ajj miles per hour1 and that in a general way this motion is from west to east1 since that is the direction of the moon's motion in its orbit4 ,the actual velocity with which the moon's shadow moves past a given station may1 however1 be considerably greater or less than this1 since on the one hand when the shadow falls very obliquely1 as when the eclipse occurs near sunrise or sunset1 the shifting of the shadow will be very much greater than the actual motion of the moon which produces it1 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 moving4 ,at the equator1 with the sun and moon overhead1 this motion of the earth subtracts about #a1jjj miles per hour from the velocity with which the shadow passes by4 ,it is chiefly on this account1 the diminished velocity with which the shadow passes by1 that total solar eclipses last longer in the tropics than in higher latitudes1 but even under the most favorable circumstances the duration of totality does not reach eight minutes at any one place1 although it may take the shadow several hours to sweep the entire length of its path across the earth4 ,according to ,whitmell the greatest possible duration of a total solar eclipse is #gm4 #djs41 and it can attain this limit only when the eclipse occurs near the beginning of ,july and is visible at a place #e north of the equator4 ,the duration of a lunar eclipse depends mainly upon the position of the moon with respect to the earth's shadow4 ,if it strikes the shadow centrally1 as at ,m1 ,fig4 #cc1 a total eclipse may last for about two hours1 with an additional hour at the beginning and end1 during which the moon is entering and leaving the earth's shadow4 ,if the moon meets the shadow at one side of the axis1 as at ,p1 the total phase of the eclipse may fail altogether1 and between these extremes the duration of totality may be anything from two hours downward4 ,illustration3 ,,fig4 #cd4--,relation of the lunar nodes to eclipses4 #fg4 ,,relation ,,of ,,the ,,lunar ,,nodes ,,to ,,eclipses4--,to show why the moon sometimes encounters the earth's shadow centrally and more frequently at full moon passes by without touching it at all1 we resort to ,fig4 #cd1 which represents a part of the orbit of the earth about the sun1 with dates showing the time in each year at which the earth passes the part of its orbit thus marked4 ,the orbit of the moon about the earth1 ,m ,m1 is also shown1 with the new moon1 ,m1 casting its shadow toward the earth and the full moon1 ,m1 apparently immersed in the earth's shadow4 ,but here appearances are deceptive1 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 taken4 ,the apparent paths of the moon and sun among the stars are great circles which lie near each other1 but are not exactly the same2 and since these great circles are only the intersections of the sky with the planes of the earth's orbit and the moon's orbit1 we see that these planes are slightly inclined to each other and must therefore intersect along some line passing through the center of the earth4 ,this line1 ,n ,n1 is shown in the figure1 and if we suppose the surface of the paper to represent the plane of the earth's orbit1 we shall have to suppose the moon's orbit to be tipped around this line1 so that the left side of the orbit lies above and the right side below the surface of the paper4 ,but since the earth's shadow lies in the plane of its orbit--i4 e41 in the surface of the paper--the full moon of ,march1 ,m1 must have passed below the shadow1 and the new moon1 ,m1 must have cast its shadow above the earth1 so that neither a lunar nor a solar eclipse could occur in that month4 ,but toward the end of ,may the earth and moon have reached a position where the line ,n ,n points almost directly toward the sun1 in line with the shadow cones which hide it4 ,note that the line ,n ,n remains very nearly parallel to its original position1 while the earth is moving along its orbit4 ,the full moon will now be very near this line and therefore very close to the plane of the earth's orbit1 if not actually in it1 and must pass through the shadow of the earth and be eclipsed4 ,so also the new moon will cast its shadow in the plane of the ecliptic1 and this shadow1 falling upon the earth1 produced the total solar eclipse of ,may #bh1 #aijj4 ,n ,n is called the line of nodes of the moon's orbit 7 #ci71 and the two positions of the earth in its orbit1 diametrically opposite each other1 at which ,n ,n points exactly toward the sun1 we shall call the nodes of the lunar orbit4 ,strictly speaking1 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 orbit4 ,bearing in mind these definitions1 we may condense much of what precedes into the proposition3 ,eclipses of either sun or moon can occur only when the earth is at or near one of the nodes of the moon's orbit4 ,corresponding to these positions of the earth there are in each year two seasons1 about six months apart1 at which times1 and at these only1 eclipses can occur4 ,thus in the year #aijj the earth passed these two points on ,june #b;d and ,november #bdth respectively1 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 dates3 ,eclipses of the ,year #aijj ,total solar eclipse ,may #bhth4 ,partial lunar eclipse ,june #abth4 ,annular 7solar7 eclipse ,november #bast4 #fh4 ,,eclipse ,,limits4--,if the earth is exactly at the node at the time of new moon1 the moon's shadow will fall centrally upon it and will produce an eclipse visible within the torrid zone1 since this is that part of the earth's surface nearest the plane of its orbit4 ,if the earth is near but not at the node1 the new moon will stand a little north or south of the plane of the earth's orbit1 and its shadow will strike the earth farther north or south than before1 producing an eclipse in the temperate or frigid zones2 or the shadow may even pass entirely above or below the earth1 producing no eclipse whatever1 or at most a partial eclipse visible near the north or south pole4 ,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 limits1 as they are called3 ,solar ,eclipse ,limits ,if at any new moon the earth is ,less than #aj days away from a node1 a central eclipse is certain4 ,between #aj and #af days some kind of eclipse is certain4 ,between #af and #ai days a partial eclipse is possible4 ,more than #ai days no eclipse is possible4 ,lunar ,eclipse ,limits ,if at any full moon the earth is ,less than #d days away from a node1 a total eclipse is certain4 ,between #d and #aj days some kind of eclipse is certain4 ,between #aj and #ad days a partial eclipse is possible4 ,more than #ad days no eclipse is possible4 ,from this table of eclipse limits we may draw some interesting conclusions about the frequency with which eclipses occur4 #fi4 ,,number ,,of ,,eclipses ,,in ,a ,,year4--,whenever the earth passes a node of the moon's orbit a new moon must occur at some time during the #b #af days that the earth remains inside the limits where some kind of eclipse is certain1 and there must therefore be an eclipse of the sun every time the earth passes a node of the moon's orbit4 ,but1 since there are two nodes past which the earth moves at least once in each year1 there must be at least two solar eclipses every year4 ,can there be more than two8 ,on the average1 will central or partial eclipses be the more numerous8 ,a similar line of reasoning will not hold true for eclipses of the moon1 since it is quite possible that no full moon should occur during the #bj days required by the earth to move past the node from the western to the eastern limit4 ,this omission of a full moon while the earth is within the eclipse limits sometimes happens at both nodes in the same year1 and then we have a year with no eclipse of the moon4 ,the student may note in the list of eclipses for #aijj that the partial lunar eclipse of ,june #abth occurred #aj days after the earth passed the node1 and was therefore within the doubtful zone where eclipses may occur and may fail1 and corresponding to this position the eclipse was a very small one1 only a thousandth part of the moon's diameter dipping into the shadow of the earth4 ,by so much the year #aijj escaped being an illustration of a year in which no lunar eclipse occurred4 ,a partial eclipse of the moon will usually occur about a fortnight before or after a total eclipse of the sun1 since the full moon will then be within the eclipse limit at the opposite node4 ,a partial eclipse of the sun will always occur about a fortnight before or after a total eclipse of the moon4 ,illustration3 ,,fig4 #ce4--,the eclipse of ,may #bh1 #aijj4 #gj4 ,,eclipse ,,maps4--,it is the custom of astronomers to prepare1 in advance of the more important eclipses1 maps showing the trace of the moon's shadow across the earth1 and indicating the times of beginning and ending of the eclipses1 as is shown in ,fig4 #ce4 ,while the actual construction of such a map requires much technical knowledge1 the principles involved are simple enough3 the straight line passed through the center of sun and moon is the axis of the shadow cone1 and the map contains little more than a graphical representation of when and where this cone meets the surface of the earth4 ,thus in the map1 the ,path of ,total ,eclipse is the trace of the shadow cone across the face of the earth1 and the width of this path shows that the earth encountered the shadow considerably inside the vertex of the cone4 ,the general direction of the path is from west to east1 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 paper4 ,on either side of the ,path of ,total ,eclipse is the region within which the eclipse was only partial1 and the broken lines marked ,begins at #c;h41 ,ends at #c;h41 show the intersection of the penumbral cone with the surface of the earth at #c ,p4 ,m41 ,greenwich time4 ,these two lines inclose every part of the earth's surface from which at that time any eclipse whatever could be seen1 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 edge1 while at the center of the penumbra1 on the ,path of ,total ,eclipse1 lay the shadow of the moon1 an oval patch whose greatest diameter was but little more than #fj miles in length1 and within which lay every part of the earth where the eclipse was total at that moment4 ,the position of the penumbra at other hours is also shown on the map1 although with more distortion1 because it then meets the surface of the earth more obliquely1 and from these lines it is easy to obtain the time of beginning and end of the eclipse at any desired place1 and to estimate by the distance of the place from the ,path of ,total ,eclipse how much of the sun's face was obscured4 ,let the student make these predictions for ,washington1 ,chicago1 ,london1 and ,algiers4 ,the points in the map marked ,first ,contact1 ,last ,contact1 show the places at which the penumbral cone first touched the earth and finally left it4 ,according to computations made as a basis for the construction of the map the ,greenwich time of ,first ,contact was #j;h4 #ab4em4 and of ,last ,contact #e;h4 #ce4fm41 and the difference between these two times gives the total duration of the eclipse upon the earth--i4 e41 #e hours #bc4a minutes4 ,illustration3 ,,fig4 #cf4--;,central eclipses for the first two decades of the twentieth century4 ,,oppolzer4 #ga4 ,,future ,,eclipses4--,an eclipse map of a different kind is shown in ,fig4 #cf1 which represents the shadow paths of all the central eclipses of the sun1 visible during the period #aijj-aiah ,a4 ,d41 in those parts of the earth north of the south temperate zone4 ,each continuous black line shows the path of the shadow in a total eclipse1 from its beginning1 at sunrise1 at the western end of the line to its end1 sunset1 at the eastern end1 the little circle near the middle of the line showing the place at which the eclipse was total at noon4 ,the broken lines represent similar data for the annular eclipses4 ,this map is one of a series prepared by the ,austrian astronomer1 ,oppolzer1 showing the path of every such eclipse from the year #abjj ,b4 ,c4 to #bafj ,a4 ,d41 a period of more than three thousand years4 ,if we examine the dates of the eclipses shown in this map we shall find that they are not limited to the particular seasons1 ,may and ,november1 in which those of the year #aijj occurred1 but are scattered through all the months of the year1 from ,january to ,december4 ,this shows at once that the line of nodes1 ,n ,n1 of ,fig4 #cd1 does not remain in a fixed position1 but turns round in the plane of the earth's orbit so that in different years the earth reaches the node in different months4 ,the precession has already furnished us an illustration of a similar change1 the slow rotation of the earth's axis1 producing a corresponding shifting of the line in which the planes of the equator and ecliptic intersect2 and in much the same way1 through the disturbing influence of the sun's attraction1 the line ,n ,n is made to revolve westward1 opposite to the arrowheads in ,fig4 #cd1 at the rate of nearly #bj per year1 so that the earth comes to each node about #ai days earlier in each year than in the year preceding1 and the eclipse season in each year comes on the average about #ai days earlier than in the year before1 although there is a good deal of irregularity in the amount of change in particular years4 #gb4 ,,recurrence ,,of ,,eclipses4--,before the beginning of the ,christian era astronomers had found out a rough-and-ready method of predicting eclipses1 which is still of interest and value4 ,the substance of the method is that if we start with any eclipse whatever--e4 g41 the eclipse of ,may #bh1 #aijj--;and reckon forward or backward from that date a period of #ah years and #aj or #aa days1 we shall find another eclipse quite similar in its general characteristics to the one with which we started4 ,thus1 from the map of eclipses 7,fig4 #cf71 we find that a total solar eclipse will occur on ,june #h1 #aiah1 #ah years and #aa days after the one illustrated in ,fig4 #ce4 ,this period of #ah years and #aa days is called saros1 an ancient word which means cycle or repetition1 and since every eclipse is repeated after the lapse of a saros1 we may find the dates of all the eclipses of #aiah by adding #aa days to the dates given in the table of eclipses for #aijj 7 #fg71 and it is to be especially noted that each eclipse of #aiah will be like its predecessor of #aijj in character--lunar1 solar1 partial1 total1 etc4 ,the eclipses of any year may be predicted by a similar reference to those which occurred eighteen years earlier4 ,consult a file of old almanacs4 ,the exact length of a saros is #bbc lunar months1 each of which is a little more than #bi4e days long1 and if we multiply the exact value of this last number 7see #fj7 by #bbc1 we shall find for the product #f1ehe4cb days1 which is equal to #ah years #aa4cb days when there are four leap years included in the #ah1 or #ah years #aj4cb days when the number of leap years is five2 and in applying the saros to the prediction of eclipses1 due heed must be paid to the number of intervening leap years4 ,to explain why eclipses are repeated at the end of the saros1 we note that the occurrence of an eclipse depends solely upon the relative positions of the earth1 moon1 and node of the moon's orbit1 and the eclipse will be repeated as often as these three come back to the position which first produced it4 ,this happens at the end of every saros1 since the saros is1 approximately1 the least common multiple of the length of the year1 the length of the lunar month1 and the length of time required by the line of nodes to make a complete revolution around the ecliptic4 ,if the saros were exactly a multiple of these three periods1 every eclipse would be repeated over and over again for thousands of years2 but such is not the case1 the saros is not an exact multiple of a year1 nor is it an exact multiple of the time required for a revolution of the line of nodes1 and in consequence the restitution which comes at the end of the saros is not a perfect one4 ,the earth at the #bbc;d new moon is in fact about half a day's motion farther west1 relative to the node1 than it was at the beginning1 and the resulting eclipse1 while very similar1 is not precisely the same as before4 ,after another #ah years1 at the second repetition1 the earth is a day farther from the node than at first1 and the eclipse differs still more in character1 etc4 ,this is shown in ,fig4 #cg1 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 saros1 #ajh years1 where the upper row of figures represents the number of repetitions of the eclipse from the beginning1 marked #j1 to the end1 #gb4 ,the solar eclipse limits1 #aj1 #af1 #ai days1 are also shown1 and all those eclipses which fall between the #aj-;day limits will be central as seen from some part of the earth1 those between #af and #ai partial wherever seen1 while between #aj and #af they may be either total or partial4 ,compare the figure with the following description given by ,professor ,newcomb3 ,a series of such eclipses commences with a very small eclipse near one pole of the earth4 ,gradually increasing for about eleven recurrences1 it will become central near the same pole4 ,forty or more central eclipses will then recur1 the central line moving slowly toward the other pole4 ,the series will then become partial1 and finally cease4 ,the entire duration of the series will be more than a thousand years4 ,a new series commences1 on the average1 at intervals of thirty years4 ,illustration3 ,,fig4 #cg4--;,graphical illustration of the saros4 ,a similar figure may be constructed to represent the recurrence of lunar eclipses2 but here1 in consequence of the smaller eclipse limits1 we shall find that a series is of shorter duration1 a little over eight centuries as compared with twelve centuries1 which is the average duration of a series of solar eclipses4 ,one further matter connected with the saros deserves attention4 ,during the period of #f1ehe4cb days the earth has #f1ehe times turned toward the sun the same face upon which the moon's shadow fell at the beginning of the saros1 but at the end of the saros the odd #j4cb of a day gives the earth time to make about a third of a revolution more before the eclipse is repeated1 and in consequence the eclipse is seen in a different region of the earth1 on the average about #aaf farther west in longitude4 ,compare in ,fig4 #cf the regions in which the eclipses of #aijj and #aiah are visible4 ,is this change in the region where the repeated eclipse is visible1 true of lunar eclipses as well as solar8 #gc4 ,,use ,,of ,,eclipses4--,at all times and among all peoples eclipses1 and particularly total eclipses of the sun1 have been reckoned among the most impressive phenomena of ,nature4 ,in early times and among uncultivated people they were usually regarded with apprehension1 often amounting to a terror and frenzy1 which civilized travelers have not scrupled to use for their own purposes with the aid of the eclipse predictions contained in their almanacs1 threatening at the proper time to destroy the sun or moon1 and pointing to the advancing eclipse as proof that their threats were not vain4 ,in our own day and our own land these feelings of awe have not quite disappeared1 but for the most part eclipses are now awaited with an interest and pleasure which1 contrasted with the former feelings of mankind1 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 enjoyment4 ,but to the astronomer an eclipse is more than a beautiful illustration of the working of natural laws2 it is in varying degree an opportunity of adding to his store of knowledge respecting the heavenly bodies4 ,the region immediately surrounding the sun is at most times closed to research by the blinding glare of the sun's own light1 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 sun4 ,more than one astronomer has reported the discovery of such planets1 and at least one of these has found a name and a description in some of the books1 but at the present time most astronomers are very skeptical about the existence of any such object of considerable size1 although there is some reason to believe that an enormous number of little bodies1 ranging in size from grains of sand upward1 do move in this region1 as yet unseen and offering to the future problems for investigation4 ,but in other directions the study of this region at the times of total eclipse has yielded far larger returns1 and in the chapter on the sun we shall have to consider the marvelous appearances presented by the solar prominences and by the corona1 an appendage of the sun which reaches out from his surface for millions of miles but is never seen save at an eclipse4 ,photographs of the corona are taken by astronomers at every opportunity1 and reproductions of some of these may be found in ,chapter ,x4 ,annular eclipses and lunar eclipses are of comparatively little consequence1 but any recorded eclipse may become of value in connection with chronology4 ,we date our letters in a particular year of the twentieth century1 and commonly suppose that the years are reckoned from the birth of ,christ2 but this is an error1 for the eclipses which were observed of old and by the chroniclers have been associated with events of his life1 when examined by the astronomers are found quite inconsistent with astronomic theory4 ,they are1 however1 reconciled with it if we assume that our system of dates has its origin four years after the birth of ,christ1 or1 in other words1 that ,christ was born in the year #d ,b4 ,c4 ,a mistake was doubtless made at the time the ,christian era was introduced into chronology4 ,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 past4 ,,chapter ,,viii ,,instruments ,,and ,,the ,,principles ,,involved ,,in ,,their ,,use #gd4 ,,two ,,familiar ,,instruments4--,in previous chapters we have seen that a clock and a divided circle 7protractor7 are needed for the observations which an astronomer makes1 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 instruments4 ,the protractor is a simple instrument1 a humble member of the family of divided circles1 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--i4 e41 #c1fjj times as accurate as the protractor furnishes4 ,the building of a good clock is equally important and has cost a like amount of labor and pains1 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 kind4 ,every such timepiece1 whether it be of the nutmeg variety which sells for a dollar1 or whether it be the standard clock of a great national observatory1 is made up of the same essential parts that fall naturally into four classes1 which we may compare with the departments of a well-ordered factory3 ,i4 ,a timekeeping department1 the pendulum or balance spring1 whose oscillations must all be of equal duration4 ,,ii4 ,a power department1 the weights or mainspring1 which1 when wound1 store up the power applied from outside and give it out piecemeal as required to keep the first department running4 ,,iii4 ,a publication department1 the dial and hands1 which give out the time furnished by ,department ,i4 ,,iv4 ,a transportation department1 the wheels1 which connect the other three and serve as a means of transmitting power and time from one to the other4 ,the case of either clock or watch is merely the roof which shelters it and forms no department of its industry4 ,of these departments the first is by far the most important1 and its good or bad performance makes or mars the credit of the clock4 ,beware of meddling with the balance wheel of your watch4 #ge4 ,,radiant ,,energy4--,but we have now to consider other instruments which in practice supplement or displace the simple apparatus hitherto employed4 ,among the most important of these modern instruments are the telescope1 the spectroscope1 and the photographic camera2 and since all these instruments deal with the light which comes from the stars to the earth1 we must for their proper understanding take account of the nature of that light1 or1 more strictly speaking1 we must take account of the radiant energy emitted by the sun and stars1 which energy1 coming from the sun1 is translated by our nerves into the two different sensations of light and heat4 ,the radiant energy which comes from the stars is not fundamentally different from that of the sun1 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 heat1 and for the same reason the vast majority of stars are invisible to the unaided eye2 they do not furnish a sufficient amount of energy to affect the optic nerves4 ,a hot brick taken into the hand reveals its presence by the two different sensations of heat and pressure 7weight72 but as there is only one brick to produce the two sensations1 so there is only one energy to produce through its action upon different nerves the two sensations of light and heat1 and this energy is called radiant because it appears to stream forth radially from everything which has the capacity of emitting it4 ,for the detailed study of radiant energy the student is referred to that branch of science called physics2 but some of its elementary principles may be learned through the following simple experiment1 which the student should not fail to perform for himself3 ,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 water4 ,these waves are a form of radiant energy1 but differing from light or heat in that they are visibly confined to a single plane1 the surface of the water1 instead of filling the entire surrounding space4 ,by varying the size of the bucket1 the depth of the water1 the weight of the bullet1 etc41 different kinds of waves1 big and little1 may be produced2 but every such set of waves may be described and defined in all its principal characteristics by means of three numbers--viz41 the vertical height of the waves from hollow to crest2 the distance of one wave from the next2 and the velocity with which the waves travel across the water4 ,the last of these quantities is called the velocity of propagation2 the second is called the wave length2 one half of the first is called the amplitude2 and all these terms find important applications in the theory of light and heat4 ,the energy of the falling bullet1 the disturbance which it produced on entering the water1 was carried by the waves from the center to the edge of the bucket but not beyond1 for the wave can go only so far as the water extends4 ,the transfer of energy in this way requires a perfectly continuous medium through which the waves may travel1 and the whole visible universe is supposed to be filled with something called ether1 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 bullet4 ,the student may think of this energy as being transmitted in spherical waves through the ether1 every glowing body1 such as a star1 a candle flame1 an arc lamp1 a hot coal1 etc41 being the origin and center of such systems of waves1 and determining by its own physical and chemical properties the wave length and amplitude of the wave systems given off4 ,the intensity of any light depends upon the amplitude of the corresponding vibration1 and its color depends upon the wave length4 ,by ingenious devices which need not be here described it has been found possible to measure the wave length corresponding to different colors--e4 g41 all of the colors of the rainbow1 and some of these wave lengths expressed in tenth meters are as follows3 ,a tenth meter is the length obtained by dividing a meter into #ajaj equal parts4 #ajaj #aj1jjj1jjj1jjj4 ,color4 ,wave length4 ,extreme limit of visible violet #c1ijj ,middle of the violet #d1jfj blue #d1gcj green #e1bgj yellow #e1haj orange #e1igj red #g1jjj ,extreme limit of visible red #g1fjj ,illustration3 ,,plate ,i4 ,,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 #c1ijj or greater than #g1fjj tenth meters4 ,radiant energy1 however1 exists in waves of both greater and shorter length than the above1 and may be readily detected by apparatus not subject to the limitations of the human eye--e4 g41 a common thermometer will show a rise of temperature when its bulb is exposed to radiant energy of wave length much greater than #g1fjj tenth meters1 and a photographic plate will be strongly affected by energy of shorter wave length than #c1ijj tenth meters4 #gf4 ,,reflection ,,and ,,condensation ,,of ,,waves4--,when the waves produced by dropping a bullet into a bucket of water meet the sides of the bucket1 they appear to rebound and are reflected back toward the center1 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 bucket4 ,there has been a condensation of energy produced by the reflection1 and this increased energy is shown by the greater amplitude of the wave4 ,the student should not fail to notice that each portion of the wave has traveled out and back over the radius of the bucket1 and that they meet simultaneously at the center because of this equality of the paths over which they travel1 and the resulting equality of time required to go out and back4 ,if the bullet were dropped at one side of the center1 would the reflected waves produce at any point a condensation of energy8 ,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 focus1 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 portion1 and all parts of the wave reach the second focus at the same time4 ,upon what geometrical principle does this depend8 ,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 simultaneously1 whether by reflection or by some other means1 as shown below4 ,the student will note that for the sake of greater precision we here say wave front instead of wave4 ,if in any wave we imagine a line drawn along the crest1 so as to touch every drop which at that moment is exactly at the crest1 we shall have what is called a wave front1 and similarly a line drawn through the trough between two waves1 or through any set of drops similarly placed on a wave1 constitutes a wave front4 #gg4 ,,mirrors ,,and ,,lenses4--,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 above1 but owing to the extreme shortness of the wave length in this case the reflecting surface should be very smooth and highly polished4 ,a piece of glass hollowed out in the center by grinding1 and with a light film of silver chemically deposited upon the hollow surface and carefully polished1 is often used by astronomers for this purpose1 and is called a concave mirror4 ,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 mirror1 and there forms an image of the star1 which may be seen with the unaided eye1 if it is held in the right place1 or may be examined through a magnifying glass4 ,similarly1 an image of the sun1 a planet1 or a distant terrestrial object is formed by the mirror1 which condenses at its appropriate place the radiant energy proceeding from each and every point in the surface of the object1 and this1 in common phrase1 produces an image of the object4 ,another device more frequently used by astronomers for the production of images 7condensation of energy7 is a lens which in its simplest form is a round piece of glass1 thick in the center and thin at the edge1 with a cross section1 such as is shown at ,a ,b in ,fig4 #ch4 ,if we suppose ,e ,g ,d to represent a small part of a wave front coming from a very distant source of radiant energy1 such as a star1 this wave front will be practically a plane surface represented by the straight line ,e ,d1 but in passing through the lens this surface will become warped1 since light travels slower in glass than in air1 and the central part of the beam1 ,g1 in its onward motion will be retarded by the thick center of the lens1 more than ,e or ,d will be retarded by the comparatively thin outer edges of ,a ,b4 ,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 made4 ,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 front1 ,e ,g ,d1 will then be condensed at ,f1 because this point is equally distant from all parts of the warped wave front1 and therefore is in a position to receive them simultaneously4 ,the distance of ,f from ,a ,b is called the focal length of the lens1 and ,f itself is called the focus4 ,the significance of this last word 7,latin1 focus fireplace7 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 hand4 ,illustration3 ,,fig4 #ch4--;,illustrating the theory of lenses4 ,all the energy transmitted by the lens in the direction ,g ,f is concentrated upon a very small area at ,f1 and an image of the object--e4 g41 a star1 from which the light came--is formed here4 ,other stars situated near the one in question will also send beams of light along slightly different directions to the lens1 and these will be concentrated1 each in its appropriate place1 in the focal plane1 ,f ,h1 passed through the focus1 ,f1 perpendicular to the line1 ,f ,g1 and we shall find in this plane a picture of all the stars or other objects within the range of the lens4 ,illustration3 ,,fig4 #ci4--;,essential parts of a reflecting telescope4 #gh4 ,,telescopes4--,the simplest kind of telescope consists of a concave mirror to produce images1 and a magnifying glass1 called an eyepiece1 through which to examine them2 but for convenience' sake1 so that the observer may not stand in his own light1 a small mirror is frequently added to this combination1 as at ,h in ,fig4 #ci1 where the lines represent the directions along which the energy is propagated4 ,by reflection from this mirror the focal plane and the images are shifted to ,f1 where they may be examined from one side through the magnifying glass ,e4 ,illustration3 ,,fig4 #dj4--;,a simple form of refracting telescope4 ,such a combination of parts is called a reflecting telescope1 while one in which the images are produced by a lens or combination of lenses is called a refracting telescope1 the adjective having reference to the bending1 refraction1 produced by the glass upon the direction in which the energy is propagated4 ,the customary arrangement of parts in such a telescope is shown in ,fig4 #dj1 where the part marked ,o is called the objective and ,v ,e 7the magnifying glass7 is the eyepiece1 or ocular1 as it is sometimes called4 ,most objects with which we have to deal in using a telescope send to it not light of one color only1 but a mixture of light of many colors1 many different wave lengths1 some of which are refracted more than others by the glass of which the lens is composed1 and in consequence of these different amounts of refraction a single lens does not furnish a single image of a star1 but gives a confused jumble of red and yellow and blue images much inferior in sharpness of outline 7definition7 to the images made by a good concave mirror4 ,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 ,fig4 #dj4 ,the two pieces of glass thus mounted in one frame constitute a compound lens having its own focal plane1 shown at ,f in the figure1 and similarly the lenses composing the eyepiece have a focal plane between the eyepiece and the objective which must also fall at ,f1 and in the use of a telescope the eyepiece must be pushed out or in until its focal plane coincides with that of the objective4 ,this process1 which is called focusing1 is what is accomplished in the ordinary opera glass by turning a screw placed between the two tubes1 and it must be carefully done with every telescope in order to obtain distinct vision4 #gi4 ,,magnifying ,,power4--,the amount by which a given telescope magnifies depends upon the focal length of the objective 7or mirror7 and the focal length of the eyepiece1 and is equal to the ratio of these two quantities4 ,thus in ,fig4 #dj the distance of the objective from the focal plane ,f is about #af times as great as the distance of the eyepiece from the same plane1 and the magnifying power of this telescope is therefore #af diameters4 ,a magnifying power of #af diameters means that the diameter of any object seen in the telescope looks #af times as large as it appears without the telescope1 and is nearly equivalent to saying that the object appears only one sixteenth as far off4 ,sometimes the magnifying power is assumed to be the number of times that the area of an object seems increased2 and since areas are proportional to the squares of lines1 the magnifying power of #af diameters might be called a power of #bef4 ,every large telescope is provided with several eyepieces of different focal lengths1 ranging from a quarter of an inch to two and a half inches1 which are used to furnish different magnifying powers as may be required for the different kinds of work undertaken with the instrument4 ,higher powers can be used with large telescopes than with small ones1 but it is seldom advantageous to use with any telescope an eyepiece giving a higher power than #fj diameters for each inch of diameter of the objective4 ,the part played by the eyepiece in determining magnifying power will be readily understood from the following experiment3 ,make a pin hole in a piece of cardboard4 ,bring a printed page so close to one eye that you can no longer see the letters distinctly1 and then place the pin hole between the eye and the page4 ,the letters which were before blurred may now be seen plainly through the pin hole1 even when the page is brought nearer to the eye than before4 ,as it is brought nearer1 notice how the letters seem to become larger1 solely because they are nearer4 ,a pin hole is the simplest kind of a magnifier1 and the eyepiece in a telescope plays the same part as does the pin hole in the experiment2 it enables the eye to be brought nearer to the image1 and the shorter the focal length of the eyepiece the nearer is the eye brought to the image and the higher is the magnifying power4 #hj4 ,,the ,,equatorial ,,mounting4--,telescopes are of all sizes1 from the modest opera glass which may be carried in the pocket and which requires no other support than the hand1 to the giant which must have a special roof to shelter it and elaborate machinery to support and direct it toward the sky4 ,but for even the largest telescopes this machinery consists of the following parts1 which are illustrated1 with exception of the last one1 in the small equatorial telescope shown in ,fig4 #da4 ,it is not customary to place a driving clock on so small a telescope as this3 7a7 ,a supporting pier or tripod4 7b7 ,an axis placed parallel to the axis of the earth4 7c7 ,another axis at right angles to b and capable of revolving upon b as an axle4 7d7 ,the telescope tube attached to c and capable of revolving about c4 7e7 ,graduated circles attached to c and b to measure the amount by which the telescope is turned on these axes4 7f7 ,a driving clock so connected with b as to make c 7and d7 revolve about b with an angular velocity equal and opposite to that with which the earth turns upon its axis4 ,illustration3 ,,fig4 #da4--;,a simple equatorial mounting4 ,illustration3 ,,fig4 #db4--;,equatorial mounting of the great telescope of the ,yerkes ,observatory4 ,such a support is called an equatorial mounting1 and the student should note from the figure that the circles1 e1 measure the hour angle and declination of any star toward which the telescope is directed1 and conversely if the telescope be so set that these circles indicate the hour angle and declination of any given star1 the telescope will then point toward that star4 ,in this way it is easy to find with the telescope any moderately bright star1 even in broad daylight1 although it is then absolutely invisible to the naked eye4 ,the rotation of the earth about its axis will speedily carry the telescope away from the star1 but if the driving clock be started1 its effect is to turn the telescope toward the west just as fast as the earth's rotation carries it toward the east1 and by these compensating motions to keep it directed toward the star4 ,in ,fig4 #db1 which represents the largest and one of the most perfect refracting telescopes ever built1 let the student pick out and identify the several parts of the mounting above described4 ,a part of the driving clock may be seen within the head of the pier4 ,in ,fig4 #dc trace out the corresponding parts in the mounting of a reflecting telescope4 ,illustration3 ,,fig4 #dc4--,the reflecting telescope of the ,paris ,observatory4 ,a telescope is often only a subordinate part of some instrument or apparatus1 and then its style of mounting is determined by the requirements of the special case2 but when the telescope is the chief thing1 and the remainder of the apparatus is subordinate to it1 the equatorial mounting is almost always adopted1 although sometimes the arrangement of the parts is very different in appearance from any of those shown above4 ,beware of the popular error that an object held close in front of a telescope can be seen by an observer at the eyepiece4 ,the numerous stories of astronomers who saw spiders crawling over the objective of their telescope1 and imagined they were beholding strange objects in the sky1 are all fictitious1 since nothing on or near the objective could possibly be seen through the telescope4 #ha4 ,,photography4--,a photographic camera consists of a lens and a device for holding at its focus a specially prepared plate or film4 ,this plate carries a chemical deposit which is very sensitive to the action of light1 and which may be made to preserve the imprint of any picture which the lens forms upon it4 ,if such a sensitive plate is placed at the focus of a reflecting telescope1 the combination becomes a camera available for astronomical photography1 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 telescope4 ,a refracting telescope may also be used for astronomical photography1 and is very much used1 but some complications occur here on account of the resolution of the light into its constituent colors in passing through the objective4 ,fig4 #dd shows such a telescope1 or rather two telescopes1 one photographic1 the other visual1 supported side by side upon the same equatorial mounting4 ,illustration3 ,,fig4 #dd4--,photographic telescope of the ,paris ,observatory4 ,one of the great advantages of photography is found in connection with what is called-- #hb4 ,,personal ,,equation4--,it is a remarkable fact1 first investigated by the ,german astronomer ,bessel1 three quarters of a century ago1 that where extreme accuracy is required the human senses can not be implicitly relied upon4 ,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 meridian2 the most skillful artists can not draw identical pictures of the same object1 etc4 ,these minor deceptions of the senses are included in the term personal equation1 which is a famous phrase in astronomy1 denoting that the observations of any given person require to be corrected by means of some equation involving his personality4 ,general health1 digestion1 nerves1 fatigue1 all influence the personal equation1 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 observing3 ,in order to avoid every physiological disturbance1 ,i have adopted the rule to abstain for one or two hours before commencing observations from every laborious occupation2 never to go to the telescope with stomach loaded with food2 to abstain from everything which could affect the nervous system1 from narcotics and alcohol1 and especially from the abuse of coffee1 which ,i have found to be exceedingly prejudicial to the accuracy of observation4#c ,a regimen suggestive of preparation for an athletic contest rather than for the more quiet labors of an astronomer4 #c ,schiaparelli1 ,osservazioni sulle ,stelle ,doppie4 #hc4 ,,visual ,,and ,,photographic ,,work4--,the photographic plate has no stomach and no nerves1 and is thus free from many of the sources of error which inhere in visual observations1 and in special classes of work it possesses other marked advantages1 such as rapidity when many stars are to be dealt with simultaneously1 permanence of record1 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 it4 ,on the other hand1 the eye has the advantage in some respects1 such as studying the minute details of a fairly bright object--e4 g41 the surface of a planet1 or the sun's corona and1 for the present at least1 neither method of observing can exclude the other4 ,for a remarkable case of discordance between the results of photographic and visual observations compare the pictures of the great nebula in the constellation ,andromeda1 which are given in ,chapter ,,xiv4 ,a partial explanation of these discordances and other similar ones is that the eye is most strongly affected by greenish-yellow light1 while the photographic plate responds most strongly to violet light2 the photograph1 therefore1 represents things which the eye has little capacity for seeing1 and vice versa4 #hd4 ,,the ,,spectroscope4--,in some respects the spectroscope is the exact counterpart of the telescope4 ,the latter condenses radiant energy and the former disperses it4 ,as a measuring instrument the telescope is mainly concerned with the direction from which light comes1 and the different colors of which that light is composed affect it only as an obstacle to be overcome in its construction4 ,on the other hand1 with the spectroscope the direction from which the radiant energy comes is of minor consequence1 and the all-important consideration is the intrinsic character of that radiation4 ,what colors are present in the light and in what proportions8 ,what can these colors be made to tell about the nature and condition of the body from which they come1 be it sun1 or star1 or some terrestrial source of light1 such as an arc lamp1 a candle flame1 or a furnace in blast8 ,these are some of the characteristic questions of the spectrum analysis1 and1 as the name implies1 they are solved by analyzing the radiant energy into its component parts1 setting down the blue light in one place1 the yellow in another1 the red in still another1 etc41 and interpreting this array of colors by means of principles which we shall have to consider4 ,something of this process of color analysis may be seen in the brilliant hues shown by a soap bubble1 or reflected from a piece of mother-of-pearl1 and still more strikingly exhibited in the rainbow1 produced by raindrops which break up the sunlight into its component colors and arrange them each in its appropriate place4 ,any of these natural methods of decomposing light might be employed in the construction of a spectroscope1 but in spectroscopes which are used for analyzing the light from feeble sources1 such as a star1 or a candle flame1 a glass prism of triangular cross section is usually employed to resolve the light into its component colors1 which it does by refracting it as shown at the edges of the lens in ,fig4 #ch4 ,illustration3 ,,fig4 #de4--,resolution of light into its component colors4 ,the course of a beam of light in passing through such a prism is shown in ,fig4 #de4 ,note that the bending of the light from its original course into a new one1 which is here shown as produced by the prism1 is quite similar to the bending shown at the edges of a lens and comes from the same cause1 the slower velocity of light in glass than in air4 ,it takes the light-waves as long to move over the path ,a ,b in glass as over the longer path #a1 #b1 #c1 #d1 of which only the middle section lies in the glass4 ,not only does the prism bend the beam of light transmitted by it1 but it bends in different degree light of different colors1 as is shown in the figure1 where the beam at the left of the prism is supposed to be made up of a mixture of blue and red light1 while at the right of the prism the greater deviation imparted to the blue quite separates the colors1 so that they fall at different places on the screen1 ,s ,s4 ,the compound light has been analyzed into its constituents1 and in the same way every other color would be put down at its appropriate place on the screen1 and a beam of white light falling upon the prism would be resolved by it into a sequence of colors1 falling upon the screen in the order red1 orange1 yellow1 green1 blue1 indigo1 violet4 ,the initial letters of these names make the word ,roygbiv1 and by means of it their order is easily remembered4 ,illustration3 ,,fig4 #df4--,principal parts of a spectroscope4 ,if the light which is to be examined comes from a star the analysis made by the prism is complete1 and when viewed through a telescope the image of the star is seen to be drawn out into a band of light1 which is called a spectrum1 and is red at one end and violet or blue at the other1 with all the colors of the rainbow intervening in proper order between these extremes4 ,such a prism placed in front of the objective of a telescope is called an objective prism1 and has been used for stellar work with marked success at the ,harvard ,college ,observatory4 ,but if the light to be analyzed comes from an object having an appreciable extent of surface1 such as the sun or a planet1 the objective prism can not be successfully employed1 since each point of the surface will produce its own spectrum1 and these will appear in the view telescope superposed and confused one with another in a very objectionable manner4 ,to avoid this difficulty there is placed between the prism and the source of light an opaque screen1 ,s1 with a very narrow slit cut in it1 through which all the light to be analyzed must pass and must also go through a lens1 ,a1 placed between the slit and the prism1 as shown in ,fig4 #df4 ,the slit and lens1 together with the tube in which they are usually supported1 are called a collimator4 ,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 spectrum1 which is in effect a series of images of the slit in light of different colors1 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 slit4 ,the length of the ribbon 7dispersion7 depends mainly upon the shape of the prism and the kind of glass of which it is made1 and it may be very greatly increased and the efficiency of the spectroscope enhanced by putting two1 three1 or more prisms in place of the single one above described4 ,when the amount of light is very great1 as in the case of the sun or an electric arc lamp1 it is advantageous to alter slightly the arrangement of the spectroscope and to substitute in place of the prism a grating--i4 e41 a metallic mirror with a great number of fine parallel lines ruled upon its surface at equal intervals1 one from another4 ,it is by virtue of such a system of fine parallel grooves that mother-of-pearl displays its beautiful color effects1 and a brilliant spectrum of great purity and high dispersion is furnished by a grating ruled with from #aj1jjj to #bj1jjj lines to the inch4 ,fig4 #dg represents1 rather crudely1 a part of the spectrum of an arc light furnished by such a grating1 or rather it shows three different spectra arranged side by side1 and looking something like a rude ladder4 ,the sides of the ladder are the spectra furnished by the incandescent carbons of the lamp1 and the cross pieces are the spectrum of the electric arc filling the space between the carbons4 ,fig4 #dh shows a continuation of the same spectra into a region where the radiant energy is invisible to the eye1 but is capable of being photographed4 ,illustration3 ,,fig4 #dg4--;,green and blue part of the spectrum of an electric arc light4 ,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 figure4 ,the purpose of the lens is to make a picture of the lamp upon the slit1 so that all the radiant energy from any one point of the arc may be brought to one part of the slit1 and thus appear in the resulting spectrum separated from the energy which comes from every other part of the arc4 ,such an instrument is called an analyzing spectroscope while one without the lens is called an integrating spectroscope1 since it furnishes to each point of the slit a sample of the radiant energy coming from every part of the source of light1 and thus produces only an average spectrum of that source without distinction of its parts4 ,when a spectroscope is attached to a telescope1 as is often done 7see ,fig4 #di71 the eyepiece is removed to make way for it1 and the telescope objective takes the part of the analyzing lens4 ,a camera is frequently combined with such an apparatus to photograph the spectra it furnishes1 and the whole instrument is then called a spectrograph4 ,illustration3 ,,fig4 #dh4--,violet and ultraviolet parts of spectrum of an arc lamp4 ,illustration3 ,,fig4 #di4--;,a spectroscope attached to the ,yerkes telescope4 #he4 ,,spectrum ,,analysis4--,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 lengths1 we have now to consider the interpretation which is to be placed upon the various kinds of spectra which may be seen1 and here we rely upon the experience of physicists and chemists1 from whom we learn as follows3 ,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 radiated1 and these atoms and molecules are able to impress upon the ether their own peculiarities in the shape of waves of different length and amplitude4 ,we have seen that by varying the conditions of the experiment different kinds of waves may be produced in a bucket of water2 and as a study of these waves might furnish an index to the conditions which produced them1 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 source4 ,thus the molecules of iron produce a system of waves peculiar to themselves and which can be duplicated by nothing else1 and every other substance gives off its own peculiar type of energy1 presenting a limited and definite number of wave lengths dependent upon the nature and condition of its molecules4 ,if these molecules are free to behave in their own characteristic fashion without disturbance or crowding1 they emit light of these wave lengths only1 and we find in the spectrum a series of bright lines1 pictures of the slit produced by light of these particular wave lengths1 while between these bright lines lie dark spaces showing the absence from the radiant energy of light of intermediate wave lengths4 ,such a spectrum is shown in the central portion of ,fig4 #dg1 which1 as we have already seen1 is produced by the space between the carbons of the arc lamp4 ,on the other hand1 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 lengths1 and this is translated by the spectroscope into a continuous ribbon of light with no dark spaces intervening1 as in the upper and lower parts of ,figs4 #dg and #dh1 produced by the incandescent solid carbons of the lamp4 ,these two types are known as the continuous and discontinuous spectrum1 and we may lay down the following principle regarding them3 ,a discontinuous spectrum1 or bright-line spectrum as it is familiarly called1 indicates that the molecules of the source of light are not crowded together1 and therefore the light must come from an incandescent gas4 ,a continuous spectrum shows only that the molecules are crowded together1 or are so numerous that the body to which they belong is not transparent and gives no further information4 ,the body may be solid1 liquid1 or gaseous1 but in the latter case the gas must be under considerable pressure or of great extent4 ,a second principle is3 ,the lines which appear in a spectrum are characteristic of the source from which the light came--e4 g41 the double line in the yellow part of the spectrum at the extreme left in ,fig4 #dg is produced by sodium vapor in and around the electric arc and is never produced by anything but sodium4 ,when by laboratory experiments we have learned the particular set of lines corresponding to iron1 we may treat the presence of these lines in another spectrum as proof that iron is present in the source from which the light came1 whether that source be a white-hot poker in the next room or a star immeasurably distant4 ,the evidence that iron is present lies in the nature of the light1 and there is no reason to suppose that nature to be altered on the way from star to earth4 ,it may1 however1 be altered by something happening to the source from which it comes--e4 g41 changing temperature or pressure may affect1 and does affect1 the spectrum which such a substance as iron emits1 and we must be prepared to find the same substance presenting different spectra under different conditions1 only these conditions must be greatly altered in order to produce radical changes in the spectrum4 ,illustration3 ,,fig4 #ej4--,the chief lines in the spectrum of sunlight4--,,herschel4 #hf4 ,,wave ,,lengths4--,to identify a line as belonging to and produced by iron or any other substance1 its position in the spectrum--i4 e41 its wave length--must be very accurately determined1 and for the identification of a substance by means of its spectrum it is often necessary to determine accurately the wave lengths of many lines4 ,a complicated spectrum may consist of hundreds or thousands of lines1 due to the presence of many different substances in the source of light1 and unless great care is taken in assigning the exact position of these lines in the spectrum1 confusion and wrong identifications are sure to result4 ,for the measurement of the required wave length a tenth meter 7 #ge7 is the unit employed1 and a scale of wave lengths expressed in this unit is presented in ,fig4 #ej4 ,the accuracy with which some of these wave lengths are determined is truly astounding2 a ten-billionth of an inch6 ,these numerical wave lengths save all necessity for referring to the color of any part of the spectrum1 and pictures of spectra for scientific use are not usually printed in colors4 #hg4 ,,absorption ,,spectra4--,there is another kind of spectrum1 of greater importance than either of those above considered1 which is well illustrated by the spectrum of sunlight 7,fig4 #ej74 ,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 spectroscope4 ,fraunhofer1 who made the first careful study of spectra1 designated some of the more conspicuous of these lines by letters of the alphabet which are shown in the plate1 and which are still in common use as names for the lines1 not only in the spectrum of sunlight but wherever they occur in other spectra4 ,thus the double line marked ,d1 wave length #ehic1 falls at precisely the same place in the spectrum as does the double 7sodium7 line which we have already seen in the yellow part of the arc-light spectrum1 which line is also called ,d and bears a very intimate relation to the dark ,d line of the solar spectrum4 ,the student who has access to colored crayons should color one edge of ,fig4 #ej in accordance with the lettering there given and1 so far as possible1 he should make the transition from one color to the next a gradual one1 as it is in the rainbow4 ,fig4 #ej is far from being a complete representation of the spectrum of sunlight4 ,not only does this spectrum extend both to the right and to the left into regions invisible to the human eye1 but within the limits of the figure1 instead of the seventy-five lines there shown1 there are literally thousands upon thousands of lines1 of which only the most conspicuous can be shown in such a cut as this4 ,the dark lines which appear in the spectrum of sunlight can1 under proper conditions1 be made to appear in the spectrum of an arc light1 and ,fig4 #ea shows a magnified representation of a small part of such a spectrum adjacent to the ,d 7sodium7 lines4 ,down the middle of each of these lines runs a black streak whose position 7wave length7 is precisely that of the ,d lines in the spectrum of sunlight1 and whose presence is explained as follows3 ,the very hot sodium vapor at the center of the arc gives off its characteristic light1 which1 shining through the outer and cooler layers of sodium vapor1 is partially absorbed by these1 resulting in a fine dark line corresponding exactly in position and wave length to the bright lines1 and seen against these as a background1 since the higher temperature at the center of the arc tends to broaden the bright lines and make them diffuse4 ,similarly the dark lines in the spectrum of the sun 7,fig4 #ej7 point to the existence of a surrounding envelope of relatively cool gases1 which absorb from the sunlight precisely those kinds of radiant energy which they would themselves emit if incandescent4 ,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 spectrum1 and they may be used to determine the chemical composition of the sun1 just as the bright lines serve to determine the chemical elements present in the electric arc4 ,with reference to the mode of their formation1 bright-line and dark-line spectra are sometimes called respectively emission and absorption spectra4 ,illustration3 ,,fig4 #ea4--,the lines reversed4 #hh4 ,,types ,,of ,,spectrum4--,the sun presents by far the most complex spectrum known1 and ,fig4 #ej shows only a small number of the more conspicuous lines which appear in it4 ,spectra of stars1 per contra1 appear relatively simple1 since their feeble light is insufficient to bring out faint details4 ,in ,chapters ,,xiii and ,,xiv there are shown types of the different kinds of spectra given by starlight1 and these are to be interpreted by the principles above established4 ,thus the spectrum of the bright star b ,aurig shows a continuous spectrum crossed by a few heavy absorption lines which are known from laboratory experiments to be produced only by hydrogen4 ,there must therefore be an atmosphere of relatively cool hydrogen surrounding this star4 ,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 sun1 while the spectrum of a ,herculis is quite different from either of the others4 ,in subsequent chapters we shall have occasion to consider more fully these different types of spectrum4 #hi4 ,,the ,,doppler ,,principle4--,this important principle of the spectrum analysis is most readily appreciated through the following experiment3 ,listen to the whistle of a locomotive rapidly approaching1 and observe how the pitch changes and the note becomes more grave as the locomotive passes by and commences to recede4 ,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 predecessor1 and in consequence the waves appear to come in quicker succession1 producing a higher note with a correspondingly shorter wave length than would be heard if the same whistle were blown with the locomotive at rest4 ,on the other hand1 the wave length is increased and the pitch of the note lowered by the receding motion of the whistle4 ,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 it1 so that a diminishing distance diminishes very slightly the wave length of every line in the spectrum produced by the light1 and an increasing distance increases these wave lengths1 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 it4 ,this change of wave length is sometimes described by saying that when a body is rapidly approaching1 the lines of its spectrum are all displaced toward the violet end of the spectrum1 and are correspondingly displaced toward the red end by a receding motion4 ,the amount of this shifting1 when it can be measured1 measures the velocity of the body along the line of sight1 but the observations are exceedingly delicate1 and it is only in recent years that it has been found possible to make them with precision4 ,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 observed1 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 position1 or show1 as they sometimes do1 a slight displacement1 as if one spectrum had been slipped past the other4 ,the difficulty of the observations lies in the extremely small amount of this slipping1 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 ,fig4 #ej4 ,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 lines1 an amount absolutely imperceptible in the most powerful spectroscope yet constructed4 ,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 principle4 #ij4 ,,other ,,instruments4--,other instruments of importance to the astronomer1 but of which only casual mention can here be made1 are the meridian-circle2 the transit1 one form of which is shown in ,fig4 #eb1 and the zenith telescope1 which furnish refined methods for making observations similar in kind to those which the student has already learned to make with plumb line and protractor2 the sextant1 which is pre-eminently the sailor's instrument for finding the latitude and longitude at sea1 by measuring the altitudes of sun and stars above the sea horizon2 the heliometer1 which serves for the very accurate measurement of small angles1 such as the angular distance between two stars not more than one or two degrees apart2 and the photometer1 which is used for measuring the amount of light received from the celestial bodies4 ,illustration3 ,,fig4 #eb4--;,a combined transit instrument and zenith telescope4 ,,chapter ,,ix ,,the ,,moon #ia4 ,,results ,,of ,,observation ,,with ,,the ,,unaided ,,eye4--,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 satellite4 ,perhaps the most striking feature brought out by them is the motion of the moon among the stars1 always from west toward east1 accompanied by that endless series of changes in shape and brightness--new moon1 first quarter1 full moon1 etc4--whose successive stages we represent by the words1 the phase of the moon4 ,from his own observation the student should be able to verify1 at least approximately1 the following statements1 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 subject3 ,a4 ,the phase of the moon depends upon the distance apart of sun and moon in the sky1 new moon coming when they are together1 and full moon when they are as far apart as possible4 ,illustration3 ,,the ,,moon1 ,,one ,,day ,,after ,,first ,,quarter4 ,from a photograph made at the ,paris ,observatory4 ,b4 ,the moon is essentially a round1 dark body1 giving off no light of its own1 but shining solely by reflected sunlight4 ,the proof of this is that whenever we see a part of the moon which is turned away from the sun it looks dark--e4 g41 at new moon1 sun and moon are in nearly the same direction from us and we see little or nothing of the moon1 since the side upon which the sun shines is turned away from us4 ,at full moon the earth is in line between sun and moon1 and we see1 round and bright1 the face upon which the sun shines4 ,at other phases1 such as the quarters1 the moon turns toward the earth a part of its night hemisphere and a part of its day hemisphere1 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 edge1 or terminator1 as it is called1 is the dividing line between day and night upon the moon4 ,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 sky1 for then the whole round disk of the moon may often be seen1 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 moon1 giving the pleasing effect which is sometimes called the old moon in the new moon's arms4 ,the new moon--i4 e41 the part illumined by the sun--usually appears to belong to a sphere of larger radius than the old moon1 but this is purely a trick played by the eyes of the observer1 and the effect disappears altogether in a telescope4 ,is there any similar effect in the few days before new moon8 ,c4 ,the moon makes the circuit of the sky from a given star around to the same star again in a little more than #bg days 7#bg4cbaff71 but the interval between successive new moons--i4 e41 from the sun around to the sun again--is more than #bi days 7#bi4ecjei74 ,this last interval1 which is called a lunar month or synodical month1 indicates what we have learned before--that the sun has changed its place among the stars during the month1 so that it takes the moon an extra two days to overtake him after having made the circuit of the sky1 just as it takes the minute hand of a clock an extra #e minutes to catch up with the hour hand after having made a complete circuit of the dial4 ,d4 ,wherever the moon may be in the sky1 it turns always the same face toward the earth1 as is shown by the fact that the dark markings which appear on its surface stand always upon 7nearly7 the same part of its disk4 ,it does not always turn the same face toward the sun1 for the boundary line between the illumined and unillumined parts of the moon shifts from one side to the other as the phase changes1 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 7#bi4e terrestrial days71 instead of being time units of different lengths as with us4 ,illustration3 ,,fig4 #ec4--,motion of moon and earth relative to the sun4 #ib4 ,,the ,,moon',s ,,motion4--,the student should compare the results of his own observations1 as well as the preceding section1 with ,fig4 #ec1 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 illustration1 any other set would do equally well4 ,the black dots1 small and large1 represent the moon revolving about the earth1 but having the circular path shown in ,fig4 #cd 7ellipse7 transformed by the earth's forward motion into the peculiar sinuous line here shown4 ,with respect to both earth and sun1 the moon's orbit deviates but little from a circle1 since the sinuous curve of ,fig4 #ec follows very closely the earth's orbit around the sun and is almost identical with it4 ,for clearness of representation the distance between earth and moon in the figure has been made ten times too great1 and to get a proper idea of the moon's orbit with reference to the sun1 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 figure4 ,when this is done1 the moon's path becomes almost indistinguishable from that of the earth1 as may be seen in the figure1 where the attempt has been made to show both lines1 and it is to be especially noted that this real orbit of the moon is everywhere concave toward the sun4 ,the phase presented by the moon at different parts of its path is indicated by the row of circles at the right1 and the student should show why a new moon is associated with ,june #cjth and a full moon with ,july #aeth1 etc4 ,what was the date of first quarter8 ,third quarter8 ,we may find in ,fig4 #ec another effect of the same kind as that noted above in ,c4 ,between noon1 ,june #cjth1 and noon1 ,july #c;d1 the earth makes upon its axis three complete revolutions with respect to the sun1 but the meridian which points toward the moon at noon on ,june #cjth will not point toward it at noon on ,july #c;d1 since the moon has moved into a new position and is now #cg away from the meridian4 ,verify this statement by measuring1 in ,fig4 #ec1 with the protractor1 the moon's angular distance from the meridian at noon on ,july #c;d4 ,when will the meridian overtake the moon8 #ic4 ,,harvest ,,moon4--,the interval between two successive transits of the meridian past the moon is called a lunar day1 and the student should show from the figure that on the average a lunar day is #ea minutes longer than a solar day--i4 e41 upon the average each day the moon comes to the meridian #ea minutes of solar time later than on the day before4 ,it is also true that on the average the moon rises and sets #ea minutes later each day than on the day before4 ,but there is a good deal of irregularity in the retardation of the time of moonrise and moonset1 since the time of rising depends largely upon the particular point of the horizon at which the moon appears1 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 value4 ,in northern latitudes this effect is particularly marked in the month of ,september1 when the eastern horizon is nearly parallel with the moon's apparent path in the sky1 and near the time of full moon in that month the moon rises on several successive nights at nearly the same hour1 and in less degree the same is true for ,october4 ,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 ,moon4 #id4 ,,size ,,and ,,mass ,,of ,,the ,,moon4--,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 angles1 and without enlarging upon the details of these observations1 we note as their result that the moon is a globe #b1afc miles in diameter1 and distant from the earth on the average about #bdj1jjj miles4 ,but1 as we have seen in ,chapter ,,vii1 this distance changes to the extent of a few thousand miles1 sometimes less1 sometimes greater1 mainly on account of the elliptic shape of the moon's orbit about the earth1 but also in part from the disturbing influence of other bodies1 such as the sun1 which pull the moon to and fro1 backward and forward1 to quite an appreciable extent4 ,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 contents4 ,leaving this as an exercise for the student1 we adopt the earth as the standard of comparison and find that the diameter of the moon is rather more than a quarter1 #d_/ae1 that of the earth1 the area of its surface is a trifle more than #a_/ad that of the earth1 and its volume a little more than #a_/di of the earth's4 ,so much is pure geometry1 but we may combine with it some mechanical principles which enable us to go a step farther and to weigh the moon--i4 e41 determine its mass and the average density of the material of which it is made4 ,we have seen that the moon moves around the sun in a path differing but little from the smooth curve shown in ,fig4 #ec1 with arrows indicating the direction of motion1 and it would follow absolutely such a smooth path were it not for the attraction of the earth1 and in less degree of some of the other planets1 which swing it about first to one side then to the other4 ,but action and reaction are equal2 the moon pulls as strongly upon the earth as does the earth upon the moon1 and if earth and moon were of equal mass1 the deviation of the earth from the smooth curve in the figure would be just as large as that of the moon4 ,it is shown in the figure that the moon does displace the earth from this curve1 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 other4 ,it may be seen from the figure that at first quarter1 about ,july #gth1 the earth is thrust ahead in the direction of its orbital motion1 while at the third quarter1 ,july #bb;d1 it is pulled back by the action of the moon1 and at all times it is more or less displaced by this action1 so that1 in order to be strictly correct1 we must amend our former statement about the moon moving around the earth and make it read1 ,both earth and moon revolve around a point on line between their centers4 ,this point is called their center of gravity1 and the earth and the moon both move in ellipses having this center of gravity at their common focus4 ,compare this with ,kepler's ,first ,law4 ,these ellipses are similarly shaped1 but of very different size1 corresponding to ,newton's third law of motion 7,chapter ,,iv71 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 orbit4 ,this is equivalent to saying that the dimensions of the two orbits are inversely proportional to the masses of the earth and the moon4 ,by observing throughout the month the direction from the earth to the sun or to a near planet1 such as ,mars or ,venus1 astronomers have determined that the diameter of the ellipse in which the earth moves is about #e1hej miles1 so that the distance of the earth from the center of gravity is #b1ibe miles1 and the distance of the moon from it is #bdj1jjj-b1ibe #bcg1jge4 ,we may now write in the form of a proportion-- ,mass of earth 3 ,mass of moon 33 #bcg1jge 3 #b1ibe1 and find from it that the mass of the earth is #ha times as great as the mass of the moon--i4 e41 leaving kind and quality out of account1 there is enough material in the earth to make #ha moons4 ,we may note in this connection that the diameter of the earth1 #g1ibf miles1 is greater than the diameter of the monthly orbit in which the moon causes it to move1 and therefore the center of gravity of earth and moon always lies inside the body of the earth1 about #a1jjj miles below the surface4 #ie4 ,,density ,,of ,,the ,,moon4--,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--metals1 minerals1 rocks1 etc4--and a part of the evidence upon which this belief is based lies in the density of the moon4 ,by density of a substance we mean the amount of it which is contained in a given volume--i4 e41 the weight of a bushel or a cubic centimeter of the stuff4 ,the density of chalk is twice as great as the density of water1 because a cubic centimeter of chalk weighs twice as much as an equal volume of water1 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 water4 ,we know the mass of the earth 7 #de71 and knowing the mass of a cubic foot of water1 it is easy1 although a trifle tedious1 to compute what would be the mass of a volume of water equal in size to the earth4 ,the quotient obtained by dividing one of these masses by the other 7mass of earth mass of water7 is the average density of the material composing the earth1 and we find numerically that this is #e4f--;i4 e41 it would take #e4f water earths to attract as strongly as does the real one4 ,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 this1 showing that the deep-lying central parts of the earth are denser than the surface parts1 as we should expect them to be1 because they have to bear the weight of all that lies above them and are compressed by it4 ,turning now to the moon1 we find in the same way as for the earth that its average density is #c4d as great as that of water4 #if4 ,,force ,,of ,,gravity ,,upon ,,the ,,moon4--,this number1 #c4d1 compared with the #e4f which we found for the earth1 shows that on the whole the moon is made of lighter stuff than is the body of the earth1 and this again is much what we should expect to find1 for weight1 the force which tends to compress the substance of the moon1 is less there than here4 ,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 it1 and this by the law of gravitation is for the earth-- ,w k 7m m7 _/ 7#cifc7b2 and for the moon-- w k m 7m_/#ha7 _/ 7#ajha7b2 from which we find by division-- w 7,w _/ #ha7 7#cifc _/ #ajha7b 7,w _/ #f7 7approximately74 ,the cubic yard of rock1 which upon the earth weighs two tons1 would1 if transported to the moon1 weigh only one third of a ton1 and would have only one sixth as much influence in compressing the rocks below it as it had upon the earth4 ,note that this rock when transported to the moon would be still attracted by the earth and would have weight toward the earth1 but it is not this of which we are speaking2 by its weight in the moon we mean the force with which the moon attracts it4 ,making due allowance for the difference in compression produced by weight1 we may say that in general1 so far as density goes1 the moon is very like a piece of the earth of equal mass set off by itself alone4 #ig4 ,,albedo4--,in another respect the lunar stuff is like that of which the earth is made3 it reflects the sunlight in much the same way and to the same amount4 ,the contrast of light and dark areas on the moon's surface shows1 as we shall see in another section1 the presence of different substances upon the moon which reflect the sunlight in different degrees4 ,this capacity for reflecting a greater or less percentage of the incident sunlight is called albedo 7,latin1 whiteness71 and the brilliancy of the full moon might lead one to suppose that its albedo is very great1 like that of snow or those masses of summer cloud which we call thunderheads4 ,but this is only an effect of contrast with the dark background of the sky4 ,the same moon by day looks pale1 and its albedo is1 in fact1 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 moon4 ,the effect produced by the differences of albedo upon the moon's face is commonly called the man in the moon1 but1 like the images presented by glowing coals1 the face in the moon is anything which we choose to make it4 ,among the ,chinese it is said to be a monkey pounding rice2 in ,india1 a rabbit2 in ,persia1 the earth reflected as in a mirror1 etc4 #ih4 ,,librations4--,we have already learned that the moon turns always the same face toward the earth1 and we have now to modify this statement and to find that here1 as in so many other cases1 the thing we learn first is only approximately true and needs to be limited or added to or modified in some way4 ,in general1 ,nature is too complex to be completely understood at first sight or to be perfectly represented by a simple statement4 ,in ,fig4 #ee we have two photographs of the moon1 taken nearly three years apart1 the right-hand one a little after first quarter and the left-hand one a little before third quarter4 ,they therefore represent different parts of the moon's surface1 but along the ragged edge the same region is shown on both photographs1 and features common to both pictures may readily be found--e4 g41 the three rings which form a right-angled triangle about one third of the way down from the top of the cut1 and the curved mountain chain just below these4 ,if the moon turned exactly the same face toward us in the two pictures1 the distance of any one of these markings from any part of the moon's edge must be the same in both pictures2 but careful measurement will show that this is not the case1 and that in the left-hand picture the upper edge of the moon is tipped toward us and the lower edge away from us1 as if the whole moon had been rotated slightly about a horizontal line and must be turned back a little 7about #g7 in order to match perfectly the other part of the picture4 ,this turning is called a libration1 and it should be borne in mind that the moon librates not only in the direction above measured1 north and south1 but also at right angles to this1 east and west1 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 face4 ,but in spite of the librations there remains on the farther side of the moon an area of #f1jjj1jjj square miles which is forever hidden from us1 and of whose character we have no direct knowledge1 although there is no reason to suppose it very different from that which is visible1 despite the fact that some of the books contain quaint speculations to the contrary4 ,the continent of ,south ,america is just about equal in extent to this unknown region1 while ,north ,america is a fair equivalent for all the rest of the moon's surface1 both those central parts which are constantly visible1 and the zone around the edge whose parts sometimes come into sight and are sometimes hidden4 ,an interesting consequence of the peculiar rotation of the moon is that from our side of it the earth is always visible4 ,sun1 stars1 and planets rise and set there as well as here1 but to an observer on the moon the earth swings always overhead1 shifting its position a few degrees one way or the other on account of the libration but running through its succession of phases1 new earth1 first quarter1 etc41 without ever going below the horizon1 provided the observer is anywhere near the center of the moon's disk4 ,illustration3 ,,fig4 #ed4--;,illustrating the moon's rotation4 #ii4 ,,cause ,,of ,,librations4--,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 earth4 ,this latter fact can have but one meaning3 the moon revolves about an axis as does the earth1 but the time required for this revolution is just equal to the time required to make a revolution in its orbit4 ,place two coins upon a table with their heads turned toward the north1 as in ,fig4 #ed1 and move the smaller one around the larger in such a way that its face shall always look away from the larger one4 ,in making one revolution in its orbit the head on this small coin will be successively directed toward every point of the compass1 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 orbit4 ,in no other way can it be made to face always away from the figure at the center of its orbit while moving around it4 ,we are now in a position to understand the moon's librations1 for1 if the small coin at any time moves faster or slower in its orbit than it turns about its axis1 a new side will be turned toward the center1 and the same may happen if the central coin itself shifts into a new position4 ,this is what happens to the moon1 for its orbital motion1 like that of ,mercury 7,fig4 #ag71 is alternately fast and slow1 and in addition to this there are present other minor influences1 such as the fact that its rotation axis is not exactly perpendicular to the plane of its orbit2 in addition to this the observer upon the earth is daily carried by its rotation from one point of view to another1 etc41 so that it is only in a general way that the rotation upon the axis and motion in the orbit keep pace with each other4 ,in a general way a cable keeps a ship anchored in the same place1 although wind and waves may cause it to librate about the anchor4 ,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 enter2 but the equality having once been established1 the mechanism by which it is preserved is simple enough4 ,the attraction of the earth for the moon has very slightly pulled the latter out of shape 7 #db71 so that the particular diameter1 which points toward the earth1 is a little longer than any other1 and thus serves as a handle which the earth lays hold of and pulls down into its lowest possible position--i4 e41 the position in which it points toward the center of the earth4 ,just how long this handle is1 remains unknown1 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 do4 #ajj4 ,,the ,,moon ,,as ,a ,,world4--,thus far we have considered the moon as a satellite of the earth1 dependent upon the earth1 and interesting chiefly because of its relation to it4 ,but the moon is something more than this2 it is a world in itself1 very different from the earth1 although not wholly unlike it4 ,the most characteristic feature of the earth's surface is its division into land and water1 and nothing of this kind can be found upon the moon4 ,it is true that the first generation of astronomers who studied the moon with telescopes fancied that the large dark patches shown in ,fig4 #ee were bodies of water1 and named them oceans1 seas1 lakes1 and ponds1 and to the present day we keep those names1 although it is long since recognized that these parts of the moon's surface are as dry as any other4 ,their dark appearance indicates a different kind of material from that composing the lighter parts of the moon1 material with a different albedo1 just as upon the earth we have light-colored and dark-colored rocks1 marble and slate1 which seen from the moon must present similar contrasts of brightness4 ,although these dark patches are almost the only features distinguishable with the unaided eye1 it is far otherwise in the telescope or the photograph1 especially along the ragged edge where great numbers of rings can be seen1 which are apparently depressions in the moon and are called craters4 ,these we find in great number all over the moon1 but1 as the figure shows1 they are seen to the best advantage near the terminator--i4 e41 the dividing line between day and night1 since the long shadows cast here by the rising or setting sun bring out the details of the surface better than elsewhere4 ,carefully examine ,fig4 #ee with reference to these features4 ,illustration3 ,,fig4 #ee4--,the moon at first and last quarter4 ,lick ,observatory photographs4 ,another feature which exists upon both earth and moon1 although far less common there than here1 is illustrated in the chain of mountains visible near the terminator1 a little above the center of the moon in both parts of ,fig4 #ee4 ,this particular range of mountains1 which is called the ,lunar ,apennines1 is by far the most prominent one upon the moon1 although others1 the ,alps and ,caucasus1 exist4 ,but for the most part the lunar mountains stand alone1 each by itself1 instead of being grouped into ranges1 as on the earth4 ,note in the figure that some of the lunar mountains stretch out into the night side of the moon1 their peaks projecting up into the sunlight1 and thus becoming visible1 while the lowlands are buried in the shadow4 ,a subordinate feature of the moon's surface is the system of rays which seem to radiate like spokes from some of the larger craters1 extending over hill and valley sometimes for hundreds of miles4 ,a suggestion of these rays may be seen in ,fig4 #ee1 extending from the great crater ,copernicus a little southwest of the end of the ,apennines1 but their most perfect development is to be seen at the time of full moon around the crater ,tycho1 which lies near the south pole of the moon4 ,look for them with an opera glass4 ,another and even less conspicuous feature is furnished by the rills1 which1 under favorable conditions of illumination1 appear like long cracks on the moon's surface1 perhaps analogous to the caons of our ,western country4 #aja4 ,,the ,,map ,,of ,,the ,,moon4--,fig4 #ee furnishes a fairly good map of a limited portion of the moon near the terminator1 but at the edges little or no detail can be seen4 ,this is always true2 the whole of the moon can not be seen to advantage at any one time1 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 best4 ,fig4 #ef shows such a map photographed from a relief model of the moon1 and representing the principal features of the lunar surface in a way they can never be seen simultaneously4 ,perhaps its most striking feature is the shape of the craters1 which are shown round in the central parts of the map and oval at the edges1 with their long diameters parallel to the moon's edge4 ,this is1 of course1 an effect of the curvature of the moon's surface1 for we look very obliquely at the edge portions1 and thus see their formations much foreshortened in the direction of the moon's radius4 ,illustration3 ,,fig4 #ef4--,relief map of the moon's surface4--,after ,,nasmyth and ,,carpenter4 ,the north and south poles of the moon are at the top and bottom of the map respectively1 and a mere inspection of the regions around them will show how much more rugged is the southern hemisphere of the moon than the northern4 ,it furnishes1 too1 some indication of how numerous are the lunar craters1 and how in crowded regions they overlap one another4 ,the student should pick out upon the map those features which he has learned to know in the photograph 7,fig4 #ee7--the ,apennines1 ,copernicus1 and the continuation of the ,apennines1 extending into the dark part of the moon4 ,illustration3 ,,fig4 #eg4--,mare ,imbrium4 ,photographed by ,g4 ,w4 ,,ritchey4 #ajb4 ,,size ,,of ,,the ,,lunar ,,features4--,we may measure distances here in the same way as upon a terrestrial map1 remembering that near the edges the scale of the map is very much distorted parallel to the moon's diameter1 and measurements must not be taken in this direction1 but may be taken parallel to the edge4 ,measuring with a millimeter scale1 we find on the map for the diameter of the crater ,copernicus1 #b4a millimeters4 ,to turn this into the diameter of the real ,copernicus in miles1 we measure upon the same map the diameter of the moon1 #gi4g millimeters1 and then have the proportion-- ,diameter of ,copernicus in miles 3 #b1afc 33 #b4a 3 #gi4g1 which when solved gives #eg miles4 ,the real diameter of ,copernicus is a trifle over #ef miles4 ,at the eastern edge of the moon1 opposite the ,apennines1 is a large oval spot called the ,mare ,crisium 7,latin1 ma-re sea74 ,measure its length4 ,the large crater to the northwest of the ,apennines is called ,archimedes4 ,measure its diameter both in the map and in the photograph 7,fig4 #ee71 and see how the two results agree4 ,the true diameter of this crater1 east and west1 is very approximately #ej miles4 ,the great smooth surface to the west of ,archimedes is the ,mare ,imbrium4 ,is it larger or smaller than ,lake ,superior8 ,fig4 #eg is from a photograph of the ,mare ,imbrium1 and the amount of detail here shown at the bottom of the sea is a sufficient indication that1 in this case at least1 the water has been drawn off1 if indeed any was ever present4 ,illustration3 ,,fig4 #eh4--,mare ,crisium4 ,lick ,observatory photographs4 ,fig4 #eh is a representation of the ,mare ,crisium at a time when night was beginning to encroach upon its eastern border1 and it serves well to show the rugged character of the ring-shaped wall which incloses this area4 ,with these pictures of the smoother parts of the moon's surface we may compare ,fig4 #ei1 which shows a region near the north pole of the moon1 and ,fig4 #fj1 giving an early morning view of ,archimedes and the ,apennines4 ,note how long and sharp are the shadows4 ,illustration3 ,,fig4 #ei4--;,illustrating the rugged character of the moon's surface4--,,nasmyth and ,,carpenter4 #ajc4 ,,the ,,moon',s ,,atmosphere4--,upon the earth the sun casts no shadows so sharp and black as those of ,fig4 #fj1 because his rays are here scattered and reflected in all directions by the dust and vapors of the atmosphere 7 #ea71 so that the place from which direct sunlight is cut off is at least partially illumined by this reflected light4 ,the shadows of ,fig4 #fj show that upon the moon it must be otherwise1 and suggest that if the moon has any atmosphere whatever1 its density must be utterly insignificant in comparison with that of the earth4 ,in its motion around the earth the moon frequently eclipses stars 7occults is the technical word71 and if the moon had an atmosphere such as is shown in ,fig4 #fa1 the light from the star ,a must shine through this atmosphere just before the moon's advancing body cuts it off1 and it must be refracted by the atmosphere so that the star would appear in a slightly different direction 7nearer to ,b7 than before4 ,the earth's atmosphere refracts the starlight under such circumstances by more than a degree1 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 arc4 ,while this hardly justifies the statement sometimes made that the moon has no atmosphere1 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 atmosphere4 ,quite in keeping with this absence of an atmosphere is the fact that clouds never float over the surface of the moon4 ,its features always stand out hard and clear1 without any of that haze and softness of outline which our atmosphere introduces into all terrestrial landscapes4 ,illustration3 ,,fig4 #fj4--;,archimedes and ,apennines4 ,,nasmyth and ,,carpenter4 #ajd4 ,,height ,,of ,,the ,,lunar ,,mountains4--,attention has already been called to the detached mountain peaks1 which in ,fig4 #ee prolong the range of ,apennines into the lunar night4 ,these are the beginnings of the ,caucasus mountains1 and from the photograph we may measure as follows the height to which they rise above the surrounding level of the moon3 ,fig4 #fb represents a part of the lunar surface along the boundary line between night and day1 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 mountain1 ,m1 whose height1 h1 is to be determined4 ,if we let ,r stand for the radius of the moon and s for the distance1 ,t ,m1 we shall have in the right-angled triangle ,m ,t ,c1 ,r#b s#b 7,r h7#b1 and we need only to measure s--that is1 the distance from the terminator to the detached mountain peak--to make this equation determine h1 since ,r is already known1 being half the diameter of the moon--#a1jha miles4 ,practically it is more convenient to use instead of this equation another form1 which the student who is expert in algebra may show to be very nearly equivalent to it3 h 7miles7 s#b _/ #bafc1 or h 7feet7 #b4dd s#b4 ,the distance s must be expressed in miles in all of these equations4 ,in ,fig4 #ee the distance from the terminator to the first detached peak of the ,caucasus mountains is #a4g millimeters #eb miles1 from which we find the height of the mountain to be #a4be miles1 or #f1fjj feet4 ,illustration3 ,,fig4 #fa4--,occultations and the moon's atmosphere4 ,illustration3 ,,fig4 #fb4--;,determining the height of a lunar mountain4 ,two things1 however1 need to be borne in mind in this connection4 ,on the earth we measure the heights of mountains above sea level1 while on the moon there is no sea1 and our #f1fjj feet is simply the height of the mountain top above the level of that particular point in the terminator1 from which we measure its distance4 ,so too it is evident from the appearance of things1 that the sunlight1 instead of just touching the top of the particular mountain whose height we have measured1 really extends some little distance down from its summit1 and the #f1fjj feet is therefore the elevation of the lowest point on the mountains to which the sunlight reaches4 ,the peak itself may be several hundred feet higher1 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 summit4 ,measure the height of the most northern visible mountain of the ,caucasus range4 ,this is one of the outlying spurs of the great mountain ,calippus1 whose principal peak1 #ai1jjj feet high1 is shown in ,fig4 #ee as the brightest part of the ,caucasus range4 ,the highest peak of the lunar ,apennines1 ,huyghens1 has an altitude of #ah1jjj feet1 and the ,leibnitz and ,doerfel ,mountains1 near the south pole of the moon1 reach an altitude #ej per cent greater than this1 and are probably the highest peaks on the moon4 ,this falls very little short of the highest mountain on the earth1 although the moon is much smaller than the earth1 and these mountains are considerably higher than anything on the western continent of the earth4 ,the vagueness of outline of the terminator makes it difficult to measure from it with precision1 and somewhat more accurate determinations of the heights of lunar mountains can be obtained by measuring the length of the shadows which they cast1 and the depths of craters may also be measured by means of the shadows which fall into them4 #aje4 ,,craters4--,fig4 #fc shows a typical lunar crater1 and conveys a good idea of the ruggedness of the lunar landscape4 ,compare the appearance of this crater with the following generalizations1 which are based upon the accurate measurement of many such3 ,a4 ,a crater is a real depression in the surface of the moon1 surrounded usually by an elevated ring which rises above the general level of the region outside1 while the bottom of the crater is about an equal distance below that level4 ,b4 ,craters are shallow1 their diameters ranging from five times to more than fifty times their depth4 ,archimedes1 whose diameter we found to be #ej miles1 has an average depth of about #d1jjj feet below the crest of its surrounding wall1 and is relatively a shallow crater4 ,illustration3 ,,fig4 #fc4--;,a typical lunar crater4--,,nasmyth and ,,carpenter4 ,c4 ,craters frequently have one or more hills rising within them which1 however1 rarely1 if ever1 reach up to the level of the surrounding wall4 ,d4 ,whatever may have been the mode of their formation1 the craters can not have been produced by scooping out material from the center and piling it up to make the wall1 for in three cases out of four the volume of the excavation is greater than the volume of material contained in the wall4 #ajf4 ,,moon ,,and ,,earth4--,we have gone far enough now to appreciate both the likeness and the unlikeness of the moon and earth4 ,they may fairly enough be likened to offspring of the same parent who have followed very different careers1 and in the fullness of time find themselves in very different circumstances4 ,the most serious point of difference in these circumstances is the atmosphere1 which gives to the earth a wealth of phenomena altogether lacking in the moon4 ,clouds1 wind1 rain1 snow1 dew1 frost1 and hail are all dependent upon the atmosphere and can not be found where it is not4 ,there can be nothing upon the moon at all like that great group of changes which we call weather1 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 moon4 ,the atmosphere is the chief agent in the propagation of sound1 and without it the moon must be wrapped in silence more absolute than can be found upon the surface of the earth4 ,so1 too1 the absence of an atmosphere shows that there can be no water or other liquid upon the moon1 for if so it would immediately evaporate and produce a gaseous envelope which we have seen does not exist4 ,with air and water absent there can be of course no vegetation or life of any kind upon the moon1 and we are compelled to regard it as an arid desert1 utterly waste4 #ajg4 ,,temperature ,,of ,,the ,,moon4--,a characteristic feature of terrestrial deserts1 which is possessed in exaggerated degree by the moon1 is the great extremes of temperature to which they and it are subject4 ,owing to its slow rotation about its axis1 a point on the moon receives the solar radiation uninterruptedly for more than a fortnight1 and that too unmitigated by any cloud or vaporous covering4 ,then for a like period it is turned away from the sun and allowed to cool off1 radiating into interplanetary space without hindrance its accumulated store of heat4 ,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 alike1 to say nothing of the ocean whose waters serve as a great balance wheel for equalizing temperatures4 ,just how hot or how cold the moon becomes is hard to determine1 and very different estimates are to be found in the books4 ,perhaps the most reliable of these are furnished by the recent researches of ,professor ,very1 whose experiments lead him to conclude that its rocky surface at midday1 in latitudes where the sun is high1 is probably hotter than boiling water and only the most terrible of earth's deserts1 where the burning sands blister the skin1 and men1 beasts1 and birds drop dead1 can approach a noontide on the cloudless surface of our satellite4 ,only the extreme polar latitudes of the moon can have an endurable temperature by day1 to say nothing of the night1 when we should have to become troglodytes to preserve ourselves from such intense cold4 ,while the night temperature of the moon1 even very soon after sunset1 sinks to something like #bjj below zero on the centigrade scale1 or #cbj below zero on the ,fahrenheit scale1 the lowest known temperature upon the earth1 according to ,general ,greely1 is #ij ,fahr4 below zero1 recorded in ,siberia in ,january1 #ahhe4 ,winter and summer are not markedly different upon the moon1 since its rotation axis is nearly perpendicular to the plane of the earth's orbit about the sun1 and the sun never goes far north or south of the moon's equator4 ,the month is the one cycle within which all seasonal changes in its physical condition appear to run their complete course4 #ajh4 ,,changes ,,in ,,the ,,moon4--,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 wilderness4 ,but minor changes there may be1 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 pronounced4 ,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 peak2 but while some things of this kind have been reported from time to time1 the evidence in their behalf has not been altogether conclusive4 ,at the present time it is an open question whether changes of this sort large enough to be seen from the earth are in progress4 ,a crater much less than a mile wide can be seen in the telescope1 but it is not easy to tell whether so minute an object has changed in size or shape during a year or a decade1 and even if changes are seen they may be apparent rather than real4 ,fig4 #fd contains two views of the crater ,archimedes1 taken under a morning and an afternoon sun respectively1 and shows a very pronounced difference between the two which proceeds solely from a difference of illumination4 ,in the presence of such large fictitious changes astronomers are slow to accept smaller ones as real4 ,illustration3 ,,fig4 #fd4--;,archimedes in the lunar morning and afternoon4--,,weinek4 ,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 made1 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 surface4 ,upon the moon this process is almost if not wholly wanting1 and the moon abides to-day much more like its primitive condition than is the earth4 #aji4 ,,the ,,moon',s ,,influence ,,upon ,,the ,,earth4--,there is a widespread popular belief that in many ways the moon exercises a considerable influence upon terrestrial affairs3 that it affects the weather for good or ill1 that crops must be planted and harvested1 pigs must be killed1 and timber cut at the right time of the moon1 etc4 ,our common word lunatic means moonstruck--i4 e41 one upon whom the moon has shone while sleeping4 ,there is not the slightest scientific basis for any of these beliefs1 and astronomers everywhere class them with tales of witchcraft1 magic1 and popular delusion4 ,for the most part the moon's influence upon the earth is limited to the light which it sends and the effect of its gravitation1 chiefly exhibited in the ocean tides4 ,we receive from the moon a very small amount of second-hand solar heat and there is also a trifling magnetic influence1 but neither of these last effects comes within the range of ordinary observation1 and we shall not go far wrong in saying that1 save the moonlight and the tides1 every supposed lunar influence upon the earth is either fictitious or too small to be readily detected4 ,,chapter ,x ,,the ,,sun #aaj4 ,,dependence ,,of ,,the ,,earth ,,upon ,,the ,,sun4--,there is no better introduction to the study of the sun than ,byron's ,ode to ,darkness1 beginning with the lines-- ,i dreamed a dream ,that was not all a dream4 ,the bright sun was extinguished1 and proceeding to depict in vivid words the consequences of this extinction4 ,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 beings4 ,the winds blow and the rivers run2 the crops grow1 are gathered and consumed1 by virtue of the solar energy4 ,factory1 locomotive1 beast1 bird1 and the human body furnish types of machines run by energy derived from the sun2 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 sun4 ,there are a few such1 but they are neither numerous nor important4 #aaa4 ,,the ,,sun',s ,,distance ,,from ,,the ,,earth4--,to the astronomer the sun presents problems of the highest consequence and apparently of very diverse character1 but all tending toward the same goal3 the framing of a mechanical explanation of the sun considered as a machine2 what it is1 and how it does its work4 ,in the forefront of these problems stand those numerical determinations of distance1 size1 mass1 density1 etc41 which we have already encountered in connection with the moon1 but which must here be dealt with in a different manner1 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 distance4 ,it would be like determining the distance of a steeple a mile away by observing its direction first from one eye1 then from the other2 too short a base for the triangle4 ,in one respect1 however1 we stand upon a better footing than in the case of the moon1 for the mass of the earth has already been found 7,chapter ,,iv7 as a fractional part of the sun's mass1 and we have only to invert the fraction in order to find that the sun's mass is #cbi1jjj times that of the earth and moon combined1 or #ccc1jjj times that of the earth alone4 ,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 follows3 ,it was suggested in #ch that ,newton proved ,kepler's three laws to be imperfect corollaries from the law of gravitation1 requiring a little amendment to make them strictly correct1 and below we give in the form of an equation ,kepler's statement of the ,third ,law together with ,newton's amendment of it4 ,in these equations-- ,t ,periodic time of any planet2 a ,one half the major axis of its orbit2 m ,its mass2 ,m ,the mass of the sun2 k ,the gravitation constant corresponding to the particular set of units in which ,t1 a1 m1 and ,m are expressed4 7,kepler7 a#c_/,t#b h2 7,newton7 a#c_/,t#b k 7,m m74 ,kepler's idea was3 ,for every planet which moves around the sun1 a#c divided by ,t#b always gives the same quotient1 h2 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--e4 g41 the earth--be taken as the units of length and time1 then the quotient will be #a4 ,newton1 on the other hand1 attached a meaning to the quotient1 and showed that it is equal to the product obtained by multiplying the sum of the two masses1 planet and sun1 by a number which is always the same when we are dealing with the action of gravitation1 whether it be between the sun and planet1 or between moon and earth1 or between the earth and a roast of beef in the butcher's scales1 provided only that we use always the same units with which to measure times1 distances1 and masses4 ,numerically1 ,newton's correction to ,kepler's ,third ,law does not amount to much in the motion of the planets4 ,jupiter1 which shows the greatest effect1 makes the circuit of his orbit in #d1ccc days instead of #d1cce1 which it would require if ,kepler's law were strictly true4 ,but in another respect the change is of the utmost importance1 since it enables us to extend ,kepler's law1 which relates solely to the sun and its planets1 to other attracting bodies1 such as the earth1 moon1 and stars4 ,thus for the moon's motion around the earth we write-- 7#bdj1jjjc7_/7bg4cbb7 k 7#a #a_/ha71 from which we may find that1 with the units here employed1 the earth's mass as the unit of mass1 the mean solar day as the unit of time1 and the mile as the unit of distance-- k #ahcj #ajaj4 ,if we introduce this value of k into the corresponding equation1 which represents the motion of the earth around the sun1 we shall have-- a#c_/7cfe4be7b #ahcj #ajaj 7#ccc1jjj #a71 where the large number in the parenthesis represents the number of times the mass of the sun is greater than the mass of the earth4 ,we shall find by solving this equation that a1 the mean distance of the sun from the earth1 is very approximately #ic1jjj1jjj miles4 #aac4 ,,another ,,method ,,of ,,determining ,,the ,,sun',s ,,distance4--,this will be best appreciated by a reference to ,fig4 #ag4 ,it appears here that the earth makes its nearest approach to the orbit of ,mars in the month of ,august1 and if in any ,august ,mars happens to be in opposition1 its distance from the earth will be very much less than the distance of the sun from the earth1 and may be measured by methods not unlike those which served for the moon4 ,if now the orbits of ,mars and the earth were circles having their centers at the sun this distance between them1 which we may represent by ,d1 would be the difference of the radii of these orbits-- ,d a - a1 where the accents 1 represent ,mars and the earth respectively4 ,kepler's ,third ,law furnishes the relation-- 7a7#c_/7,t7#b 7a7#c_/7,t7#b2 and since the periodic times of the earth and ,mars1 ,t1 ,t1 are known to a high degree of accuracy1 these two equations are sufficient to determine the two unknown quantities1 a1 a--i4 e41 the distance of the sun from ,mars as well as from the earth4 ,the first of these equations is1 of course1 not strictly true1 on account of the elliptical shape of the orbits1 but this can be allowed for easily enough4 ,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 ,mars1 and great interest has been aroused among astronomers by the discovery1 in #ahih1 of an asteroid1 or planet1 ,eros1 which at times comes much closer to the earth than does ,mars or any other heavenly body except the moon1 and which will at future oppositions furnish a more accurate determination of the sun's distance than any hitherto available4 ,observations for this purpose are being made at the present time 7,october1 #aijj74 ,many other methods of measuring the sun's distance have been devised by astronomers1 some of them extremely ingenious and interesting1 but every one of them has its weak point--e4 g41 the determination of the mass of the earth in the first method given above and the measurement of ,d in the second method1 so that even the best results at present are uncertain to the extent of #bjj1jjj miles or more1 and astronomers1 instead of relying upon any one method1 must use all of them1 and take an average of their results4 ,according to ,professor ,harkness1 this average value is #ib1gif1iej miles1 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 sun1 but whether on the nearer or the farther side of the center1 or exactly at it1 no man knows4 #aad4 ,,parallax ,,and ,,distance4--,it is quite customary among astronomers to speak of the sun's parallax1 instead of its distance from the earth1 meaning by parallax its difference of direction as seen from the center and surface of the earth--i4 e41 the angle subtended at the sun by a radius of the earth placed at right angles to the line of sight4 ,the greater the sun's distance the smaller will this angle be1 and it therefore makes a substitute for the distance which has the advantage of being represented by a small number1 #h4h1 instead of a large one4 ,the books abound with illustrations intended to help the reader comprehend how great is a distance of #ic1jjj1jjj miles1 but a single one of these must suffice here4 ,to ride #ajj miles a day #cfe days in the year would be counted a good bicycling record1 but the rider who started at the beginning of the ,christian era and rode at that rate toward the sun from the year #a ,a4 ,d4 down to the present moment would not yet have reached his destination1 although his journey would be about three quarters done4 ,he would have crossed the orbit of ,venus about the time of ,charlemagne1 and that of ,mercury soon after the discovery of ,america4 #aae4 ,,size ,,and ,,density ,,of ,,the ,,sun4--,knowing the distance of the sun1 it is easy to find from the angle subtended by its diameter 7#cb minutes of arc7 that the length of that diameter is #hfe1jjj miles4 ,we recall in this connection that the diameter of the moon's orbit is only #dhj1jjj miles1 but little more than half the diameter of the sun1 thus affording abundant room inside the sun1 and to spare1 for the moon to perform the monthly revolution about its orbit1 as shown in ,fig4 #fe4 ,illustration3 ,,fig4 #fe4--,the sun's size4--,,young4 ,in the same manner in which the density of the moon was found from its mass and diameter1 the student may find from the mass and diameter of the sun given above that its mean density is #a4d times that of water4 ,this is about the same as the density of gravel or soft coal1 and is just about one quarter of the average density of the earth4 ,we recall that the small density of the moon was accounted for by the diminished weight of objects upon it1 but this explanation can not hold in the case of the sun1 for not only is the density less but the force of gravity 7weight7 is there #bh times as great as upon the earth4 ,the athlete who here weighs #age pounds1 if transported to the surface of the sun would weigh more than an elephant does here1 and would find his bones break under his own weight if his muscles were strong enough to hold him upright4 ,the tremendous pressure exerted by gravity at the surface of the sun must be surpassed below the surface1 and as it does not pack the material together and make it dense1 we are driven to one of two conclusions3 ,either the stuff of which the sun is made is altogether unlike that of the earth1 not so readily compressed by pressure1 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 terrestrial4 #aaf4 ,,material ,,of ,,which ,,the ,,sun ,,is ,,made4--,as to the first of these alternatives1 the spectroscope comes to our aid and shows in the sun's spectrum 7,fig4 #ej7 the characteristic line marked ,d1 which we know always indicates the presence of sodium and identifies at least one terrestrial substance as present in the sun in considerable quantity4 ,the lines marked ,c and ,f are produced by hydrogen1 which is one of the constituents of water1 ,e shows calcium to be present in the sun1 b magnesium1 etc4 ,in this way it has been shown that about one half of our terrestrial elements1 mainly the metallic ones1 are present as gases on or near the sun's surface1 but it must not be inferred that elements not found in this way are absent from the sun4 ,they may be there1 probably are there1 but the spectroscopic proof of their presence is more difficult to obtain4 ,professor ,rowland1 who has been prominent in the study of the solar spectrum1 says3 ,were the whole earth heated to the temperature of the sun1 its spectrum would probably resemble that of the sun very closely4 ,some of the common terrestrial elements found in the sun are3 ,aluminium4 ,calcium4 ,carbon4 ,copper4 ,hydrogen4 ,iron4 ,lead4 ,nickel4 ,potassium4 ,silicon4 ,silver4 ,sodium4 ,tin4 ,zinc4 ,oxygen 787 ,whatever differences of chemical structure may exist between the sun and the earth1 it seems that we must regard these bodies as more like than unlike to each other in substance1 and we are brought back to the second of our alternatives3 there must be some influence opposing the force of gravity and making the substance of the sun light instead of heavy1 and we need not seek far to find it in-- #aag4 ,,the ,,heat ,,of ,,the ,,sun4--,that the sun is hot is too evident to require proof1 and it is a familiar fact that heat expands most substances and makes them less dense4 ,the sun's heat falling upon the earth expands it and diminishes its density in some small degree1 and we have only to imagine this process of expansion continued until the earth's diameter becomes #eh per cent larger than it now is1 to find the earth's density reduced to a level with that of the sun4 ,just how much the temperature of the earth must be raised to produce this amount of expansion we do not know1 neither do we know accurately the temperature of the sun1 but there can be no doubt that heat is the cause of the sun's low density and that the corresponding temperature is very high4 ,before we inquire more closely into the sun's temperature1 it will be well to draw a sharp distinction between the two terms heat and temperature1 which are often used as if they meant the same thing4 ,heat is a form of energy which may be found in varying degree in every substance1 whether warm or cold--a block of ice contains a considerable amount of heat--while temperature corresponds to our sensations of warm and cold1 and measures the extent to which heat is concentrated in the body4 ,it is the amount of heat per molecule of the body4 ,a barrel of warm water contains more heat than the flame of a match1 but its temperature is not so high4 ,bearing in mind this distinction1 we seek to determine not the amount of heat contained in the sun but the sun's temperature1 and this involves the same difficulty as does the question1 ,what is the temperature of a locomotive8 ,it is one thing in the fire box and another thing in the driving wheels1 and still another at the headlight2 and so with the sun1 its temperature is certainly different in different parts--one thing at the center and another at the surface4 ,even those parts which we see are covered by a veil of gases which produce by absorption the dark lines of the solar spectrum1 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 streams4 ,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 investigators1 who have assigned to it values ranging from #a1djj ,c4 to more than #e1jjj1jjj ,c4 ,quite recently1 however1 improved methods and a better understanding of the problem have brought about a better agreement of results1 and it now seems probable that the temperature of the visible surface of the sun lies somewhere between #e1jjj and #aj1jjj ,c41 say #ae1jjj of the ,fahrenheit scale4 #aah4 ,,determining ,,the ,,sun',s ,,temperature4--,one ingenious method which has been used for determining this temperature is based upon the principle stated above1 that every object1 whether warm or cold1 contains heat and gives it off in the form of radiant energy4 ,the radiation from a body whose temperature is lower than #ejj ,c4 is made up exclusively of energy whose wave length is greater than #g1fjj tenth meters1 and is therefore invisible to the eye1 although a thermometer or even the human hand can often detect it as radiant heat4 ,a brick wall in the summer sunshine gives off energy which can be felt as heat but can not be seen4 ,when such a body is further heated it continues to send off the same kinds 7wave lengths7 of energy as before1 but new and shorter waves are added to its radiation1 and when it begins to emit energy of wave length #g1ejj or #g1fjj tenth meters1 it also begins to shine with a dull-red light1 which presently becomes brighter and less ruddy and changes to white as the temperature rises1 and waves of still shorter length are thereby added to the radiation4 ,we say1 in common speech1 the body becomes first red hot and then white hot1 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 temperature4 ,the greater the proportion of energy of short wave lengths the higher is the temperature of the radiating body4 ,in sunlight the maximum of brilliancy to the eye lies at or near the wave length1 #e1fjj tenth meters1 but the greatest intensity of radiation of all kinds 7light included7 is estimated to fall somewhere between green and blue in the spectrum at or near the wave length #e1jjj tenth meters1 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 #bg1jjj1jjj by the wave length corresponding to maximum radiation--we shall find at once for the absolute temperature of the sun's surface #e1djj ,c4 ,paschen's law has been shown to hold true1 at least approximately1 for lower temperatures and longer wave lengths than are here involved1 but as it is not yet certain that it is strictly true and holds for all temperatures1 too great reliance must not be attached to the numerical result furnished by it4 ,illustration3 ,,fig4 #ff4--,the sun1 ,august #aa1 #ahid4 ,photographed at the ,goodsell ,observatory4 ,illustration3 ,,fig4 #fg4--,the sun1 ,august #ad1 #ahid4 ,photographed at the ,goodsell ,observatory4 #aai4 ,,the ,,sun',s ,,surface4--,a marked contrast exists between the faces of sun and moon in respect of the amount of detail to be seen upon them1 the sun showing nothing whatever to correspond with the mountains1 craters1 and seas of the moon4 ,the unaided eye in general finds in the sun only a blank bright circle as smooth and unmarked as the surface of still water1 and even the telescope at first sight seems to show but little more4 ,there may usually be found upon the sun's face a certain number of black patches called sun spots1 such as are shown in ,figs4 #ff to #fi1 and occasionally these are large enough to be seen through a smoked glass without the aid of a telescope4 ,when seen near the edge of the sun they are quite frequently accompanied1 as in ,fig4 #fi1 by vague patches called facul 7,latin1 facula a little torch71 which look a little brighter than the surrounding parts of the sun4 ,so1 too1 a good photograph of the sun usually shows that the central parts of the disk are rather brighter than the edge1 as indeed we should expect them to be1 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 center4 ,see ,fig4 #gj1 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 center4 ,illustration3 ,,fig4 #fh4--,the sun1 ,august #ah1 #ahid4 ,photographed at the ,goodsell ,observatory4 ,examine the sun spots in the four photographs1 ,figs4 #ff to #fi1 and note that the two spots which appear at the extreme left of the first photograph1 very much distorted and foreshortened by the curvature of the sun's surface1 are seen in a different part of the second picture1 and are not only more conspicuous but show better their true shape4 ,illustration3 ,,plate ,,ii4 ,,the ,,equatorial ,,constellations #abj4 ,,the ,,sun',s ,,rotation4--,the changed position of these spots shows that the sun rotates about an axis at right angles to the direction of the spot's motion1 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 photographs4 ,this rotation in the space of three days has carried the spots from the edge halfway to the center of the disk1 and the student should note the progress of the spots in the two later photographs1 that of ,august #bast showing them just ready to disappear around the farther edge of the sun4 ,illustration3 ,,fig4 #fi4--,the sun1 ,august #ba1 #ahid4 ,photographed at the ,goodsell ,observatory4 ,plot accurately in one of these figures the positions of the spots as shown in the other three1 and observe whether the path of the spots across the sun's face is a straight line4 ,is there any reason why it should not be straight8 ,these four pictures may be made to illustrate many things about the sun4 ,thus the sun's axis is not parallel to that of the earth1 for the letters ,n ,s mark the direction of a north and south line across the face of the sun1 and this line1 of course1 is parallel to the earth's axis1 while it is evidently not parallel to the sun's axis4 ,the group of spots took more than ten days to move across the sun's face1 and as at least an equal time must be required to move around the opposite side of the sun1 it is evident that the period of the sun's rotation is something more than #bj days4 ,it is1 in fact1 rather more than #be days1 for this same group of spots reappeared again on the left-hand edge of the sun on ,september #eth4 ,illustration3 ,,fig4 #gj4--;,absorption at the sun's edge4 #aba4 ,,sun ,,spots4--,another significant fact comes out plainly from the photographs4 ,the spots are not permanent features of the sun's face1 since they changed their size and shape very appreciably in the few days covered by the pictures4 ,compare particularly the photographs of ,august #adth and ,august #ahth1 where the spots are least distorted by the curvature of the sun's surface4 ,by ,september #afth this group of spots had disappeared absolutely from the sun's face1 although when at its largest the group extended more than #hj1jjj miles in length1 and several of the individual spots were large enough to contain the earth if it had been dropped upon them4 ,from ,fig4 #fg determine in miles the length of the group on ,august #adth4 ,fig4 #ga shows an enlarged view of these spots as they appeared on ,august #agth1 and in this we find some details not so well shown in the preceding pictures4 ,the larger spots consist of a black part called the nucleus or umbra 7,latin1 shadow71 which is surrounded by an irregular border called the penumbra 7partial shadow71 which is intermediate in brightness between the nucleus and the surrounding parts of the sun4 ,it should not be inferred from the picture that the nucleus is really black or even dark4 ,it shines1 in fact1 with a brilliancy greater than that of an electric lamp1 but the background furnished by the sun's surface is so much brighter that by contrast with it the nucleus and penumbra appear relatively dark4 ,illustration3 ,,fig4 #ga4--,sun spots1 ,august #ag1 #ahid4 ,goodsell ,observatory4 ,illustration3 ,,fig4 #gb4--,sun spot of ,march #e1 #ahgc4--;,from ,,langley1 ,the ,new ,astronomy4 ,by permission of the publishers4 ,the bright shining surface of the sun1 the background for the spots1 is called the photosphere 7,greek1 light sphere71 and1 as ,fig4 #ga shows1 it assumes under a suitable magnifying power a mottled aspect quite different from the featureless expanse shown in the earlier pictures4 ,the photosphere is1 in fact1 a layer of little clouds with darker spaces between them1 and the fine detail of these clouds1 their complicated structure1 and the way in which1 when projected against the background of a sun spot1 they produce its penumbra1 are all brought out in ,fig4 #gb4 ,note that the little patch in one corner of this picture represents ,north and ,south ,america drawn to the same scale as the sun spots4 ,illustration3 ,,fig4 #gc4--,spectroheliograph1 showing distribution of facul upon the sun4--,,hale4 ,illustration3 ,,fig4 #gd4--;,eclipse of ,july #bj1 #ahgh4--,,trouvelot4 #abb4 ,,facul4--,we have seen in ,fig4 #fi a few of the bright spots called facul4 ,at the telescope or in the ordinary photograph these can be seen only at the edge of the sun1 because elsewhere the background furnished by the photosphere is so bright that they are lost in it4 ,it is possible1 however1 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 background1 much more than the brightness of the facul is diminished1 and in this way to obtain a photograph of the sun's surface which shall show them wherever they occur1 and such a photograph1 showing faintly the spectral lines1 is reproduced in ,fig4 #gc4 ,the facul are the bright patches which stretch inconspicuously across the face of the sun1 in two rather irregular belts with a comparatively empty lane between them4 ,this lane lies along the sun's equator1 and it is upon either side of it between latitudes #e and #dj that facul seem to be produced4 ,it is significant of their connection with sun spots that the spots occur in these particular zones and are rarely found outside them4 ,illustration3 ,,fig4 #ge4--;,eclipse of ,april #af1 #ahic4--,,schaeberle4 #abc4 ,,invisible ,,parts ,,of ,,the ,,sun4 ,,the ,,corona4--,thus far we have been dealing with parts of the sun that may be seen and photographed under all ordinary conditions4 ,but outside of and surrounding these parts is an envelope1 or rather several envelopes1 of much greater extent than the visible sun4 ,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 eclipse4 ,illustration3 ,,fig4 #gf4--;,eclipse of ,january #ba1 #ahih4--;,,campbell4 ,fig4 #gd is from a drawing1 and ,figs4 #ge and #gf are from eclipse photographs showing this region1 in which the most conspicuous object is the halo of soft light called the corona1 that completely surrounds the sun but is seen to be of differing shapes and differing extent at the several eclipses here shown1 although a large part of these apparent differences is due to technical difficulties in photographing1 and reproducing an object with outlines so vague as those of the corona4 ,the outline of the corona is so indefinite and its outer portions so faint that it is impossible to assign to it precise dimensions1 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 sun4 ,despite its huge bulk1 it is of most unsubstantial character1 an airy nothing through which comets have been known to force their way around the sun from one side to the other1 literally for millions of miles1 without having their course influenced or their velocity checked to any appreciable extent4 ,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 experiments4 ,it seems odd that a vacuum should give off so bright a light as the coronal pictures show1 and the exact character of that light and the nature of the corona are still subjects of dispute among astronomers1 although it is generally agreed that1 in part at least1 its light is ordinary sunlight faintly reflected from the widely scattered molecules composing the substance of the corona4 ,it is also probable that in part the light has its origin in the corona itself4 ,a curious and at present unconfirmed result announced by one of the observers of the eclipse of ,may #bh1 #aijj1 is that the corona is not hot1 its effective temperature being lower than that of the instrument used for the observation4 ,illustration3 ,,fig4 #gg4--,solar prominence of ,march #be1 #ahie4--;,,hale4 #abd4 ,,the ,,chromosphere4--,between the corona and the photosphere there is a thin separating layer called the chromosphere 7,greek1 color sphere71 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 surface1 as in a fountain a jet of water is thrown up from the basin and remains for a few moments suspended in mid-air4 ,not infrequently in such a fountain foreign matter is swept up by the rush of the water--dirt1 twigs1 small fish1 etc4--and in like manner the prominences often carry along with them parts of the underlying layers of the sun1 photosphere1 facul1 etc41 which reveal their presence in the prominence by adding their characteristic lines to the spectrum1 like that of the chromosphere1 which the prominence presents when they are absent4 ,none of the eclipse photographs 7,figs4 #gd to #gf7 show the chromosphere1 because the color effect is lacking in them1 but a great curving prominence may be seen near the bottom of ,fig4 #ge1 and smaller ones at other parts of the sun's edge4 ,illustration3 ,,fig4 #gh4--;,a solar prominence4--,,hale4 #abe4 ,,prominences4--,fig4 #gg shows upon a larger scale one of these prominences rising to a height of #afj1jjj miles above the photosphere2 and another photograph1 taken #ah minutes later1 but not reproduced here1 showed the same prominence grown in this brief interval to a stature of #bhj1jjj miles4 ,these pictures were not taken during an eclipse1 but in full sunlight1 using the same spectroscopic apparatus which was employed in connection with the facul to diminish the brightness of the background without much enfeebling the brilliancy of the prominence itself4 ,the dark base from which the prominence seems to spring is not the sun's edge1 but a part of the apparatus used to cut off the direct sunlight4 ,fig4 #gh contains a series of photographs of another prominence taken within an interval of #a hour #dg 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 ,fig4 #gg4 ,illustration3 ,,fig4 #gi4--;,contrasted forms of solar prominences4--,,zoellner4 ,the preceding pictures are from photographs1 and with them the student may compare ,fig4 #gi1 which is constructed from drawings made at the spectroscope by the ,german astronomer ,zoellner4 ,the changes here shown are most marked in the prominence at the left1 which is shaped like a broken tree trunk1 and which appears to be vibrating from one side to the other like a reed shaken in the wind4 ,such a prominence is frequently called an eruptive one1 a name suggested by its appearance of having been blown out from the sun by something like an explosion1 while the prominence at the right in this series of drawings1 which appears much less agitated1 is called by contrast with the other a quiescent prominence4 ,these quiescent prominences are1 as a rule1 much longer-lived than the eruptive ones4 ,one more picture of prominences 7,fig4 #hj7 is introduced to show the continuous stretch of chromosphere out of which they spring4 ,illustration3 ,,fig4 #hj4--,prominences and chromosphere4--,,hale4 ,prominences are seen only at the edge of the sun1 because it is there alone that the necessary background can be obtained1 but they must occur at the center of the sun and elsewhere quite as well as at the edge1 and it is probable that quiescent prominences are distributed over all parts of the sun's surface1 but eruptive prominences show a strong tendency toward the regions of sun spots and facul as if all three were intimately related phenomena4 #abf4 ,,the ,,sun ,,as ,a ,,machine4--,thus far we have considered the anatomy of the sun1 dissecting it into its several parts1 and our next step should be a consideration of its physiology1 the relation of the parts to each other1 and their function in carrying on the work of the solar organism1 but this step1 unfortunately1 must be a lame one4 ,the science of astronomy to-day possesses no comprehensive and well-established theory of this kind1 but looks to the future for the solution of this the greatest pending problem of solar physics4 ,progress has been made toward its solution1 and among the steps of this progress that we shall have to consider1 the first and most important is the conception of the sun as a kind of heat engine4 ,in a steam engine coal is burned under the boiler1 and its chemical energy1 transformed into heat1 is taken up by the water and delivered1 through steam as a medium1 to the engine1 which again transforms and gives it out as mechanical work in the turning of shafts1 the driving of machinery1 etc4 ,now1 the function of the sun is exactly opposite to that of the engine and boiler3 it gives out1 instead of receiving1 radiant energy2 but1 like the engine1 it must be fed from some source2 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 boiler4 ,we know that for some thousands of years the sun has been furnishing light and heat to the earth in practically unvarying amount1 and not to the earth alone1 but it has been pouring forth these forms of energy in every direction1 without apparent regard to either use or economy4 ,of all the radiant energy given off by the sun1 only two parts out of every thousand million fall upon any planet of the solar system1 and of this small fraction the earth takes about one tenth for the maintenance of its varied forms of life and action4 ,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 diminution1 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 it1 although they may be in some small measure re-enforced by minor influences1 such as the fall of meteoric dust and stones into the sun4 ,every boy who has inflated a bicycle tire with a hand pump knows that the pump grows warm during the operation1 on account of the compression of the air within the cylinder4 ,a part of the muscular force 7energy7 expended in working the pump reappears in the heat which warms both air and pump1 and a similar process is forever going on in the sun1 only in place of muscular force we must there substitute the tremendous attraction of gravitation1 #bh times as great as upon the earth4 ,the matter in the interior of the sun must be as a shuttlecock between the stupendous pressure and the enormously high temperature1 the one tending to compress and the other to expand it1 but with this important difference between them3 the temperature steadily tends to fall as the heat energy is wasted away1 while the gravitative force suffers no corresponding diminution1 and in the long run must gain the upper hand1 causing the sun to shrink and become more dense4 ,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 heat4 ,according to ,lord ,kelvin1 each centimeter of shrinkage in the sun's diameter furnishes the energy required to keep up its radiation for something more than an hour1 and1 on account of the sun's great distance1 the shrinkage might go on at this rate for many centuries without producing any measurable effect in the sun's appearance4 #abg4 ,,gaseous ,,constitution ,,of ,,the ,,sun4--,but ,helmholtz's dynamical theory of the maintenance of the sun's heat1 which we are here considering1 includes one essential feature that is not sufficiently stated above4 ,in order that the explanation may hold true1 it is necessary that the sun should be in the main a gaseous body1 composed from center to circumference of gases instead of solid or liquid parts4 ,pumping air warms the bicycle pump in a way that pumping water or oil will not4 ,the high temperature of the sun itself furnishes sufficient reason for supposing the solar material to be in the gaseous state1 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 earth1 since its average density is #a1jjj times as great as that of air1 and its consistence and mechanical behavior must be more like that of honey or tar than that of any gas with which we are familiar4 ,it is worth noting1 however1 that if a hole were dug into the crust of the earth to a depth of #ae or #bj 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 gases4 #abh4 ,,the ,,sun',s ,,circulation4--,it is plain that under the conditions which exist in the sun the outer portions1 which can radiate their heat freely into space1 must be cooler than the inner central parts1 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 place4 ,so1 too1 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 drops1 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 surface1 while above and below is the gaseous atmosphere4 ,in the case of the sun this cloud layer is always present and is that part which we have learned to call the photosphere4 ,above the photosphere lies the chromosphere1 composed of gases less easily liquefied1 hydrogen is the chief one1 while between photosphere and chromosphere is a thin layer of metallic vapors1 perhaps indistinguishable from the top crust of the photosphere itself1 which by absorbing the light given off from the liquid photosphere produces the greater part of the ,fraunhofer lines in the solar spectrum4 ,from time to time the hot matter struggling up from below breaks through the photosphere and1 carrying with it a certain amount of the metallic vapors1 is launched into the upper and cooler regions of the sun1 where1 parting with its heat1 it falls back again upon the photosphere and is absorbed into it4 ,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 miles1 or even sufficient to carry them off never to return4 ,the matter of the corona must certainly be in a state of the most lively agitation1 its particles being alternately hurled up from the photosphere and falling back again like fireworks1 the particles which make up the corona of to-day being quite a different set from those of yesterday or last week4 ,it seems beyond question that the prominences and facul too are produced in some way by this up-and-down circulation of the sun's matter1 and that any mechanical explanation of the sun must be worked out along these lines2 but the problem is an exceedingly difficult one1 and must include and explain many other features of the sun's activity of which only a few can be considered here4 #abi4 ,,the ,,sun-,,spot ,,period4--,sun spots come and go1 and at best any particular spot is but short-lived1 rarely lasting more than a month or two1 and more often its duration is a matter of only a few days4 ,they are not equally numerous at all times1 but1 like swarms of locusts1 they seem to come and abound for a season and then almost to disappear1 as if the forces which produced them were of a periodic character alternately active and quiet4 ,the effect of this periodic activity since #ahgj is shown in ,fig4 #ha1 where the horizontal line is a scale of times1 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 year4 ,this indicates very plainly that #ahgj1 #ahhc1 and #ahic were years of great sun-spot activity1 while #ahgi and #ahhi were years in which few spots appeared4 ,the older records1 covering a period of two centuries1 show the same fluctuations in the frequency of sun spots and from these records curves 7which may be found in ,young's1 ,the ,sun7 have been plotted1 showing a succession of waves extending back for many years4 ,illustration3 ,,fig4 #ha4--,the curve of sun-spot frequency4 ,the sun-spot period is the interval of time from the crest or hollow of one wave to the corresponding part of the next one1 and on the average this appears to be a little more than eleven years1 but is subject to considerable variation4 ,in accordance with this period there is drawn in broken lines at the right of ,fig4 #ha a predicted continuation of the sun-spot curve for the first decade of the twentieth century4 ,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 made2 but in a general way #aija and #aiaa will probably be years of few sun spots1 while they will be numerous in #aije1 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 period4 ,determine from ,fig4 #ha as accurately as possible the length of the sun-spot period4 ,it is hard to tell the exact position of a crest or hollow of the curve4 ,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--e4 g41 in #ahgd and #ahhe8 ,illustration3 ,,fig4 #hb4--;,illustrating change of the sun-spot zones4 #acj4 ,,the ,,sun-,,spot ,,zones4--,it has been already noted that sun spots are found only in certain zones of latitude upon the sun1 and that facul and eruptive prominences abound in these zones more than elsewhere1 although not strictly confined to them4 ,we have now to note a peculiarity of these zones which ought to furnish a clew to the sun's mechanism1 although up to the present time it has not been successfully traced out4 ,just before a sun-spot minimum the few spots which appear are for the most part clustered near the sun's equator4 ,as these spots die out two new groups appear1 one north the other south of the sun's equator and about #be or #cj distant from it1 and as the period advances toward a maximum these groups shift their positions more and more toward the equator1 thus approaching each other but leaving between them a vacant lane1 which becomes steadily narrower until at the close of the period1 when the next minimum is at hand1 it reaches its narrowest dimensions1 but does not altogether close up even then4 ,in ,fig4 #hb these relations are shown for the period falling between #ahgi and #ahij1 by means of the horizontal lines2 for each year one line in the northern and one in the southern hemisphere of the sun1 their lengths being proportional to the number of spots which appeared in the corresponding hemisphere during the year1 and their positions on the sun's disk showing the average latitude of the spots in question4 ,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 spots1 and this appears to be generally the case1 although the difference is not usually as great as in this particular decade4 #aca4 ,,influence ,,of ,,the ,,sun-,,spot ,,period4--,sun spots are certainly less hot than the surrounding parts of the sun's surface1 and1 in view of the intimate dependence of the earth upon the solar radiation1 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 earth1 raising and lowering its temperature and quite possibly affecting it in other ways4 ,ingenious men have suggested many such kinds of influence1 which1 according to their investigations1 appear to run in cycles of eleven years4 ,abundant and scanty harvests1 cyclones1 tornadoes1 epidemics1 rainfall1 etc41 are among these alleged effects1 and it is possible that there may be a real connection between any or all of them and the sun-spot period1 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 kind4 ,the magnetic condition of the earth and its disturbances1 which are called magnetic storms1 do certainly follow in a very marked manner the course of sun-spot activity1 and perhaps there should be added to this the statement that auroras 7northern lights7 stand in close relation to these magnetic disturbances and are most frequent at the times of sun-spot maxima4 ,upon the sun1 however1 the influence of the spot period is not limited to things in and near the photosphere1 but extends to the outermost limits of the corona4 ,determine from ,fig4 #ha 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 corona1 while the pictures taken at a time of maximum activity of the sun spots show a very differently shaped and much smaller corona4 #acb4 ,,the ,,law ,,of ,,the ,,sun',s ,,rotation4--,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 disk1 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 result4 ,each particular parallel of latitude has its own period of rotation different from that of its neighbors on either side1 so that there can be no such thing as a fixed geography of the sun's surface4 ,every part of it is constantly taking up a new position with respect to every other part1 much as if the ,gulf of ,mexico should be south of the ,united ,states this year1 southeast of it next year1 and at the end of a decade should have shifted around to the opposite side of the earth from us4 ,a meridian of longitude drawn down the ,mississippi ,valley remains always a straight line1 or1 rather1 great circle1 upon the surface of the earth1 while ,fig4 #hc shows what would become of such a meridian drawn through the equatorial parts of the sun's disk4 ,in the first diagram it appears as a straight line running down the middle of the sun's disk4 ,twenty-five days later1 when the same face of the sun comes back into view again1 after making a complete revolution about the axis1 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 diagram1 and still more warped after another and another revolution1 as shown in the figure4 ,illustration3 ,,fig4 #hc4--;,effect of the sun's peculiar rotation in warping a meridian1 originally straight4 ,at least such is the case if the spots truly represent the way in which the sun turns round4 ,there is1 however1 a possibility that the spots themselves drift with varying speeds across the face of the sun1 and that the differences which we find in their rates of motion belong to them rather than to the photosphere4 ,just what happens in the regions near the poles is hard to say1 for the sun spots only extend about halfway from the equator to the poles1 and the spectroscope1 which may be made to furnish a certain amount of information bearing upon the case1 is not as yet altogether conclusive1 nor are the facul which have also been observed for this purpose4 ,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 period1 the variations in the corona1 the peculiar character of the sun's rotation1 etc41 and we have still unsolved in the mechanical theory of the sun one of the noblest problems of astronomy1 and one upon which both observers and theoretical astronomers are assiduously working at the present time4 ,a close watch is kept upon sun spots and prominences1 the corona is observed at every total eclipse1 and numerous are the ingenious methods which are being suggested and tried for observing it without an eclipse in ordinary daylight4 ,attempts1 more or less plausible1 have been made and are now pending to explain photosphere1 spots and the reversing layer by means of the refraction of light within the sun's outer envelope of gases1 and it seems altogether probable1 in view of these combined activities1 that a considerable addition to our store of knowledge concerning the sun may be expected in the not distant future4 ,,chapter ,,xi ,,the ,,planets #acc4 ,,planets4--,circling about the sun1 under the influence of his attraction1 is a family of planets each member of which is1 like the moon1 a dark body shining by reflected sunlight1 and therefore presenting phases2 although only two of them1 ,mercury and ,venus1 run through the complete series--new1 first quarter1 full1 last quarter--which the moon presents4 ,the way in which their orbits are grouped about the sun has been considered in ,chapter ,,iii1 and ,figs4 #af and #ag of that chapter may be completed so as to represent all of the planets by drawing in ,fig4 #af two circles with radii of #g4i and #ab4d centimeters respectively1 to represent the orbits of the planets ,uranus and ,neptune1 which are more remote from the sun than ,saturn1 and by introducing a little inside the orbit of ,jupiter about #ejj ellipses of different sizes1 shapes1 and positions to represent a group of minor planets or asteroids as they are often called4 ,it is convenient to regard these asteroids as composing by themselves a class of very small planets1 while the remaining #h larger planets fall naturally into two other classes1 a group of medium-sized ones--,mercury1 ,venus1 ,earth1 and ,mars--called inner planets by reason of their nearness to the sun2 and the outer planets--,jupiter1 ,saturn1 ,uranus1 ,neptune--each of which is much larger and more massive than any planet of the inner group4 ,compare in ,figs4 #hd and #he their relative sizes4 ,the earth1 ,e1 is introduced into ,fig4 #he as a connecting link between the two figures4 ,some of these planets1 like the earth1 are attended by one or more moons1 technically called satellites1 which also shine by reflected sunlight and which move about their respective planets in accordance with the law of gravitation1 much as the moon moves around the earth4 ,illustration3 ,,fig4 #hd4--,the inner planets and the moon4 ,illustration3 ,,fig4 #he4--,the outer planets4 #acd4 ,,distances ,,of ,,the ,,planets ,,from ,,the ,,sun4--,it is a comparatively simple matter to observe these planets year after year as they move among the stars1 and to find from these observations how long each one of them requires to make its circuit around the sun--that is1 its periodic time1 ,t1 which figures in ,kepler's ,third ,law1 and when these periodic times have been ascertained1 to use them in connection with that law to determine the mean distance of each planet from the sun4 ,thus1 ,jupiter requires #d1ccc days to move completely around its orbit2 and comparing this with the periodic time and mean distance of the earth we find-- a#c _/ 7#dcccb7 7#ic1jjj1jjjc7 _/ 7#cfe4beb71 which when solved gives as the mean distance of ,jupiter from the sun1 #dhc1gcj1jjj miles1 or #e4bj times as distant as the earth4 ,if we make a similar computation for each planet1 we shall find that their distances from the sun show a remarkable agreement with an artificial series of numbers called ,bode's law4 ,we write down the numbers contained in the first line of figures below1 each of which1 after the second1 is obtained by doubling the preceding one1 add #d to each number and point off one place of decimals2 the resulting number is 7approximately7 the distance of the corresponding planet from the sun4 ,mercury4 ,venus4 ,earth4 ,mars4 ,jupiter4 ,saturn4 ,uranus4 ,neptune4 #j #c #f #ab #bd #dh #if #aib #chd #d #d #d #d #d #d #d #d #d ---------------------------------------- ------------------------------- #j4d #j4g #a4j #a4f #b4h #e4b #aj4j #ai4f #ch4h #j4d #j4g #a4j #a4e #b4h #e4b #i4e #ai4b #cj4a ,the last line of figures shows the real distance of the planet as determined from ,kepler's law1 the earth's mean distance from the sun being taken as the unit for this purpose4 ,with exception of ,neptune1 the agreement between ,bode's law and the true distances is very striking1 but most remarkable is the presence in the series of a number1 #b4h1 with no planet corresponding to it4 ,this led astronomers at the time ,bode published the law1 something more than a century ago1 to give new heed to a suggestion made long before by ,kepler1 that there might be an unknown planet moving between the orbits of ,mars and ,jupiter1 and a number of them agreed to search for such a planet1 each in a part of the sky assigned him for that purpose4 ,but they were anticipated by ,piazzi1 an ,italian1 who found the new planet1 by accident1 on the first day of the nineteenth century1 moving at a distance from the sun represented by the number #b4gg4 ,this planet was the first of the asteroids1 and in the century that has elapsed hundreds of them have been discovered1 while at the present time no year passes by without several more being added to the number4 ,while some of these are nearer to the sun than is the first one discovered1 and others are farther from it1 their average distance is fairly represented by the number #b4h4 ,why ,bode's law should hold true1 or even so nearly true as it does1 is an unexplained riddle1 and many astronomers are inclined to call it no law at all1 but only a chance coincidence--an illustration of the inherent capacity of figures to be juggled with2 but if so1 it is passing strange that it should represent the distance of the asteroids and of ,uranus1 which was also an undiscovered planet at the time the law was published4 #ace4 ,,the ,,planets ,,compared ,,with ,,each ,,other4--,when we pass from general considerations to a study of the individual peculiarities of the planets1 we find great differences in the extent of knowledge concerning them1 and the reason for this is not far to seek4 ,neptune and ,uranus1 at the outskirts of the solar system1 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 size1 mass1 density1 the character of their orbits1 etc4 ,the asteroids are so small that in the telescope they look like mere points of light1 absolutely indistinguishable in appearance from the fainter stars4 ,mercury1 although closer at hand and presenting a disk of considerable size1 always stands so near the sun that its observation is difficult on this account4 ,something of the same kind is true for ,venus1 although in much less degree2 while ,mars1 ,jupiter1 and ,saturn are comparatively easy objects for telescopic study1 and our knowledge of them1 while far from complete1 is considerably greater than for the other planets4 ,figs4 #hd and #he show the relative sizes of the planets composing the inner and outer groups respectively1 and furnish the numerical data concerning their diameters1 masses1 densities1 etc41 which are of most importance in judging of their physical condition4 ,each planet1 save ,saturn1 is represented by two circles1 of which the outer is drawn proportional to the size of the planet1 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 water4 ,note the great difference in thickness of shell between the two groups4 ,saturn1 having a mean density less than that of water1 must have something loaded upon it1 instead of removed1 in order that it should float just submerged4 ,,jupiter #acf4 ,,appearance4--,commencing our consideration of the individual planets with ,jupiter1 which is by far the largest of them1 exceeding both in bulk and mass all the others combined1 we have in ,fig4 #hf four representations of ,jupiter and his family of satellites as they may be seen in a very small telescope--e4 g41 an opera glass--save that the little dots which here represent the satellites are numbered #a1 #b1 #c1 #d1 in order to preserve their identity in the successive pictures4 ,the chief interest of these pictures lies in the satellites1 but1 reserving them for future consideration1 we note that the planet itself resembles in shape the full moon1 although in respect of brightness it sends to us less than #a_/fjjj part as much light as the moon4 ,from a consideration of the motion of ,jupiter and the earth in ,fig4 #af1 show that ,jupiter can not present any such phases as does the moon1 but that its disk must be at all times nearly full4 ,as seen from ,saturn1 what kind of phases would ,jupiter present8 #acg4 ,,the ,,belts4--,even upon the small scale of ,fig4 #hf we detect the most characteristic feature of ,jupiter's appearance in the telescope1 the two bands extending across his face parallel to the line of the satellites1 and in ,fig4 #hg these same dark bands may be recognized amid the abundance of detail which is here brought out by a large telescope4 ,photography does not succeed as a means of reproducing this detail1 and for it we have to rely upon the skill of the artist astronomer4 ,the lettering shows the ,pacific ,standard time at which the sketches were made1 and also the longitude of the meridian of ,jupiter passing down the center of the planet's disk4 ,illustration3 ,,fig4 #hf4--;,jupiter and his satellites4 ,illustration3 ,,fig4 #hg4--;,drawings of ,jupiter made at the #cf-;inch telescope of the ,lick ,observatory4--,,keeler4 ,the dark bands are called technically the belts of ,jupiter2 and a comparison of these belts in the second and third pictures of the group1 in which nearly the same face of the planet is turned toward us1 will show that they are subject to considerable changes of form and position even within the space of a few days4 ,so1 too1 by a comparison of such markings as the round white spots in the upper parts of the disks1 and the indentations in the edges of the belts1 we may recognize that the planet is in the act of turning round1 and must therefore have an axis about which it turns1 and poles1 an equator1 etc4 ,the belts are in fact parallel to the planet's equator2 and generalizing from what appears in the pictures1 we may say that there is always a strongly marked belt on each side of the equator with a lighter colored streak between them1 and that farther from the equator are other belts variable in number1 less conspicuous1 and less permanent than the two first seen4 ,compare the position of the principal belts with the position of the zones of sun-spot activity in the sun4 ,a feature of the planet's surface1 which can not be here reproduced1 is the rich color effect to be found upon it4 ,the principal belts are a brick-red or salmon color1 the intervening spaces in general white but richly mottled1 and streaked with purples1 browns1 and greens4 ,the drawings show the planet as it appeared in the telescope1 inverted1 and they must be turned upside down if we wish the points of the compass to appear as upon a terrestrial map4 ,bearing this in mind1 note in the last picture the great oval spot in the southern hemisphere of ,jupiter4 ,this is a famous marking1 known from its color as the great red spot1 which appeared first in #ahgh and has persisted to the present day 7#aijj71 sometimes the most conspicuous marking on the planet1 at others reduced to a mere ghost of itself1 almost invisible save for the indentation which it makes in the southern edge of the belt near it4 #ach4 ,,rotation ,,and ,,flattening ,,at ,,the ,,poles4--,one further significant fact with respect to ,jupiter may be obtained from a careful measurement of the drawings2 the planet is flattened at the poles1 so that its polar diameter is about one sixteenth part shorter than the equatorial diameter4 ,the flattening of the earth amounts to only one three-hundredth part1 and the marked difference between these two numbers finds its explanation in the greater swiftness of ,jupiter's rotation about its axis1 since in both cases it is this rotation which makes the flattening4 ,it is not easy to determine the precise dimensions of the planet1 since this involves a knowledge both of its distance from us and of the angle subtended by its diameter1 but the most recent determinations of this kind assign as the equatorial diameter #ij1bjj miles1 and for the polar diameter #hd1djj miles4 ,determine from either of these numbers the size of the great red spot4 ,the earth turns on its axis once in #bd hours but no such definite time can be assigned to ,jupiter1 which1 like the sun1 seems to have different rotation periods in different latitudes--#i;h4 #ejm4 in the equatorial belt and #i;h4 #efm4 in the dark belts and higher latitudes4 ,there is some indication that the larger part of the visible surface rotates in #i;h4 #ee4fm41 while a broad stream along the equator flows eastward some #bgj miles per hour1 and thus comes back to the center of the planet1 as seen from the earth1 five or six minutes earlier than the parts which do not share in this motion4 ,judged by terrestrial standards1 #bgj miles per hour is a great velocity1 but ,jupiter is constructed on a colossal scale1 and1 too1 we have to compare this movement1 not to a current flowing in the ocean1 but to a wind blowing in the upper regions of the earth's atmosphere4 ,the visible surface of ,jupiter is only the top of a cloud formation1 and contains nothing solid or permanent1 if indeed there is anything solid even at the core of the planet4 ,the great red spot during the first dozen years of its existence1 instead of remaining fixed relative to the surrounding formations1 drifted two thirds of the way around the planet1 and having come to a standstill about #ahia1 it is now slowly retracing its path4 #aci4 ,,physical ,,condition4--,for a better understanding of the physical condition of ,jupiter1 we have now to consider some independent lines of evidence which agree in pointing to the conclusion that ,jupiter1 although classed with the earth as a planet1 is in its essential character much more like the sun4 ,appearance4--,the formations which we see in ,fig4 #hg look like clouds4 ,they gather and disappear1 and the only element of permanence about them is their tendency to group themselves along zones of latitude4 ,if we measure the light reflected from the planet we find that its albedo is very high1 like that of snow or our own cumulus clouds1 and it is of course greater from the light parts of the disk than from the darker bands4 ,the spectroscope shows that the sunlight reflected from these darker belts is like that reflected from the lighter parts1 save that a larger portion of the blue and violet rays has been absorbed out of it1 thus producing the ruddy tint of the belts1 as sunset colors are produced on the earth1 and showing that here the light has penetrated farther into the planet's atmosphere before being thrown back by reflection from lower-lying cloud surfaces4 ,the dark bands are therefore to be regarded as rifts in the clouds1 reaching down to some considerable distance and indicating an atmosphere of great depth4 ,the great red spot1 #bh1jjj miles long1 and obviously thrusting back the white clouds on every side of it1 year after year1 can hardly be a mere patch on the face of the planet1 but indicates some considerable depth of atmosphere4 ,density4--,so1 too1 the small mean density of the planet1 only #a4c times that of water and actually less than the density of the sun1 suggests that the larger part of the planet's bulk may be made of gases and clouds1 with very little solid matter even at the center2 but here we get into a difficulty from which there seems but one escape4 ,the force of gravity at the visible surface of ,jupiter may be found from its mass and dimensions to be #b4f times as great as at the surface of the earth1 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 planet4 ,some idea of this compression may be obtained from ,fig4 #hh1 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 #af miles1 the density at any level being proportional to the distance of the curved line from the straight one near it4 ,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 ,jupiter1 and indicates a much greater rate of increase4 ,starting from the upper surface of the cloud in ,jupiter's atmosphere1 if we descend1 not #af miles1 but #a1fjj or #af1jjj1 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 planet8 ,we are here in a dilemma between density on the one hand and the effects of gravity on the other1 and the only escape from it lies in the assumption that the interior of ,jupiter is tremendously hot1 and that this heat expands the substance of the planet in spite of the pressure to which it is subject1 making a large planet with a low density1 possibly gaseous at the very center1 but in its outer part surrounded by a shell of clouds condensed from the gases by radiating their heat into the cold of outer space4 ,illustration3 ,,fig4 #hh4--;,increase of density in the atmospheres of ,jupiter and the earth4 ,this is essentially the same physical condition that we found for the sun1 and we may add1 as further points of resemblance between it and ,jupiter1 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 northern1 and that has its periods of maximum and minimum activity1 which1 curiously enough1 seem to coincide with periods of maximum and minimum sun-spot development4 ,of this1 however1 we can not be entirely sure1 since it is only in recent years that it has been studied with sufficient care1 and further observations are required to show whether the agreement is something more than an accidental and short-lived coincidence4 ,temperature4--,the temperature of ,jupiter must1 of course1 be much lower than that of the sun1 since the surface which we see is not luminous like the sun's2 but below the clouds it is not improbable that ,jupiter may be incandescent1 white hot1 and it is surmised with some show of probability that a little of its light escapes through the clouds from time to time1 and helps to produce the striking brilliancy with which this planet shines4 #adj4 ,,the ,,satellites ,,of ,,jupiter4--,the satellites bear much the same relation to ,jupiter that the moon bears to the earth1 revolving about the planet in accordance with the law of gravitation1 and conforming to ,kepler's three laws1 as do the planets in their courses about the sun4 ,observe in ,fig4 #hf the position of satellite ,no4 #a on the four dates1 and note how it oscillates back and forth from left to right of ,jupiter1 apparently making a complete revolution in about two days1 while ,no4 #d moves steadily from left to right during the entire period1 and has evidently made only a fraction of a revolution in the time covered by the pictures4 ,this quicker motion1 of course1 means that ,no4 #a is nearer to ,jupiter than ,no4 #d1 and the numbers given to the satellites show the order of their distances from the planet4 ,the peculiar way in which the satellites are grouped1 always standing nearly in a straight line1 shows that their orbits must lie nearly in the same plane1 and that this plane1 which is also the plane of the planets' equator1 is turned edgewise toward the earth4 ,these satellites enjoy the distinction of being the first objects ever discovered with the telescope1 having been found by ,galileo almost immediately after its invention1 ,a4 ,d4 #afaj4 ,it is quite possible that before this time they may have been seen with the naked eye1 for in more recent years reports are current that they have been seen under favorable circumstances by sharp-eyed persons1 and very little telescopic aid is required to show them4 ,look for them with an opera or field glass4 ,they bear the names ,io1 ,europa1 ,ganymede1 ,callisto1 which1 however1 are rarely used1 and1 following the custom of astronomers1 we shall designate them by the ,roman numerals ,i1 ,,ii1 ,,iii1 ,,iv4 ,illustration3 ,,fig4 #hi4--,orbits of ,jupiter's satellites4 ,for nearly three centuries 7#afaj to #ahib7 astronomers spoke of the four satellites of ,jupiter2 but in ,september1 #ahib1 a fifth one was added to the number by ,professor ,barnard1 who1 observing with the largest telescope then extant1 found very close to ,jupiter a tiny object only #a_/fjj part as bright as the other satellites1 but1 like them1 revolving around ,jupiter1 a permanent member of his system4 ,this is called the fifth satellite1 and ,fig4 #hi shows the orbits of these satellites around ,jupiter1 which is here represented on the same scale as the orbits themselves4 ,the broken line just inside the orbit of ,i represents the size of the moon's orbit4 ,the cut shows also the periodic times of the satellites expressed in days1 and furnishes in this respect a striking illustration of the great mass of ,jupiter4 ,satellite ,i is a little farther from ,jupiter than is the moon from the earth1 but under the influence of a greater attraction it makes the circuit of its orbit in #a4gg days1 instead of taking #bi4ec days1 as does the moon4 ,determine from the figure by the method employed in #aaa how much more massive is ,jupiter than the earth4 ,small as these satellites seem in ,fig4 #hf1 they are really bodies of considerable size1 as appears from ,fig4 #ij1 where their dimensions are compared with those of the earth and moon1 save that the fifth satellite is not included4 ,this one is so small as to escape all attempts at measuring its diameter1 but1 judging from the amount of light it reflects1 the period printed with the legend of the figure represents a gross exaggeration of this satellite's size4 ,illustration3 ,,fig4 #ij4--;,jupiter's satellites compared with the earth and moon4 ,like the moon1 each of these satellites may fairly be considered a world in itself1 and as such a fitting object of detailed study1 but1 unfortunately1 their great distance from us makes it impossible1 even with the most powerful telescope1 to see more upon their surfaces than occasional vague markings1 which hardly suffice to show the rotations of the satellites upon their axes4 ,one striking feature1 however1 comes out from a study of their influence in disturbing each other's motion about ,jupiter4 ,their masses and the resulting densities of the satellites are smaller than we should have expected to find1 the density being less than that of the moon1 and averaging only a little greater than the density of ,jupiter itself4 ,at the surface of the third satellite the force of gravity is but little less than on the moon1 although the moon's density is nearly twice as great as that of ,,iii1 and there can be no question here of accounting for the low density through expansion by great heat1 as in the case of the sun and ,jupiter4 ,it has been surmised that these satellites are not solid bodies1 like the earth and moon1 but only shoals of rock and stone1 loosely piled together and kept from packing into a solid mass by the action of ,jupiter in raising tides within them4 ,but the explanation can hardly be regarded as an accepted article of astronomical belief1 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 them4 #ada4 ,,eclipses ,,of ,,the ,,satellites4--,it may be seen from ,fig4 #hi that in their motion around the planet ,jupiter's satellites must from time to time pass through his shadow and be eclipsed1 and that the shadows of the satellites will occasionally fall upon the planet1 producing to an observer upon ,jupiter an eclipse of the sun1 but to an observer on the earth presenting only the appearance of a round black spot moving slowly across the face of the planet4 ,occasionally also a satellite will pass exactly between the earth and ,jupiter1 and may be seen projected against the planet as a background4 ,all of these phenomena are duly predicted and observed by astronomers1 but the eclipses are the only ones we need consider here4 ,the importance of these eclipses was early recognized1 and astronomers endeavored to construct a theory of their recurrence which would permit accurate predictions of them to be made4 ,but in this they met with no great success1 for while it was easy enough to foretell on what night an eclipse of a given satellite would occur1 and even to assign the hour of the night1 it was not possible to make the predicted minute agree with the actual time of eclipse until after ,roemer1 a ,danish astronomer of the seventeenth century1 found where lay the trouble4 ,his discovery was1 that whenever the earth was on the side of its orbit toward ,jupiter the eclipses really occurred before the predicted time1 and when the earth was on the far side of its orbit they came a few minutes later than the predicted time4 ,he correctly inferred that this was to be explained1 not by any influence which the earth exerted upon ,jupiter and his satellites1 but through the fact that the light by which we see the satellite and its eclipse requires an appreciable time to cross the intervening space1 and a longer time when the earth is far from ,jupiter than when it is near4 ,for half a century ,roemer's views found little credence1 but we know now that he was right1 and that on the average the eclipses come #hm4 #ahs4 early when the earth is nearest to ,jupiter1 and #hm4 #ahs4 late when it is on the opposite side of its orbit4 ,this is equivalent to saying that light takes #hm4 #ahs4 to cover the distance from the sun to the earth1 so that at any moment we see the sun not as it then is1 but as it was #h minutes earlier4 ,it has been found possible in recent years to measure by direct experiment the velocity with which light travels--#ahf1ccg miles per second--and multiplying this number by the #dihs4 7 #hm4 #ahs47 we obtain a new determination of the sun's distance from the earth4 ,the product of the two numbers is #ib1gie1hbf1 in very fair agreement with the #ic1jjj1jjj miles found in ,chapter ,x2 but1 as noted there1 this method1 like every other1 has its weak side1 and the result may be a good many thousands of miles in error4 ,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 ,law1 while the result obtained from ,jupiter's satellites is entirely independent of this law1 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 eclipses4 ,this mode of proof1 by comparing the numerical results furnished by two or more different principles1 and showing that they agree or disagree1 is of wide application and great importance in physical science4 ,,saturn #adb4 ,,the ,,ring ,,of ,,saturn4--,in respect of size and mass ,saturn stands next to ,jupiter1 and although far inferior to him in these respects1 it contains more material than all the remaining planets combined4 ,but the unique feature of ,saturn which distinguishes it from every other known body in the heavens is its ring1 which was long a puzzle to the astronomers who first studied the planet with a telescope 7one of them called ,saturn a planet with ears71 but1 was after nearly half a century correctly understood and described by ,huyghens1 whose ,latin text we translate into--,it is surrounded by a ring1 thin1 flat1 nowhere touching it1 and making quite an angle with the ecliptic4 ,illustration3 ,,fig4 #ia4--;,aspects of ,saturn's rings4 ,compare with this description ,fig4 #ia1 which shows some of the appearances presented by the ring at different positions of ,saturn in its orbit4 ,it was their varying aspects that led ,huyghens to insert the last words of his description1 for1 if the plane of the ring coincided with the plane of the earth's orbit1 then at all times the ring must be turned edgewise toward the earth1 as shown in the middle picture of the group4 ,fig4 #ib shows the sun and the orbit of the earth placed near the center of ,saturn's orbit1 across whose circumference are ruled some oblique lines representing the plane of the ring1 the right end always tilted up1 no matter where the planet is in its orbit4 ,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 ,s1 as is shown in the first and third pictures of ,fig4 #ia1 while midway between these positions the edge of the ring will be presented to the earth4 ,illustration3 ,,fig4 #ib4--;,aspects of the ring in their relation to ,saturn's orbital motion4 ,the last occasion of this kind was in ,october1 #ahia1 and with the large telescope of the ,washburn ,observatory the writer at that time saw ,saturn without a trace of a ring surrounding it4 ,the ring is so thin that it disappears altogether when turned edgewise4 ,the names of the zodiacal constellations are inserted in ,fig4 #ib in their proper direction from the sun1 and from these we learn that the ring will disappear1 or be exceedingly narrow1 whenever ,saturn is in the constellation ,pisces or near the boundary line between ,leo and ,virgo4 ,it will be broad and show its northern side when ,saturn is in ,scorpius or ,sagittarius1 and its southern face when the planet is in ,gemini4 ,what will be its appearance in #aijg at the date marked in the figure8 #adc4 ,,nature ,,of ,,the ,,ring4--,it is apparent from ,figs4 #ia and #ic 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 which1 though narrow1 is as clean and sharp as if cut with a knife4 ,also1 the inner edge of the ring fades off into an obscure border called the dusky ring or crape ring4 ,this requires a pretty good telescope to show it1 as may be inferred from the fact that it escaped notice for more than two centuries during which the planet was assiduously studied with telescopes1 and was discovered at the ,harvard ,college ,observatory as recently as #ahej4 ,although the rings appear oval in all of the pictures1 this is mainly an effect of perspective1 and they are in fact nearly circular with the planet at their center4 ,the extreme diameter of the ring is #agb1jjj miles1 and from this number1 by methods already explained 7,chapter ,,ix71 the student should obtain the width of the rings1 their distance from the ball of the planet1 and the diameter of the ball4 ,as to thickness1 it is evident1 from the disappearance of the ring when its edge is turned toward the earth1 that it is very thin in comparison with its diameter1 probably not more than #ajj miles thick1 although no exact measurement of this can be made4 ,illustration3 ,,fig4 #ic4--,saturn4 ,from theoretical reasons based upon the law of gravitation astronomers have held that the rings of ,saturn could not possibly be solid or liquid bodies4 ,the strains impressed upon them by the planet's attraction would tear into fragments steel rings made after their size and shape4 ,quite recently ,professor ,keeler has shown1 by applying the spectroscope 7,doppler's principle7 to determine the velocity of the ring's rotation about ,saturn1 that the inner parts of the ring move1 as ,kepler's ,third ,law requires1 more rapidly than do the outer parts1 thus furnishing a direct proof that they are not solid1 and leaving no doubt that they are made up of separate fragments1 each moving about the planet in its own orbit1 like an independent satellite1 but standing so close to its neighbors that the whole space reflects the sunlight as completely as if it were solid4 ,with this understanding of the rings it is easy to see why they are so thin4 ,like ,jupiter1 ,saturn is greatly flattened at the poles1 and this flattening1 or rather the protuberant mass about the equator1 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 there4 ,the ring lies in the plane of ,saturn's equator because each particle is constrained to move there4 ,the division of the ring into two parts1 an outer and an inner ring1 is usually explained as follows3 ,saturn is surrounded by a numerous brood of satellites1 which by their attractions produce perturbations in the material composing the rings1 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 effect4 ,the dividing line between the rings is therefore a narrow lane1 #b1djj miles wide1 from which the fragments have been swept clean away by the perturbing action of the satellites4 ,less conspicuous divisions are seen from time to time in other parts of the ring1 where the perturbations1 though less1 are still appreciable4 ,but it is open to some question whether this explanation is sufficient4 ,the curious darkness of the inner or crape ring is easily explained4 ,the particles composing it are not packed together so closely as in the outer ring1 and therefore reflect less sunlight4 ,indeed1 so sparsely strewn are the particles in this ring that it is in great measure transparent to the sunlight1 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 ring1 but disappeared in total eclipse when it entered the shadow cast by the bright ring4 #add4 ,,the ,,ball ,,of ,,saturn4--,the ball of the planet is in most respects a smaller copy of ,jupiter4 ,with an equatorial diameter of #gf1jjj miles1 a polar diameter of #fi1jjj miles1 and a mass #ie times that of the earth1 its density is found to be the least of any planet in the solar system1 only #j4gj of the density of water1 and about one half as great as is the density of ,jupiter4 ,the force of gravity at its surface is only a little greater 7#a4ah7 than on the earth2 and this1 in connection with the low density1 leads1 as in the case of ,jupiter1 to the conclusion that the planet must be mainly composed of gases and vapors1 very hot within1 but inclosed by a shell of clouds which cuts off their glow from our eyes4 ,like ,jupiter in another respect1 the planet turns very swiftly upon its axis1 making a revolution in #aj hours #ad minutes1 but up to the present it remains unknown whether different parts of the surface have different rotation times4 #ade4 ,,the ,,satellites4--,saturn is attended by a family of nine satellites1 a larger number than belongs to any other planet1 but with one exception they are exceedingly small and difficult to observe save with a very large telescope4 ,indeed1 the latest one is said to have been discovered in #ahih by means of the image which it impressed upon a photographic plate1 and it has never been seen4 ,titan1 the largest of them1 is distant #gga1jjj miles from the planet and bears much the same relation to ,saturn that ,satellite ,,iii bears to ,jupiter1 the similarity in distance1 size and mass being rather striking1 although1 of course1 the smaller mass of ,saturn as compared with ,jupiter makes the periodic time of ,titan--#ae days #bc hours--much greater than that of ,,iii4 ,can you apply ,kepler's ,third ,law to the motion of ,titan so as to determine from the data given above1 the time required for a particle at the outer or inner edge of the ring to revolve once around ,saturn8 ,japetus1 the second satellite in point of size1 whose distance from ,saturn is about ten times as great as the moon's distance from the earth1 presents the remarkable peculiarity of being always brighter in one part of its orbit than in another1 three or four times as bright when west of ,saturn as when east of it4 ,this probably indicates that1 like our own moon1 the satellite turns always the same face toward its planet1 and further1 that one side of the satellite reflects the sunlight much better than the other side--i4 e41 has a higher albedo4 ,with these two assumptions it is easily seen that the satellite will always turn toward the earth one face when west1 and the other face when east of ,saturn1 and thus give the observed difference of brightness4 ,,uranus ,,and ,,neptune #adf4 ,,chief ,,characteristics4--,the two remaining large planets are interesting chiefly as modern additions to the known members of the sun's family4 ,the circumstances leading to the discovery of ,neptune have been touched upon in ,chapter ,,iv1 and for ,uranus we need only note that it was found by accident in the year #agha by ,william ,herschel1 who for some time after the discovery considered it to be only a comet4 ,it was the first planet ever discovered1 all of its predecessors having been known from prehistoric times4 ,illustration3 ,,william ,,herschel 7#agch-ahbb74 ,uranus has four satellites1 all of them very faint1 which present only one feature of special importance4 ,instead of moving in orbits which are approximately parallel to the plane of the ecliptic1 as do the satellites of the inner planets1 their orbit planes are tipped up nearly perpendicular to the planes of the orbits of both ,uranus and the earth4 ,the one satellite which ,neptune possesses has the same peculiarity in even greater degree1 for its motion around the planet takes place in the direction opposite to that in which all the planets move around the sun1 much as if the orbit of the satellite had been tipped over through an angle of #aej4 ,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 #ahj4 ,both ,uranus and ,neptune are too distant to allow much detail to be seen upon their surfaces1 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 earth4 ,in respect of density and the force of gravity at their surfaces1 they are not very unlike ,saturn1 although their density is greater and gravity less than his1 leading to the supposition that they are for the most part gaseous bodies1 but cooler and probably more nearly solid than either ,jupiter or ,saturn4 ,under favorable circumstances ,uranus may be seen with the naked eye by one who knows just where to look for it4 ,neptune is never visible save in a telescope4 #adg4 ,,the ,,inner ,,planets4--,in sharp contrast with the giant planets which we have been considering stands the group of four inner planets1 or five if we count the moon as an independent body1 which resemble each other in being all small1 dense1 and solid bodies1 which by comparison with the great distances separating the outer planets may fairly be described as huddled together close to the sun4 ,their relative sizes are shown in ,fig4 #hd1 together with the numerical data concerning size1 mass1 density1 etc41 which we have already found important for the understanding of a planet's physical condition4 ,,venus ,illustration3 ,,fig4 #id4--,the phases of ,venus4--,,antoniadi4 #adh4 ,,appearance4--,omitting the earth1 ,venus is by far the most conspicuous member of this group1 and when at its brightest is1 with exception of the sun and moon1 the most brilliant object in the sky1 and may be seen with the naked eye in broad daylight if the observer knows just where to look for it4 ,but its brilliancy is subject to considerable variations on account of its changing distance from the earth1 and the apparent size of its disk varies for the same reason1 as may be seen from ,fig4 #id4 ,these drawings bring out well the phases of the planet1 and the student should determine from ,fig4 #ag what are the relative positions in their orbits of the earth and ,venus at which the planet would present each of these phases4 ,as a guide to this1 observe that the dark part of ,venus's earthward side is always proportional in area to the angle at ,venus between the earth and sun4 ,in the first picture of ,fig4 #id about two thirds of the surface corresponding to the full hemisphere of the planet is dark1 and the angle at ,venus between earth and sun is therefore two thirds of #ahj--;i4 e41 #abj4 ,in ,fig4 #ag find a place on the orbit of ,venus from which if lines be drawn to the sun and earth1 as there shown1 the angle between them will be #abj4 ,make a similar construction for the fourth picture in ,fig4 #id4 ,which of these two positions is farther from the earth8 ,how do the distances compare with the apparent size of ,venus in the two pictures8 ,what is the phase of ,venus to-day8 ,the irregularities in the shading of the illuminated parts of the disk are too conspicuous in ,fig4 #id1 on account of difficulties of reproduction2 these shadings are at the best hard to see in the telescope1 and distinct permanent markings upon the planet are wholly lacking4 ,this absence of markings makes almost impossible a determination of the planet's time of rotation about its axis1 and astronomers are divided in this respect into two parties1 one of which maintains that ,venus1 like the earth1 turns upon its axis in some period not very different from #bd hours1 while the other contends that1 like the moon1 it turns always the same face toward the center of its orbit1 making a rotation upon its axis in the same period in which it makes a revolution about the sun4 ,the reason why no permanent markings are to be seen on this planet is easily found4 ,like ,jupiter and ,saturn1 its atmosphere is at all times heavily cloud-laden1 so that we seldom1 if ever1 see down to the level of its solid parts4 ,there is1 however1 no reason here to suppose the interior parts hot and gaseous4 ,it is much more probable that ,venus1 like the earth1 possesses a solid crust whose temperature we should expect to be considerably higher than that of the earth1 because ,venus is nearer the sun4 ,but the cloud layer in its atmosphere must modify the temperature in some degree1 and we have practically no knowledge of the real temperature conditions at the surface of the planet4 ,it is the clouds of ,venus which in great measure are responsible for its marked brilliancy1 since they are an excellent medium for reflecting the sunlight1 and give to its surface an albedo greater than that of any other planet1 although ,saturn is nearly equal to it4 ,of course1 the presence of such cloud formations indicates that ,venus is surrounded by a dense atmosphere1 and we have independent evidence of this in the shape of its disk when the planet is very nearly between the earth and sun4 ,the illuminated part1 from tip to tip of the horns1 then stretches more than halfway around the planet's circumference1 and shows that a certain amount of light must have been refracted through its atmosphere1 thus making the horns of the crescent appear unduly prolonged4 ,this atmosphere is shown by the spectroscope to be not unlike that of the earth1 although1 possibly1 more dense4 ,,mercury #adi4 ,,chief ,,characteristics4--,mercury1 on account of its nearness to the sun1 is at all times a difficult object to observe1 and ,copernicus1 who spent most of his life in ,poland1 is said1 despite all his efforts1 to have gone to his grave without ever seeing it4 ,in our more southern latitude it can usually be seen for about a fortnight at the time of each elongation--i4 e41 when at its greatest angular distance from the sun--and the student should find from ,fig4 #af the time at which the next elongation occurs and look for the planet1 shining like a star of the first magnitude1 low down in the sky just after sunset or before sunrise1 according as the elongation is to the east or west of the sun4 ,when seen in the morning sky the planet grows brighter day after day until it disappears in the sun's rays1 while in the evening sky its brilliancy as steadily diminishes until the planet is lost4 ,it should therefore be looked for in the evening as soon as possible after it emerges from the sun's rays4 ,mercury1 as the smallest of the planets1 is best compared with the moon1 which it does not greatly surpass in size and which it strongly resembles in other respects4 ,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 moon1 but also that its light changes with the varying phase of the planet in almost exactly the same way as the amount of moonlight changes4 ,we may therefore infer that its surface is like that of the moon1 a rough and solid one1 with few or no clouds hanging over it1 and most probably covered with very little or no atmosphere4 ,like ,venus1 its rotation period is uncertain1 with the balance of probability favoring the view that it rotates upon its axis once in #hh days1 and therefore always turns the same face toward the sun4 ,if such is the case1 its climate must be very peculiar3 one side roasted in a perpetual day1 where the direct heating power of the sun's rays1 when the planet is at perihelion1 is ten times as great as on the moon1 and which six weeks later1 when the planet is at its farthest from the sun1 has fallen off to less than half of this4 ,on the opposite side of the planet there must reign perpetual night and perpetual cold1 mitigated by some slight access of warmth from the day side1 and perhaps feebly imitating the rapid change of season which takes place on the day side of the planet4 ,this view1 however1 takes no account of a possible deviation of the planet's axis from being perpendicular to the plane of its orbit1 or of the librations which must be produced by the great eccentricity of the orbit1 either of which would complicate without entirely destroying the ideal conditions outlined above4 ,,mars #aej4 ,,appearance4--,the one remaining member of the inner group1 ,mars1 has in recent years received more attention than any other planet1 and the newspapers and magazines have announced marvelous things concerning it3 that it is inhabited by a race of beings superior in intelligence to men2 that the work of their hands may be seen upon the face of the planet2 that we should endeavor to communicate with them1 if indeed they are not already sending messages to us1 etc4--all of which is certainly important1 if true1 but it rests upon a very slender foundation of evidence1 a part of which we shall have to consider4 ,beginning with facts of which there is no doubt1 this ruddy-colored planet1 which usually shines about as brightly as a star of the first magnitude1 sometimes displays more than tenfold this brilliancy1 surpassing every other planet save ,venus and presenting at these times especially favorable opportunities for the study of its surface4 ,the explanation of this increase of brilliancy is1 of course1 that the planet approaches unusually near to the earth1 and we have already seen from a consideration of ,fig4 #ag that this can only happen in the months of ,august and ,september4 ,the last favorable epoch of this kind was in #ahid4 ,from ,fig4 #ag the student should determine when the next one will come4 ,illustration3 ,,fig4 #ie4--,mars4--,,schaeberle4 ,fig4 #ie presents nine drawings of the planet made at one of the epochs of close approach to the earth1 and shows that its face bears certain faint markings which1 though inconspicuous1 are fixed and permanent features of the planet4 ,the dark triangular projection in the lower half of the second drawing was seen and sketched by ,huyghens1 #afei ,a4 ,d4 ,in ,fig4 #if some of these markings are shown much more plainly1 but ,fig4 #ie gives a better idea of their usual appearance in the telescope4 ,illustration3 ,,fig4 #if4--;,four views of ,mars differing #ij in longitude4--,,barnard4 #aea4 ,,rotation4--,it may be seen readily enough1 from a comparison of the first two sketches of ,fig4 #ie1 that the planet rotates about an axis1 and from a more extensive study it is found to be very like the earth in this respect1 turning once in #bd;h4 #cgm4 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 axis4 ,since it is this inclination of the axis which is the cause of changing seasons upon the earth1 there must be similar changes1 winter and summer1 as well as day and night1 upon ,mars1 only each season is longer there than here in the same proportion that its year is longer than ours--i4 e41 nearly two to one4 ,it is summer in the northern hemisphere of ,mars whenever the sun1 as seen from ,mars1 stands in that constellation which is nearest the point of the sky toward which the planet's axis points4 ,but this axis points toward the constellation ,cygnus1 and ,alpha ,cygni is the bright star nearest the north pole of ,mars4 ,as ,pisces is the zodiacal constellation nearest to ,cygnus1 it must be summer in the northern hemisphere of ,mars when the sun is in ,pisces1 or1 turning the proposition about1 it must be summer in the southern hemisphere of ,mars when the planet1 as seen from the sun1 lies in the direction of ,pisces4 #aeb4 ,,the ,,polar ,,caps4--,one effect of the changing seasons upon ,mars is shown in ,fig4 #ig1 where we have a series of drawings of the region about its south pole made in #ahid1 on dates between ,may #bast and ,december #ajth4 ,show from ,fig4 #ag that during this time it was summer in the region here shown4 ,mars crossed the prime radius in #ahid on ,september #eth4 ,the striking thing in these pictures is the white spot surrounding the pole1 which shrinks in size from the beginning to near the end of the series1 and then disappears altogether4 ,the spot came back again a year later1 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 succession4 ,illustration3 ,,fig4 #ig4--,the south polar cap of ,mars in #ahid4--;,,barnard4 ,sir ,w4 ,herschel1 who studied these appearances a century ago1 compared them with the snow fields which every winter spread out from the region around the terrestrial pole1 and in the summer melt and shrink1 although with us they do not entirely disappear4 ,this explanation of the polar caps of ,mars has been generally accepted among astronomers1 and from it we may draw one interesting conclusion3 the temperature upon ,mars between summer and winter oscillates above and below the freezing point of water1 as it does in the temperate zones of the earth4 ,but this conclusion plunges us into a serious difficulty4 ,the temperature of the earth is made by the sun1 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 earth1 so that1 if ,mars is to be kept at the same temperature as the earth1 there must be some peculiar means for storing the solar heat and using it more economically than is done here4 ,possibly there is some such mechanism1 although no one has yet found it1 and some astronomers are very confident that it does not exist1 and assert that the comparison of the polar caps with snow fields is misleading1 and that the temperature upon ,mars must be at least #ajj1 and perhaps #bjj or more1 below zero4 #aec4 ,,atmosphere ,,and ,,climate4--,in this connection one feature of ,mars is of importance4 ,the markings upon its surface are always visible when turned toward the earth1 thus showing that the atmosphere contains no such amount of cloud as does our own1 but on the whole is decidedly clear and sunny1 and presumably much less dense than ours4 ,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 subject2 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 earth4 ,indeed1 this cloudlessness must mean one of two things3 either the temperature is so low that vapors can not exist in any considerable quantity1 or the surface of ,mars is so dry that there is little water or other liquid to be evaporated4 ,the latter alternative is adopted by those astronomers who look upon the polar caps as true snow fields1 which serve as the chief reservoir of the planet's water supply1 and who find in ,fig4 #ih evidence that as the snow melts and the water flows away over the flat1 dry surface of the planet1 vegetation springs up1 as shown by the dark markings on the disk1 and gradually dies out with the advancing season4 ,note that in the first of these pictures the season upon ,mars corresponds to the end of ,may with us1 and in the last picture to the beginning of ,august1 a period during which in much of our western country the luxuriant vegetation of spring is burned out by the scorching sun4 ,from this point of view the permanent dark spots are the low-lying parts of the planet's surface1 in which at all times there is a sufficient accumulation of water to support vegetable life4 ,illustration3 ,,fig4 #ih4--,the same face of ,mars at three different seasons4--,,lowell4 #aed4 ,,the ,,canals4--,in ,fig4 #ih the lower part of the disk of ,mars shows certain faint dark lines which are generally called canals1 and in ,plate ,,iii there is given a map of ,mars showing many of these canals running in narrow1 dusky streaks across the face of the planet according to a pattern almost as geometrical as that of a spider's web4 ,this must not be taken for a picture of the planet's appearance in a telescope4 ,no man ever saw ,mars look like this1 but the map is useful as a plain representation of things dimly seen4 ,some of the regions of this map are marked ,mare 7sea71 in accordance with the older view which regarded the darker parts of the planet--and of the moon--as bodies of water1 but this is now known to be an error in both cases4 ,the curved surface of a planet can not be accurately reproduced upon the flat surface of paper1 but is always more or less distorted by the various methods of projecting it which are in use4 ,compare the map of ,mars in ,plate ,,iii with ,fig4 #ii1 in which the projection represents very well the equatorial parts of the planet1 but enormously exaggerates the region around the poles4 ,it is a remarkable feature of the canals that they all begin and end in one of these dark parts of the planet's surface2 they show no loose ends lying on the bright parts of the planet4 ,another even more remarkable feature is that while the larger canals are permanent features of the planet's surface1 they at times appear doubled--i4 e41 in place of one canal two parallel ones side by side1 lasting for a time and then giving place again to a single canal4 ,it is exceedingly difficult to frame any reasonable explanation of these canals and the varied appearances which they present4 ,the source of the wild speculations about ,mars1 to which reference is made above1 is to be found in the suggestion frequently made1 half in jest and half in earnest1 that the canals are artificial water courses constructed upon a scale vastly exceeding any public works upon the earth1 and testifying to the presence in ,mars of an advanced civilization4 ,the distinguished ,italian astronomer1 ,schiaparelli1 who has studied these formations longer than any one else1 seems inclined to regard them as water courses lined on either side by vegetation1 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 overcome4 ,illustration3 ,,fig4 #ii4--;,a chart of ,mars1 #ahih-'ii4--;,,cerulli4 ,illustration3 ,,plate ,,iii4 ,,map ,,of ,,mars 7,,after ,,schiaparelli7 #aee4 ,,satellites4--,in #ahgg1 one of the times of near approach1 ,professor ,hall1 of ,washington1 discovered two tiny satellites revolving about ,mars in orbits so small that the nearer one1 ,phobos1 presents the remarkable anomaly of completing the circuit of its orbit in less time than the planet takes for a rotation about its axis4 ,this satellite1 in fact1 makes three revolutions in its orbit while the planet turns once upon its axis1 and it therefore rises in the west and sets in the east1 as seen from ,mars1 going from one horizon to the other in a little less than #f hours4 ,the other satellite1 ,deimos1 takes a few hours more than a day to make the circuit of its orbit1 but the difference is so small that it remains continuously above the horizon of any given place upon ,mars for more than #fj hours at a time1 and during this period runs twice through its complete set of phases--new1 first quarter1 full1 etc4 ,in ordinary telescopes these satellites can be seen only under especially favorable circumstances1 and are far too small to permit of any direct measurement of their size4 ,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 moons1 and1 judging from this comparison1 their diameters can not much exceed a half dozen miles1 unless their albedo is far less than that of ,mars1 which does not seem probable4 ,,the ,,asteroids #aef4 ,,minor ,,planets4--,these may be dismissed with few words4 ,there are about #ejj of them known1 all discovered since the beginning of the nineteenth century1 and new ones are still found every year4 ,no one pretends to remember the names which have been assigned them1 and they are commonly represented by a number inclosed in a circle1 showing the order in which they were discovered--e4 g41 circle #a ,ceres1 circle #dcc ,eros1 etc4 ,for the most part they are little more than chips1 world fragments1 adrift in space1 and naturally it was the larger and brighter of them that were first discovered4 ,the size of the first four of them--,ceres1 ,pallas1 ,juno1 and ,vesta--compared with the size of the moon1 according to ,professor ,barnard1 is shown in ,fig4 #ajj4 ,the great majority of them must be much smaller than the smallest of these1 perhaps not more than a score of miles in diameter4 ,a few of the asteroids present problems of special interest1 such as ,eros1 on account of its close approach to the earth2 ,polyhymnia1 whose very eccentric orbit makes it a valuable means for determining the mass of ,jupiter1 etc42 but these are special cases and the average asteroid now receives scant attention1 although half a century ago1 when only a few of them were known1 they were regarded with much interest1 and the discovery of a new one was an event of some consequence4 ,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 ,jupiter1 but which1 by some mischance1 had been blown into pieces4 ,this is now known to be well-nigh impossible1 for every fragment which after the explosion moved in an elliptical orbit1 as all the asteroids do move1 would be brought back once in every revolution to the place of the explosion1 and all the asteroid orbits must therefore intersect at this place4 ,but there is no such common point of intersection4 ,illustration3 ,,fig4 #ajj4--,the size of the first four asteroids4--,,barnard4 #aeg4 ,,life ,,on ,,the ,,planets4--,there is a belief firmly grounded in the popular mind1 and not without its advocates among professional astronomers1 that the planets are inhabited by living and intelligent beings1 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 belief1 and what support1 if any1 they lend to it4 ,at the outset we must observe that the word life is an elastic term1 hard to define in any satisfactory way1 and yet standing for something which we know here upon the earth4 ,it is this idea1 our familiar though crude knowledge of life1 which lies at the root of the matter4 ,life1 if it exists in another planet1 must be in its essential character like life upon the earth1 and must at least possess those features which are common to all forms of terrestrial life4 ,it is an abuse of language to say that life in ,mars may be utterly unlike life in the earth2 if it is absolutely unlike1 it is not life1 whatever else it may be4 ,now1 every form of life found upon the earth has for its physical basis a certain chemical compound1 called protoplasm1 which can exist and perpetuate itself only within a narrow range of temperature1 roughly speaking1 between #j and #ajj centigrade1 although these limits can be considerably overstepped for short periods of time4 ,moreover1 this protoplasm can be active only in the presence of water1 or water vapor1 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 #ajj or below #j1 ,c41 and water must be present in that place in some form4 ,with these conditions before us it is plain that life can not exist in the sun on account of its high temperature4 ,it is conceivable that active and intelligent beings1 salamanders1 might exist there1 but they could not properly be said to live4 ,in ,jupiter and ,saturn the same condition of high temperature prevails1 and probably also in ,uranus and ,neptune1 so that it seems highly improbable that any of these planets should be the home of life4 ,of the inner planets1 ,mercury and the moon seem destitute of any considerable atmospheres1 and are therefore lacking in the supply of water necessary for life1 and the same is almost certainly true of all the asteroids4 ,there remain ,venus1 ,mars1 and the satellites of the outer planets1 which latter1 however1 we must drop from consideration as being too little known4 ,on ,venus there is an atmosphere probably containing vapor of water1 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 limits4 ,it would1 however1 be straining our actual knowledge to affirm that such is the case1 or to insist that if such were the case1 life would necessarily exist upon the planet4 ,on ,mars we encounter the fundamental difficulty of temperature already noted in #aeb4 ,if in some unknown way the temperature is maintained sufficiently high for the polar caps to be real snow1 thawing and forming again with the progress of the seasons1 the necessary conditions of life would seem to be fulfilled here and life if once introduced upon the planet might abide and flourish4 ,but of positive proof that such is the case we have none4 ,on the whole1 our survey lends little encouragement to the belief in planetary life1 for aside from the earth1 of all the hundreds of bodies in the solar system1 not one is found in which the necessary conditions of life are certainly fulfilled1 and only two exist in which there is a reasonable probability that these conditions may be satisfied4 ,,chapter ,,xii ,,comets ,,and ,,meteors #aeh4 ,,visitors ,,in ,,the ,,solar ,,system4--,all of the objects--sun1 moon1 planets1 stars--which we have thus far had to consider1 are permanent citizens of the sky1 and we have no reason to suppose that their present appearance differs appreciably from what it was #a1jjj years or #aj1jjj years ago4 ,but there is another class of objects--comets1 meteors--which appear unexpectedly1 are visible for a time1 and then vanish and are seen no more4 ,on account of this temporary character the astronomers of ancient and medival times for the most part refused to regard them as celestial bodies but classed them along with clouds1 fogs1 ,jack-o'-lanterns1 and fireflies1 as exhalations from the swamps or the volcano2 admitting them to be indeed important as harbingers of evil to mankind1 but having no especial significance for the astronomer4 ,the comet of #afah ,a4 ,d4 inspired the lines-- ,eight things there be a ,comet brings1 ,when it on high doth horrid range3 ,wind1 ,famine1 ,plague1 and ,death to ,kings1 ,war1 ,earthquakes1 ,floods1 and ,direful ,change1 which1 according to ,white 7,history of the ,doctrine of ,comets71 were to be taught in all seriousness to peasants and school children4 ,it was by slow degrees1 and only after direct measurements of parallax had shown some of them to be more distant than the moon1 that the tide of old opinion was turned and comets were transferred from the sublunary to the celestial sphere1 and in more recent times meteors also have been recognized as coming to us from outside the earth4 ,a meteor1 or shooting star as it is often called1 is one of the commonest of phenomena1 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 place1 dashed swiftly across a portion of the sky and then vanished4 ,it is this misleading appearance that probably is responsible for the name shooting star4 ,illustration3 ,,fig4 #aja4--;,donati's comet4--,,bond4 #aei4 ,,comets4--,comets are less common and much longer-lived than meteors1 lasting usually for several weeks1 and may be visible night after night for many months1 but never for many years1 at a time4 ,during the last decade there is no year in which less than three comets have appeared1 and #ahih is distinguished by the discovery of ten of these bodies1 the largest number ever found in one year4 ,on the average1 we may expect a new comet to be found about once in every ten weeks1 but for the most part they are small affairs1 visible only in the telescope1 and a fine large one1 like ,donati's comet of #aheh 7,fig4 #aja71 or the ,great ,comet of ,september1 #ahhb1 which was visible in broad daylight close beside the sun1 is a rare spectacle1 and as striking and impressive as it is rare4 ,illustration3 ,,fig4 #ajb4--,some famous comets4 ,note in ,fig4 #ajb the great variety of aspect presented by some of the more famous comets1 which are here represented upon a very small scale4 ,fig4 #ajc is from a photograph of one of the faint comets of the year #ahic1 which appears here as a rather feeble streak of light amid the stars which are scattered over the background of the picture4 ,an apparently detached portion of this comet is shown at the extreme left of the picture1 looking almost like another independent comet4 ,the clean1 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 photographed4 ,a more striking representation of a moderately bright telescopic comet is contained in ,figs4 #ajd and #aje1 which present two different views of the same comet1 showing a considerable change in its appearance4 ,a striking feature of ,fig4 #aje is the star images1 which are here drawn out into short lines all parallel with each other4 ,during the exposure of #b;h4 #bjm4 required to imprint this picture upon the photographic plate1 the comet was continually changing its position among the stars on account of its orbital motion1 and the plate was therefore moved from time to time1 so as to follow the comet and make its image always fall at the same place4 ,hence the plate was continually shifted relative to the stars whose images1 drawn out into lines1 show the direction in which the plate was moved--i4 e41 the direction in which the comet was moving across the sky4 ,the same effect is shown in the other photographs1 but less conspicuously than here on account of their shorter exposure times4 ,these pictures all show that one end of the comet is brighter and apparently more dense than the other1 and it is customary to call this bright part the head of the comet1 while the brushlike appendage that streams away from it is called the comet's tail4 ,illustration3 ,,fig4 #ajc4--;,brooks's comet1 ,november #ac1 #ahic4 ,,barnard4 #afj4 ,,the ,,parts ,,of ,a ,,comet4--,it is not every comet that has a tail1 though all the large ones do1 and in ,fig4 #ajc the detached piece of cometary matter at the left of the picture represents very well the appearance of a tailless comet1 a rather large but not very bright star of a fuzzy or hairy appearance4 ,the word comet means long-haired or hairy star4 ,something of this vagueness of outline is found in all comets1 whose exact boundaries are hard to define1 instead of being sharp and clean-cut like those of a planet or satellite4 ,often1 however1 there is found in the head of a comet a much more solid appearing part1 like the round white ball at the center of ,fig4 #ajf1 which is called the nucleus of the comet1 and appears to be in some sort the center from which its activities radiate4 ,as shown in ,figs4 #ajf and #ajg1 the nucleus is sometimes surrounded by what are called envelopes1 which have the appearance of successive wrappings or halos placed about it1 and odd1 spurlike projections1 called jets1 are sometimes found in connection with the envelopes or in place of them4 ,these figures also show what is quite a common characteristic of large comets1 a dark streak running down the axis of the tail1 showing that the tail is hollow1 a mere shell surrounding empty space4 ,illustration3 ,,fig4 #ajd4--,swift's comet1 ,april #ag1 #ahib4--;,,barnard4 ,the amount of detail shown in ,figs4 #ajf and #ajg is1 however1 quite exceptional1 and the ordinary comet is much more like ,fig4 #ajc or #ajd4 ,even a great comet when it first appears is not unlike the detached fragment in ,fig4 #ajc1 a faint and roundish patch of foggy light which grows through successive stages to its maximum estate1 developing a tail1 nucleus1 envelopes1 etc41 only to lose them again as it shrinks and finally disappears4 ,illustration3 ,,fig4 #aje4--,swift's comet1 ,april #bd1 #ahib4--;,,barnard4 #afa4 ,,the ,,orbits ,,of ,,comets4--,it will be remembered that ,newton found1 as a theoretical consequence of the law of gravitation1 that a body moving under the influence of the sun's attraction might have as its orbit any one of the conic sections1 ellipse1 parabola1 or hyperbola1 and among the #djj and more comet orbits which have been determined every one of these orbit forms appears1 but curiously enough there is not a hyperbola among them which1 if drawn upon paper1 could be distinguished by the unaided eye from a parabola1 and the ellipses are all so long and narrow1 not one of them being so nearly round as is the most eccentric planet orbit1 that astronomers are accustomed to look upon the parabola as being the normal type of comet orbit1 and to regard a comet whose motion differs much from a parabola as being abnormal and calling for some special explanation4 ,the fact that comet orbits are parabolas1 or differ but little from them1 explains at once the temporary character and speedy disappearance of these bodies4 ,they are visitors to the solar system and visible for only a short time1 because the parabola in which they travel is not a closed curve1 and the comet1 having passed once along that portion of it near the earth and the sun1 moves off along a path which ever thereafter takes it farther and farther away1 beyond the limit of visibility4 ,the development of the comet during the time it is visible1 the growth and disappearance of tail1 nucleus1 etc41 depend upon its changing distance from the sun1 the highest development and most complex structure being presented when it is nearest to the sun4 ,illustration3 ,,fig4 #ajf4--;,head of ,coggia's comet1 ,july #ac1 #ahgd4--,,trouvelot4 ,fig4 #ajh shows the path of the ,great ,comet of #ahhb during the period in which it was seen1 from ,september #c1 #ahhb1 to ,may #bf1 #ahhc4 ,these dates--,,ix1 #c1 and ,v1 #bf--;are marked in the figure opposite the parts of the orbit in which the comet stood at those times4 ,similarly1 the positions of the earth in its orbit at the beginning of ,september1 ,october1 ,november1 etc41 are marked by the ,roman numerals ,,ix1 ,x1 ,,xi1 etc4 ,the line ,s ,v shows the direction from the sun to the vernal equinox1 and ,s is the line along which the plane of the comet's orbit intersects the plane of the earth's orbit--i4 e41 it is the line of nodes of the comet orbit4 ,since the comet approached the sun from the south side of the ecliptic1 all of its orbit1 save the little segment which falls to the left of ,s 1 lies below 7south7 of the plane of the earth's orbit1 and the part which would be hidden if this plane were opaque is represented by a broken line4 ,illustration3 ,,fig4 #ajg4--;,head of ,donati's comet1 ,september #cj1 ,october #b1 #aheh4--;,,bond4 #afb4 ,,elements ,,of ,a ,,comet',s ,,orbit4--,there is a theorem of geometry to the effect that through any three points not in the same straight line one circle1 and only one1 can be drawn4 ,corresponding to this there is a theorem of celestial mechanics1 that through any three positions of a comet one conic section1 and only one1 can be passed along which the comet can move in accordance with the law of gravitation4 ,this conic section is1 of course1 its orbit1 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 7right ascensions and declinations7 necessary for determining the particular orbit in which it moves4 ,the circle1 to which reference was made above1 is completely ascertained and defined when we know its radius and the position of its center4 ,a parabola is not so simply defined1 and five numbers1 called the elements of its orbit1 are required to fix accurately a comet's path around the sun4 ,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 ecliptic2 a third fixes the direction of the axis of the orbit in its plane1 and the remaining two1 which are of more interest to us1 are the date at which the comet makes its nearest approach to the sun 7perihelion passage7 and its distance from the sun at that date 7perihelion distance74 ,the date1 ,september #agth1 placed near the center of ,fig4 #ajh1 is the former of these elements1 while the latter1 which is too small to be accurately measured here1 may be found from ,fig4 #aji to be #j4hb of the sun's diameter1 or1 in terms of the earth's distance from the sun1 #j4jjh4 ,illustration3 ,,fig4 #ajh4--,orbits of the earth and the ,great ,comet of #ahhb4 ,fig4 #aji shows on a large scale the shape of that part of the orbit near the sun and gives the successive positions of the comet1 at intervals of #b_/aj of a day1 on ,september #afth and #agth1 showing that in less than #aj hours--#ag4j to #ag4d--the comet swung around the sun through an angle of more than #bdj4 ,when at its perihelion it was moving with a velocity of #cjj miles per second6 ,this very unusual velocity was due to the comet's extraordinarily close approach to the sun4 ,the earth's velocity in its orbit is only #ai miles per second1 and the velocity of any comet at any distance from the sun1 provided its orbit is a parabola1 may be found by dividing this number by the square root of half the comet's distance--e4 g41 #cjj miles per second equals #ai #j4jjda_/b4 ,illustration3 ,,fig4 #aji4--,motion of the ,great ,comet of #ahhc in passing around the sun4 ,most of the visible comets have their perihelion distances included between #a_/c and #d_/c of the earth's distance from the sun1 but occasionally one is found1 like the second comet of #ahhe1 whose nearest approach to the sun lies far outside the earth's orbit1 in this case halfway out to the orbit of ,jupiter2 but such a comet must be a very large one in order to be seen at all from the earth4 ,there is1 however1 some reason for believing that the number of comets which move around the sun without ever coming inside the orbit of ,jupiter1 or even that of ,saturn1 is much larger than the number of those which come close enough to be discovered from the earth4 ,in any case we are reminded of ,kepler's saying1 that comets in the sky are as plentiful as fishes in the sea1 which seems to be very little exaggerated when we consider that1 according to ,kleiber1 out of all the comets which enter the solar system probably not more than #b or #c per cent are ever discovered4 ,illustration3 ,,fig4 #aaj4--,the ,great ,comet of #ahdc4 #afc4 ,,dimensions ,,of ,,comets4--,the comet whose orbit is shown in ,figs4 #ajh and #aji is the finest and largest that has appeared in recent years4 ,its tail1 which at its maximum extent would have more than bridged the space between sun and earth 7#ajj1jjj1jjj miles71 is made very much too short in ,fig4 #aji1 but when at its best was probably not inferior to that of the ,great ,comet of #ahdc1 shown in ,fig4 #aaj4 ,as we shall see later1 there is a peculiar and special relationship between these two comets4 ,the head of the comet of #ahhb was not especially large--about twice the diameter of the ball of ,saturn--but its nucleus1 according to an estimate made by ,dr4 ,elkin when it was very near perihelion1 was as large as the moon4 ,the head of the comet shown in ,fig4 #ajg was too large to be put in the space between the earth and the moon1 and the ,great ,comet of #ahaa had a head considerably larger than the sun itself4 ,from these colossal sizes down to the smallest shred just visible in the telescope1 comets of all dimensions may be found1 but the smaller the comet the less the chance of its being discovered1 and a comet as small as the earth would probably go unobserved unless it approached very close to us4 #afd4 ,,the ,,mass ,,of ,a ,,comet4--,there is no known case in which the mass of a comet has ever been measured1 yet nothing about them is more sure than that they are bodies with mass which is attracted by the sun and the planets1 and which in its turn attracts both sun and planets and produces perturbations in their motion4 ,these perturbations are1 however1 too small to be measured1 although the corresponding perturbations in the comet's motion are sometimes enormous1 and since these mutual perturbations are proportional to the masses of comet and planet1 we are forced to say that1 by comparison with even such small bodies as the moon or ,mercury1 the mass of a comet is utterly insignificant1 certainly not as great as a ten-thousandth part of the mass of the earth4 ,in the case of the ,great ,comet of #ahhb1 if we leave its hundred million miles of tail out of account and suppose the entire mass condensed into its head1 we find by a little computation that the average density of the head under these circumstances must have been less than #a_/aejj of the density of air4 ,in ordinary laboratory practice this would be called a pretty good vacuum4 ,a striking observation made on ,september #ag1 #ahhb1 goes to confirm the very small density of this comet4 ,it is shown in ,fig4 #aji that early on that day the comet crossed the line joining earth and sun1 and therefore passed in transit over the sun's disk4 ,two observers at the ,cape of ,good ,hope saw the comet approach the sun1 and followed it with their telescopes until the nucleus actually reached the edge of the sun and disappeared1 behind it as they supposed1 for no trace of the comet1 not even its nucleus1 could be seen against the sun1 although it was carefully looked for4 ,now1 the figure shows that the comet passed between the earth and sun1 and its densest parts were therefore too attenuated to cut off any perceptible fraction of the sun's rays4 ,in other cases stars have been seen through the head of a comet1 shining apparently with undimmed luster1 although in some cases they seem to have been slightly refracted out of their true positions4 #afe4 ,,meteors4--,before proceeding further with the study of comets it is well to turn aside and consider their humbler relatives1 the shooting stars4 ,on some clear evening1 when the moon is absent from the sky1 watch the heavens for an hour and count the meteors visible during that time4 ,note their paths1 the part of the sky where they appear and where they disappear1 their brightness1 and whether they all move with equal swiftness4 ,out of such simple observations with the unaided eye there has grown a large and important branch of astronomical science1 some parts of which we shall briefly summarize here4 ,a particular meteor is a local phenomenon seen over only a small part of the earth's surface1 although occasionally a very big and bright one may travel and be visible over a considerable territory4 ,such a one in ,december1 #ahgf1 swept over the ,united ,states from ,kansas to ,pennsylvania1 and was seen from eleven different ,states4 ,but the ordinary shooting star is much less conspicuous1 and1 as we know from simultaneous observations made at neighboring places1 it makes its appearance at a height of some #ge miles above the earth's surface1 occupies something like a second in moving over its path1 and then disappears at a height of about #ej miles or more1 although occasionally a big one comes down to the very surface of the earth with force sufficient to bury itself in the ground1 from which it may be dug up1 handled1 weighed1 and turned over to the chemist to be analyzed4 ,the pieces thus found show that the big meteors1 at least1 are masses of stone or mineral2 iron is quite commonly found in them1 as are a considerable number of other terrestrial substances combined in rather peculiar ways4 ,but no chemical element not found on the earth has ever been discovered in a meteor4 #aff4 ,,nature ,,of ,,meteors4--,the swiftness with which the meteors sweep down shows that they must come from outside the earth1 for even half their velocity1 if given to them by some terrestrial volcano or other explosive agent1 would send them completely away from the earth never to return4 ,we must therefore look upon them as so many projectiles1 bullets1 fired against the earth from some outside source and arrested in their motion by the earth's atmosphere1 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 life4 ,the speed of the meteor is checked by the resistance which the atmosphere offers to its motion1 and the energy represented by that speed is transformed into heat1 which in less than a second raises the meteor and the surrounding air to incandescence1 melts the meteor either wholly or in part1 and usually destroys its identity1 leaving only an impalpable dust1 which cools off as it settles slowly through the lower atmosphere to the ground4 ,the heating effect of the air's resistance is proportional to the square of the meteor's velocity1 and even at such a moderate speed as #a mile per second the effect upon the meteor is the same as if it stood still in a bath of red-hot air4 ,now1 the actual velocity of meteors through the air is often #cj or #dj times as great as this1 and the corresponding effect of the air in raising its temperature is more than #a1jjj times that of red heat4 ,small wonder that the meteor is brought to lively incandescence and consumed even in a fraction of a second4 #afg4 ,,the ,,number ,,of ,,meteors4--,a single observer may expect to see in the evening hours about one meteor every #aj minutes on the average1 although1 of course1 in this respect much irregularity may occur4 ,later in the night they become more frequent1 and after #b ,a4 ,m4 there are about three times as many to be seen as in the evening hours4 ,but no one person can keep a watch upon the whole sky1 high and low1 in front and behind1 and experience shows that by increasing the number of observers and assigning to each a particular part of the sky1 the total number of meteors counted may be increased about five-fold4 ,so1 too1 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 station1 say #ej or #ajj miles1 and to watch every part of that atmosphere would require a large number of stations1 estimated at something more than #aj1jjj1 scattered systematically over the whole face of the earth4 ,if we piece together the several numbers above considered1 taking #ad as a fair average of the hourly number of meteors to be seen by a single observer at all hours of the night1 we shall find for the total number of meteors encountered by the earth in #bd hours1 #ad #e #aj1jjj #bd #af1hjj1jjj4 ,without laying too much stress upon this particular number1 we may fairly say that the meteors picked up by the earth every day are to be reckoned by millions1 and since they come at all seasons of the year1 we shall have to admit that the region through which the earth moves1 instead of being empty space1 is really a dust cloud1 each individual particle of dust being a prospective meteor4 ,on the average these individual particles are very small and very far apart2 a cloud of silver dimes each about #bej miles from its nearest neighbor is perhaps a fair representation of their average mass and distance from each other1 but1 of course1 great variations are to be expected both in the size and in the frequency of the particles4 ,there must be great numbers of them that are too small to make shooting stars visible to the naked eye1 and such are occasionally seen darting by chance across the field of view of a telescope4 #afh4 ,,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 orbit4 ,it is a faint and diffuse stream of light1 something like the ,milky ,way1 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 degrees1 possibly around the entire circumference of the sky4 ,it may be seen at any season of the year1 although it shows to the best advantage in spring evenings and autumn mornings4 ,look for it4 #afi4 ,,great ,,meteors4--,but there are other meteors1 veritable fireballs in appearance1 far more conspicuous and imposing than the ordinary shooting star4 ,such a one exploded over the city of ,madrid1 ,spain1 on the morning of ,february #aj1 #ahif1 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 artillery4 ,fig4 #aaa shows a large meteor which was seen in ,california in the early evening of ,july #bg1 #ahid1 and which left behind it a luminous trail or cloud visible for more than half an hour4 ,not infrequently large meteors are found traveling together1 two or three or more in company1 making their appearance simultaneously as did the ,california meteor of ,october #bb1 #ahif1 which is described as triple1 the trio following one another like a train of cars1 and ,arago cites an instance1 from the year #ahcj1 where within a short space of time some forty brilliant meteors crossed the sky1 all moving in the same direction with a whistling noise and displaying in their flight all the colors of the rainbow4 ,the mass of great meteors such as these must be measured in hundreds if not thousands of pounds1 and stories are current1 although not very well authenticated1 of even larger ones1 many tons in weight1 having been found partially buried in the ground4 ,of meteors which have been actually seen to fall from the sky1 the largest single fragment recovered weighs about #ejj pounds1 but it is only a fragment of the original meteor1 which must have been much more massive before it was broken up by collision with the atmosphere4 ,illustration3 ,,fig4 #aaa4--,the ,california meteor of ,july #bg1 #ahid4 #agj4 ,,the ,,velocity ,,of ,,meteors4--,every meteor1 big or little1 is subject to the law of gravitation1 and before it encounters the earth must be moving in some kind of orbit having the sun at its focus1 the particular species of orbit--ellipse1 parabola1 hyperbola--depending upon the velocity and direction of its motion4 ,now1 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 observers1 but the velocity can not be so readily found1 since the meteors go too fast for any ordinary process of timing4 ,but by photographing one of them two or three times on the same plate1 with an interval of only a tenth of a second between exposures1 ,dr4 ,elkin has succeeded in showing1 in a few cases1 that their velocities varied from #bj to #be miles per second1 and must have been considerably greater than this before the meteors encountered the earth's atmosphere4 ,this is a greater velocity than that of the earth in its orbit1 #ai miles per second1 as might have been anticipated1 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 earth1 for1 counting in the direction of the earth's motion1 the region of sunset and evening is always on the rear side of the earth1 and meteors in order to strike this region must overtake it by their swifter motion4 ,we have here1 in fact1 the reason why meteors are especially abundant in the morning hours2 at this time the observer is on the front side of the earth which catches swift and slow meteors alike1 while the rear is pelted only by the swifter ones which follow it4 ,a comparison of the relative number of morning and evening meteors makes it probable that the average meteor moves1 relative to the sun1 with a velocity of about #bf miles per second1 which is very approximately the average velocity of comets when they are at the earth's distance from the sun4 ,astronomers1 therefore1 consider meteors as well as comets to have the parabola and the elongated ellipse as their characteristic orbits4 #aga4 ,,meteor ,,showers--,,the ,,radiant4--,there is evident among meteors a distinct tendency for individuals1 to the number of hundreds or even hundreds of millions1 to travel together in flocks or swarms1 all going the same way in orbits almost exactly alike4 ,this gregarious tendency is made manifest not only by the fact that from time to time there are unusually abundant meteoric displays1 but also by a striking peculiarity of their behavior at such times4 ,the meteors all seem to come from a particular part of the heavens1 as if here were a hole in the sky through which they were introduced1 and from which they flow away in every direction1 even those which do not visibly start from this place having paths among the stars which1 if prolonged backward1 would pass through it4 ,the cause of this appearance may be understood from ,fig4 #aab1 which represents a group of meteors moving together along parallel paths toward an observer at ,d4 ,traveling unseen above the earth until they encounter the upper strata of its atmosphere1 they here become incandescent and speed on in parallel paths1 #a1 #b1 #c1 #d1 #e1 #f1 which1 as seen by the observer1 are projected back against the sky into luminous streaks that1 as is shown by the arrowheads1 b1 c1 d1 all seem to radiate from the point a--i4 e41 from the point in the sky whose direction from the observer is parallel to the paths of the meteors4 ,illustration3 ,,fig4 #aab4--;,explanation of the radiant of a meteoric shower4--,,denning4 ,such a display is called a meteor shower1 and the point a is called its radiant4 ,note how those meteors which appear near the radiant all have short paths1 while those remote from it in the sky have longer ones4 ,query3 ,as the night wears on and the stars shift toward the west1 will the radiant share in their motion or will it be left behind8 ,would the luminous part of the path of any of these meteors pass across the radiant from one side to the other8 ,is such a crossing of the radiant possible under any circumstances8 ,fig4 #aac shows how the meteor paths are grouped around the radiant of a strongly marked shower4 ,select from it the meteors which do not belong to this shower4 ,illustration3 ,,fig4 #aac4--,the radiant of a meteoric shower1 showing also the paths of three meteors which do not belong to this shower4--,,denning4 ,many hundreds of these radiants have been observed in the sky1 each of which represents an orbit along which a group of meteors moves1 and the relation of one of these orbits to that of the earth is shown in ,fig4 #aad4 ,the orbit of the meteors is an ellipse extending out beyond the orbit of ,uranus1 but so eccentric that a part of it comes inside the orbit of the earth1 and the figure shows only that part of it which lies nearest the sun4 ,the ,roman numerals which are placed along the earth's orbit show the position of the earth at the beginning of the tenth month1 eleventh month1 etc4 ,the meteors flow along their orbit in a long procession1 whose direction of motion is indicated by the arrow heads1 and the earth1 coming in the opposite direction1 plunges into this stream and receives the meteor shower when it reaches the intersection of the two orbits4 ,the long arrow at the left of the figure represents the direction of motion of another meteor shower which encounters the earth at this point4 ,illustration3 ,,fig4 #aad4--,the orbits of the earth and the ,november meteors4 ,can you determine from the figure answers to the following questions8 ,on what day of the year will the earth meet each of these showers8 ,will the radiant points of the showers lie above or below the plane of the earth's orbit8 ,will these meteors strike the front or the rear of the earth8 ,can they be seen in the evening hours8 ,from many of the radiants year after year1 upon the same day or week in each year1 there comes a swarm of shooting stars1 showing that there must be a continuous procession of meteors moving along this orbit1 so that some are always ready to strike the earth whenever it reaches the intersection of its orbit with theirs4 ,such is the explanation of the shower which appears each year in the first half of ,august1 and whose meteors are sometimes called ,perseids1 because their radiant lies in the constellation ,perseus1 and a similar explanation holds for all the star showers which are repeated year after year4 #agb4 ,,the ,,leonids4--,there is1 however1 a kind of star shower1 of which the ,leonids 7radiant in ,leo7 is the most conspicuous type1 in which the shower1 although repeated from year to year1 is much more striking in some years than in others4 ,thus1 to quote from the historian3 ,in #ahcc the shower was well observed along the whole eastern coast of ,north ,america from the ,gulf of ,mexico to ,halifax4 ,the meteors were most numerous at about #e ,a4 ,m4 on ,november #acth1 and the rising sun could not blot out all traces of the phenomena1 for large meteors were seen now and then in full daylight4 ,within the scope that the eye could contain1 more than twenty could be seen at a time shooting in every direction4 ,not a cloud obscured the broad expanse1 and millions of meteors sped their way across in every point of the compass4 ,their coruscations were bright1 gleaming1 and incessant1 and they fell thick as the flakes in the early snows of ,december4 ,but1 so far as is known1 none of them reached the ground4 ,an illiterate man on the following day remarked3 ,the stars continued to fall until none were left4 ,i am anxious to see how the heavens will appear this evening1 for ,i believe we shall see no more stars4 ,an eyewitness in the ,southern ,states thus describes the effect of this shower upon the plantation negroes3 ,upward of a hundred lay prostrate upon the ground1 some speechless and some with the bitterest cries1 but with their hands upraised1 imploring ,god to save the world and them4 ,the scene was truly awful1 for never did rain fall much thicker than the meteors fell toward the earth--east1 west1 north1 and south it was the same4 ,in the preceding year a similar but feebler shower from the same radiant created much alarm in ,france1 and through the old historic records its repetitions may be traced back at intervals of #cc or #cd years1 although with many interruptions1 to ,october #ab1 #ijb1 ,o4 ,s41 when an immense number of falling stars were seen to spread themselves over the face of the sky like rain4 ,such a star shower differs from the one repeated every year chiefly in the fact that its meteors1 instead of being drawn out into a long procession1 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 orbit1 but which is far from extending entirely around it1 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 earth4 ,the fact that the ,leonid shower is repeated at intervals of #cc or #cd years 7it appeared in #agii1 #ahcb-'cc1 #ahff-'fg7 shows that this is the periodic time in its orbit1 which latter must of course be an ellipse1 and presumably a long and narrow one4 ,it is this orbit which is shown in ,fig4 #aad1 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 shower2 the earth and the meteors would pass by without a collision4 ,now1 the meteors in their motion are subject to perturbations1 particularly by the large planets ,jupiter1 ,saturn1 and ,uranus1 which slightly change the meteor orbit1 and it seems certain that the changes thus produced will sometimes thrust the swarm inside or outside the orbit of the earth1 and thus cause a failure of the shower at times when it is expected4 ,the meteors were due at the crossing of the orbits in ,november1 #ahii and #aijj1 and1 although a few were then seen1 the shower was far from being a brilliant one1 and its failure was doubtless caused by the outer planets1 which switched the meteors aside from the path in which they had been moving for a century4 ,whether they will be again switched back so as to produce future showers is at the present time uncertain4 #agc4 ,,capture ,,of ,,the ,,leonids4--,but a far more striking effect of perturbations is to be found in ,fig4 #aae1 which shows the relation of the ,leonid orbit to those of the principal planets1 and illustrates a curious chapter in the history of the meteor swarm that has been worked out by mathematical analysis1 and is probably a pretty good account of what actually befell them4 ,early in the second century of the ,christian era this flock of meteors came down toward the sun from outer space1 moving along a parabolic orbit which would have carried it just inside the orbit of ,jupiter1 and then have sent it off to return no more4 ,but such was not to be its fate4 ,as it approached the orbit of ,uranus1 in the year #abf ,a4 ,d41 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 figure1 and in this new orbit they have moved from that time to this1 permanent instead of transient members of the solar system4 ,the perturbations1 however1 did not end with the year in which the meteors were captured and annexed to the solar system1 but ever since that time ,jupiter1 ,saturn1 and ,uranus have been pulling together upon the orbit1 and have gradually turned it around into its present position as shown in the figure1 and it is chiefly this shifting of the orbit's position in the thousand years that have elapsed since #ijb ,a4 ,d4 that makes the meteor shower now come in ,november instead of in ,october as it did then4 ,illustration3 ,,fig4 #aae4--,supposed capture of the ,november meteors by ,uranus4 #agd4 ,,breaking ,,up ,a ,,meteor ,,swarm4--,how closely packed together these meteors were at the time of their annexation to the solar system is unknown1 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 orbit1 as the ,perseids are distributed1 and1 given sufficient time1 it will accomplish this1 but up to the present the work is only partly done4 ,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 procession1 so that there is a thin stream of them extending entirely around the orbit and furnishing in every ,november a ,leonid shower2 but by far the larger part of the meteors still cling together1 although drawn out into a stream or ribbon1 which1 though very thin1 is so long that it takes some three years to pass through the perihelion of its orbit4 ,it is only when the earth plunges through this ribbon1 as it should in #ahii1 #aijj1 #aija1 that brilliant ,leonid showers can be expected4 #age4 ,,relation ,,of ,,comets ,,and ,,meteors4--,it appears from the foregoing that meteors and comets move in similar orbits1 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 orbit1 or at least in orbits so like that an appreciable difference between them is hardly to be found4 ,thus a comet which was discovered and observed early in the year #ahff1 moves in the same orbit with the ,leonid meteors1 passing its perihelion about ten months ahead of the main body of the meteors4 ,if it were set back in its orbit by ten months' motion1 it would be a part of the meteor swarm4 ,similarly1 the ,perseid meteors have a comet moving in their orbit actually immersed in the stream of meteor particles1 and several other of the more conspicuous star showers have comets attending them4 ,perhaps the most remarkable case of this character is that of a shower which comes in the latter part of ,november from the constellation ,andromeda1 and which from its association with the comet called ,biela 7after the name of its discoverer7 is frequently referred to as the ,bielid shower4 ,this comet1 an inconspicuous one moving in an unusually small elliptical orbit1 had been observed at various times from #aggb down to #ahdf without presenting anything remarkable in its appearance2 but about the beginning of the latter year1 with very little warning1 it broke in two1 and for three months the pieces were watched by astronomers moving off1 side by side1 something more than half as far apart as are the earth and moon4 ,it disappeared1 made the circuit of its orbit1 and six years later came back1 with the fragments nearly ten times as far apart as before1 and after a short stay near the earth once more disappeared in the distance1 never to be seen again1 although the fragments should have returned to perihelion at least half a dozen times since then4 ,in one respect the orbit of the comet was remarkable3 it passed through the place in which the earth stands on ,november #bgth of each year1 so that if the comet were at that particular part of its orbit on any ,november #bgth1 a collision between it and the earth would be inevitable4 ,so far as is known1 no such collision with the comet has ever occurred1 but the ,bielid meteors which are strung along its orbit do encounter the earth on that date1 in greater or less abundance in different years1 and are watched with much interest by the astronomers who look upon them as the final appearance of the dbris of a worn-out comet4 #agf4 ,,periodic ,,comets4--,the ,biela comet is a specimen of the type which astronomers call periodic comets--i4 e41 those which move in small ellipses and have correspondingly short periodic times1 so that they return frequently and regularly to perihelion4 ,the comets which accompany the other meteor swarms--,leonids1 ,perseids1 etc4--also belong to this class as do some #cj or #dj others which have periodic times less than a century4 ,as has been already indicated1 these deviations from the normal parabolic orbit call for some special explanation1 and the substance of that explanation is contained in the account of the ,leonid meteors and their capture by ,uranus4 ,any comet may be thus captured by the attraction of a planet near which it passes4 ,it is only necessary that the perturbing action of the planet should result in a diminution of the comet's velocity1 for we have already learned that it is this velocity which determines the character of the orbit1 and anything less than the velocity appropriate to a parabola must produce an ellipse--i4 e41 a closed orbit around which the body will revolve time after time in endless succession4 ,we note in ,fig4 #aae 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 thereby4 ,it might have passed behind ,uranus1 it would have passed behind had it come a little later1 and the effect would then have been just the opposite4 ,its velocity would have been increased1 its orbit changed to a hyperbola1 and it would have left the solar system more rapidly than it came into it1 thrust out instead of held in by the disturbing planet4 ,of such cases we can expect no record to remain1 but the captured comet is its own witness to what has happened1 and bears imprinted upon its orbit the brand of the planet which slowed down its motion4 ,thus in ,fig4 #aae the changed orbit of the meteors has its aphelion 7part remotest from the sun7 quite close to the orbit of ,uranus1 and one of its nodes1 mho1 the point in which it cuts through the plane of the ecliptic from north to south side1 is also very near to the same orbit4 ,it is these two marks1 aphelion and node1 which by their position identify ,uranus as the planet instrumental in capturing the meteor swarm1 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 node4 ,jupiter1 by reason of his great mass1 is an especially efficient capturer of comets1 and ,fig4 #aaf shows his group of captives1 his family of comets as they are sometimes called4 ,the several orbits are marked with the names commonly given to the comets4 ,frequently this is the name of their discoverer1 but often a different system is followed--e4 g41 the name #ahhf1 ,,iv1 means the fourth comet to pass through perihelion in the year #ahhf4 ,the other great planets--,saturn1 ,uranus1 ,neptune--have also their families of captured comets1 and according to ,schulhof1 who does not entirely agree with the common opinion about captured comets1 the earth has caught no less than nine of these bodies4 ,illustration3 ,,fig4 #aaf4--;,jupiter's family of comets4 #agg4 ,,comet ,,groups4--,but there is another kind of comet family1 or comet group as it is called1 which deserves some notice1 and which is best exemplified by the ,great ,comet of #ahhb and its relatives4 ,no less than four other comets are known to be traveling in substantially the same orbit with this one1 the group consisting of comets #affh1 ,i2 #ahdc1 ,i2 #ahhj1 ,i2 #ahhb1 ,,ii2 #ahhg1 ,i4 ,the orbit itself is not quite a parabola1 but a very elongated ellipse1 whose major axis and corresponding periodic time can not be very accurately determined from the available data1 but it certainly extends far beyond the orbit of ,neptune1 and requires not less than #ejj years for the comet to complete a revolution in it4 ,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 #affh brought back ahead of time by unknown perturbations4 ,there is still a possibility of this1 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 orbit4 ,this common orbit suggests a common origin for the comets1 but leaves us to conjecture how they became separated4 ,the observed orbits of these five comets present some slight discordances among themselves1 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 time4 ,they have all receded from the sun nearly on line toward the bright star ,sirius1 and were all of them1 at the beginning of the year #aijj1 standing nearly motionless inside of a space not bigger than the sun and distant from the sun about #aej radii of the earth's orbit4 ,the great rapidity with which they swept through that part of their orbit near the sun 7see #afb7 is being compensated by the present extreme slowness of their motions1 so that the comets of #affh and #ahhb1 whose passages through the solar system were separated by an interval of more than two centuries1 now stand together near the aphelion of their orbits1 separated by a distance only #ej per cent greater than the diameter of the moon's orbit1 and they will continue substantially in this position for some two or three centuries to come4 ,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--viz43 r#c _/ ,t#b #agh1 where ,t is the time1 in years1 required for the comet to move from its perihelion to any remote part of the orbit1 whose distance from the sun is represented1 in radii of the earth's orbit1 by r4 ,if the comet of #affh had moved in a parabola instead of the ellipse supposed above1 how many years would have been required to reach its present distance from the sun8 #agh4 ,,relation ,,of ,,comets ,,to ,,the ,,solar ,,system4--,the orbits of these comets illustrate a tendency which is becoming ever more strongly marked4 ,because comet orbits are nearly parabolas1 it used to be assumed that they were exactly parabolic1 and this carried with it the conclusion that comets have their origin outside the solar system4 ,it may be so1 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 planets2 and by the further fact that1 unlike the planets1 the comets show no marked tendency to move around their orbits in the direction in which the sun rotates upon his axis4 ,there is1 in fact1 the utmost confusion among them in this respect1 some going one way and some another4 ,the law of the solar system 7gravitation7 is impressed upon their movements1 but its order is not4 ,but as observations grow more numerous and more precise1 and comet orbits are determined with increasing accuracy1 there is a steady gain in the number of elliptic orbits at the expense of the parabolic ones1 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 system1 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 paths4 ,a striking instance of what may befall a comet in this way is shown in ,fig4 #aag1 where the tail of a comet appears sadly distorted and broken by what is presumed to have been a collision with a meteor swarm4 ,a more famous case of impeded motion is offered by the comet which bears the name of ,encke4 ,this has a periodic time less than that of any other known comet1 and at intervals of forty months comes back to perihelion1 each time moving in a little smaller orbit than before1 unquestionably on account of some resistance which it has suffered4 ,illustration3 ,,fig4 #aag4--;,brooks's comet1 ,october #ba1 #ahic4--;,,barnard4 #agi4 ,,the ,,development ,,of ,a ,,comet4--,we saw in #agd that the sun's action upon a meteor swarm tends to break it up into a long stream1 and the same tendency to break up is true of comets whose attenuated substance presents scant resistance to this force4 ,according to the mathematical analysis of ,roche1 if the comet stood still the sun's tidal force would tend first to draw it out on line with the sun1 just as the earth's tidal force pulled the moon out of shape 7 #db71 and then it would cause the lighter part of the comet's substance to flow away from both ends of this long diameter4 ,this destructive action of the sun is not limited to comets and meteor streams1 for it tends to tear the earth and moon to pieces as well2 but the densities and the resulting mutual attractions of their parts are far too great to permit this to be accomplished4 ,as a curiosity of mathematical analysis we may note that a spherical cloud of meteors1 or dust particles weighing a gramme each1 and placed at the earth's distance from the sun1 will be broken up and dissipated by the sun's tidal action if the average distance between the particles exceeds two yards4 ,now1 the earth is far more dense than such a cloud1 whose extreme tenuity1 however1 suggests what we have already learned of the small density of comets1 and prepares us in their case for an outflow of particles at both ends of the diameter directed toward the sun4 ,something of this kind actually occurs1 for the tail of a comet streams out on the side opposite to the sun1 and in general points away from the sun1 as is shown in ,fig4 #aji1 and the envelopes and jets rise up toward the sun2 but an inspection of ,fig4 #ajf will show that the tail and the envelope are too unlike to be produced by one and the same set of forces4 ,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 gravity4 ,we think naturally in this connection of the repelling force which a charge of electricity exerts upon a similar charge placed on a neighboring body1 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' tails2 for the force of gravity would operate between the substance of sun and comet1 and on the whole would be the controlling force1 while the electric charges would produce a repulsion1 relatively feeble for the big particles and strong for the little ones1 since an electric charge lies wholly on the surface1 while gravity permeates the whole mass of a body1 and the ratio of volume 7gravity7 to surface 7electric charge7 increases rapidly with increasing size4 ,the repelling force would thrust back toward the comet those particles which flowed out toward the sun1 while it would urge forward those which flowed away from it1 thus producing the difference in appearance between tail and envelopes1 the latter being regarded from this standpoint as stunted tails strongly curved backward4 ,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 repulsion4 #ahj4 ,,comet ,,tails4--,according to ,bredichin1 a comet's tail is formed by something like the following process3 ,in the head of the comet itself a certain part of its matter is broken up into fine bits1 single molecules perhaps1 which1 as they no longer cling together1 may be described as in the condition of vapor4 ,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 velocities1 the heavy ones slowly and the light ones faster1 much as particles of smoke stream away from a smokestack1 making for the comet a tail which like a trail of smoke is composed of constantly changing particles4 ,the result of this process is shown in ,fig4 #aah1 where the positions of the comet in its orbit on successive days are marked by the ,roman numerals1 and the broken lines represent the paths of molecules m,i1 m,,ii1 m,,iii1 etc41 expelled from it on their several dates and traveling thereafter in orbits determined by the combined effect of the sun's attraction1 the sun's repulsion1 and the comet's repulsion4 ,the comet's attraction 7gravity7 is too small to be taken into account4 ,the line drawn upward from ,,vi represents the positions of these molecules on the sixth day1 and shows that all of them are arranged in a tail pointing nearly away from the sun4 ,a similar construction for the other dates gives the corresponding positions of the tail1 always pointing away from the sun4 ,illustration3 ,,fig4 #aah4--;,formation of a comet's tail4 ,only the lightest kind of molecules--e4 g41 hydrogen--could drift away from the comet so rapidly as is here shown4 ,the heavier ones1 such as carbon and iron1 would be repelled as strongly by the electric forces1 but they would be more strongly pulled back by the gravitative forces1 thus producing a much slower separation between them and the head of the comet4 ,construct a figure such as the above1 in which the molecules shall recede from the comet only one eighth as fast as in ,fig4 #aah1 and note what a different position it gives to the comet's tail4 ,instead of pointing directly away from the sun1 it will be bent strongly to one side1 as is the large plume-shaped tail of the ,donati comet shown in ,fig4 #aja4 ,but observe that this comet has also a nearly straight tail1 like the theoretical one of ,fig4 #aah4 ,we have here two distinct types of comet tails1 and according to ,bredichin there is still another but unusual type1 even more strongly bent to one side of the line joining comet and sun1 and appearing quite short and stubby4 ,the existence of these three types1 and their peculiarities of shape and position1 are all satisfactorily accounted for by the supposition that they are made of different materials4 ,the relative molecular weights of hydrogen1 some of the hydrocarbons1 and iron1 are such that tails composed of these molecules would behave just as do the actual tails observed and classified into these three types4 ,the spectroscope shows that these materials--hydrogen1 hydrocarbons1 and iron--are present in comets1 and leaves little room for doubt of the essential soundness of ,bredichin's theory4 #aha4 ,,disintegration ,,of ,,comets4--,we must regard the tail as waste matter cast off from the comet's head1 and although the amount of this matter is very small1 it must in some measure diminish the comet's mass4 ,this process is1 of course1 most active at the time of perihelion passage1 and if the comet returns to perihelion time after time1 as the periodic ones which move in elliptic orbits must do1 this waste of material may become a serious matter1 leading ultimately to the comet's destruction4 ,it is significant in this connection that the periodic comets are all small and inconspicuous1 not one of them showing a tail of any considerable dimensions1 and it appears probable that they are far advanced along the road which1 in the case of ,biela's comet1 led to its disintegration4 ,their fragments are in part strewn through the solar system1 making some small fraction of its cloud of cosmic dust1 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 comet4 ,but it is not through the tail only that the disintegrating process is worked out4 ,while ,biela's comet is perhaps the most striking instance in which the head has broken up1 it is by no means the only one4 ,the ,great ,comet of #ahhb 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 same4 ,an even more striking phenomenon was the gradual breaking up of the nucleus of the same comet1 #ahhb1 ,,ii1 into a half dozen nuclei arranged in line like beads upon a string1 and pointing along the axis of the tail4 ,see ,fig4 #aai1 which shows the series of changes observed in the head of this comet4 #ahb4 ,,comets ,,and ,,the ,,spectroscope4--,the spectrum presented by comets was long a puzzle1 and still retains something of that character1 although much progress has been made toward an understanding of it4 ,in general it consists of two quite distinct parts--first1 a faint background of continuous spectrum due to ordinary sunlight reflected from the comet2 and1 second1 superposed upon this1 three bright bands like the carbon band shown at the middle of ,fig4 #dh1 only not so sharply defined4 ,these bands make a discontinuous spectrum quite similar to that given off by compounds of hydrogen and carbon1 and of course indicate that a part of the comet's light originates in the body itself1 which must therefore be incandescent1 or at least must contain some incandescent portions4 ,illustration3 ,,fig4 #aai4--,the head of the ,great ,comet of #ahhb4--,,winlock4 ,by heating hydrocarbons in our laboratories until they become incandescent1 something like the comet spectrum may be artificially produced1 but the best approximation to it is obtained by passing a disruptive electrical discharge through a tube in which fragments of meteors have been placed4 ,a flash of lightning is a disruptive electrical discharge upon a grand scale4 ,now1 meteors and electric phenomena have been independently brought to our notice in connection with comets1 and with this suggestion it is easy to frame a general idea of the physical condition of these objects--for example1 a cloud of meteors of different sizes so loosely clustered that the average density of the swarm is very low indeed2 the several particles in motion relative to each other1 as well as to the sun1 and disturbed in that motion by the sun's tidal action4 ,each particle carries its own electric charge1 which may be of higher or lower tension than that of its neighbor1 and is ready to leap across the intervening gap whenever two particles approach each other4 ,to these conditions add the inductive effect of the sun's electric charge1 which tends to produce a particular and artificial distribution of electricity among the comet's particles1 and we may expect to find an endless succession of sparks1 tiny lightning flashes1 springing from one particle to another1 most frequent and most vivid when the comet is near the sun1 but never strong enough to be separately visible4 ,their number is1 however1 great enough to make the comet in part self-luminous with three kinds of light--i4 e41 the three bright bands of its spectrum1 whose wave lengths show in the comet the same elements and compounds of the elements--carbon1 hydrogen1 and oxygen--which chemical analysis finds in the fallen meteor4 ,it is not to be supposed that these are the only chemical elements in the comet1 as they certainly are not the only ones in the meteor4 ,they are the easy ones to detect under ordinary circumstances1 but in special cases1 like that of the ,great ,comet of #ahhb1 whose near approach to the sun rendered its whole substance incandescent1 the spectrum glows with additional bright lines of sodium1 iron1 etc4 #ahc4 ,,collisions4--,a question sometimes asked1 ,what would be the effect of a collision between the earth and a comet8 finds its answer in the results reached in the preceding sections4 ,there would be a star shower1 more or less brilliant according to the number and size of the pieces which made up the comet's head4 ,if these were like the remains of the ,biela comet1 the shower might even be a very tame one2 but a collision with a great comet would certainly produce a brilliant meteoric display if its head came in contact with the earth4 ,if the comet were built of small pieces whose individual weights did not exceed a few ounces or pounds1 the earth's atmosphere would prove a perfect shield against their attacks1 reducing the pieces to harmless dust before they could reach the ground1 and leaving the earth uninjured by the encounter1 although the comet might suffer sadly from it4 ,but big stones in the comet1 meteors too massive to be consumed in their flight through the air1 might work a very different effect1 and by their bombardment play sad havoc with parts of the earth's surface1 although any such result as the wrecking of the earth1 or the destruction of all life upon it1 does not seem probable4 ,the #dj meteors of #afi may stand for a collision with a small comet4 ,consult the ,bible 7,joshua x1 #aa7 for an example of what might happen with a larger one4 ,,chapter ,,xiii ,,the ,,fixed ,,stars #ahd4 ,,the ,,constellations4--,in the earlier chapters the student has learned to distinguish between wandering stars 7planets7 and those fixed luminaries which remain year after year in the same constellation1 shining for the most part with unvarying brilliancy1 and presenting the most perfect known image of immutability4 ,homer and ,job and prehistoric man saw ,orion and the ,pleiades much as we see them to-day1 although the precession1 by changing their relation to the pole of the heavens1 has altered their risings and settings1 and it may be that their luster has changed in some degree as they grew old with the passing centuries4 ,illustration3 ,,fig4 #abj4--;,illustrating the division of the sky into constellations4 ,the division of the sky into constellations dates back to the most primitive times1 long before the ,christian era1 and the crooked and irregular boundaries of these constellations1 shown by the dotted lines in ,fig4 #abj1 such as no modern astronomer would devise1 are an inheritance from antiquity1 confounded and made worse in its descent to our day4 ,the boundaries assigned to constellations near the south pole are much more smooth and regular1 since this part of the sky1 invisible to the peoples from whom we inherit1 was not studied and mapped until more modern times4 ,the old traditions associated with each constellation a figure1 often drawn from classical mythology1 which was supposed to be suggested by the grouping of the stars3 thus ,ursa ,major is a great bear1 stalking across the sky1 with the handle of the ,dipper for his tail2 ,leo is a lion2 ,cassiopeia1 a lady in a chair2 ,andromeda1 a maiden chained to a rock1 etc42 but for the most part the resemblances are far-fetched and quite too fanciful to be followed by the ordinary eye4 #ahe4 ,,the ,,number ,,of ,,stars4--,as numerous as the stars of heaven is a familiar figure of speech for expressing the idea of countless number1 but as applied to the visible stars of the sky the words convey quite a wrong impression1 for1 under ordinary circumstances1 in a clear sky every star to be seen may be counted in the course of a few hours1 since they do not exceed #c1jjj or #d1jjj1 the exact number depending upon atmospheric conditions and the keenness of the individual eye4 ,test your own vision by counting the stars of the ,pleiades4 ,six are easily seen1 and you may possibly find as many as ten or twelve2 but however many are seen1 there will be a vague impression of more just beyond the limit of visibility1 and doubtless this impression is partly responsible for the popular exaggeration of the number of the stars4 ,in fact1 much more than half of what we call starlight comes from stars which are separately too small to be seen1 but whose number is so great as to more than make up for their individual faintness4 ,the ,milky ,way is just such a cloud of faint stars1 and the student who can obtain access to a small telescope1 or even an opera glass1 should not fail to turn it toward the ,milky ,way and see for himself how that vague stream of light breaks up into shining points1 each an independent star4 ,these faint stars1 which are found in every part of the sky as well as in the ,milky ,way1 are usually called telescopic1 in recognition of the fact that they can be seen only in the telescope1 while the other brighter ones are known as lucid stars4 #ahf4 ,,magnitudes4--,the telescopic stars show among themselves an even greater range of brightness than do the lucid ones1 and the system of magnitudes 7 #i7 has accordingly been extended to include them1 the faintest star visible in the greatest telescope of the present time being of the sixteenth or seventeenth magnitude1 while1 as we have already learned1 stars on the dividing line between the telescopic and the lucid ones are of the sixth magnitude4 ,to compare the amount of light received from the stars with that from the planets1 and particularly from the sun and moon1 it has been found necessary to prolong the scale of magnitudes backward into the negative numbers1 and we speak of the sun as having a stellar magnitude represented by the number -#bf4e4 ,the full moon's stellar magnitude is -#ab1 and the planets range from -#c 7,venus7 to #h 7,neptune74 ,even a very few of the stars are so bright that negative magnitudes must be used to represent their true relation to the fainter ones4 ,sirius1 for example1 the brightest of the fixed stars1 is of the -#a magnitude1 and such stars as ,arcturus and ,vega are of the #j magnitude4 ,the relation of these magnitudes to each other has been so chosen that a star of any one magnitude is very approximately #b4e times as bright as one of the next fainter magnitude1 and this ratio furnishes a convenient method of comparing the amount of light received from different stars4 ,thus the brightness of ,venus is #b4e #b4e times that of ,sirius4 ,the full moon is #b4ei times as bright as ,venus1 etc42 only it should be observed that the number #b4e is not exactly the value of the light ratio between two consecutive magnitudes4 ,strictly this ratio is the #ajja_/e #b4eaai1 so that to be entirely accurate we must say that a difference of five magnitudes gives a hundredfold difference of brightness4 ,in mathematical symbols1 if ,b represents the ratio of brightness 7quantity of light7 of two stars whose magnitudes are m and n1 then ,b 7#ajj77m-n7_/#e ,how much brighter is an ordinary first-magnitude star1 such as ,aldebaran or ,spica1 than a star just visible to the naked eye8 ,how many of the faintest stars visible in a great telescope would be required to make one star just visible to the unaided eye8 ,how many full moons must be put in the sky in order to give an illumination as bright as daylight8 ,how large a part of the visible hemisphere would they occupy8 #ahg4 ,,classification ,,by ,,magnitudes4--,the brightness of all the lucid stars has been carefully measured with an instrument 7photometer7 designed for that special purpose1 and the following table shows1 according to the ,harvard ,photometry1 the number of stars in the whole sky1 from pole to pole1 which are brighter than the several magnitudes named in the table3 ,the number of stars brighter than magnitude #a4j is #aa #b4j #ci #c4j #adb #d4j #dfc #e4j #a1dhc #f4j #d1cbf ,it must not be inferred from this table that there are in the whole sky only #d1cbf stars visible to the naked eye4 ,the actual number is probably #ej or #fj per cent greater than this1 and the normal human eye sees stars as faint as the magnitude #f4d or #f4e1 the discordance between this number and the previous statement1 that the sixth magnitude is the limit of the naked-eye vision1 having been introduced in the attempt to make precise and accurate a classification into magnitudes which was at first only rough and approximate4 ,this same striving after accuracy leads to the introduction of fractional numbers to represent gradations of brightness intermediate between whole magnitudes4 ,thus of the #b1hdc stars included between the fifth and sixth magnitudes a certain proportion are said to be of the #e4a magnitude1 #e4b magnitude1 and so on to the #e4i magnitude1 even hundredths of a magnitude being sometimes employed4 ,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 it1 and similarly we may find the number included between each other pair of consecutive magnitudes1 as follows3 ,magnitude #j #a #b #c #d #e #f ,number of stars #aa #bh #ajc #cba #a1jbj #b1hdc #d #cm #ab #cf #ajh #cbd #igb #b1iaf ,in the last line each number after the first is found by multiplying the preceding one by #c1 and the approximate agreement of each such number with that printed above it shows that on the whole1 as far as the table goes1 the fainter stars are approximately three times as numerous as those a magnitude brighter4 ,the magnitudes of the telescopic stars have not yet been measured completely1 and their exact number is unknown2 but if we apply our principle of a threefold increase for each successive magnitude1 we shall find for the fainter stars--those of the tenth and twelfth magnitudes--prodigious numbers which run up into the millions1 and even these are probably too small1 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 ratio4 ,this is balanced in some degree by the less rapid increase which is known to exist in magnitudes still fainter2 and applying our formula without regard to these variations in the rate of increase1 we obtain as a rude approximation to the total number of stars down to the fifteenth magnitude1 #hf1jjj1jjj4 ,the ,herschels1 father and son1 actually counted the number of stars visible in nearly #h1jjj sample regions of the sky1 and1 inferring the character of the whole sky from these samples1 we find it to contain #eh1ejj1jjj stars2 but the magnitude of the faintest star visible in their telescope1 and included in their count1 is rather uncertain4 ,how many first-magnitude stars would be needed to give as much light as do the #b1hdc stars of magnitude #e4j to #f4j8 ,how many tenth-magnitude stars are required to give the same amount of light8 ,to the modern man it seems natural to ascribe the different brilliancies of the stars to their different distances from us2 but such was not the case #b1jjj years ago1 when each fixed star was commonly thought to be fastened to a crystal sphere1 which carried them with it1 all at the same distance from us1 as it turned about the earth4 ,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 beyond1 it was easy to fall into the opposite error and to think of the stars as being much alike one with another1 and1 like pebbles on the beach1 scattered throughout space with some rough degree of uniformity1 so that in every direction there should be found in equal measure stars near at hand and stars far off1 each shining with a luster proportioned to its remoteness4 #ahh4 ,,distances ,,of ,,the ,,stars4--,now1 in order to separate the true from the false in this last mode of thinking about the stars1 we need some knowledge of their real distances from the earth1 and in seeking it we encounter what is perhaps the most delicate and difficult problem in the whole range of observational astronomy4 ,as shown in ,fig4 #aba1 the principles involved in determining these distances are not fundamentally different from those employed in determining the moon's distance from the earth4 ,thus1 the ellipse at the left of the figure represents the earth's orbit and the position of the earth at different times of the year4 ,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 sky4 ,a similar construction is made for the star ,b1 and it is readily seen that owing to the changing position of the observer as he moves around the earth's orbit1 both ,a and ,b will appear to move upon the background in orbits shaped like that of the earth as seen from the star1 but having their size dependent upon the star's distance1 the apparent orbit of ,a being larger than that of ,b1 because ,a is nearer the earth4 ,by measuring the angular distance between ,a and ,b at opposite seasons of the year 7e4 g41 the angles ,a--,jan4--,b1 and ,a--,july--,b7 the astronomer determines from the change in this angle how much larger is the one path than the other1 and thus concludes how much nearer is ,a than ,b4 ,strictly1 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 orbit1 and if ,b were so far away that the angle ,jan4--,b--,july were nothing at all we should get immediately from the observations the angle ,jan4--,a--,july1 which would suffice to determine the stars' distance4 ,supposing the diameter of the earth's orbit and the angle at ,a to be known1 can you make a graphical construction that will determine the distance of ,a from the earth8 ,illustration3 ,,fig4 #aba4--;,determining a star's parallax4 ,the angle subtended at ,a by the radius of the earth's orbit--i4 e41 #a_/b 7,jan4--,a--,july7--is called the star's parallax1 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 orbit4 ,the distance of a star is equal to the radius of the earth's orbit divided by the parallax1 in seconds of arc1 and multiplied by the number #bjfbfe4 ,a weak point of this method of measuring stellar distances is that it always gives what is called a relative parallax--i4 e41 the difference between the parallaxes of ,a and ,b2 and while it is customary to select for ,b a star or stars supposed to be much farther off than ,a1 it may happen1 and sometimes does happen1 that these comparison stars as they are called are as near or nearer than ,a1 and give a negative parallax--i4 e41 the difference between the angles at ,a and ,b proves to be negative1 as it must whenever the star ,b is nearer than ,a4 ,the first really successful determinations of stellar parallax were made by ,struve and ,bessel a little prior to #ahdj1 and since that time the distances of perhaps #ajj stars have been measured with some degree of reliability1 although the parallaxes themselves are so small--never as great as #a''--that it is extremely difficult to avoid falling into error1 since even for the nearest star the problem of its distance is equivalent to finding the distance of an object more than #e miles away by looking at it first with one eye and then with the other4 ,too short a base line4 #ahi4 ,,the ,,sun ,,and ,,his ,,neighbors4--,the distances of the sun's nearer neighbors among the stars are shown in ,fig4 #abb1 where the two circles having the sun at their center represent distances from it equal respectively to #a1jjj1jjj and #b1jjj1jjj times the distance between earth and sun4 ,in the figure the direction of each star from the sun corresponds to its right ascension1 as shown by the ,roman numerals about the outer circle2 the true direction of the star from the sun can not1 of course1 be shown upon the flat surface of the paper1 but it may be found by elevating or depressing the star from the surface of the paper through an angle1 as seen from the sun1 equal to its declination1 as shown in the fifth column of the following table1 ,the ,sun's ,nearest ,neighbors ---------------------------------------- ---------------------- ,no4 ,,star4 ,magnitude4 ,r4 ,a4 ,dec4 ,parallax4,distance4 ---------------------------------------- ---------------------- #a a ,centauri #j4g #ad4e;h4 -#fj #j4ge #j4bg #b ,ll4 #ba1ahe #f4h #aa4j #cg #j4de #j4df #c #fa ,cygni #e4j #ba4j #ch #j4dj #j4ea #d ,herculis #c4f #af4g #ci #j4dj #j4ea #e ,sirius -#a4d #f4g -#ag #j4cg #j4ef #f ,s #b1cih #h4b #ah4g #ei #j4ce #j4eh #g ,procyon #j4e #g4f #e #j4cd #j4fj #h g ,draconis #d4h #ag4e #ee #j4cj #j4fh #i ,gr4 #cd #g4i #j4b #dc #j4bi #j4ga #aj ,lac4 #i1ceb #g4e #bc4j -#cf #j4bh #j4gd #aa s ,draconis #d4h #ai4e #fi #j4be #j4hb #ab ,a4 ,o4 #ag1dae-f #i4j #ag4f #fh #j4be #j4hb #ac ,cassiopei #c4d #j4g #eg #j4be #j4hb #ad ,altair #a4j #ai4h #i #j4ba #j4ig #ae e ,indi #e4b #ba4i -#eg #j4bj #a4jc #af ,gr4 #a1fah #f4g #aj4a #ej #j4bj #a4jc #ag #aj ,urs ,majoris #d4b #h4i #db #j4bj #a4jc #ah ,castor #a4e #g4e #cb #j4bj #a4jc #ai ,ll4 #ba1beh #h4e #aa4j #dd #j4bj #a4jc #bj o#b ,eridani #d4e #d4b - #h #j4ai #a4jh #ba ,a4 ,o4 #aa1fgg #i4j #aa4b #ff #j4ai #a4jh #bb ,ll4 #ah1aae #h4j #i4a #ec #j4ah #a4ad #bc ,b4 ,d4 #cf1 #c1hhc #g4a #bj4j #cf #j4ah #a4ad #bd ,gr4 #a1fah #f4e #aj4a #ej #j4ag #a4ba #be b ,cassiopei #b4c #j4a #ei #j4af #a4bh #bf #gj ,ophiuchi #d4d #ah4j #b #j4af #a4bh #bg ,s #a1eaf #f4e #aa4b #gd #j4ae #a4ch #bh ,gr4 #a1hcj #f4f #aa4h #ci #j4ae #a4ch #bi m ,cassiopei #e4d #a4j #ed #j4ad #a4dg #cj e ,eridani #d4d #c4e -#aj #j4ad #a4dg #ca i ,urs ,majoris #c4b #h4i #dh #j4ac #a4eh #cb b ,hydri #b4i #j4c -#gh #j4ac #a4eh #cc ,fomalhaut #a4j #bb4i -#cj #j4ac #a4eh #cd ,br4 #c1jgg #f4j #bc4a #eg #j4ac #a4eh #ce e ,cygni #b4e #bj4h #cc #j4ab #a4ga #cf b ,com #d4e #ac4a #bh #j4aa #a4hg #cg ps#e ,aurig #h4h #f4f #dd #j4aa #a4hg #ch p ,herculis #c4c #ag4b #cg #j4aa #a4hg #ci ,aldebaran #a4a #d4e #af #j4aj #b4jf #dj ,capella #j4a #e4a #df #j4aj #b4jf #da ,b4 ,d4 #ce1 #d1jjc #i4b #bj4a #ce #j4aj #b4jf #db ,gr4 #a1fdf #f4c #aj4c #di #j4aj #b4jf #dc g ,cygni #b4c #bj4c #dj #j4aj #b4jf #dd ,regulus #a4b #aj4j #ab #j4aj #b4jf #de ,vega #j4b #ah4f #ci #j4aj #b4jf ---------------------------------------- ---------------------- in which the numbers in the first column are those placed adjacent to the stars in the diagram to identify them4 ,illustration3 ,,fig4 #abb4--,stellar neighbors of the sun4 #aij4 ,,light ,,years4--,the radius of the inner circle in ,fig4 #abb1 #a1jjj1jjj times the earth's distance from the sun1 is a convenient unit in which to express the stellar distances1 and in the preceding table the distances of the stars from the sun are expressed in terms of this unit4 ,to express them in miles the numbers in the table must be multiplied by #ic1jjj1jjj1jjj1jjj4 ,the nearest star1 a ,centauri1 is #be1jjj1jjj1jjj1jjj miles away4 ,but there is another unit in more common use--i4 e41 the distance traveled over by light in the period of one year4 ,we have already found 7 #ada7 that it requires light #hm4 #ahs4 to come from the sun to the earth1 and it is a simple matter to find from this datum that in a year light moves over a space equal to #fc1cfh radii of the earth's orbit4 ,this distance is called a light year1 and the distance of the same star1 a ,centauri1 expressed in terms of this unit1 is #d4bf years--i4 e41 it takes light that long to come from the star to the earth4 ,in ,fig4 #abb 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 #cj light years from the sun bright stars and faint ones are mixed up together1 and that1 so far as distance is concerned1 the sun is only a member of this swarm of stars1 whose distances apart1 each from its nearest neighbor1 are of the same order of magnitude as those which separate the sun from the three or four stars nearest it4 ,fig4 #abb is not to be supposed complete4 ,doubtless other stars will be found whose distance from the sun is less than #b1jjj1jjj radii of the earth's orbit1 but it is not probable that they will ever suffice to more than double or perhaps treble the number here shown4 ,the vast majority of the stars lie far beyond the limits of the figure4 #aia4 ,,proper ,,motions4--,it is evident that these stars are too far apart for their mutual attractions to have much influence one upon another1 and that we have here a case in which1 according to #cd1 each star is free to keep unchanged its state of rest or motion with unvarying velocity along a straight line4 ,their very name1 fixed stars1 implies that they are at rest1 and so astronomers long believed4 ,hipparchus 7#abe ,b4 ,c47 and ,ptolemy 7#acj ,a4 ,d47 observed and recorded many allineations among the stars1 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 sky4 ,for example1 they found at the beginning of the ,christian era that the four stars1 ,capella1 e ,persei1 a and b ,arietis1 stood in a straight line--i4 e41 upon a great circle of the sky4 ,verify this by direct reference to the sky1 and see how nearly these stars have kept the same position for nearly twenty centuries4 ,three of them may be identified from the star maps1 and the fourth1 e ,persei1 is a third-magnitude star between ,capella and the other two4 ,other allineations given by ,ptolemy are3 ,spica1 ,arcturus and b ,bootis2 ,spica1 d ,corvi and g ,corvi2 a ,libr1 ,arcturus and z ,urs ,majoris4 ,arcturus does not now fit very well to these alignments1 and nearly two centuries ago it1 together with ,aldebaran and ,sirius1 was on other grounds suspected to have changed its place in the sky since the days of ,ptolemy4 ,this discovery1 long since fully confirmed1 gave a great impetus to observing with all possible accuracy the right ascensions and declinations of the stars1 with a view to finding other cases of what was called proper motion--i4 e41 a motion peculiar to the individual star as contrasted with the change of right ascension and declination produced for all stars by the precession4 ,since the middle of the eighteenth century there have been made many thousands of observations of this kind1 whose results have gone into star charts and star catalogues1 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 magnitude1 with a view to ultimately determining all their proper motions4 ,the complete achievement of this result is1 of course1 a thing of the remote future1 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 motion1 although in most cases it is very small1 there being less than #ajj known stars in which it amounts to so much as #a per annum--i4 e41 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 diameter4 ,the most rapid known proper motion is that of a telescopic star midway between the equator and the south pole1 which changes its position at the rate of nearly #i per annum1 and the next greatest is that of another telescopic star1 in the northern sky1 ,no4 #bh of ,fig4 #abb4 ,it is not until we reach the tenth place in a list of large proper motions that we find a bright lucid star1 ,no4 #a of ,fig4 #abb4 ,it is a significant fact that for the most part the stars with large proper motions are precisely the ones shown in ,fig4 #abb1 which is designed to show stars near the earth4 ,this connection between nearness and rapidity of proper motions is indeed what we should expect to find1 since a given amount of real motion of the star along its orbit will produce a larger angular displacement1 proper motion1 the nearer the star is to the earth1 and this fact has guided astronomers in selecting the stars to be observed for parallax1 the proper motion being determined first and the parallax afterward4 #aib4 ,,the ,,paths ,,of ,,the ,,stars4--,we have already seen reason for thinking that the orbit along which a star moves is practically a straight line1 and from a study of proper motions1 particularly their directions across the sky1 it appears that these orbits point in all possible ways--north1 south1 east1 and west--so that some of them are doubtless directed nearly toward or from the sun2 others are square to the line joining sun and star2 while the vast majority occupy some position intermediate between these two4 ,now1 our relation to these real motions of the stars is well illustrated in ,fig4 #aab1 where the observer finds in some of the shooting stars a tremendous proper motion across the sky1 but sees nothing of their rapid approach to him1 while others appear to stand motionless1 although1 in fact1 they are moving quite as rapidly as are their fellows4 ,the fixed star resembles the shooting star in this respect1 that its proper motion is only that part of its real motion which lies at right angles to the line of sight1 and this needs to be supplemented by that other part of the motion which lies parallel to the line of sight1 in order to give us any knowledge of the star's real orbit4 ,illustration3 ,,fig4 #abc4--,motion of ,polaris in the line of sight as determined by the spectroscope4 ,,frost4 #aic4 ,,motion ,,in ,,the ,,line ,,of ,,sight4--,it is only within the last #be years that anything whatever has been accomplished in determining these stellar motions of approach or recession1 but within that time much progress has been made by applying the ,doppler principle 7 #hi7 to the study of stellar spectra1 and at the present time nearly every great telescope in the world is engaged upon work of this kind4 ,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 star1 but this shifting1 which must be determined by comparing the star's spectrum with that of some artificial light showing corresponding lines1 is so small in amount that its accurate measurement is a matter of extreme difficulty1 as may be seen from ,fig4 #abc4 ,this cut shows along its central line a part of the spectrum of ,polaris1 between wave lengths #d1dej and #d1fjj tenth meters1 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 ,polaris4 ,this comparison spectrum is1 as it should be1 a discontinuous or bright-line one1 while the spectrum of the star is a continuous one1 broken only by dark gaps or lines1 many of which have no corresponding lines in the comparison spectrum4 ,but a certain number of lines in the two spectra do correspond1 save that the dark line is always pushed a very little toward the direction of shorter wave lengths1 showing that this star is approaching the earth4 ,this spectrum was photographed for the express purpose of determining the star's motion in the line of sight1 and with it there should be compared ,figs4 #abd and #abe1 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 telescope4 ,the lower section of each figure shows an enlargement of the original photograph1 bringing out its details in a way not visible to the unaided eye4 ,in the enlarged spectrum of b ,aurig a rate of motion equal to that of the earth in its orbit would be represented by a shifting of #j4jc of a millimeter in the position of the broad1 hazy lines4 ,illustration3 ,,fig4 #abd4--,spectrum of b ,aurig4--,,pickering4 ,despite the difficulty of dealing with such small quantities as the above1 very satisfactory results are now obtained1 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 orbits1 ranging all the way from #j to #fj miles per second--more than #bjj1jjj miles per hour--which latter velocity1 according to ,campbell1 is the rate at which m ,cassiopei is approaching the sun4 ,the student should not fail to note one important difference between proper motions and the motions determined spectroscopically3 the latter are given directly in miles per second1 or per hour1 while the former are expressed in angular measure1 seconds of arc1 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 measure4 ,we are brought thus to the very heart of the matter2 parallax1 proper motion1 and motion in the line of sight are intimately related quantities1 all of which are essential to a knowledge of the real motions of the stars4 ,illustration3 ,,fig4 #abe4--,spectrum of ,pollux4--,,pickering4 #aid4 ,,star ,,drift4--,an illustration of how they may be made to work together is furnished by some of the stars--which make up the ,great ,dipper--b1 g1 e1 and z ,urs ,majoris1 whose proper motions have long been known to point in nearly the same direction across the sky and to be nearly equal in amount4 ,more recently it has been found that these stars are all moving toward the sun with approximately the same velocity--#ah miles per second4 ,one other star of the ,dipper1 d ,urs ,majoris1 shares in the common proper motion1 but its velocity in the line of sight has not yet been determined with the spectroscope4 ,these similar motions make it probable that the stars are really traveling together through space along parallel lines2 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 sight1 together with their unknown distances and the unknown direction and velocity of their real motion along their orbits4 ,solving these equations for the values of the unknown quantities1 it is found that the five stars probably lie in a plane which is turned nearly edgewise toward us1 and that in this plane they are moving about twice as fast as the earth moves around the sun1 and are at a distance from us represented by a parallax of less than #j4jb--;i4 e41 six times as great as the outermost circle in ,fig4 #abb4 ,a most extraordinary system of stars which1 although separated from each other by distances as great as the whole breadth of ,fig4 #abb1 yet move along in parallel paths which it is difficult to regard as the result of chance1 and for which it is equally difficult to frame an explanation4 ,illustration3 ,,fig4 #abf4--,the ,great ,dipper1 past1 present1 and future4 ,the stars a and of the ,great ,dipper do not share in this motion1 and must ultimately part company with the other five1 to the complete destruction of the ,dipper's shape4 ,fig4 #abf illustrates this change of shape1 the upper part of the figure 7a7 showing these seven stars as they were grouped at a remote epoch in the past1 while the lower section 7c7 shows their position for an equally remote epoch in the future4 ,there is no resemblance to a dipper in either of these configurations1 but it should be observed that in each of them the stars a and keep their relative position unaltered1 and the other five stars also keep together1 the entire change of appearance being due to the changing positions of these two groups with respect to each other4 ,this phenomenon of groups of stars moving together is called star drift1 and quite a number of cases of it are found in different parts of the sky4 ,the ,pleiades are perhaps the most conspicuous one1 for here some sixty or more stars are found traveling together along similar paths4 ,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 motion1 and therefore are not to be considered as members of the group1 but rather as isolated stars which1 for a time1 chance to be nearly on line with the ,pleiades1 and probably farther off1 since their proper motions are smaller4 ,to rightly appreciate the extreme slowness with which proper motions alter the constellations1 the student should bear in mind that the changes shown in passing from one section of ,fig4 #abf to the next represent the effect of the present proper motions of the stars accumulated for a period of #bjj1jjj years4 ,will the stars continue to move in straight paths for so long a time8 #aie4 ,,the ,,sun',s ,,way4--,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 stars4 ,the principle involved is simple enough4 ,if the sun moves with respect to the stars and carries the earth and the other planets year after year into new regions of space1 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 motion1 and even these will show its effect by their apparent motion of approach or recession along the line of sight4 ,so far as their own orbital motions are concerned1 there is no reason to suppose that more stars move north than south1 or that more go east than west2 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 sky1 we infer that this does not come from any general drift of the stars in that direction1 but that it marks the course of the sun among them4 ,that it is moving along a straight line pointing toward ,vega1 and that at least a part of the velocities which the spectroscope shows in the line of sight1 comes from the motion of the sun and earth4 ,working along these lines1 ,kapteyn finds that the sun is moving through space with a velocity of #aa miles per second1 which is decidedly below the average rate of stellar motion--#ai miles per second4 #aif4 ,,distance ,,of ,,sirian ,,and ,,solar ,,stars4--,by combining this rate of motion of the sun with the average proper motions of the stars of different magnitudes1 it is possible to obtain some idea of the average distance from us of a first-magnitude star or a sixth-magnitude star1 which1 while it gives no information about the actual distance of any particular star1 does show that on the whole the fainter stars are more remote4 ,but here a broad distinction must be drawn4 ,by far the larger part of the stars belong to one of two well-marked classes1 called respectively ,sirian and solar stars1 which are readily distinguished from each other by the kind of spectrum they furnish4 ,thus b ,aurig belongs to the ,sirian class1 as does every other star which has a spectrum like that of ,fig4 #abd1 while ,pollux is a solar star presenting in ,fig4 #abe a spectrum like that of the sun1 as do the other stars of this class4 ,two thirds of the sun's near neighbors1 shown in ,fig4 #abb1 have spectra of the solar type1 and in general stars of this class are nearer to us than are the stars with spectra unlike that of the sun4 ,the average distance of a solar star of the first magnitude is very approximately represented by the outer circle in ,fig4 #abb1 #b1jjj1jjj times the distance of the sun from the earth2 while the corresponding distance for a ,sirian star of the first magnitude is represented by the number #d1fjj1jjj4 ,a third-magnitude star is on the average twice as far away as one of the first magnitude1 a fifth-magnitude star four times as far off1 etc41 each additional two magnitudes doubling the average distance of the stars1 at least down to the eighth magnitude and possibly farther1 although beyond this limit we have no certain knowledge4 ,put in another way1 the naked eye sees many ,sirian stars which may have gone out and ceased to shine centuries ago1 for the light by which we now see them left those stars before the discovery of ,america by ,columbus4 ,for the student of mathematical tastes we note that the results of ,kapteyn's investigation of the mean distances 7,d7 of the stars of magnitude 7m7 may be put into two equations3 ,for ,solar ,stars1 ,d #bc #bm_/#b ,for ,sirian ,stars1 ,d #eb #bm_/#b where the coefficients #bc and #eb are expressed in light years4 ,how long a time is required for light to come from an average solar star of the sixth magnitude8 #aig4 ,,consequences ,,of ,,stellar ,,distance4--,the amount of light which comes to us from any luminous body varies inversely as the square of its distance1 and since many of the stars are changing their distance from us quite rapidly1 it must be that with the lapse of time they will grow brighter or fainter by reason of this altered distance4 ,but the distances themselves are so great that the most rapid known motion in the line of sight would require more than #a1jjj years 7probably several thousand7 to produce any perceptible change in brilliancy4 ,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 object1 and we may apply this law to determine the sun's rank among the stars4 ,if it were removed to the distance of an average first-1 or second-1 or third-magnitude star1 how would its light compare with that of the stars8 ,the average distance of a third-magnitude star of the solar type is1 as we have seen above1 #d1jjj1jjj times the sun's distance from the earth1 and since #d1jjj1jjj #ajf4f1 we find that at this distance the sun's stellar magnitude would be altered by #f4f #e magnitudes1 and would therefore be -#bf4e #cc4j #f4e--;i4 e41 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 visibility4 ,it must therefore be relatively small and feeble as compared with the brightness of the average star4 ,it is only its close proximity to us that makes the sun look brighter than the stars4 ,the fixed stars may have planets circling around them1 but an application of the same principles will show how hopeless is the prospect of ever seeing them in a telescope4 ,if the sun's nearest neighbor1 a ,centauri1 were attended by a planet like ,jupiter1 this planet would furnish to us no more light than does a star of the twenty-second magnitude--i4 e41 it would be absolutely invisible1 and would remain invisible in the most powerful telescope yet built1 even though its bulk were increased to equal that of the sun4 ,let the student make the computation leading to this result1 assuming the stellar magnitude of ,jupiter to be -#a4g4 #aih4 ,,double ,,stars4--,in the constellation ,taurus1 not far from ,aldebaran1 is the fourth-magnitude star th ,tauri1 which can readily be seen to consist of two stars close together4 ,the star a ,capricorni is plainly double1 and a sharp eye can detect that one of the faint stars which with ,vega make a small equilateral triangle1 is also a double star4 ,look for them in the sky4 ,in the strict language of astronomy the term double star would not be applied to the first two of these objects1 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--i4 e41 their angular separation is measured by a few seconds or fractions of a single second1 instead of the six minutes which separate the component stars of th ,tauri or a ,capricorni4 ,there are found in the sky many thousands of these close double stars1 of which some are only optically double--i4 e41 two stars nearly on line with the earth but at very different distances from it--while more of them are really what they seem1 stars near each other1 and in many cases near enough to influence each other's motion4 ,these are called binary systems1 and in cases of this kind the principles of celestial mechanics set forth in ,chapter ,,iv hold true1 and we may expect to find each component of a double star moving in a conic section of some kind1 having its focus at the common center of gravity of the two stars4 ,we are thus presented with problems of orbital motion quite similar to those which occur in the solar system1 and careful telescopic observations are required year after year to fix the relative positions of the two stars--i4 e41 their angular separation1 which it is customary to call their distance1 and their direction one from the other1 which is called position angle4 #aii4 ,,orbits ,,of ,,double ,,stars4--,the sun's nearest neighbor1 a ,centauri1 is such a double star1 whose position angle and distance have been measured by successive generations of astronomers for more than a century1 and ,fig4 #abg shows the result of plotting their observations4 ,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 one1 which is represented by the small circle at the intersection of the lines inside the ellipse4 ,it appears from the figure that during this time the one star has gone completely around the other1 as a planet goes around the sun1 and the true orbit must therefore be an ellipse having one of its foci at the center of gravity of the two stars4 ,the other star moves in an ellipse of precisely similar shape1 but probably smaller size1 since the dimensions of the two orbits are inversely proportional to the masses of the two bodies1 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 orbits4 ,this practice1 which has been followed in ,fig4 #abg1 gives correctly the relative positions of the two stars1 and makes one orbit do the work of two4 ,illustration3 ,,fig4 #abg4--,the orbit of a ,centauri4--,,see4 ,in ,fig4 #abg the bright star does not fall anywhere near the focus of the ellipse marked out by the smaller one1 and from this we infer that the figure does not show the true shape of the orbit1 which is certainly distorted1 foreshortened1 by the fact that we look obliquely down upon its plane4 ,it is possible1 however1 by mathematical analysis1 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 star1 and thus give the true shape and size of the orbit4 ,see ,fig4 #abh for a case in which the true orbit is turned exactly edgewise toward the earth1 and the small star1 which really moves in an ellipse like that shown in the figure1 appears to oscillate to and fro along a straight line drawn through the principal star1 as shown at the left of the figure4 ,in the case of a ,centauri the true orbit proves to have a major axis #dg times1 and a minor axis #dj times1 as great as the distance of the earth from the sun4 ,the orbit1 in fact1 is intermediate in size between the orbits of ,uranus and ,neptune1 and the periodic time of the star in this orbit is #ha years1 a little less than the period of ,uranus4 ,illustration3 ,,fig4 #abh4--;,apparent orbit and real orbit of the double star #db ,com ,berenicis4--,,see4 #bjj4 ,,masses ,,of ,,double ,,stars4--,if we apply to this orbit ,kepler's ,third ,law in the form given it at page #agi1 we shall find-- a#c _/ ,t#b 7#bc4e7c _/ 7#ha7b k 7,m m71 where ,m and m represent the masses of the two stars4 ,we have already seen that k1 the gravitation constant1 is equal to #a when the masses are measured in terms of the sun's mass taken as unity1 and when ,t and a are expressed in years and radii of the earth's orbit respectively1 and with this value of k we may readily find from the above equation1 ,m m #b4e--;i4 e41 the combined mass of the two components of a ,centauri is equal to rather more than twice the mass of the sun4 ,it is not every double star to which this process of weighing can be applied4 ,the major axis of the orbit1 a1 is found from the observations in angular measure1 #ce in this case1 and it is only when the parallax of the star is known that this can be converted into the required linear units1 radii of the earth's orbit1 by dividing the angular major axis by the parallax2 #dg #ce #j4ge4 ,our list of distances 7 #ahi7 contains four double stars whose periodic times and major axes have been fairly well determined1 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 move3 ---------------------------------------- ------------ ,,star4 ,major ,minor ,periodic ,mass4 axis4 axis4 time4 ---------------------------------------- ------------ a ,centauri #dg #dj #ha y4 #b #gj ,ophiuchi #ef #dh #hh #c ,procyon #cd #ca #dj #c ,sirius #dc #cd #eb #d ---------------------------------------- ------------ ,the orbit of ,uranus1 diameter #ch1 and ,neptune1 diameter #fj1 are of much the same size as these double-star orbits2 but the planetary orbits are nearly circular1 while in every case the double stars show a substantial difference between the long and short diameters of their orbits4 ,this is a characteristic feature of most double-star orbits1 and seems to stand in some relation to their periodic times1 for1 on the average1 the longer the time required by a star to make its orbital revolution the more eccentric is its orbit likely to prove4 ,another element of the orbits of double stars1 which stands in even closer relation to the periodic time1 is the major axis2 the smaller the long diameter of the orbit the more rapid is the motion and the shorter the periodic time1 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 telescope4 ,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 move1 this is by no means true of all the double stars1 many of which have periods running up into the hundreds if not thousands of years1 while a few complete their orbital revolutions in periods comparable with1 or even shorter than1 that of ,jupiter4 #bja4 ,,dark ,,stars4--,procyon1 the next to the last star of the preceding table1 calls for some special mention1 as the determination of its mass and orbit stands upon a rather different basis from that of the other stars4 ,more than half a century ago it was discovered that its proper motion was not straight and uniform after the fashion of ordinary stars1 but presented a series of loops like those marked out by a bright point on the rim of a swiftly running bicycle wheel4 ,the hub may move straight forward with uniform velocity1 but the point near the tire goes up and down1 and1 while sharing in the forward motion of the hub1 runs sometimes ahead of it1 sometimes behind1 and such seemed to be the motion of ,procyon and of ,sirius as well4 ,bessel1 who discovered it1 did not hesitate to apply the laws of motion1 and to affirm that this visible change of the star's motion pointed to the presence of an unseen companion1 which produced upon the motions of ,sirius and ,procyon just such effects as the visible companions produce in the motions of double stars4 ,a new kind of star1 dark instead of bright1 was added to the astronomer's domain1 and its discoverer boldly suggested the possible existence of many more4 ,that countless stars are visible is clearly no argument against the existence of as many more invisible ones4 ,there is no reason to think radiance a necessary property of celestial bodies4 ,but most astronomers were incredulous1 and it was not until #ahfb that1 in the testing of a new and powerful telescope just built1 a dark star was brought to light and the companion of ,sirius actually seen4 ,the visual discovery of the dark companion of ,procyon is of still more recent date 7,november1 #ahif71 when it was detected with the great telescope of the ,lick ,observatory4 ,this discovery is so recent that the orbit is still very uncertain1 being based almost wholly upon the variations in the proper motion of the star1 and while the periodic time must be very nearly correct1 the mass of the stars and dimensions of the orbit may require considerable correction4 ,the companion of ,sirius is about ten magnitudes and that of ,procyon about twelve magnitudes fainter than the star itself4 ,how much more light does the bright star give than its faint companion8 ,despite the tremendous difference of brightness represented by the answer to this question1 the mass of ,sirius is only about twice as great as that of its companion1 and for ,procyon the ratio does not exceed five or six4 ,the visual discovery of the companions to ,sirius and ,procyon removes them from the list of dark stars1 but others still remain unseen1 although their existence is indicated by variable proper motions or by variable orbital motion1 as in the case of z ,cancri1 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 seen4 #bjb4 ,,multiple ,,stars4--,combinations of three1 four1 or more stars close to each other1 like z ,cancri1 are called multiple stars1 and while they are far from being as common as are double stars1 there is a considerable number of them in the sky1 #ajj or more as against the more than #aj1jjj double stars that are known4 ,that their relative motions are subject to the law of gravitation admits of no serious doubt1 but mathematical analysis breaks down in face of the difficulties here presented1 and no astronomer has ever been able to determine what will be the general character of the motions in such a system4 ,illustration3 ,,fig4 #abi4--;,illustrating the motion of a spectroscopic binary4 #bjc4 ,,spectroscopic ,,binaries4--,in the year #ahij ,professor ,pickering1 of the ,harvard ,observatory1 announced the discovery of a new class of double stars1 invisible as such in even the most powerful telescope1 and producing no perturbations such as have been considered above1 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 star4 ,in ,fig4 #abi we suppose ,a and ,b to be the two components of a double star1 each moving in its own orbit about their common center of gravity1 ,c1 whose distance from the earth is several million times greater than the distance between the stars themselves4 ,under such circumstances no telescope could distinguish between the two stars1 which would appear fused into one2 but the smaller the orbit the more rapid would be their motion in it1 and if this orbit were turned edgewise toward the earth1 as is supposed in the figure1 whenever the stars were in the relative position there shown1 ,a would be rapidly approaching the earth by reason of its orbital motion1 while ,b would move away from it1 so that in accordance with the ,doppler principle the lines composing their respective spectra would be shifted in opposite directions1 thus producing a doubling of the lines1 each single line breaking up into two1 like the double-sodium line ,d1 only not spaced so far apart4 ,when the stars have moved a quarter way round their orbit to the points ,a1 ,b1 their velocities are turned at right angles to the line of sight and the spectrum returns to the normal type with single lines1 only to break up again when after another quarter revolution their velocities are again parallel with the line of sight4 ,the interval of time between consecutive doublings of the lines in the spectrum thus furnishes half the time of a revolution in the orbit4 ,the distance between the components of a double line shows by means of the ,doppler principle how fast the stars are traveling1 and this in connection with the periodic times fixes the size of the orbit1 provided we assume that it is turned exactly edgewise to the earth4 ,this assumption may not be quite true1 but even though the orbit should deviate considerably from this position1 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 orbits1 since the spectroscope measures only that component of the whole velocity which is directed toward the earth1 and it is important to note that the real orbits and masses of these spectroscopic binaries1 as they are called1 will usually be somewhat larger than those indicated by the spectroscope1 since it is only in exceptional cases that the orbit will be turned exactly edgewise to us4 ,the bright star ,capella is an excellent illustration of these spectroscopic binaries4 ,at intervals of a little less than a month the lines of its spectrum are alternately single and double1 their maximum separation corresponding to a velocity in the line of sight amounting to #cg miles per second4 ,each component of a doubled line appears to be shifted an equal amount from the position occupied by the line when it is single1 thus indicating equal velocities and equal masses for the two component stars whose periodic time in their orbit is #ajd days4 ,from this periodic time1 together with the velocity of the star's motion1 let the student show that the diameter of the orbit--i4 e41 the distance of the stars from each other--is approximately #ec1jjj1jjj miles1 and that their combined mass is a little less than that of a ,centauri1 provided that their orbit plane is turned exactly edgewise toward the earth4 ,there are at the present time 7#aija7 #cd spectroscopic binaries known1 including among them such stars as ,polaris1 ,capella1 ,algol1 ,spica1 b ,aurig1 z ,urs ,majoris1 etc41 and their number is rapidly increasing1 about one star out of every seven whose motion in the line of sight is determined proving to be a binary or1 as in the case of ,polaris1 possibly triple4 ,on account of smaller distance apart their periodic times are much shorter than those of the ordinary double stars1 and range from a few days up to several months--more than two years in the case of ,pegasi1 which has the longest known period of any star of this class4 ,spectroscopic binaries agree with ordinary double stars in having masses rather greater than that of the sun1 but there is as yet no assured case of a mass ten times as great as that of the sun4 #bjd4 ,,variable ,,stars4--,attention has already been drawn 7 #bc7 to the fact that some stars shine with a changing brightness--e4 g41 ,algol1 the most famous of these variable stars1 at its maximum of brightness furnishes three times as much light as when at its minimum1 and other variable stars show an even greater range4 ,the star o ,ceti has been named ,mira 7,latin1 the wonderful71 from its extraordinary range of brightness1 more than six-hundred-fold4 ,for the greater part of the time this star is invisible to the naked eye1 but during some three months in every year it brightens up sufficiently to be seen1 rising quite rapidly to its maximum brilliancy1 which is sometimes that of a second-magnitude star1 but more frequently only third or even fourth magnitude1 and1 after shining for a few weeks with nearly maximum brilliancy1 falling off to become invisible for a time and then return to its maximum brightness after an interval of eleven months from the preceding maximum4 ,in #aija it should reach its greatest brilliancy about midsummer1 and a month earlier than this for each succeeding year4 ,find it by means of the star map1 and by comparing its brightness from night to night with neighboring stars of about the same magnitude see how it changes with respect to them4 ,the interval of time from maximum to maximum of brightness--#cca4f days for ,mira--is called the star's period1 and within its period a star regularly variable runs through all its changes of brilliancy1 much as the weather runs through its cycle of changes in the period of a year4 ,but1 as there are wet years and dry ones1 hot years and cold1 so also with variable stars1 many of them show differences more or less pronounced between different periods1 and one such difference has already been noted in the case of ,mira2 its maximum brilliancy is different in different years4 ,so1 too1 the length of the period fluctuates in many cases1 as does every other circumstance connected with it1 and predictions of what such a variable star will do are notoriously unreliable4 #bje4 ,,the ,,algol ,,variables4--,on the other hand1 some variable stars present an almost perfect regularity1 repeating their changes time after time with a precision like that of clockwork4 ,algol is one type of these regular variables1 having a period of #fh4haed hours1 during six sevenths of which time it shines with unchanging luster as a star of the #b4c magnitude1 but during the remaining #i hours of each period it runs down to the #c4e magnitude1 and comes back again1 as is shown by a curve in ,fig4 #acj4 ,the horizontal scale here represents hours1 reckoned from the time of the star's minimum brightness1 and the vertical scale shows stellar magnitudes4 ,such a diagram is called the star's light curve1 and we may read from it that at any time between #e;h4 and #cb;h4 after the time of minimum the star's magnitude is #b4cb2 at #b;h4 after a minimum the magnitude is #b4hh1 etc4 ,what is the magnitude an hour and a half before the time of minimum8 ,what is the magnitude #dc days after a minimum8 ,illustration3 ,,fig4 #acj4--,the light curve of ,algol4 ,the arrows shown in ,fig4 #acj are a feature not usually found with light curves1 but in this case each one represents a spectroscopic determination of the motion of ,algol in the line of sight4 ,these observations extended over a period of more than two years1 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 light1 and each arrow shows not only the direction of the star's motion along the line of sight1 the arrows pointing down denoting approach of the star toward the earth1 but also its velocity1 each square of the ruling corresponding to #aj kilometers 7#f4b miles per second74 ,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 are1 but there can be no doubt that before minimum the star is moving away from the earth1 and after minimum is approaching it4 ,it is evident from these observations that in ,algol we have to do with a spectroscopic binary1 one of whose components is a dark star which1 once in each revolution1 partially eclipses the bright star and produces thus the variations in its light4 ,by combining the spectroscopic observations with the variations in the star's light1 ,vogel finds that the bright star1 ,algol1 itself has a diameter somewhat greater than that of the sun1 but is of low density1 so that its mass is less than half that of the sun1 while the dark star is a very little smaller than the sun and has about a quarter of its mass4 ,the distance between the two stars1 dark and bright1 is #c1bjj1jjj miles4 ,fig4 #abi1 which is drawn to scale1 shows the relative positions and sizes of these stars as well as the orbits in which they move4 ,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 eclipses1 and corresponding to this probability there are already known no less than #ae stars of the ,algol type of eclipse variables1 and only a beginning has been made in the search for them4 ,illustration3 ,,fig4 #aca4--,the light curve of b ,lyr4 #bjf4 ,,variables ,,of ,,the b ,,lyr ,,type4--,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 course4 ,capella would be such a variable if its orbit plane were directed exactly toward the earth1 and the fact that its light is not variable shows conclusively that such is not the position of the orbit4 ,fig4 #aca represents the light curve of one of the best-known variable systems of this second type1 that of b ,lyr1 whose period is #ab days #ba4h hours1 and the student should read from the curve the magnitude of the star for different times during this interval4 ,according to ,myers1 this light curve and the spectroscopic observations of the star point to the existence of a binary star of very remarkable character1 such as is shown1 together with its orbit and a scale of miles1 in ,fig4 #acb4 ,note the tide which each of these stars raises in the other1 thus changing their shapes from spheres into ellipsoids4 ,the astonishing dimensions of these stars are in part compensated by their very low density1 which is less than that of air1 so that their masses are respectively only #aj times and #ba times that of the sun6 ,but these dimensions and masses perhaps require confirmation1 since they depend upon spectroscopic observations of doubtful interpretation4 ,in ,fig4 #acb what relative positions must the stars occupy in their orbit in order that their combined light should give b ,lyr its maximum brightness8 ,what position will furnish a minimum brightness8 ,illustration3 ,,fig4 #acb4--,the system of b ,lyr4--,,myers4 #bjg4 ,,variables ,,of ,,long ,,and ,,short ,,periods4--,it must not be supposed that all variable stars are binaries which eclipse each other4 ,by far the larger part of them1 like ,mira1 are not to be accounted for in this way1 and a distinction which is pretty well marked in the length of their periods is significant in this connection4 ,there is a considerable number of variable stars with periods shorter than a month1 and there are many having periods longer than #f months1 but there are very few having periods longer than #ah months1 or intermediate between #a month and #f months1 so that it is quite customary to divide variable stars into two classes--those of long period1 #f months or more1 and those of short period less than #f months1 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 color1 while the short-period stars are almost without exception white or very pale yellow4 ,in fact1 the longer the period the redder the star1 although it is not to be inferred that all red stars are variable2 a considerable percentage of them shine with constant light4 ,the eclipse explanation of variability holds good only for short-period variables1 and possibly not for all of them1 while for the long-period variables there is no explanation which commands the general assent of astronomers1 although unverified hypotheses are plenty4 ,the number of stars known to be variable is about #djj1 while a considerable number of others are suspected1 and it would not be surprising if a large fraction of all the stars should be found to fluctuate a little in brightness4 ,the sun's spots may suffice to make it a variable star with a period of #aa years4 ,the discovery of new variables is of frequent occurrence1 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 ,fig4 #acc4 ,a given region of the sky--e4 g41 the ,northern ,crown--is photographed repeatedly upon the same plate1 which is shifted a little at each new exposure1 so that the stars shall fall at new places upon it4 ,the finally developed plate shows a row of images corresponding to each star1 and if the star's light is constant the images in any given row will all be of the same size1 as are most of those in ,fig4 #acc2 but a variable star such as is shown by the arrowhead reveals its presence by the broken aspect of its row of dots1 a minimum brilliancy being shown by smaller and a maximum by larger ones4 ,in this particular case1 at two exposures the star was too faint to print its image upon the plate4 ,illustration3 ,,fig4 #acc4--;,discovery of a variable star by means of photography4--,,pickering4 #bjh4 ,,new ,,stars4--,next to the variable stars of very long or very irregular period stand the so-called new or temporary stars1 which appear for the most part suddenly1 and after a brief time either vanish altogether or sink to comparative insignificance4 ,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 #afgj to #ahdh ,a4 ,d41 for since that time there have been no less than five of them visible to the naked eye and others telescopic4 ,in so far as these new stars are not ordinary variables 7,mira1 first seen in #aeif1 was long counted as a new star71 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 other4 ,the actual collision of two dark bodies moving with high velocities is clearly sufficient to produce a luminous star--e4 g41 meteors--and even the close approach of two cooled-off stars1 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 brightness4 ,the most famous of all new stars is that which1 according to ,tycho ,brahe's report1 appeared in the year #aegb1 and was so bright when at its best as to be seen with the naked eye in broad daylight4 ,it continued visible1 though with fading light1 for about #af months1 and finally disappeared to the naked eye1 although there is some reason to suppose that it can be identified with a ruddy star of the eleventh magnitude in the constellation ,cassiopeia1 whose light still shows traces of variability4 ,no modern temporary star approaches that of ,tycho in splendor1 but in some respects the recent ones surpass it in interest1 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 alone4 ,one of the most extraordinary of new stars1 and the most brilliant one since that of ,tycho1 appeared suddenly in the constellation ,perseus in ,february1 #aija1 and for a short time equaled ,capella in brightness4 ,but its light rapidly waned1 with periodic fluctuations of brightness like those of a variable star1 and at the present time 7,september1 #aijb7 it is lost to the naked eye1 although in the telescope it still shines like a star of the ninth or tenth magnitude4 ,by the aid of powerful photographic apparatus1 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 nebul had been thrown off by the star at the time of its sudden outburst of light4 ,but the extraordinary velocity of this nebular motion1 nearly a billion miles per hour1 makes such an explanation almost incredible1 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 matter1 into which a rapidly moving dark star plunged and1 after the fashion of terrestrial meteors1 was raised to brilliant incandescence by the collision4 ,if we assume this to be the true explanation of these extraordinary phenomena1 it is possible to show from the known velocity with which light travels through space and from the rate at which the nebula spread1 that the distance of ,nova ,persei1 as the new star is called1 corresponds to a parallax of about one one-hundredth of a second1 a result that is1 in substance1 confirmed by direct telescopic measurements of its parallax4 ,another modern temporary star is ,nova ,aurig1 which appeared suddenly in ,december1 #ahia1 waned1 and in the following ,april vanished1 only to reappear three months later for another season of renewed brightness4 ,the spectra of both these modern ,nov contain both dark and bright lines displaced toward opposite ends of the spectrum1 and suggesting the ,doppler effect that would be produced by two or more glowing bodies having rapid and opposite motions in the line of sight4 ,but the most recent investigations cast discredit on this explanation and leave the spectra of temporary stars still a subject of debate among astronomers1 with respect both to the motion they indicate and the intrinsic nature of the stars themselves4 ,the varying aspect of the spectra suggested at one time the sun's chromosphere1 at another time the conditions that are present in nebul1 etc4 ,,chapter ,,xiv ,,stars ,,and ,,nebul #bji4 ,,stellar ,,colors4--,we have already seen that one star differs from another in respect of color as well as brightness1 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 heavens1 while at the other end of the scale a ,orionis and ,aldebaran are strongly ruddy1 and ,antares presents an even deeper tone of red4 ,between these extremes the light of every star shows a mixture of the rainbow hues1 in which a very pale yellow is the predominant color1 shading off1 as we have seen1 to white at one end of the scale and red at the other4 ,there are no green stars1 or blue stars1 or violet stars1 save in one exceptional class of cases--viz41 where the two components of a double star are of very different brightness1 it is quite the usual thing for them to have different colors1 and then1 almost without exception1 the color of the fainter star lies nearer to the violet end of the spectrum than does the color of the bright one1 and sometimes shows a distinctly blue or green hue4 ,a fine type of such double star is b ,cygni1 in which the components are respectively yellow and blue1 and the yellow star furnishes eight times as much light as the blue one4 ,the exception which double stars thus make to the general rule of stellar colors1 yellow and red1 but no color of shorter wave length1 has never been satisfactorily explained1 but the rule itself presents no difficulties4 ,each star is an incandescent body1 giving off radiant energy of every wave length within the limits of the visible spectrum1 and1 indeed1 far beyond these limits4 ,if this radiant energy could come unhindered to our eyes every star would appear white1 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 and1 like the earth's atmosphere1 take a heavier toll from the violet than from the red end of the spectrum4 ,the greater the absorption in the star's atmosphere1 therefore1 the feebler and the ruddier will be its light1 and corresponding to this the red stars are as a class fainter than the white ones4 #baj4 ,,chemistry ,,of ,,the ,,stars4--,the spectroscope is pre-eminently the instrument to deal with this absorption of light in the stellar atmospheres1 just as it deals with that absorption in the sun's atmosphere to which are due the dark lines of the solar spectrum1 although the faintness of starlight1 compared with that of the sun1 presents a serious obstacle to its use4 ,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 made4 ,such familiar chemical elements as hydrogen and iron1 carbon1 sodium1 and calcium are scattered broadcast throughout the visible universe1 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 sun1 it is evident that in a broad way their substance is like rather than unlike that composing the solar system1 and is subject to the same physical and chemical laws which obtain here4 ,galileo and ,newton extended to the heavens the terrestrial sciences of mathematics and mechanics1 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 earth4 #baa4 ,,stellar ,,spectra4--,when the spectra of great numbers of stars are compared one with another1 it is found that they bear some relation to the colors of the stars1 as1 indeed1 we should expect1 since spectrum and color are both produced by the stellar atmospheres1 and it is found useful to classify these spectra into three types1 as follows3 ,type ,i4 ,sirian stars4--,speaking generally1 the stars which are white or very faintly tinged with yellow1 furnish spectra like that of ,sirius1 from which they take their name1 or that of b ,aurig 7,fig4 #abd71 which is a continuous spectrum1 especially rich in energy of short wave length--i4 e41 violet and ultraviolet light1 and is crossed by a relatively small number of heavy dark lines corresponding to the spectrum of hydrogen4 ,sometimes1 however1 these lines are much fainter than is here shown1 and we find associated with them still other faint ones pointing to the presence of other metallic substances in the star's atmosphere4 ,these metallic lines are not always present1 and sometimes even the hydrogen lines themselves are lacking1 but the spectrum is always rich in violet and ultraviolet light4 ,since with increasing temperature a body emits a continually increasing proportion of energy of short wave length 7 #aah71 the richness of these spectra in such energy points to a very high temperature in these stars1 probably surpassing in some considerable measure that of the sun4 ,stars with this type of spectrum are more numerous than all others combined1 but next to them in point of numbers stands-- ,type ,,ii4 ,solar stars4--,to this type of spectrum belong the yellow stars1 which show spectra like that of the sun1 or of ,pollux 7,fig4 #abe74 ,these are not so rich in violet light as are those of ,type ,i1 but in complexity of spectrum and in the number of their absorption lines they far surpass the ,sirian stars4 ,they are supposed to be at a lower temperature than the ,sirian stars1 and a much larger number of chemical elements seems present and active in the reversing layer of their atmospheres4 ,the strong resemblance which these spectra bear to that of the sun1 together with the fact that most of the sun's stellar neighbors have spectra of this type1 justify us in ranking both them and it as members of one class1 called solar stars4 ,type ,,iii4 ,red stars4--,a small number of stars show spectra comparable with that of a ,herculis 7,fig4 #acd71 in which the blue and the violet part of the spectrum is almost obliterated1 and the remaining yellow and red parts show not only dark lines1 but also numerous broad dark bands1 sharp at one edge1 and gradually fading out at the other4 ,it is this selective absorption1 extinguishing the blue and leaving the red end of the spectrum1 which produces the ruddy color of these stars1 while the bands in their spectra are characteristic of chemical combinations1 and their presence 444 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 7,scheiner-,frost74 ,one of the chemical compounds here indicated is a hydrocarbon similar to that found in comets4 ,in the white and yellow stars the temperatures are so high that the same chemical elements1 although present1 can not unite one with another to form compound substances4 ,illustration3 ,,fig4 #acd4--,the spectrum of a ,herculis4--,,espin4 ,most of the variable stars are red and have spectra of the third type2 but this does not hold true for the eclipse variables like ,algol1 all of which are white stars with spectra of the first type4 ,the ordinary variable star is therefore one with a dense atmosphere of relatively low temperature and complex structure1 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 longer1 red waves to escape4 ,although their exact nature is not understood1 there can be little doubt that the fluctuation in the light of these stars is due to processes taking place within the star itself1 but whether above or below its photosphere is still uncertain4 #bab4 ,,classes ,,of ,,stars4--,there is no hard-and-fast dividing line between these types of stellar spectra1 but the change from one to another is by insensible gradations1 like the transition from youth to manhood and from manhood to old age1 and along the line of transition are to be found numberless peculiarities and varieties of spectra not enumerated above--e4 g41 a few stars show not only dark absorption lines in their spectra but bright lines as well1 which1 like those in ,fig4 #dh1 point to the presence of incandescent vapors1 even in the outer parts of their atmospheres4 ,among the lucid stars about #ge per cent have spectra of the first type1 #bc per cent are of the second type1 #a per cent of the third type1 and the remaining #a per cent are peculiar or of doubtful classification4 ,among the telescopic stars it is probable that much the same distribution holds1 but in the present state of knowledge it is not prudent to speak with entire confidence upon this point4 ,that the great number of stars whose spectra have been studied should admit of a classification so simple as the above1 is an impressive fact which1 when supplemented by the further fact of a gradual transition from one type of spectrum to the next1 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 development1 and that the sun is only one of these individuals1 of something less than medium size and in a stage of development which is not at all peculiar1 since it is shared by nearly a fourth of all the stars4 #bac4 ,,star ,,clusters4--,in previous chapters we have noted the ,pleiades and ,prsepe as star clusters visible to the naked eye1 and to them we may add the ,hyades1 near ,aldebaran1 and the little constellation ,coma ,berenices4 ,but more impressive than any of these1 although visible only in a telescope1 is the splendid cluster in ,hercules1 whose appearance in a telescope of moderate size is shown in ,fig4 #ace1 while ,fig4 #acf is a photograph of the same cluster taken with a very large reflecting telescope4 ,this is only a type of many telescopic clusters which are scattered over the sky1 and which are made up of stars packed so closely together as to become indistinguishable1 one from another1 at the center of the cluster4 ,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 neighbors1 but whose apparent nearness to each other is doubtless due to their great distance from us4 ,it is quite probable that even at the center of this cluster1 where more than a thousand stars are included within a radius of #afj1 the actual distances separating adjoining stars are much greater than that separating earth and sun1 but far less than that separating the sun from its nearest stellar neighbor4 ,illustration3 ,,fig #ace4--,star cluster in ,hercules4 ,an interesting discovery of recent date1 made by ,professor ,bailey in photographing star clusters1 is that some few of them1 which are especially rich in stars1 contain an extraordinary number of variable stars1 mostly very faint and of short period4 ,two clusters1 one in the northern and one in the southern hemisphere1 contain each more than a hundred variables1 and an even more extraordinary case is presented by a cluster1 called ,messier #e1 not far from the star a ,serpentis1 which contains no less than sixty-three variables1 all about of the fourteenth magnitude1 all having light periods which differ but little from half a day1 all having light curves of about the same shape1 and all having a range of brightness from maximum to minimum of about one magnitude4 ,an extraordinary set of coincidences which points unmistakably to a common origin and cause of variability4 ,illustration3 ,,fig4 #acf4--,star cluster in ,hercules4--,,keeler4 ,illustration3 ,,fig4 #acg4--,the ,andromeda nebula as seen in a very small telescope4 ,illustration3 ,,fig4 #ach4--,the ,andromeda nebula and ,holmes's comet4 ,photographed by ,,barnard4 ,illustration3 ,,fig4 #aci4--;,a drawing of the ,andromeda nebula4 ,illustration3 ,,fig4 #adj4--;,a photograph of the ,andromeda nebula4--,,roberts4 #bad4 ,,nebul4--,returning to ,fig4 #acf1 we note that its background has a hazy appearance1 and that at its center the stars can no longer be distinguished1 but blend one with another so as to appear like a bright cloud4 ,the outer part of the cluster is resolved into stars1 while in the picture the inner portion is not so resolved1 although in the original photographic plate the individual stars can be distinguished to the very center of the cluster4 ,in many cases1 however1 this is not possible1 and we have an irresolvable cluster which it is customary to call a nebula 7,latin1 little cloud74 ,the most conspicuous example of this in the northern heavens is the great nebula in ,andromeda 7,r4 ,a4 #j;h #cgm1 ,dec4 #da71 which may be seen with the naked eye as a faint patch of foggy light4 ,look for it4 ,this appears in an opera glass or very small telescope not unlike ,fig4 #acg1 which is reproduced from a sketch4 ,fig4 #ach is from a photograph of the same object showing essentially the same shape as in the preceding figure1 but bringing out more detail4 ,note the two small nebul adjoining the large one1 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 taken4 ,fig4 #aci is from another drawing of this nebula1 although it is hardly to be recognized as a representation of the same thing2 but its characteristic feature1 the two dark streaks near the center of the picture1 is justified in part by ,fig4 #adj1 which is from a photograph made with a large reflecting telescope4 ,illustration3 ,,fig4 #ada4--,types of nebul4 ,a comparison of these several representations of the same thing will serve to illustrate the vagueness of its outlines1 and how much the impressions to be derived from nebul depend upon the telescopes employed and upon the observer's own prepossessions4 ,the differences among the pictures can not be due to any change in the nebula itself1 for half a century ago it was sketched much as shown in the latest of them 7,fig4 #adj74 ,illustration3 ,,fig4 #adb4--,the ,trifid nebula4--,,keeler4 #bae4 ,,typical ,,nebul4--,some of the fantastic forms which nebul present in the telescope are shown on a small scale in ,fig4 #ada1 but in recent years astronomers have learned to place little reliance upon drawings such as these1 which are now almost entirely supplanted by photographs made with long exposures in powerful telescopes4 ,one of the most exquisite of these modern photographs is that of the ,trifid nebula in ,sagittarius 7,fig4 #adb74 ,note especially the dark lanes that give to this nebula its name1 ,trifid1 and which run through its brightest parts1 breaking it into seemingly independent sections4 ,the area of the sky shown in this cut is about #ae per cent less than that covered by the full moon4 ,illustration3 ,,fig4 #adc4--;,a nebula in ,cygnus4--,,keeler4 ,fig4 #adc shows a very different type of nebula1 found in the constellation ,cygnus1 which appears made up of filaments closely intertwined1 and stretches across the sky for a distance considerably greater than the moon's diameter4 ,illustration3 ,,fig4 #add4--,spiral nebula in ,canes ,venatici4--,,keeler4 ,a much smaller but equally striking nebula is that in the constellation ,canes ,venatici 7,fig4 #add71 which shows a most extraordinary spiral structure1 as if the stars composing it were flowing in along curved lines toward a center of condensation4 ,the diameter of the circular part of this nebula1 omitting the projection toward the bottom of the picture1 is about five minutes of arc1 a sixth part of the diameter of the moon1 and its thickness is probably very small compared with its breadth1 perhaps not much exceeding the width of the spiral streams which compose it4 ,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 them4 ,this characteristic grouping of the stars1 which is followed in many other nebul1 shows that they are really part and parcel of the nebula and not merely on line with it4 ,fig4 #ade shows how a great nebula is associated with the star r ,ophiuchi4 ,illustration3 ,,fig4 #ade4--;,great nebula about the star r ,ophiuchi4--,,barnard4 ,probably the most impressive of all nebul is the great one in ,orion 7,fig4 #adf71 whose position is shown on the star map between ,rigel and z ,orionis4 ,look for it with an opera glass or even with the unaided eye4 ,this is sometimes called an amorphous--i4 e41 shapeless--nebula1 because it presents no definite form which the eye can grasp and little trace of structure or organization4 ,it is without form and void at least in its central portions1 although on its edges curved filaments may be traced streaming away from the brighter parts of the central region4 ,this nebula1 as shown in ,fig4 #adf1 covers an area about equal to that of the full moon1 without counting as any part of this the companion nebula shown at one side1 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 ,orion4 ,indeed1 over a large part of the entire sky the background is faintly covered with nebulous light whose brighter portions1 if each were counted as a separate nebula1 would carry the total number of such objects well into the hundreds of thousands4 ,illustration3 ,,fig4 #adf4--,the ,orion nebula4 ,the ,pleiades 7,plate ,,iv7 present a case of a resolvable star cluster projected against such a nebulous background whose varying intensity should be noted in the figure4 ,a part of this nebulous matter is shown in wisps extending from one star to the next1 after the fashion of a bridge1 and leaving little doubt that the nebula is actually a part of the cluster and not merely a background for it4 ,illustration3 ,,the ,,pleiades 7,,after ,a ,,photograph7 ,fig4 #adg shows a series of so-called double nebul perhaps comparable with double stars1 although the most recent photographic work seems to indicate that they are really faint spiral nebul in which only the brightest parts are shown by the telescope4 ,according to ,keeler1 the spiral is the prevailing type of nebul1 and while ,fig4 #add presents the most perfect example of such a nebula1 the student should not fail to note that the ,andromeda nebula 7,fig4 #adj7 shows distinct traces of a spiral structure1 only here we do not see its true shape1 the nebula being turned nearly edgewise toward us so that its presumably circular outline is foreshortened into a narrow ellipse4 ,illustration3 ,,fig4 #adg4--;,double nebul4 ,,herschel4 ,another type of nebula of some consequence presents in the telescope round disks like those of ,uranus or ,neptune1 and this appearance has given them the name planetary nebul4 ,the comet in ,fig4 #ach1 if smaller1 would represent fairly well the nebul of this type4 ,sometimes a planetary nebula has a star at its center1 and sometimes it appears hollow1 like a smoke ring1 and is then called a ring nebula4 ,the most famous of these is in the constellation ,lyra1 not far from ,vega4 #baf4 ,,spectra ,,of ,,nebul4--,a star cluster1 like the one in ,hercules1 shows1 of course1 stellar spectra1 and even when irresolvable the spectrum is a continuous one1 testifying to the presence of stars1 although they stand too close together to be separately seen4 ,but in a certain number of nebul the spectrum is altogether different1 a discontinuous one containing only a few bright lines1 showing that here the nebular light comes from glowing gases which are subject to no considerable pressure4 ,the planetary nebul all have spectra of this kind and make up about half of all the known gaseous nebul4 ,it is worthy of note that a century ago ,sir ,william ,herschel had observed a green shimmer in the light of certain nebul which led him to believe that they were not of a starry nature1 a conclusion which has been abundantly confirmed by the spectroscope4 ,the green shimmer is1 in fact1 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 nebul4 ,in faint nebul this line constitutes the whole of their visible spectrum1 but in brighter ones two or three other and fainter lines are usually associated with it1 and a very bright nebula1 like that in ,orion1 may show a considerable number of extra lines1 but for the most part they can not be identified in the spectrum of any terrestrial substances4 ,an exception to this is found in the hydrogen lines1 which are well marked in most spectra of gaseous nebul1 and there are indications of one or two other known substances4 #bag4 ,,density ,,of ,,nebul4--,it is known from laboratory experiments that diminishing the pressure to which an incandescent gas is subject1 diminishes the number of lines contained in its spectrum1 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 density4 ,but this is far from showing that the nebula itself is correspondingly attenuated1 for we must not assume that this shining gas is all that exists in the nebula2 so far as telescope or camera are concerned1 there may be associated with it any amount of dark matter which can not be seen because it sends to us no light4 ,it is easy to think in this connection of meteoric dust or the stuff of which comets are made1 for these seem to be scattered broadcast on every side of the solar system and may1 perchance1 extend out to the region of the nebul4 ,but1 whatever may be associated in the nebula with the glowing gas which we see1 the total amount of matter1 invisible as well as visible1 must be very small1 or rather its average density must be very small1 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 space4 ,the brighter parts of this nebula as seen from the earth subtend an angle of about half a degree1 and while we know nothing of its distance from us1 it is easy to see that the farther it is away the greater must be its real dimensions1 and that this increase of bulk and mass with increasing distance will just compensate the diminishing intensity of gravity at great distances1 so that for a given angular diameter--e4 g41 half a degree--the force with which this nebula attracts the sun depends upon its density but not at all upon its distance4 ,now1 the nebula must attract the sun in some degree1 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 view1 and this changed point of view should produce a change in the apparent direction of the nebula from us--i4 e41 a proper motion1 whose amount would depend upon the attracting force1 and therefore upon the density of the attracting matter4 ,observations of the ,orion nebula show that its proper motion is wholly inappreciable1 certainly far less than half a second of arc per year1 and corresponding to this amount of proper motion the mean density of the nebula must be some millions of times 7#ajaj according to ,ranyard7 less than that of air at sea level--i4 e41 the average density throughout the nebula is comparable with that of those upper parts of the earth's atmosphere in which meteors first become visible4 #bah4 ,,motion ,,of ,,nebul4--,the extreme minuteness of their proper motions is a characteristic feature of all nebul4 ,indeed1 there is hardly a known case of sensible proper motion of one of these bodies1 although a dozen or more of them show velocities in the line of sight ranging in amount from #cj to -#dj miles per second1 the plus sign indicating an increasing distance4 ,while a part of these velocities may be only apparent and due to the motion of earth and sun through space1 a part at least is real motion of the nebul themselves4 ,these seem to move through the celestial spaces in much the same way and with the same velocities as do the stars1 and their smaller proper motions across the line of sight 7angular motions7 are an index of their great distance from us4 ,no one has ever succeeded in measuring the parallax of a nebula or star cluster4 ,illustration3 ,,fig4 #adh4--;,a part of the ,milky ,way4 ,the law of gravitation presumably holds sway within these bodies1 and the fact that their several parts and the stars which are involved within them1 although attracted by each other1 have shown little or no change of position during the past century1 is further evidence of their low density and feeble attraction4 ,in a few cases1 however1 there seem to be in progress within a nebula changes of brightness1 so that what was formerly a faint part has become a brighter one1 or vice versa2 but1 on the whole1 even these changes are very small4 ,illustration3 ,,fig4 #adi4--,the ,milky ,way near th ,ophiuchi4--,,barnard4 #bai4 ,,the ,,milky ,,way4--,closely related to nebul and star clusters is another feature of the sky1 the galaxy or ,milky ,way1 with whose appearance to the unaided eye the student should become familiar by direct study of the thing itself4 ,figs4 #adh and #adi are from photographs of two small parts of it1 and serve to bring out the small stars of which it is composed4 ,every star shown in these pictures is invisible to the naked eye1 although their combined light is easily seen4 ,the general course of the galaxy across the heavens is shown in the star maps1 but these contain no indication of the wealth of detail which even the naked eye may detect in it4 ,bright and faint parts1 dark rifts which cut it into segments1 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 examination4 ,illustration3 ,,fig4 #aej4--,the ,milky ,way near b ,cygni4--,,barnard4 ,speaking generally1 the course of the ,milky ,way is a great circle completely girdling the sky and having its north pole in the constellation ,coma ,berenices4 ,the width of this stream of light is very different in different parts of the heavens1 amounting where it is widest1 in ,lyra and ,cygnus1 to something more than #cj1 although its boundaries are too vague and ill defined to permit much accuracy of measurement4 ,observe the very bright part between b and g ,cygni1 nearly opposite ,vega1 and note how even an opera glass will partially resolve the nebulous light into a great number of stars1 which are here rather brighter than in other parts of its course4 ,but the resolution into stars is only partial1 and there still remains a background of unresolved shimmer4 ,fig4 #aej is a photograph of a small part of this region in which1 although each fleck of light represents a separate star1 the galaxy is not completely resolved4 ,compare with this region1 rich in stars1 the nearly empty space between the branches of the galaxy a little west of ,altair4 ,another hole in the ,milky ,way may be found a little north and east of a ,cygni1 and between the extremes of abundance and poverty here noted there may be found every gradation of nebulous light4 ,the ,milky ,way is not so simple in its structure as might at first be thought1 but a clear and moonless night is required to bring out its details4 ,the nature of these details1 the structure of the galaxy1 its shape and extent1 the arrangement of its parts1 and their relation to stars and nebul in general1 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 heavens4 #bbj4 ,,distribution ,,of ,,the ,,stars4--,how far out into space do the stars extend8 ,are they limited or infinite in number8 ,do they form a system of mutually related parts1 or are they bunched promiscuously1 each for itself1 without reference to the others8 ,here is what has been well called the most important problem of stellar astronomy1 the acquisition of well-founded ideas about the distribution of the stars4 ,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 wrong1 and few of their speculations along this line are demonstrably true1 the theme itself is of such grandeur and permanent interest as to demand at least a brief consideration4 ,but before proceeding to its speculative side we need to collect facts upon which to build1 and these1 however inadequate1 are in the main simple and not far to seek4 ,parallaxes1 proper motions1 motions in the line of sight1 while pertinent to the problem of stellar distribution1 are of small avail1 since they are far too scanty in number and relate only to limited classes of stars1 usually the very bright ones or those nearest to the sun4 ,almost the sole available data are contained in the brightness of the stars and the way in which they seem scattered in the sky4 ,the most casual survey of the heavens is enough to show that the stars are not evenly sprinkled upon it4 ,the lucid stars are abundant in some regions1 few in others1 and the laborious star gauges1 actual counting of the stars in sample regions of the sky1 which have been made by the ,herschels1 ,celoria1 and others1 suffice to show that this lack of uniformity in distribution is even more markedly true of the telescopic stars4 ,the rate of increase in the number of stars from one magnitude to the next1 as shown in #ahg1 is proof of another kind of irregularity in their distribution4 ,it is not difficult to show1 mathematically1 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 sun1 then the stars of any particular magnitude ought to be four times as numerous as those of the next brighter magnitude--e4 g41 four times as many sixth-magnitude stars as there are fifth-magnitude ones4 ,but1 as we have already seen in #ahg1 by actual count there are only three times as many1 and from the discrepancy between these numbers1 an actual threefold increase instead of a fourfold one1 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 space4 #bba4 ,,the ,,stellar ,,system4--,but the arrangement of the stars is not altogether lawless and chaotic2 there are traces of order and system1 and among these the ,milky ,way is the dominant feature4 ,telescope and photographic plate alike show that it is made up of stars which1 although quite irregularly scattered along its course1 are on the average some twenty times as numerous in the galaxy as at its poles1 and which thin out as we recede from it on either side1 at first rapidly and then more slowly4 ,this tendency to cluster along the ,milky ,way is much more pronounced among the very faint telescopic stars than among the brighter ones1 for the lucid stars and the telescopic ones down to the tenth or eleventh magnitude1 while very plainly showing the clustering tendency1 are not more than three times as numerous in the galaxy as in the constellations most remote from it4 ,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 #ab on either side of the center line of the galaxy4 ,in addition to this general condensation of stars toward the ,milky ,way1 there are peculiarities in the distribution of certain classes of stars which are worth attention4 ,planetary nebul and new stars are seldom1 if ever1 found far from the ,milky ,way1 and stars with bright lines in their spectra especially affect this region of the sky4 ,stars with spectra of the first type--,sirian stars--are much more strongly condensed toward the ,milky ,way than are stars of the solar type1 and in consequence of this the ,milky ,way is peculiarly rich in light of short wave lengths4 ,resolvable star clusters are so much more numerous in the galaxy than elsewhere1 that its course across the sky would be plainly indicated by their grouping upon a map showing nothing but clusters of this kind4 ,on the other hand1 nebul as a class show a distinct aversion for the galaxy1 and are found most abundantly in those parts of the sky farthest from it1 much as if they represented raw material which was lacking along the ,milky ,way1 because already worked up to make the stars which are there so numerous4 #bbb4 ,,relation ,,of ,,the ,,sun ,,to ,,the ,,milky ,,way4--,the fact that the galaxy is a great circle of the sky1 but only of moderate width1 shows that it is a widely extended and comparatively thin stratum of stars within which the solar system lies1 a member of the galactic system1 and probably not very far from its center4 ,this position1 however1 is not to be looked upon as a permanent one1 since the sun's motion1 which lies nearly in the plane of the ,milky ,way1 is ceaselessly altering its relation to the center of that system1 and may ultimately carry us outside its limits4 ,the ,milky ,way itself is commonly thought to be a ring1 or series of rings1 like the coils of the great spiral nebula in ,andromeda1 and separated from us by a space far greater than the thickness of the ring itself4 ,note in ,figs4 #adi and #aej how the background is made up of bright and dark parts curiously interlaced1 and presenting much the appearance of a thin sheet of cloud through which we look to barren space beyond4 ,while1 mathematically1 this appearance can not be considered as proof that the galaxy is in fact a distant ring1 rather than a sheet of starry matter stretching continuously from the nearer stellar neighbors of the sun into the remotest depths of space1 nevertheless1 most students of the question hold it to be such a ring of stars1 which are relatively close together while its center is comparatively vacant1 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 placed4 #bbc4 ,,dimensions ,,of ,,the ,,galaxy4--,the dimensions of this stellar system are wholly unknown1 but there can be no doubt that it extends farther in the plane of the ,milky ,way than at right angles to that plane1 for stars of the fifteenth and sixteenth magnitudes are common in the galaxy1 and testify by their feeble light to their great distance from the earth1 while near the poles of the ,milky ,way there seem to be few stars fainter than the twelfth magnitude4 ,herschel1 with his telescope of #ah inches aperture1 could count in the ,milky ,way more than a dozen times as many stars per square degree as could ,celoria with a telescope of #d inches aperture2 but around the poles of the galaxy the two telescopes showed practically the same number of stars1 indicating that here even the smaller telescope reached to the limits of the stellar system4 ,very recently1 indeed1 the telescope with which ,fig4 #adj was photographed seems to have reached the farthest limit of the ,milky ,way1 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 them4 #bbd4 ,,beyond ,,the ,,milky ,,way4--,each additional step into the depths of space brings us into a region of which less is known1 and what lies beyond the ,milky ,way is largely a matter of conjecture4 ,we shrink from thinking it an infinite void1 endless emptiness1 and our intellectual sympathies go out to ,lambert's speculation of a universe filled with stellar systems1 of which ours1 bounded by the galaxy1 is only one4 ,there is1 indeed1 little direct evidence that other such systems exist1 but the ,andromeda nebula is not altogether unlike a galaxy with a central cloud of stars1 and in the southern hemisphere1 invisible in our latitudes1 are two remarkable stellar bodies like the ,milky ,way in appearance1 but cut off from all apparent connection with it1 much as we might expect to find independent stellar systems1 if such there be4 ,these two bodies are known as the ,magellanic clouds1 and individually bear the names of ,major and ,minor ,nubecula4 ,according to ,sir ,john ,herschel1 the ,nubecula ,major1 like the ,minor1 consists partly of large tracts and ill-defined patches of irresolvable nebula1 and of nebulosity in every stage of resolution up to perfectly resolved stars like the ,milky ,way1 as also of regular and irregular nebul 444 of globular clusters in every stage of resolvability1 and of clustering groups sufficiently insulated and condensed to come under the designation of clusters of stars4 ,its outlines are vague and somewhat uncertain1 but surely include an area of more than #dj square degrees--i4 e41 as much as the bowl of the ,big ,dipper--and within this area ,herschel counted several hundred nebul and clusters which far exceeds anything that is to be met with in any other region of the heavens4 ,although its excessive complexity of detail baffled ,herschel's attempts at artistic delineation1 it has yielded to the modern photographic processes1 which show the ,nubecula ,major to be an enormous spiral nebula made up of subordinate stars1 nebul1 and clusters1 as is the ,milky ,way4 ,compared with the ,andromeda nebula1 its greater angular extent suggests a smaller distance1 although for the present all efforts at determining the parallax of either seem hopeless4 ,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 sun1 a humble member of a great cluster of stars which is roughly globular in shape1 but flattened at the poles of the galaxy and completely encircled by its coils4 ,however plausible such a view may appear1 it is for the present1 at least1 pure hypothesis1 although vigorously advocated by ,easton1 who bases his argument upon the appearance of the galaxy itself4 #bbe4 ,,absorption ,,of ,,starlight4--,we have had abundant occasion to learn that at least within the confines of the solar system meteoric matter1 cosmic dust1 is profusely scattered1 and it appears not improbable that the same is true1 although in smaller degree1 in even the remoter parts of space4 ,in this case the light which comes from the farther stars over a path requiring many centuries to travel1 must be in some measure absorbed and enfeebled by the obstacles which it encounters on the way4 ,unless celestial space is transparent to an improbable degree the remoter stars do not show their true brightness2 there is a certain limit beyond which no star is able to send its light1 and beyond which the universe must be to us a blank4 ,a lighthouse throws into the fog its beams only to have them extinguished before a single mile is passed1 and though the celestial lights shine farther1 a limit to their reach is none the less certain if meteoric dust exists outside the solar system4 ,if there is such an absorption of light in space1 as seems plausible1 the universe may well be limitless and the number of stellar systems infinite1 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 them4 ,,chapter ,,xv ,,growth ,,and ,,decay #bbf4 ,,nature ,,of ,,the ,,problem4--,to use a common figure of speech1 the universe is alive4 ,we have found it filled with an activity that manifests itself not only in the motions of the heavenly bodies along their orbits1 but which extends to their minutest parts1 the molecules and atoms1 whose vibrations furnish the radiant energy given off by sun and stars4 ,some of these activities1 such as the motions of the heavenly bodies in their orbits1 seem fitted to be of endless duration2 while others1 like the radiation of light and heat1 are surely temporary1 and sooner or later must come to an end and be replaced by something different4 ,the study of things as they are thus leads inevitably to questions of what has been and what is to be4 ,a sound science should furnish some account of the universe of yesterday and to-morrow as well as of to-day1 and we need not shrink from such questions1 although answers to them must be vague and in great measure speculative4 ,the historian of ,america finds little difficulty with events of the nineteenth century or even the eighteenth1 but the sources of information about ,america in the fifteenth century are much less definite2 the tenth century presents almost a blank1 and the history of ,american mankind in the first century of the ,christian era is wholly unknown4 ,so1 as we attempt to look into the past or the future of the heavens1 we must expect to find the mists of obscurity grow denser with remoter periods until even the vaguest outlines of its development are lost1 and we are compelled to say1 beyond this lies the unknown4 ,our account of growth and decay in the universe1 therefore1 can not aspire to cover the whole duration of things1 but must be limited in its scope to certain chapters whose epochs lie near to the time in which we live1 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 us4 #bbg4 ,,logical ,,bases ,,and ,,limitations4--,the first of these bases is3 ,an adequate knowledge of the present universe4 ,our only hope of reading the past and future lies in an understanding of the present2 not necessarily a complete knowledge of it1 but one which is sound so far as it goes4 ,our position is like that of a detective who is called upon to unravel a mystery or crime1 and who must commence with the traces that have been left behind in its commission4 ,the foot print1 the blood stain1 the broken glass must be examined and compared1 and fashioned into a theory of how they came to be2 and as a wrong understanding of these elements is sure to vitiate the theories based upon them1 so a false science of the universe as it now is1 will surely give a false account of what it has been2 while a correct but incomplete knowledge of the present does not wholly bar an understanding of the past1 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 him4 ,the second basis of our inquiry is3 ,the assumed permanence of natural laws4 ,the law of gravitation certainly held true a century ago as well as a year ago1 and for aught we know to the contrary it may have been a law of the universe for untold millions of years2 but that it has prevailed for so long a time is a pure assumption1 although a necessary one for our purpose4 ,so with those other laws of mathematics and mechanics and physics and chemistry to which we must appeal2 if there was ever a time or place in which they did not hold true1 that time and place lie beyond the scope of our inquiry1 and are in the domain inaccessible to scientific research4 ,it is for this reason that science knows nothing and can know nothing of a creation or an end of the universe1 but considers only its orderly development within limited periods of time4 ,what kind of a past universe would1 under the operation of known laws1 develop into the present one1 is the question with which we have to deal1 and of it we may say with ,helmholtz3 ,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 laws4 ,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 different1 and1 having found these1 to trace their effects into both past and future4 ,any force1 however small1 or any process1 however slow1 may produce great results if it works always and ceaselessly in the same direction1 and it is in these processes1 whose trend is never reversed1 that we find a partial clew to both past and future4 #bbh4 ,,the ,,sun',s ,,development4--,the first of these to claim our attention is the shrinking of the sun's diameter which1 as we have seen in ,chapter ,x1 is the means by which the solar output of radiant energy is maintained from year to year4 ,its amount1 only a few feet per annum1 is far too small to be measured with any telescope2 but it is cumulative1 working century after century in the same direction1 and1 given time enough1 it will produce in the future1 and must have produced in the past1 enormous transformations in the sun's bulk and equally significant changes in its physical condition4 ,thus1 as we attempt to trace the sun's history into the past1 the farther back we go the greater shall we expect to find its diameter and the greater the space 7volume7 through which its molecules are spread4 ,by reason of this expansion its density must have been less then than now1 and by going far enough back we may even reach a time at which the density was comparable with what we find in the nebul of to-day4 ,if our ideas of the sun's present mechanism are sound1 then1 as a necessary consequence of these1 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 other4 ,as we have seen in #abf1 this condensation necessarily developed heat1 a part of which was radiated away as fast as produced1 while the remainder was stored up1 and served to raise the temperature of the sun to what we find it now4 ,at the present time this temperature is a chief obstacle to further shrinkage1 and so powerfully opposes the gravitative forces as to maintain nearly an equilibrium with them1 thus causing a very slow rate of further condensation4 ,but it is not probable that this was always so4 ,in the early stages of the sun's history1 when the temperature was low1 contraction of its bulk must have been more rapid1 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 orbit4 ,of course1 numerical precision is not to be expected in results of this kind1 but1 from a consideration of the greatest amount of heat that could be furnished by the shrinkage of a mass equal to that of the sun1 it seems that the period of this development is to be measured in tens of millions or possibly hundreds of millions of years1 but almost certainly does not reach a thousand millions4 #bbi4 ,,the ,,sun',s ,,future4--,the future duration of the sun as a source of radiant energy is surely to be measured in far smaller numbers than these4 ,its career as a dispenser of light and heat is much more than half spent1 for the shrinkage results in an ever-increasing density1 which makes its gaseous substance approximate more and more toward the behavior of a liquid or solid1 and we recall that these forms of matter can not by any further condensation restore the heat whose loss through radiation caused them to contract4 ,they may continue to shrink1 but their temperature must fall1 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 space1 and must congeal into a crust which1 although at first incandescent1 will speedily become dark and opaque1 cutting off the light of the central portions1 save as it may be rent from time to time by volcanic outbursts of the still incandescent mass beneath4 ,but such outbursts can be of short duration only1 and its final condition must be that of a dark body1 like the earth or moon1 no longer available as a source of radiant energy4 ,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 it1 as is now the case with ,jupiter and ,saturn4 ,it is believed that these planets were formerly incandescent1 and at the present time are in a state of development through which the earth has passed and toward which the sun is moving4 ,according to ,newcomb1 the future during which the sun can continue to furnish light and heat at its present rate is not likely to exceed #aj1jjj1jjj years4 ,this idea of the sun as a developing body whose present state is only temporary1 furnishes a clew to some of the vexing problems of solar physics4 ,thus the sun-spot period1 the distribution of the spots in latitude1 and the peculiar law of rotation of the sun in different latitudes1 may be1 and very probably are1 results not of anything now operating beneath its photosphere1 but of something which happened to it in the remote past--e4 g41 an unsymmetrical shrinkage or possibly a collision with some other body4 ,at sea the waves continue to toss long after the storm which produced them has disappeared1 and1 according to the mathematical researches of ,wilsing1 a profound agitation of the sun's mass might well require tens of thousands1 or even hundreds of thousands of years to subside1 and during this time its effects would be visible1 like the waves1 as phenomena for which the actual condition of things furnishes no apparent cause4 #bcj4 ,,the ,,nebular ,,hypothesis4--,the theory of the sun's progressive contraction as a necessary result of its radiation of energy is comparatively modern1 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 planet4 ,laplace1 whose speculations upon this subject have had a dominant influence during the nineteenth century1 has left1 in a popular treatise upon astronomy1 an admirable statement of the phenomena of planetary motion1 which suggest and lead up to the nebular theory of the sun's development1 and in presenting this theory we shall follow substantially his line of thought1 but with some freedom of translation and many omissions4 ,he says3 ,to trace out the primitive source of the planetary movements1 we have the following five phenomena3 7#a7 ,these movements all take place in the same direction and nearly in the same plane4 7#b7 ,the movements of the satellites are in the same direction as those of the planets4 7#c7 ,the rotations of the planets and the sun are in the same direction as the orbital motions and nearly in the same plane4 7#d7 ,planets and satellites alike have nearly circular orbits4 7#e7 ,the orbits of comets are wholly unlike these by reason of their great eccentricities and inclinations to the ecliptic4 ,that these coincidences should be purely the result of chance seemed to ,laplace incredible1 and1 seeking a cause for them1 he continues3 ,whatever its nature may be1 since it has produced or controlled the motions of the planets1 it must have reached out to all these bodies1 and1 in view of the prodigious distances which separate them1 the cause can have been nothing else than a fluid of great extent which must have enveloped the sun like an atmosphere4 ,a consideration of the planetary motions leads us to think that 444 the sun's atmosphere formerly extended far beyond the orbits of all the planets and has shrunk by degrees to its present dimensions4 ,this is not very different from the idea developed in #bbh from a consideration of the sun's radiant energy2 but in ,laplace's day the possibility of generating the sun's heat by contraction of its bulk was unknown1 and he was compelled to assume a very high temperature for the primitive nebulous sun1 while we now know that this is unnecessary4 ,whether the primitive nebula was hot or cold the shrinkage would take place in much the same way1 and would finally result in a star or sun of very high temperature1 but its development would be slower if it were hot in the beginning than if it were cold4 ,but again ,laplace3 ,how did the sun's atmosphere determine the rotations and revolutions of planets and satellites8 ,if these bodies had been deeply immersed in this atmosphere its resistance to their motion would have made them fall into the sun1 and we may therefore conjecture that the planets were formed1 one by one1 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 equator4 ,here he proceeds to show by an appeal to dynamical principles that something of this kind must happen1 and that the matter sloughed off by the nebula in the form of a ring1 perhaps comparable to the rings of ,saturn or the asteroid zone1 would ultimately condense into a planet1 which in its turn might shrink and cast off rings to produce satellites4 ,illustration3 ,,pierre ,,simon ,,laplace 7#agdi-ahbg74 ,planets and satellites would then all have similar motions1 as noted at the beginning of this section1 since in every case this motion is an inheritance from a common source1 the rotation of the primitive nebula about its own axis4 ,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 rapid1 this rotation should take place in less time than is required for the orbital revolution of any of the bodies which have been cast off1 and this holds true for the sun as compared with the planets4 #bca4 ,,objections ,,to ,,the ,,nebular ,,hypothesis4--,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 itself1 but1 as we have seen in ,chapter ,,xi1 this ring is made up of a great number of independent particles which move at different rates of speed1 and comparing1 through ,kepler's ,third ,law1 the motion of the inner edge of the ring with the known periodic time of the satellites1 we may find that these particles must rotate about ,saturn more rapidly than the planet turns upon its axis4 ,similarly the inner satellite of ,mars completes its revolution in about one third of a ,martian day1 and we find in cases like this grounds for objection to the nebular theory4 ,compare also ,laplace's argument with the peculiar rotations of ,uranus1 ,neptune1 and their satellites 7,chapter ,,xi74 ,do these fortify or weaken his case8 ,despite these objections and others equally serious that have been raised1 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 system2 but at some points--e4 g41 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 theory4 ,one proposed modification1 much discussed in recent years1 consists in substituting for the primitive gaseous nebula imagined by ,laplace1 a very diffuse cloud of meteoric matter which in the course of its development would become transformed into the gaseous state by rising temperature4 ,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 planets4 ,chamberlin and ,moulton1 who have recently given much attention to this subject1 in dissenting from some of ,laplace's views1 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 mass1 high momentum1 and irregular distribution to the outer part1 and high mass1 low momentum1 and sphericity to the central part1 and they suggest a possible oblique collision of a small nebula with the outer parts of a large one4 #bcb4 ,,bode',s ,,law4--,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 7 #acd74 ,this law1 stated in mathematical form1 makes a geometrical series1 and similar geometrical series apply to the distances of the satellites of ,jupiter and ,saturn from these planets4 ,now1 ,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 law1 save that it involves the amount of time that has elapsed since the beginning of the shrinking process4 ,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--i4 e41 that ,mars is as much older than the earth as the earth is older than ,venus1 etc4 ,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 planets4 ,but too much stress should not be placed upon this conclusion4 ,so long as the manner in which the planets came into being continues an open question1 conclusions about their time of birth must remain of doubtful validity4 #bcc4 ,,tidal ,,friction ,,between ,,earth ,,and ,,moon4--,an important addition to theories of development within the solar system has been worked out by ,prof4 ,g4 ,h4 ,darwin1 who1 starting with certain very simple assumptions as to the present condition of things in earth and moon1 derives from these1 by a strict process of mathematical reasoning1 far-reaching conclusions of great interest and importance4 ,the key to these conclusions lies in recognition of the fact that through the influence of the tides 7 #db7 there is now in progress and has been in progress for a very long time1 a gradual transfer of motion 7moment of momentum7 from the earth to the moon4 ,the earth's motion of rotation is being slowly destroyed by the friction of the tides1 as the motion of a bicycle is destroyed by the friction of a brake1 and1 in consequence of this slowing down1 the moon is pushed farther and farther away from the earth1 so that it now moves in a larger orbit than it had some millions of years ago4 ,fig4 #bd has been used to illustrate the action of the moon in raising tides upon the earth1 but in accordance with the third law of motion 7 #cf7 this action must be accompanied by an equal and contrary reaction whose nature may readily be seen from the same figure4 ,the moon moves about its orbit from west to east and the earth rotates about its axis in the same direction1 as shown by the curved arrow in the figure4 ,the tidal wave1 ,i1 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 figure4 ,it is true that the tidal wave at ,i pulls back and tends to neutralize the effect of the wave at ,i1 but on the whole the tidal wave nearer the moon has the stronger influence1 and the moon on the whole moves a very little faster1 and by virtue of this added impetus draws continually a little farther away from the earth than it would if there were no tides4 #bcd4 ,,consequences ,,of ,,tidal ,,friction ,,upon ,,the ,,earth4--,this process of moving the moon away from the earth is a cumulative one1 going on century after century1 and with reference to it the moon's orbit must be described not as a circle or ellipse1 or any other curve which returns into itself1 but as a spiral1 like the balance spring of a watch1 each of whose coils is a little larger than the preceding one1 although this excess is1 to be sure1 very small1 because the tides themselves are small and the tidal influence feeble when compared with the whole attraction of the earth for the moon4 ,but1 given time enough1 even this small force may accomplish great results1 and something like #ajj1jjj1jjj 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 position4 ,for millions of years to come1 if moon and earth endure so long1 the distance between them must go on increasing1 although at an ever slower rate1 since the farther away the moon goes the smaller will be the tides and the slower the working out of their results4 ,on the other hand1 when the moon was nearer the earth than now1 tidal influences must have been greater and their effects more rapidly produced than at the present time1 particularly if1 as seems probable1 at some past epoch the earth was hot and plastic like ,jupiter and ,saturn4 ,then1 instead of tides in the water of the sea1 such as we now have1 the whole substance of the earth would respond to the moon's attraction in bodily tides of semi-fluid matter not only higher1 but with greater internal friction of their molecules one upon another1 and correspondingly greater effect in checking the earth's rotation4 ,but1 whether the tide be a bodily one or confined to the waters of the sea1 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 wheel1 slowing down its motion1 and producing thus a longer day as well as a longer month on account of the moon's increased distance4 ,slowing down the earth's rotation is the direct action of the moon upon the earth4 ,pushing the moon away is the form in which the earth's equal and contrary reaction manifests itself4 #bce4 ,,consequences ,,of ,,tidal ,,friction ,,upon ,,the ,,moon4--,when the moon was plastic the earth must have raised in it a bodily tide manifold greater than the lunar tides upon the earth1 and1 as we have seen in ,chapter ,,ix1 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 earth4 ,these two processes1 slowing down the rotation and pushing away the disturbing body1 are inseparable--one requires the other2 and it is worth noting in this connection that when for any reason the tide ceases to flow1 and the tidal wave takes up a permanent position1 as it has in the moon 7 #ii71 its work is ended1 for when there is no motion of the wave there can be no friction to further reduce the rate of rotation of the one body1 and no reaction to that friction to push away the other4 ,but this permanent and stationary tidal wave in the moon1 or elsewhere1 means that the satellite presents always the same face toward its planet1 moving once about its orbit in the time required for one revolution upon its axis1 and the tide raised by the moon upon the earth tends to produce here the result long since achieved in our satellite1 to make our day and month of equal length1 and to make the earth turn always the same side toward the moon4 ,but the moon's tidal force is small compared with that of the earth1 and has a vastly greater momentum to overcome1 so that its work upon the earth is not yet complete4 ,according to ,thomson and ,tait1 the moon must be pushed off another hundred thousand miles1 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 length1 and the moon thereby permanently hidden from one hemisphere of the earth4 #bcf4 ,,the ,,earth-,,moon ,,system4--,retracing into the past the course of development of the earth and moon1 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 now1 but it has not been found possible to trace out the mode of their separation from one body into two1 as is supposed in the nebular theory4 ,in the earliest part of their history accessible to mathematical analysis they are distinct bodies at some considerable distance from each other1 with the earth rotating about an axis more nearly perpendicular to the moon's orbit and to the ecliptic than is now the case4 ,starting from such a condition1 the lunar tides1 according to ,darwin1 have been instrumental in tipping the earth's rotation axis into its present oblique position1 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 month4 #ccg4 ,,tidal ,,friction ,,upon ,,the ,,planets4--,the satellites of the outer planets are equally subject to influences of this kind1 and there appears to be independent evidence that some of them1 at least1 turn always the same face toward their respective planets1 indicating that the work of tidal friction has here been accomplished4 ,we saw in ,chapter ,,xi that it is at present an open question whether the inner planets1 ,venus and ,mercury1 do not always turn the same face toward the sun1 their day and year being of equal length4 ,in addition to the direct observational evidence upon this point1 ,schiaparelli has sought to show by an appeal to tidal theory that such is probably the case1 at least for ,mercury1 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 satellite1 ,japetus4 ,the same line of reasoning would show that every satellite in the solar system1 save possibly the newly discovered ninth satellite of ,saturn1 must1 as a consequence of tidal friction1 turn always the same face toward its planet4 #bch4 ,,the ,,solar ,,tide4--,the sun also raises tides in the earth1 and their influence must be similar in character to that of the lunar tides1 checking the rotation of the earth and thrusting earth and sun apart1 although quantitatively these effects are small compared with those of the moon4 ,they must1 however1 continue so long as the solar tide lasts1 possibly until the day and year are made of equal length--i4 e41 they may continue long after the lunar tidal influence has ceased to push earth and moon apart4 ,should this be the case1 a curious inverse effect will be produced4 ,the day being then longer than the month1 the moon will again raise a tide in the earth which will run around it from west to east1 opposite to the course of the present tide1 thus tending to accelerate the earth's rotation1 and by its reaction to bring the moon back toward the earth again1 and ultimately to fall upon it4 ,we may note that an effect of this kind must be in progress now between ,mars and its inner satellite1 ,phobos1 whose time of orbital revolution is only one third of a ,martian day4 ,it seems probable that this satellite is in the last stages of its existence as an independent body1 and must ultimately fall into ,mars4 #bci4 ,,roche',s ,,limit4--,in looking forward to such a catastrophe1 however1 due regard must be paid to a dynamical principle of a different character4 ,the moon can never be precipitated upon the earth entire1 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 side4 ,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 satellite1 if it turns always the same face toward the planet1 can not come without being broken into fragments4 ,if we represent the radius of the planet by r1 and the quotient obtained by dividing the density of the planet by the density of the satellite by q1 then ,roche's limit #b4dd r q#a_/c4 ,thus in the case of earth and moon we find from the densities given in #ie1 q #a4fe1 and with r #c1ifc miles we obtain #aa1djj 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 sides4 ,we must observe1 however1 that ,roche's limit takes no account of molecular forces1 the adhesion of one molecule to another1 by virtue of which a stick or stone resists fracture1 but is concerned only with the gravitative forces by which the molecules are attracted toward the moon's center and toward the earth4 ,within a stone or rock of moderate size these gravitative forces are insignificant1 and cohesion is the chief factor in preserving its integrity1 but in a large body like the moon1 the case is just reversed1 cohesion plays a small part and gravitation a large one in holding the body together4 ,we may conclude1 therefore1 that at a proper distance these forces are capable of breaking up the moon1 or any other large body1 into fragments of a size such that molecular cohesion instead of gravitation is the chief agent in preserving them from further disintegration4 #bdj4 ,,saturn',s ,,rings4--,saturn's rings are of peculiar interest in this connection4 ,the outer edge of the ring system lies just inside of ,roche's limit for this planet1 and we have already seen that the rings are composed of small fragments independent of each other4 ,whatever may have been the process by which the nine satellites of ,saturn came into existence1 we have in ,roche's limit the explanation why the material of the ring was not worked up into satellites2 the forces exerted by ,saturn would tear into pieces any considerable satellite thus formed and equally would prevent the formation of one from raw material4 ,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 limit1 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 feature4 ,the drawings of ,saturn made two centuries ago agree among themselves in representing the rings as larger than they now appear1 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 planet4 ,but the direct evidence of such a progress that can be drawn from present data is too scanty to justify positive conclusions in the matter4 ,on the other hand1 ,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 limit1 and that the very small inner satellites of ,saturn may have been thus formed at the expense of the ring4 ,the inner satellite of ,mars is very close to ,roche's limit for that planet1 and1 as we have seen above1 must be approaching still nearer to the danger line4 #bda4 ,,the ,,moon',s ,,development4--,the fine series of photographs of the moon obtained within the last few years at ,paris1 have been used by the astronomers of that observatory for a minute study of the lunar formations1 much as geologists study the surface of the earth to determine something about the manner in which it was formed4 ,their conclusions are1 in general1 that at some past time the moon was a hot and fluid body which1 as it cooled and condensed1 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 matter1 whose latest and feeblest stages produced the lunar craters1 while traces of the earlier ones1 connected with a general settling of the crust1 although nearly obliterated1 are still preserved in certain large but vague features of the lunar topography1 such as the distribution of the seas1 etc4 ,they find also in certain markings of the surface what they consider convincing evidence of the existence in past times of a lunar atmosphere4 ,but this seems doubtful1 since the force of gravity at the moon's surface is so small that an atmosphere similar to that of the earth1 even though placed upon the moon1 could not permanently endure1 but would be lost by the gradual escape of its molecules into the surrounding space4 ,the molecules of a gas are quite independent one of another1 and are in a state of ceaseless agitation1 each one darting to and fro1 colliding with its neighbors or with whatever else opposes its forward motion1 and traveling with velocities which1 on the average1 amount to a good many hundreds of feet per second1 although in the case of any individual molecule they may be much less or much greater than the average value1 an occasional molecule having possibly a velocity several times as great as the average4 ,in the upper regions of our own atmosphere1 if one of these swiftly moving particles of oxygen or nitrogen were headed away from the earth with a velocity of seven miles per second1 the whole attractive power of the earth would be insufficient to check its motion1 and it would therefore1 unless stopped by some collision1 escape from the earth and return no more4 ,but1 since this velocity of seven miles per second is more than thirty times as great as the average velocity of the molecules of air1 it must be very seldom indeed that one is found to move so swiftly1 and the loss of the earth's atmosphere by leakage of this sort is insignificant4 ,but upon the moon1 or any other body where the force of gravity is small1 conditions are quite different1 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 atmosphere4 ,this velocity1 only five times the average1 would be frequently attained1 particularly in former times when the moon's temperature was high1 for then the average velocity of all the molecules would be considerably increased1 and the amount of leakage might become1 and probably would become1 a serious matter1 steadily depleting the moon's atmosphere and leading finally to its present state of exhaustion4 ,it is possible that the moon may at one time have had an atmosphere1 but if so it could have been only a temporary possession1 and the same line of reasoning may be applied to the asteroids and to most of the satellites of the solar system1 and also1 though in less degree1 to the smaller planets1 ,mercury and ,mars4 #bdb4 ,,stellar ,,development4--,we have already considered in this chapter the line of development followed by one star1 the sun1 and treating this as a typical case1 it is commonly believed that the life history of a star1 in so far as it lies within our reach1 begins with a condition in which its matter is widely diffused1 and presumably at a low temperature4 ,contracting in bulk under the influence of its own gravitative forces1 the star's temperature rises to a maximum1 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 cases1 such as are noted in ,chapter ,,xiii4 ,the most systematic development of this idea is due to ,lockyer1 who looks upon all the celestial bodies--sun1 moon and planets1 stars1 nebul1 and comets--as being only collections of meteoric matter in different stages of development1 and who has sought by means of their spectra to classify these bodies and to determine their stage of advancement4 ,while the fundamental ideas involved in this meteoritic hypothesis are not seriously controverted1 the detailed application of its principles is open to more question1 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 statements4 ,illustration3 ,,fig4 #aea4--,types of stellar spectra substantially according to ,,secchi4 #bdc4 ,,stellar ,,spectra4--,thus the types of stellar spectra shown in ,fig4 #aea are supposed to illustrate successive stages in the development of an average star4 ,type ,i corresponds to the period in which its temperature is near the maximum2 ,type ,,ii belongs to a later stage in which the temperature has commenced to fall2 and ,type ,,iii to the period immediately preceding extinction4 ,while human life1 or even the duration of the human race1 is too short to permit a single star to be followed through all the stages of its career1 an adequate picture of that development might be obtained by examining many stars1 each at a different stage of progress1 and1 following this idea1 numerous subdivisions of the types of stellar spectra shown in ,fig4 #aea have been proposed in order to represent with more detail the process of stellar growth and decay2 but for the most part these subdivisions and their interpretation are accepted by astronomers with much reserve4 ,it is significant that there are comparatively few stars with spectra of ,type ,,iii1 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 life4 ,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 life4 ,the period in which the sun belongs1 represented by ,type ,,ii1 probably has a duration intermediate between the others4 ,since most of the variable stars1 save those of the ,algol class1 have spectra of the third type1 we conclude that variability1 with its associated ruddy color and great atmospheric absorption of light1 is a sign of old age and approaching extinction4 ,the ,algol or eclipse variables1 on the other hand1 having spectra of the first type1 are comparatively young stars1 and1 as we shall see a little later1 the shortness of their light periods in some measure confirms this conclusion drawn from their spectra4 ,we have noted in #aif that the sun's near neighbors are prevailingly stars with spectra of the second type1 while the ,milky ,way is mainly composed of first-type stars1 and from this we may now conclude that in our particular part of the entire celestial space the stars are1 as a rule1 somewhat further developed than is the case elsewhere4 #bdd4 ,,double ,,stars4--,the double stars present special problems of development growing out of the effects of tidal friction1 which must operate in them much as it does between earth and moon1 tending steadily to increase the distance between the components of such a star4 ,so1 too1 in such a system as is shown in ,fig4 #acb1 gravity must tend to make each component of the double star shrink to smaller dimensions1 and this shrinkage must result in faster rotation and increased tidal friction1 which in turn must push the components apart1 so that in view of the small density and close proximity of those particular stars we may fairly regard a star like b ,lyr as in the early stages of its career and destined with increasing age to lose its variability of light1 since the eclipses which now take place must cease with increasing distance between the components unless the orbit is turned exactly edgewise toward the earth4 ,close proximity and the resulting shortness of periodic time in a double star seem1 therefore1 to be evidence of its youth1 and since this shortness of periodic time is characteristic of both ,algol variables and spectroscopic binaries as a class1 we may set them down as being1 upon the whole1 stars in the early stages of their career4 ,on the other hand1 it is generally true that the larger the orbit1 and the greater the periodic time in the orbit1 the farther is the star advanced in its development4 ,in his theory of tidal friction1 ,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 axis1 the effect of the tides is to increase the eccentricity of the orbit1 and1 following this indication1 ,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 eccentric1 so that we have in the shape of such orbits a new index of stellar development2 the more eccentric the orbit1 the farther advanced are the stars4 ,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 supposed1 and which1 being found to hold true1 confirms in some degree the criteria of stellar age which are furnished by the theory of tidal friction4 #bde4 ,,nebul4--,the nebular hypothesis of ,laplace has inclined astronomers to look upon nebul in general as material destined to be worked up into stars1 but which is now in a very crude and undeveloped stage4 ,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 stars4 ,but even among nebul there are to be found very different stages of development4 ,the irregular nebula1 shapeless and void like that of ,orion2 the spiral1 ring1 and planetary nebul and the star cluster1 clearly differ in amount of progress toward their final goal4 ,but it is by no means sure that these several types are different stages in one line of development2 for example1 the primitive nebula which grows into a spiral may never become a ring or planetary nebula1 and vice versa4 ,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 ,fig4 #abb4 #bdf4 ,,classification4--,considering the heavenly bodies with respect to their stage of development1 and arranging them in due order1 we should probably find lowest down in the scale of progress the irregular nebul of chaotic appearance such as that represented in ,fig4 #adf4 ,above these in point of development stand the spiral1 ring1 and planetary nebul1 although the exact sequence in which they should be arranged remains a matter of doubt4 ,still higher up in the scale are star clusters whose individual members1 as well as isolated stars1 are to be classified by means of their spectra1 as shown in ,fig4 #aea1 where the order of development of each star is probably from ,type ,i1 through ,,ii1 into ,,iii and beyond1 to extinction of its light and the cutting off of most of its radiant energy4 ,jupiter and ,saturn are to be regarded as stars which have recently entered this dark stage4 ,the earth is further developed than these1 but it is not so far along as are ,mars and ,mercury2 while the moon is to be looked upon as the most advanced heavenly body accessible to our research1 having reached a state of decrepitude which may almost be called death--a stage typical of that toward which all the others are moving4 ,meteors and comets are to be regarded as fragments of celestial matter1 chips1 too small to achieve by themselves much progress along the normal lines of development1 but destined sooner or later1 by collision with some larger body1 to share thenceforth in its fortunes4 #bdg4 ,,stability ,,of ,,the ,,universe4--,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 bodies1 but could never bring about collisions among them or greatly alter their existing orbits4 ,but in the proof of this great theorem two influences were neglected1 either of which is fatal to its validity4 ,one of these--tidal friction--as we have already seen1 tends to wreck the systems of satellites1 and the same effect must be produced upon the planets by any other influence which tends to impede their orbital motion4 ,it is the inertia of the planet in its forward movement that balances the sun's attraction1 and any diminution of the planet's velocity will give this attraction the upper hand and must ultimately precipitate the planet into the sun4 ,the meteoric matter with which the earth comes ceaselessly into collision must have just this influence1 although its effects are very small1 and something of the same kind may come from the medium which transmits radiant energy through the interstellar spaces4 ,it seems incredible that the luminiferous ether1 which is supposed to pervade all space1 should present absolutely no resistance to the motion of stars and planets rushing through it with velocities which in many cases exceed #ej1jjj miles per hour4 ,if there is a resistance to this motion1 however small1 we may extend to the whole visible universe the words of ,thomson and ,tait1 who say in their great ,treatise on ,natural ,philosophy1 ,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 move2 but1 whatever it may be1 there can be but one ultimate result for such a system as that of the sun and planets1 if continuing long enough under existing laws and not disturbed by meeting with other moving masses in space4 ,that result is the falling together of all into one mass1 which1 although rotating for a time1 must in the end come to rest relatively to the surrounding medium4 ,compare with this the words of a great poet who in ,the ,tempest puts into the mouth of ,prospero the lines3 ,the cloud-capp'd towers1 the gorgeous palaces1 ,the solemn temples1 the great globe itself1 ,yea1 all which it inherit1 shall dissolve2 ,and1 like this insubstantial pageant faded1 ,leave not a rack behind4 #bdh4 ,,the ,,future4--,in spite of statements like these1 it lies beyond the scope of scientific research to affirm that the visible order of things will ever come to naught1 and the outcome of present tendencies1 as sketched above1 may be profoundly modified in ages to come1 by influences of which we are now ignorant4 ,we have already noted that the farther our speculation extends into either past or future1 the more insecure are its conclusions1 and the remoter consequences of present laws are to be accepted with a corresponding reserve4 ,but the one great fact which stands out clear in this connection is that of change4 ,the old concept of a universe created in finished form and destined so to abide until its final dissolution1 has passed away from scientific thought and is replaced by the idea of slow development4 ,a universe which is ever becoming something else and is never finished1 as shadowed forth by ,goethe in the lines3 ,thus work ,i at the roaring loom of ,time1 ,and weave for ,deity a living robe sublime4 ,,appendix ,,the ,,greek ,,alphabet ,the ,greek letters are so much used by astronomers in connection with the names of the stars1 and for other purposes1 that the ,greek alphabet is printed below--not necessarily to be learned1 but for convenient reference3 ,greek4 ,name4 ,english4 ,a a ,alpha a ,b b ,beta b ,g g ,gamma g ,d d ,delta d ,e e or e ,epsilon 7e ,z z ,zeta z ,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 7o ,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 ,omega o ,,popular ,,literature ,,of ,,astronomy ,the following brief bibliography1 while making no pretense at completeness1 may serve as a useful guide to supplementary reading3 ,general ,treatises ,,young4 ,general ,astronomy4 ,an admirable general survey of the entire field4 ,,newcomb4 ,popular ,astronomy4 ,the second edition of a ,german translation of this work by ,engelmann and ,vogel is especially valuable4 ,,ball4 ,story of the ,heavens4 ,somewhat easier reading than either of the preceding4 ,,chambers4 ,descriptive ,astronomy4 ,an elaborate but elementary work in three volumes4 ,,langley4 ,the ,new ,astronomy4 ,treats mainly of the physical condition of the celestial bodies4 ,,proctor and ,,ranyard4 ,old and ,new ,astronomy4 ,special ,treatises ,,proctor4 ,the ,moon4 ,a general treatment of the subject4 ,,nasmyth and ,,carpenter4 ,the ,moon4 ,an admirably illustrated but expensive work dealing mainly with the topography and physical conditions of the moon4 ,there is a cheaper and very good edition in ,german4 ,,young4 ,the ,sun4 ,international ,scientific ,series4 ,the most recent and authoritative treatise on this subject4 ,,proctor4 ,other ,worlds than ,ours4 ,an account of planets1 comets1 etc4 ,,newton4 ,meteor4 ,encyclopdia ,britannica4 ,,airy4 ,gravitation4 ,a non-mathematical exposition of the laws of planetary motion4 ,,stokes4 ,on ,light as a ,means of ,investigation4 ,burnett ,lectures4 ,,ii4 ,the basis of spectrum analysis4 ,,schellen4 ,spectrum ,analysis4 ,,thomson 7,sir ,w41 ,lord ,,kelvin71 ,popular ,lectures1 etc4 ,lectures on the ,tides1 ,the ,sun's ,heat1 etc4 ,,ball4 ,time and ,tide4 ,an exposition of the researches of ,g4 ,h4 ,darwin upon tidal friction4 ,,gore4 ,the ,visible ,universe4 ,deals with a class of problems inadequately treated in most popular astronomies4 ,,darwin4 ,the ,tides4 ,an admirable elementary exposition4 ,,clerke4 ,the ,system of the ,stars4 ,stellar astronomy4 ,,newcomb4 ,chapters on the ,stars1 in ,popular ,science ,monthly for #aijj4 ,,clerke4 ,history of ,astronomy during the ,nineteenth ,century4 ,an admirable work4 ,,wolf4 ,geschichte der ,astronomie4 ,mnchen1 #ahgg4 ,an excellent ,german work4 ,a ,,list ,,of ,,stars ,,for ,,time ,,observations ,see #bj4 ---------------------------------------- ------------------------ ,,name4 ,magnitude4 ,right ,ascension4 ,declination4 ---------------------------------------- ------------------------ h4 m4 b ,ceti #b #j #ch4f - #ah4e ,ceti #c #a #c4f - #aj4g a ,ceti #c #b #eg4a #c4g g ,eridani #c #c #ec4d - #ac4h ,aldebaran #a #d #cj4b #af4c ,rigel #j #e #i4g - #h4c k ,orionis #b #e #dc4j - #i4g b ,canis ,majoris #b #f #ah4c - #ag4i ,sirius -#a #f #dj4g - #af4f ,procyon #j #g #cd4a #e4e a ,hydr #b #i #bb4g - #h4b ,regulus #a #aj #c4j #ab4e n ,hydr #c #aj #dd4g - #ae4g e ,corvi #c #ab #e4j - #bb4a g ,corvi #c #ab #aj4g - #ag4j ,spica #a #ac #ai4i - #aj4f z ,virginis #c #ac #bi4f - #j4a a ,libr #c #ad #de4c - #ae4f b ,libr #c #ae #aa4f - #i4j ,antares #a #af #bc4c - #bf4b a ,ophiuchi #b #ag #cj4c #ab4f e ,sagittarii #b #ah #ag4e - #cd4d d ,aquil #c #ai #bj4e #b4i ,altair #a #ai #de4i #h4f b ,aquarii #c #ba #bf4c - #f4j a ,aquarii #c #bb #j4f - #j4h ,fomalhaut #a #bb #eb4a - #cj4b ---------------------------------------- ------------------------ ,,index ,the references are to section numbers4 ,absorption of starlight1 #bbe4 ,absorption spectra1 #hg4 ,accelerating force1 #ce4 ,adjustment of observations1 #b4 ,albedo of moon1 #ig4 of ,venus1 #adh4 ,algol1 #bje4 ,altitudes1 #d1 #ba4 ,andromeda nebula1 #bad4 ,angles1 measurement of1 #b4 ,angular diameter1 #g4 ,annular eclipse1 #fd4 ,asteroids1 #aef4 ,atmosphere of the earth1 #di4 of the moon1 #ajc4 of ,jupiter1 #aci4 of ,mars1 #aec4 ,aurora1 #ea4 ,azimuth1 #e1 #ba4 ,biela's comet1 #aha4 ,bode's law1 #acd1 #bcb4 ,bredichin's theory of comet tails1 #ahj4 ,calendar1 ,o4 ,s4 and ,n4 ,s41 #fa4 ,capture of comets and meteors1 #agf4 ,canals of ,mars1 #aed4 ,celestial mechanics1 #cb4 ,changes upon the moon1 #ajh4 ,chemical constitution of sun1 #aaf4 of stars1 #baj4 ,chromosphere1 the sun's1 #abd4 ,chronology1 #ei4 ,classification of stars1 #bab4 ,clocks and watches1 #gd4 sidereal clock1 #ab4 ,collisions with comets1 #ahc4 ,colors of stars1 #bji4 ,comets1 general characteristics1 #aeh-afd4 development of1 #agi1 #aha4 groups1 #agg4 orbits1 #afa4 periodic1 #agf4 spectra1 #ahb4 tails1 #ahj4 ,comets and meteors1 relation of1 #age4 ,conic sections1 #ch4 ,constellations1 #ahd4 ,corona1 the sun's1 #abc4 ,craters1 lunar1 #aje4 ,dark stars1 #bja4 ,day1 #eb1 #fb4 ,declination1 #ba4 ,development of comet1 #agi4 of moon1 #bda4 of nebul1 #bde4 of stars1 #bdb1 #bdd4 of sun1 #bbh4 of universe1 #bbf4 ,distribution of stars and nebul1 #bbj4 ,diurnal motion1 #aj1 #ae4 ,doppler principle1 #hi4 ,double nebul1 #bae4 ,double stars1 #aih4 development of1 #bdd4 ,driving clock1 #hj4 ,earth1 atmosphere1 #dh4 mass1 #de4 size and shape1 #dd4 warming of the earth1 #dg4 ,eclipses1 nature of1 #fc4 annular eclipse1 #fd4 eclipse limits1 #fh4 eclipse maps1 #gj1 #ga4 number of1 in a year1 #fi4 partial eclipse1 #fd4 prediction of1 #gj1 #ga4 recurrence of1 #gb4 shadow cone1 #fd1 #ff4 total eclipse1 #fd4 uses of1 #gc4 ,eclipses of ,jupiter's satellites1 #ada4 ,eclipse theory of variable stars1 #bje4 ,ecliptic1 #bf4 obliquity of1 #be4 ,ellipse1 #cc4 ,epochs for planetary motion1 #cj4 ,energy1 radiant1 #ge4 condensation of1 #gf4 ,epicycle1 #cb4 ,equation of time1 #ec4 ,equator1 #af1 #ba4 ,equatorial mounting1 #hj4 ,equinoxes1 #be4 ,ether1 #ge4 ,evening star1 #ca4 ,facul1 #abb4 ,falling bodies1 law of1 #ce4 ,finding the stars1 #ad4 ,fraunhofer lines1 #hg4 ,galaxy1 #bai4 ,geography of the sky1 #af4 ,graphical representation1 #f4 ,grating1 diffraction1 #hd4 ,gravitation1 law of1 #cg4 ,harvest moon1 #ic4 ,heat of the sun1 #aah1 #abf4 ,helmholtz1 contraction theory of the sun1 #abf1 #bbh4 ,horizon1 #d1 #ba4 ,hour angle1 #ba4 ,hour circle1 #ba4 ,hyperbola1 #ch4 ,japetus1 satellite of ,saturn1 #ade4 ,jupiter1 #acf4 atmosphere1 #aci4 belts1 #acg4 invisible from fixed stars1 #aig4 orbit of1 #bi4 physical condition1 #aci4 rotation and flattening1 #ach4 satellites1 #adj4 surface markings1 #acg4 ,kepler's laws1 #cc1 #aaa4 ,latitude1 determination of1 #ah4 ,leap year1 #fa4 ,lenses1 #gg4 ,leonid meteor shower1 #agb4 perturbations of1 #agd4 ,librations of moon1 #ih4 ,life upon the planets1 #aeg4 ,light curves1 #bje4 ,light1 nature of1 #ge4 ,light year1 #aij4 ,limits of eclipses1 #fh4 ,longitude1 #ef4 determination of1 #eh4 ,lunation1 #fj4 ,magnifying power of telescope1 #gi4 ,magnitude1 stellar1 #i1 #ahf4 ,mars1 atmosphere1 temperature1 #aej4 canals1 #aed4 orbit1 #cj4 polar caps1 #aeb4 rotation1 #aea4 satellites1 #aee4 surface markings1 #aej4 ,mass1 determination of1 #cg4 of comets1 #afd4 of double stars1 #bjj4 of moon1 #id4 of planets1 #dj1 #acc4 ,measurements1 accurate1 #a4 ,mercury1 #adi4 motion of its perihelion1 #dc4 orbit of1 #cj4 ,meridian1 #ai1 #ba4 ,meteors1 nature of1 #afe1 #afi4 number of1 #afg4 velocity1 #agj4 ,meteors and comets1 relation of1 #age4 ,meteor showers1 radiant1 #aga4 ,leonids1 capture of1 #agb1 #agc4 perturbations1 #agd4 ,milky ,way1 #bai4 ,mira1 o ,ceti1 #bjd4 ,mirrors1 #gg4 ,month1 #fj4 ,moon1 #ia4 albedo1 #ig4 atmosphere1 #ajc4 changes in1 #ajh4 density1 surface gravity1 #ie4 development of1 #bda4 harvest moon1 #ic4 influence upon the earth1 #aji1 #bcc4 librations1 #ih4 map of1 #aja4 mass and size1 #id4 motion1 #bd1 #ib4 mountains and craters1 #ajd4 phases1 #ia1 #ib4 physical condition1 #ajj1 #ajg4 ,month1 #fj4 ,morning star1 #ca4 ,motion in line of sight1 #hi1 #aic4 ,multiple stars1 #bjb4 ,names of stars1 #h4 ,nebul1 #bad4 density1 #bag4 development of1 #bde4 motion1 #bah4 spectra1 #baf4 types and classes of1 #bae4 ,nebular hypothesis1 #bcj4 objections to1 #bca4 ,neptune1 #adf4 discovery of1 #da4 ,newton's laws of motion1 #cd4 law of gravitation1 #cg1 #dc4 ,nodes1 #ci4 relation to eclipses1 #fg1 #ga4 ,nucleus1 of comet1 #afj4 ,objective1 of telescope1 #gh4 ,obliquity of ecliptic1 #be4 ,observations1 of stars1 #aj4 ,occultation of stars1 #ajc4 ,orbits1 of comets1 #afa4 of double stars1 #aii4 of moon1 #ib4 of planets1 #bh4 ,orion nebula1 #bae4 ,parabola1 #ce1 #ch1 #afa4 ,parabolic velocity1 #ch4 ,parallax1 #aad1 #ahh4 ,penumbra1 #fd1 #aba4 ,perihelion1 #ch4 ,periodic comets1 #agf4 ,personal equation1 #hb4 ,perturbations1 #ci4 of meteors1 #agd4 ,phases1 of the moon1 #ia1 #ib4 ,photography1 #ha4 of stars1 #ac4 ,photosphere1 of sun1 #aba4 ,planets1 #bf1 #acc4 distances from the sun1 #acd4 how to find1 #bi4 mass1 density1 size1 #acc4 motion of1 #bg1 #ch4 periodic times of1 #cj4 ,planetary nebul1 #bae4 ,pleiades1 #af1 #bae4 ,plumb-line apparatus1 #aa1 #ah4 ,poles1 #ba4 ,precession1 #df4 ,prisms1 #hd4 ,problem of three bodies1 #ci4 ,prominences1 solar1 #abe4 ,proper motions1 #aia4 ,protractor1 #b4 ,ptolemaic system1 #cb4 ,radiant energy1 #ge4 ,radiant1 of meteor shower1 #aga4 ,radius victor1 #cc4 ,reference lines and circles1 #ag4 ,refraction1 #ej4 ,right ascension1 #af1 #bj1 #ba4 ,roche's limit1 #bci4 ,rotation1 of earth1 #ee4 of ,mars1 #aea4 of moon1 #ii4 of ,jupiter1 #ach4 of ,saturn1 #add4 of sun1 #abj1 #acb4 ,saros1 #gb4 ,satellites1 of ,jupiter1 #acf1 #adj4 of ,mars1 #aee4 of ,saturn1 #ade4 ,saturn1 #adb4 ball of1 #add4 orbit1 #bi4 rings1 #adb4 rotation1 #add4 satellites1 #ade4 ,seasons1 on the earth1 #dg4 on ,mars1 #aea4 ,shadow cone1 #fd1 #ff4 ,sidereal time1 #bj1 #ed4 ,shooting stars1 #aeh4 7,see ,meteor47 ,spectroscope1 #hd4 ,spectroscopic binaries1 #bjc4 ,spectrum1 #hd1 #hg4 of comets1 #ahb4 of nebul1 #baf4 of stars1 #baa4 types of1 #hh4 ,spectrum analysis1 #he4 ,spiral nebul1 #bae4 ,standard time1 #eg4 ,stars1 #h1 #ahd4 classes of1 #bab4 clusters1 #bac4 colors1 #bji4 dark stars1 #bja4 development of1 #bdb4 distances from the sun1 #ahh1 #aif4 distribution of1 #bbj4 double stars1 #aih1 #bjc4 drift1 #aid4 magnitudes1 #i1 #aif4 number of1 #ahe4 spectra1 #baa4 temporary1 #bjh4 variable1 #bjd4 ,starlight1 absorption of1 #bbe4 ,star maps1 construction of1 #bc4 ,stellar system1 extent of1 #bbc4 ,sun's apparent motion1 #be4 real motion1 #aie4 ,sun1 #aaj4 chemical composition1 #aaf4 chromosphere1 #abd4 corona1 #abc4 distance from the earth1 #aaa4 facul1 #aai1 #abb4 gaseous constitution1 #abg4 heat of1 #aag4 mechanism of1 #abf4 physical properties1 #aae-abj4 prominences1 #abe4 rotation1 #abj1 #acb4 surface of1 #aai4 temperature1 #aah4 ,sun spots1 #aai1 #aba4 period1 #abi1 #aca4 zones1 #acj4 ,telescopes1 #gh4 equatorial mounting for1 #hj4 magnifying power of1 #gi4 ,temperature of ,jupiter1 #aci4 of ,mars1 #aeb4 of ,mercury1 #adi4 of moon1 #ajg4 of sun1 #aah4 ,temporary stars1 #bjh4 ,terminator1 #ia4 ,tenth meter1 #ge4 ,tidal friction1 #bcc-bch4 ,tides1 #db4 ,time1 sidereal1 #bj1 #ed4 solar1 #eb4 determination of1 #bj4 equation of1 #ec4 standard1 #eg4 ,triangulation1 #c4 ,trifid nebula1 #bae4 ,twilight1 #ea4 ,twinkling1 of stars1 #dh4 ,universe1 development of1 #bbf4 stability of1 #bdg4 ,uranus1 #adf4 ,variable stars1 #bjd4 ,velocity1 its relation to orbital motion1 #ch4 ,venus1 #adh4 orbit of1 #cj4 ,vernal equinox1 #ba1 #be4 ,vertical circle1 #ba4 ,wave front1 #gf4 ,wave lengths1 #ge1 #hf4 ,year1 #be4 leap year1 #fa4 sidereal year1 #ei4 tropical year1 #fj4 ,zenith1 #ba4 ,zodiac1 #bf4 ,zodiacal light1 #afh4 ,,the ,,end