,illustration3 ,the ,lunar 8,crater0 ,copernicus ,photographed from ,nasmyth and ,carpenter's plaster-of-paris model of the moon4 ,in this model the topography of the moon is faithfully represented as seen with powerful telescopes4 ---------------------------------------- -------------------------------- ,astronomy in a ,nutshell ,the ,chief ,facts and ,principles ,explained in ,popular ,language for the ,general ,reader and for ,schools ,by ,garrett ,p4 ,serviss ,with #dg ,illustrations ,g4 ,p4 ,putnam's ,sons ,new ,york and ,london ,the ,knickerbocker ,press #aiab ---------------------------------------- -------------------------------- ,,copyright1 #aiab ,,by ,,garrett ,p4 ,,serviss ,the ,knickerbocker ,press1 ,new ,york ---------------------------------------- -------------------------------- ,,preface ,how many thousands of educated people1 trained in the best schools1 or even graduates of the great universities1 have made the confession3 8,i never got a grip on astronomy in my student days4 ,they didn't make it either plain or interesting to me2 and now ,i am sorry for it40 ,the purpose of the writer of this book is to supply the need of such persons1 either in school1 or at home1 after school-days are ended4 ,he does not address himself to special students of the subject--although they1 too1 may find the book useful at the beginning--but to that vast1 intelligent public for whom astronomy is1 more or less1 a 8mystical midland10 from which1 occasionally1 fascinating news comes to their ears4 ,the ordinary text-book is too overladen with technical details1 and too summary in its treatment of the general subject1 to catch and hold the attention of those who have no special preliminary interest in astronomy4 ,the aim here is to tell all that really needs to be told1 and no more1 and to put it as perspicuously1 compactly1 and interestingly1 as possible4 ,for that reason the book is called a 8nutshell40 99 99 99 99 99 ,the author has been sparing in the use of diagrams1 because he believes that1 in many cases1 they have been over-pressed4 ,there is a tendency to try to represent everything to the eye4 ,this is well to a certain extent1 but there is danger that by pursuing this method too far the power of mental comprehension will be weakened4 ,after all1 it is only by an intelligent use of the imagination that progress can be made in such a science as astronomy4 ,the reader is urged to make a serious effort to understand what is said in the text1 and to picture it in his mind's eye1 before referring to the diagrams4 ,after he has thus presented the subject to his imagination1 he may refer to the illustrations1 and correct with their aid any misapprehension4 ,for this reason the cuts1 with their descriptions1 have been made independent of the regular text1 although they are placed in their proper connections throughout the book4 ,g4 ,p4 ,s4 ,april1 #aiab4 ---------------------------------------- -------------------------------- ,,contents ,,part ,i--,,the ,,celestial ,,sphere4 ,,pages ,definition of ,astronomy--,fundamental ,law of the #c-fd ,stars--,relations of the ,earth to the ,universe--,ordinary ,appearance of the ,sky--,the ,horizon1 the ,zenith1 and the ,meridian--,locating the ,stars--,altitude and ,azimuth--,circular or ,angular ,measure--,altitude ,circles and ,vertical ,circles--,the ,apparent ,motion of the ,heavens--,the ,north ,star and ,phenomena ,connected with it--,revolution of the ,stars round the ,pole--,locating the ,stars on the ,celestial ,sphere--,astronomical ,equivalents of ,latitude and ,longitude--,parallels of ,declination and ,hour ,circles--8,the ,greenwich of the ,sky0--,effects ,produced by ,changing the ,observer's ,place on the ,earth--,the ,parallel ,sphere1 the ,right ,sphere1 and the ,oblique ,sphere--,the ,astronomical ,clock--,the ,ecliptic--,apparent ,annual ,revolution of the ,sun round the ,earth--,inclination of the ,ecliptic to the ,equator3 its ,cause and its ,effects--,the ,equinoxes--,importance of the ,vernal ,equinox--,the ,equinoctial ,colure--,the ,solstices--,poles of the ,ecliptic--,celestial ,latitude and ,longitude--,the ,zodiac--,the ,precession of the ,equinoxes3 its ,cause and ,effects--,revolution of the ,celestial ,poles--,past and ,future ,pole ,stars ,,part ,,ii--,,the ,,earth4 ,,pages ,nature1 ,shape1 and ,size of the ,earth--,the ,polar #fg-abc ,compression and ,equatorial ,protuberance1 and their ,cause--,the ,attraction of ,gravitation--,the ,mass of the ,earth3 how ,found--,how the ,earth ,holds the ,moon1 and the ,sun the ,planets--,the ,tides--,how the ,moon and ,sun ,produce ,tides--,spring ,tides and ,neap ,tides--,the ,atmosphere--,the ,law and ,effects of ,refraction--,dip of the ,horizon--,the ,aberration of ,light--,time3 how ,measured--,sidereal1 ,apparent ,solar1 and ,mean ,solar ,time--,the ,clock and the ,sun--,day and ,night--,where the ,days ,begin--,the ,seasons--,effects of the ,varying ,declination of the ,sun--,polar and ,equatorial ,day and ,night--,the ,tropics and the ,polar ,circles--,inequality of ,length of the ,seasons--,when the ,seasons in the ,two ,hemispheres will be ,reversed--,the ,calendar1 the ,year1 and the ,month--,reformations of the ,calendar--,different ,measures of the ,month ,,part ,,iii--,,the ,,solar ,,system4 ,,pages ,the ,sun--,distance1 ,size1 and ,condition of the #abg-bae ,sun--,temperature of the ,sun--,solar ,heat on the ,earth1 and its ,mechanical ,equivalent--,peculiar ,rotation of the ,sun--,sun-spots1 their ,appearance and ,probable ,cause--,facul--,the ,photosphere--,solar ,prominences--,explosive ,prominences--,the ,solar ,corona--,parallax1 and the ,measure of ,distances--,spectroscopic ,analysis--,how the ,elements in the ,sun ,reveal their ,presence--,list of the ,principal ,solar ,elements--,the ,moon--,origin of the ,moon--,appearance of its ,surface--,gravity on the ,moon--,the ,phases of the ,moon--,causes of the ,absence of a ,lunar ,atmosphere--,eclipses--,how the ,moon ,causes ,eclipses of the ,sun--,the ,laws ,governing ,eclipses--,the ,shadow during a ,solar ,eclipse--,eclipses of the ,moon--,number of ,eclipses in a ,year--,the ,saros--,the ,planets--,kepler's ,laws of ,planetary ,motion--,mercury--,venus--,mars1 and its ,so-called ,canals--,theories about ,mars--,jupiter1 its ,belts and its ,satellites--,the ,great ,red ,spot0--,saturn1 its ,rings and its ,satellites--,composition of the ,rings--,uranus and ,neptune--,comets1 and the ,laws of their ,motion--,composition of ,comets--,the ,pressure of ,light and its ,connection with ,comets' ,tails--,breaking up of ,comets--,meteors and their ,relations to ,comets--,the ,november ,meteors and ,other ,celebrated ,showers--,meteorites or ,bolides which ,fall upon the ,earth--,the ,question of their ,origin ,,part ,,iv--,,the ,,fixed ,,stars4 ,,pages ,division of the ,stars into ,magnitudes--,division of #bai-beg the ,stars according to their ,spectra--,stars ,larger and ,smaller than the ,sun--,the ,distances of the ,stars--,variable ,stars--,double and ,binary ,stars--,spectroscopic ,binaries and how they are ,discovered--,proper ,motions of the ,stars--,number of the ,stars--,new1 or ,temporary ,stars--,the ,milky ,way--,the ,nebul--,the ,two ,kinds of ,nebul--,spiral ,nebul--,the ,nebular ,hypothesis--,applications of ,photography to ,stars and ,nebul--,the ,constellations--,how to ,learn the ,constellations--,their ,antiquity--,description of the ,principal ,constellations ,visible from the ,northern ,hemisphere at ,various ,times of the ,year ,,index #bei ---------------------------------------- -------------------------------- ,,illustrations ,,page ,,the ,,lunar 8,,crater0 ,,copernicus ,frontispiece ,,photograph ,,of ,,south ,,polar #h ,,region ,,of ,,the ,,moon ,,the ,,moon ,,near ,,the 8,,crater0 #bj ,,tycho ,,drawing ,,of ,,jupiter #bh ,,drawing ,,of ,,jupiter #bh ,,jupiter #ch ,,saturn #df ,,saturn #df ,,the ,,milky ,,way ,,about ,,chi ,,cygni #eh ,,the ,,great ,,southern #fd ,,star-,,cluster ,,in ,,centauri ,,photograph ,,of ,a ,,group ,,of #gf ,,sun-,,spots ,,polar ,,streamers ,,of ,,the ,,sun1 #hi ,,eclipse ,,of #ahhi ,,solar ,,corona ,,at ,,the ,,eclipse ,,of #hi #ahga ,,morehouse',s ,,comet1 ,,october #ae1 #if #aijh ,,morehouse',s ,,comet1 ,,november #if #ae1 #aijh ,,head ,,of ,,the ,,great ,,comet ,,of #aje #ahfa ,,halley',s ,,comet1 ,,may #e1 #aiaj #aje ,,the ,,six-,,tailed ,,comet ,,of #agdd #aab ,,spiral ,,nebula ,,in ,,ursa ,,major 7,m #abd #aja7 ,,the ,,whirlpool ,,nebula ,,in ,,canes #abd ,,venatici ,,tress ,,nebula 7,n4 ,g4 ,c4 #fiib7 #acb ,,in ,,cygnus ,,the ,,great ,,andromeda ,,nebula #adj ,,spiral ,,nebula ,,in ,,cepheus 7,h4 #aed ,,iv4 #gf7 ,,nebulous ,,groundwork ,,in ,,taurus #aed ,,nebula ,,in ,,sagittarius 7,m4 #h7 #afb ,,the ,,great ,,nebula ,,in ,,orion #ahj ,,photographs ,,of ,,mars #bjj ,,schiaparrelli',s ,,chart ,,of #bbj ,,martian 8,,canals0 ,,illustrations ,,in ,,the ,,text ,,the ,,rational ,,and ,,the ,,sensible #ab ,,horizon ,,altitude ,,and ,,azimuth #ad ,,right ,,ascension ,,and #ce ,,declination ,,the ,,ecliptic ,,and ,,celestial #ea ,,latitude ,,and ,,longitude ,,how ,,the ,,earth ,,controls ,,the #ge ,,moon ,,the ,,tidal ,,force ,,of ,,the ,,moon #gi ,,refraction #he ,,dip ,,of ,,the ,,horizon #hg ,,sidereal ,,and ,,solar ,,time #ic ,,the ,,change ,,of ,,day #aja ,,the ,,seasons #ajg ,,parallax ,,of ,,the ,,moon #aci ,,parallax ,,of ,,the ,,sun ,,from #ada ,,transit ,,of ,,venus ,,spectrum ,,analysis #adg ,,the ,,phases ,,of ,,the ,,moon #afj ,,orbits ,,of ,,mars ,,and ,,the ,,earth #ahc ,,ellipse1 ,,parabola1 ,,and #bjc ,,hyperbola ,,the ,,north ,,circumpolar ,,stars #bdd ,,key ,,to ,,north ,,circumpolar ,,stars #bde ---------------------------------------- -------------------------------- ,,part ,i4 ,,the ,,celestial ,,sphere4 ---------------------------------------- -------------------------------- ,,part ,i4 ,,the ,,celestial ,,sphere4 #a4 ,definition of ,astronomy4 ,astronomy has to do with the earth1 sun1 moon1 planets1 comets1 meteors1 stars1 and nebul2 in other words1 with the universe1 or 8the aggregate of existing things40 ,it is the most ancient of all sciences4 ,the derivation of the name from two ,greek words1 aster1 8star10 and nomos1 8law10 indicates its nature4 ,it deals with the law of the stars--the word 8star0 being understood1 in its widest signification1 as including every heavenly body of whatever kind4 ,the earth itself is such a body4 ,since we happen to live on the earth1 it becomes our standpoint in space1 from which we look out at the others4 ,but1 if we lived on some other planet1 we would see the earth as a distant body in the sky1 just as we now see ,jupiter or ,mars4 ,astronomy teaches us that everything in the universe1 from the sun and the moon to the most remote star or the most extraordinary nebula1 is related to the earth4 ,all are made of similar elementary substances and all obey similar physical laws4 ,the same substance which is a solid upon the earth may be a gas or a vapour in the sun1 but that does not alter its essential nature4 ,iron appears in the sun in the form of a hot vapour1 but fundamentally it is the same substance which exists on the earth as a hard1 tough1 and heavy metal4 ,its different states depend upon the temperature to which it is subjected4 ,the earth is a cool body1 while the sun is an intensely hot one2 consequently iron is solid on the earth and vaporous in the sun1 just as in winter water is solid ice on the surface of a pond and steamy vapour over the boiler in the kitchen4 ,even on the earth we can make iron liquid in a blast furnace1 and with the still greater temperatures obtainable in a laboratory we can turn it into vapour1 thus reducing it to something like the state in which it regularly exists in the sun4 ,this fact1 that the entire universe is made up of similar substances1 differing only in state according to the local circumstances affecting them1 is the greatest thing that astronomy has to tell us4 ,it may be regarded as the fundamental law of the stars4 #b4 ,the ,situation of the ,earth in the ,heavens4 ,one of the greatest triumphs of human intelligence is the discovery of the real place which the earth occupies in the universe4 ,this discovery has been made in spite of the most deceptive appearances4 ,if we accepted the sole evidence of our eyes1 as men once did1 we could only conclude that the earth was the centre of the universe4 ,in the daytime we see the sun apparently moving through the sky from east to west1 as if it were travelling in a circle round the earth1 overhead by day and underfoot at night4 ,in the night-time1 we see the stars apparently travelling round the earth in the same way as the sun4 ,the fact is1 that all of them are virtually motionless with regard to the earth1 and their apparent movements through the sky are produced by the earth's rotation on its axis4 ,the earth turns round on itself once every twenty-four hours1 like a spinning ball4 ,imagine a fly on a rotating school globe2 the whole room would appear to the fly to be revolving round it as the heavens appear to revolve round the earth4 ,it would have to be a very intelligent insect to correct the deceptive evidence of its eyes4 ,the actual facts1 revealed by many centuries of observation and reasoning1 are that the earth is a rotating globe1 turning once on its axis every twenty-four hours and revolving once round the sun every three hundred and sixty-five days4 ,the sun is also a globe1 #a1cjj1jjj times larger than the earth1 but so hot that it glows with intense brilliance1 while the substances of which it consists are kept in a gaseous or vaporous state4 ,besides the earth there are seven other principal globes1 or planets1 which revolve round the sun1 at various distances and in various periods1 and1 in addition to these1 there are hundreds of smaller bodies1 called asteroids or small planets4 ,there are also many singular bodies called comets1 and swarms of still smaller ones called meteors1 which likewise revolve round the sun4 ,the earth and the other bodies of which we have just spoken are not only cooler than the sun1 but most of them are in a solid state and do not shine with light of their own4 ,the sun furnishes both heat and light to the smaller and cooler bodies revolving round it4 ,in fact1 the sun is simply a star1 resembling the thousands of other stars which surround us in the sky1 and its apparent superiority to them is due only to the fact that it is relatively near-by while they are far away4 ,it is probable that all1 or most1 of the stars also have planets1 comets1 and meteors revolving round them1 but invisible owing to their immense distance4 ,the 8paths0 in which the earth and the other planets and bodies travel in their revolutions round the sun are called their orbits4 ,these orbits are all elliptical in shape1 but those of the earth and the other large planets are not very different from circles4 ,some of the asteroids1 and all of the comets1 however1 travel in elliptical orbits of considerable eccentricity1 i4 e41 which differ markedly from circles4 ,the orbit of the earth differs so slightly from a circle that the eccentricity amounts to only about one-sixtieth4 ,the distance of the earth from the sun being1 on the average1 #ic1jjj1jjj miles1 the eccentricity of its orbit causes it to approach to within about #ia1ejj1jjj miles in winter 7of the northern hemisphere7 and to recede to about #id1ejj1jjj miles in summer4 ,the point in its orbit where the earth is nearest the sun is called perihelion1 and the point where it is farthest from the sun1 aphelion4 ,the earth is at perihelion about ,jan4 #a1 and at aphelion about ,july #d4 ,now1 in order to make a general picture in the mind of the earth's situation1 let the reader suppose himself to be placed out in space as far from the sun as from the other stars4 ,then1 if he could see it1 he would observe the earth as a little speck1 shining like a mote in the sunlight1 and circling in its orbit close around the sun4 ,the universe would appear to him to be somewhat like an immense spherical room filled with scattered electric-light bulbs1 suspended above1 below1 and all around him1 each of these bulbs representing a sun1 and if there were minute insects flying around each light1 these insects would represent the planets belonging to the various suns4 ,one of the glowing bulbs among the multitude would stand for our sun1 and one of the insects circling round it would be the earth4 ,illustration3 ,photograph of the ,south ,polar ,region of the ,moon ,made by ,g4 ,w4 ,ritchey with the forty-inch refractor of the ,yerkes ,observatory4 ,we have already remarked that the rotation of the earth on its axis causes all the other heavenly bodies to appear to revolve round it once every twenty-four hours1 and we must now add that the earth's revolution round the sun causes the same bodies to appear to make another1 slower revolution round it once every year4 ,this introduces a complication of apparent motions which it is the business of astronomy to deal with1 and which we shall endeavour to explain4 #c4 ,the ,horizon1 the ,zenith1 and the ,meridian4 ,first1 let us consider what is the ordinary appearance of the sky4 ,when we go out of doors on a clear night we see the heavens in the shape of a great dome arched above us and filled with stars4 ,what we thus see is one half of the spherical shell of the heavens which surrounds us on all sides1 the earth being apparently placed at its centre4 ,the other half is concealed from our sight behind1 or below1 the earth4 ,this spherical shell1 of which only one half is visible to us at a time1 is called the celestial sphere4 ,now1 the surface of the earth seems to us 7for this is another of the deceptive appearances which astronomy has to correct7 to be a vast flat expanse1 whose level is broken by hills and mountains1 and the visible half of the celestial sphere seems to bend down on all sides and to rest upon the earth in a circle which extends all around us4 ,this circle1 where the heavens and the earth appear to meet1 is called the horizon4 ,as we ordinarily see it1 the horizon appears irregular and broken on account of the unevenness of the earth's surface1 but if we are at sea1 or in the midst of a great level prairie1 the horizon appears as a smooth circle1 everywhere equally distant from the eye4 ,this circle is called the sensible horizon4 ,but there is another1 ideal1 horizon1 used in astronomy1 which is called the rational horizon4 ,it is of the utmost importance that we should clearly understand what is meant by the rational horizon1 and for this purpose we must consider another fact concerning the dome of the sky4 ,we now turn our attention to the centre of that dome1 which1 of course1 is the point directly overhead4 ,this point1 which is of primary importance1 is called the zenith4 ,the position of the zenith is indicated by the direction of a plumb-line4 ,if we imagine a plumb-line to be suspended from the centre of the sky overhead1 and to pass into the earth at our feet1 it would run through the centre of the earth1 and1 if it were continued onward in the same direction1 it would1 after emerging from the other side of the earth1 reach the centre of the invisible half of the sky-dome at a point diametrically opposite to the zenith4 ,this central point of the invisible half of the celestial sphere1 lying under our feet1 is called the nadir4 ,keeping in mind the definitions of zenith and nadir that have just been given1 we are in a position to understand what the rational horizon is4 ,it is a great circle whose plane cuts through the centre of the earth1 and which is situated exactly half-way between the zenith and the nadir4 ,this plane is necessarily perpendicular1 or at right angles1 to the plumb-line joining the zenith and the nadir4 ,in other words1 the rational horizon divides the celestial sphere into two precisely equal halves1 an upper and a lower half4 ,in a hilly or mountainous country the sensible or visible horizon differs widely from the rational1 or true horizon1 but at sea the two are nearly identical4 ,this arises from the fact1 that the earth is so excessively small in comparison with the distances of most of the heavenly bodies that it may be regarded as a mere point in the midst of the celestial sphere4 ,illustration3 ,fig4 #a4 ,the ,rational and the ,sensible ,horizon4 ,let ,c be the earth's centre1 ,o the place of the observer1 and ,h ,d the rational horizon passing through the centre of the earth4 ,for an object situated near the earth1 as at ,a1 the sensible horizon makes a large angle with the rational horizon4 ,if the object is farther away1 as at ,b1 the angle becomes less2 and still less1 again1 if the object is at ,d4 ,it is evident that if the object be immensely distant1 like a star1 the sensible horizon ,o ,s will be practically parallel with the rational horizon1 and will blend with it1 because the radius1 or semi-diameter1 of the earth1 ,o ,c1 is virtually nothing in comparison with the distance of the star4 ,besides the horizon and the zenith there is one other thing of fundamental importance which we must learn about before proceeding further1--the meridian4 ,the meridian is an imaginary line1 or semicircle1 beginning at the north point on the horizon1 running up through the zenith1 and then curving down to the south point4 ,it thus divides the visible sky into two exactly equal halves1 an eastern and a western half4 ,in the ordinary affairs of life we usually think only of that part of the meridian which extends from the zenith to the south point on the horizon 7which is sometimes called the noon-line0 because the sun crosses it at noon71 but in astronomy the northern half of the meridian is as important as the southern4 #d4 ,altitude and ,azimuth4 ,now1 suppose that we wish to indicate the location of a star1 or other object1 in the sky4 ,to do so1 we must have some fixed basis of reference1 and such a basis is furnished by the horizon and the zenith4 ,if we tried to describe the position of a star1 the most natural thing would be1 first1 to estimate1 or measure1 its height above the horizon1 and1 second1 to indicate the direction in which it was situated with regard to the points of the compass4 ,these two measures1 if they were accurately made1 would enable another person to find the star in the sky4 ,and this is precisely what is done in astronomy4 ,the height above the horizon is called altitude1 and the bearing with reference to the points of the compass is called azimuth4 ,together these are known as co-ordinates4 ,in order to systematise this method of measuring the location of a star1 the astronomer uses imaginary circles drawn on the celestial sphere4 ,the horizon and the meridian are two of these circles4 ,in addition to these1 other imaginary circles are drawn parallel to the horizon and becoming smaller and smaller until the uppermost one may run close round the zenith1 which is the common centre of the entire set4 ,these are called altitude circles1 because each one throughout its whole extent is at an unvarying height1 or altitude1 above the horizon4 ,such circles may be drawn anywhere we please1 so as to pass through any chosen star or stars4 ,if two stars in different quarters of the sky are found to lie on the same circle1 then we know that both have the same altitude4 ,illustration3 ,fig4 #b4 ,altitude and ,azimuth4 ,c is the place of the observer4 ,n ,c ,s1 a north-and-south line drawn in the plane of the horizon4 ,e ,c ,w1 an east-and-west line in the plane of the horizon4 ,n ,e ,s ,w1 the circle of the horizon4 ,z1 the observer's zenith4 ,n ,z ,s1 vertically above ,n ,c ,s1 the meridian4 ,e ,z ,w1 the prime vertical4 ,z s s1 part of a vertical circle drawn through the star s4 ,the circle through s parallel to the horizon is an altitude circle4 ,the angle s ,c s1 or the arc s s1 represents the star's altitude4 ,the angle s ,c ,z1 or the arc ,z s1 is the star's zenith distance4 ,to find the azimuth1 the angular distance round the horizon from ,s 7#j71 through ,w1 ,n1 ,e1 to the point where the star's vertical circle meets the horizon1 is measured4 ,in this case it is #cae4 ,but if we measured it eastward from the south point it would be--#de4 ,then another set of circles is drawn perpendicular to the horizon1 and all intersecting at the zenith and the nadir4 ,these are called vertical circles1 from the fact that they are upright to the horizon4 ,that one of the vertical circles which cuts the horizon at the north-and-south points coincides with the meridian1 which we have already described4 ,the vertical circle at right angles to the meridian is called the prime vertical4 ,it cuts the horizon at the east and west points1 dividing the visible sky into a northern and a southern half4 ,like the altitude circles1 vertical circles may be drawn anywhere we please so as to pass through a star in any quarter of the sky--but the meridian and the prime vertical are fixed4 ,with the two sets of circles that have just been described1 it is possible to indicate accurately the location of any heavenly body1 at any particular moment4 ,its altitude is ascertained by measuring1 along the vertical circle passing through it1 its distance from the horizon4 7,sometimes it is convenient to measure1 instead of the altitude of a star1 its zenith distance1 which is also reckoned on the vertical circle47 ,to ascertain the azimuth1 we must first choose a point of beginning on the horizon4 ,any of the cardinal points1 i4e41 east1 west1 north1 or south1 may be employed for this purpose1 but in astronomy it is customary to use only the south point1 and to carry the measure westward all round the circle of the horizon1 and so back to the point of beginning in the south4 ,this involves circular1 or degree1 measure1 to which a few words must now be devoted4 ,every circle1 no matter how large or how small1 is divided into #cfj equal parts1 called degrees1 usually indicated by the sign 772 each degree is subdivided into #fj equal parts called minutes1 indicated by the sign 772 and each minute is subdivided into #fj equal parts called seconds1 indicated by the sign 774 ,thus there are #cfj1 or #ba1fjj1 or #a1bif1jjj in every complete circle4 ,the actual length of a degree in inches1 yards1 or miles1 depends upon the size of the circle1 but no circle ever has more than #cfj1 and a degree of any particular circle is precisely equal to any other degree of that same circle4 ,thus1 if a circle is #cfj miles in circumference1 every one of its degrees will be one mile long4 ,in mathematics1 a degree usually means not a distance measured along the circumference of a circle1 but an angle formed at the centre of the circle between two lines called radii 7radius in the singular71 which lines1 where they intersect the circumference1 are separated by a distance equal to one #cfjth of the entire circle4 ,but1 for ordinary purposes1 it is simpler to think of a degree as an arc equal in length to one #cfjth of the circle4 ,now1 since the horizon1 and the other imaginary lines drawn in the sky1 are all circles1 it is evident that the principle of circular measure may be applied to them1 and indeed must be so applied in order that they shall be of use to us in indicating the position of a star4 ,to return1 then1 to the measurement of the azimuth of a star4 ,since the south point is the place of beginning1 we mark it #j1 and we divide the circle of the horizon into #cfj1 counting round westward4 ,suppose we see a star somewhere in the south-western quarter of the sky2 then the point where the vertical circle passing through that star intersects the horizon will indicate its azimuth4 ,suppose that this point is found to be #be west of south2 then #be will be the star's azimuth4 ,suppose it is #ij2 then the azimuth is #ij1 and the star must be on the prime vertical in the west1 because west1 being one quarter of the way round the horizon from south1 is #ij in angular distance from the south point4 ,suppose the azimuth is #ahj2 then the star must be on the meridian north of the zenith1 because north is exactly half-way1 or #ahj round the horizon from the south point4 ,suppose the azimuth is #bgj2 then the star must be on the prime vertical in the east1 because east is #bgj1 or three quarters of the way round from the south point4 ,if the star is on the meridian in the south its azimuth may be called either #j or #cfj1 because on any graduated circle the mark indicating #cfj coincides in position with #j1 that being at the same time the point of beginning and the point of ending4 ,the same system of angular measure is applied in ascertaining a star's altitude4 ,since the horizon is half-way between the zenith and the nadir it must be just #ij from either4 ,if a star is in the zenith1 then its altitude is #ij1 and if it is below the zenith its altitude lies somewhere between #j and #ij4 ,in any case it cannot be less than #j nor more than #ij4 ,having measured the altitude and the azimuth we have the two co-ordinates which are needed to indicate accurately the place of a star in the sky4 ,but1 as we shall see in a moment1 other co-ordinates beside altitude and azimuth are needed for a complete description of the places of the stars on the celestial sphere4 ,owing to the apparent revolution of the heavens round the earth1 the altitudes and azimuths of the celestial bodies are continually changing4 ,we shall now study the causes of these changes4 #e4 ,the ,apparent ,motion of the ,heavens4 ,we have likened the earth to a rotating school globe4 ,as such a globe turns1 any particular spot on it is presented in succession toward the various sides of the room4 ,in precisely the same way any spot on the earth is turned by its rotation successively toward various parts of the surrounding sky4 ,to understand the effect of this1 a little patient watching of the actual heavens will be required1 but this has the charm of all out-of-doors observation of nature1 and it will be found of fascinating interest as the facts begin to unfold themselves4 ,illustration3 ,the ,moon ,near the 8,crater0 ,tycho ,photographed at the ,lick ,observatory under the direction of ,e4 ,s4 ,holden4 ,tycho is the regular oval depression a little below the centre of the view4 ,the vast depression1 #adj miles across1 with a row of smaller craters within1 below the centre of the view at the top1 is ,clavius4 ,the photograph was made when sundown was approaching on that part of the moon4 ,observe the jagged line of advancing night lying across the rugged surface on the western 7left-hand7 side4 ,it is best to begin by finding the ,north ,star1 or pole star4 ,if you are living not far from latitude #dj north1 which is the median latitude of the ,united ,states1 you must1 after determining as closely as you can the situation of the north point1 look upward along the meridian in the north until your eyes are directed to a point about #dj above the horizon4 ,forty degrees is somewhat less than half-way from the horizon to the zenith1 which1 as we have seen1 are separated by an arc of #ij4 ,at that point you will notice a lone star of what astronomers call the second magnitude4 ,this is the celebrated ,north ,star4 ,it is the most useful to man of all the stars1 except the sun1 and it differs from all the others in a way presently to be explained4 ,but first it is essential that you should make no mistake in identifying it4 ,there are certain landmarks in the sky which make such identification certain4 ,in the first place1 it is always so close to the meridian in the north1 that by naked-eye observation you would probably never suspect that it was not exactly on the meridian4 ,then1 its altitude is always equal1 or very nearly equal1 to the latitude of the place where you happen to be on the earth1 so that if you know your latitude you know how high to carry your eye above the northern horizon4 ,if you are in latitude #ej1 the star will be at #ej altitude1 and if your latitude is #cj1 the altitude of the star will be #cj4 ,next you will notice that the ,north ,star is situated at the end of the handle of a kind of dipper-shaped figure formed by stars1 the handle being bent the wrong way4 ,all of the stars forming this 8dipper0 are faint1 except the two which are farthest from the ,north ,star1 in the outer edge of the bowl1 one of which is about as bright as the ,north ,star itself4 ,again1 if you carry your eye along the handle to the bowl1 and then continue onward about as much farther1 you will be led to another1 larger1 more conspicuous1 and more perfect1 dipper-shaped figure1 which is in the famous constellation of ,ursa ,major1 or the ,great ,bear4 ,this striking figure is called the ,great ,dipper 7known in ,england as ,the ,wain74 ,it contains seven conspicuous stars1 all of which1 with one exception1 are equal in brightness to the ,north ,star4 ,now1 look particularly at the two stars which indicate the outer side of the bowl of this dipper1 and you will find that if you draw an imaginary line through them toward the meridian in the north1 it will lead your eye directly back to the ,north ,star4 ,these two significant stars are often called ,the ,pointers4 ,with their aid you can make sure that you have really found the ,north ,star4 ,having found it1 begin by noting the various groups of stars1 or constellations1 in the northern part of the sky1 and1 as the night wears on1 observe whether any change takes place in their position4 ,to make our description more definite1 we will suppose that the observations begin at nine o'clock ,p4,m4 about the #ast of ,july4 ,at that hour and date1 and from the middle latitudes of the ,united ,states1 the ,great ,dipper is seen in a south-westerly direction from the ,north ,star1 with its handle pointing overhead4 ,at the same time1 on the opposite side of the ,north ,star1 and low in the north-east1 appears the remarkable constellation of ,cassiopeia1 easily recognisable by a zigzag figure1 roughly resembling the letter ,w1 formed by its five principal stars4 ,fix the relative positions of these constellations in the memory1 and an hour later1 at #aj ,p4,m41 look at them again4 ,you will find that they have moved1 the ,great ,dipper sinking1 while ,cassiopeia rises4 ,make a third observation at #aa ,p4,m41 and you will perceive that the motion has continued1 ,the ,pointers having descended in the north-west1 until they are on a level with the ,north ,star1 while ,cassiopeia has risen to nearly the same level in the north-east4 ,in the meantime1 the ,north ,star has remained apparently motionless in its original position4 ,if you repeat the observation at midnight1 you will find that the ,great ,dipper has descended so far that its centre is on a level with the ,north ,star1 and that ,cassiopeia has proportionally risen in the north-east4 ,it is just as if the two constellations were attached to the ends of a rod pivoted at the centre upon the ,north ,star and twirling about it4 ,in the meantime you will have noticed that the figure of the 8,little ,dipper10 attached to the ,north ,star1 which had its bowl toward the zenith at #i ,p4,m41 has swung round so that at midnight it is extended toward the south-west4 ,thus1 you will perceive that the ,north ,star is like a hub round which the heavens appear to turn1 carrying the other stars with them4 ,to convince yourself that this motion is common to the stars in all parts of the sky1 you should also watch the conduct of those which pass overhead1 and those which are in the southern quarter of the heavens4 ,for instance1 at #i ,p4,m4 7same date71 you will see near the zenith a beautiful coronet which makes a striking appearance although all but one of its stars are relatively faint4 ,this is the constellation ,corona ,borealis1 or the ,northern ,crown4 ,as the hours pass you will see the ,crown swing slowly westward1 descending gradually toward the horizon1 and if you persevere in your observations until about #e ,a4,m41 you will see it set in the north-west4 ,the curve that it describes is concentric with those followed by the ,great ,dipper and ,cassiopeia1 but1 being farther from the ,north ,star than they are1 and at a distance greater than the altitude of the ,north ,star1 it sinks below the horizon before it can arrive at a point directly underneath that star4 ,then take a star far in the south4 ,at #i o'clock1 you will perceive the bright reddish star ,antares1 in the constellation ,scorpio1 rather low in the south and considerably east of the meridian4 ,hour after hour it will move westward1 in a curve larger than that of the ,northern ,crown1 but still concentric with it4 ,a little before #aj ,p4,m41 it will cross the meridian1 and between #a and #b ,a4,m41 it will sink beneath the horizon at a point south of west4 ,so1 no matter in what part of the heavens you watch the stars1 you will see not only that they move from east to west1 but that this motion is performed in curves concentric round the ,north ,star1 which alone appears to maintain its place unchanged4 ,along the eastern horizon you will perceive stars continually rising2 in the middle of the sky you will see others continually crossing the meridian--a majestic march of constellations1--and along the western horizon you will find still others continually setting4 ,if you could watch the stars uninterruptedly throughout the twenty-four hours 7if daylight did not hide them from sight during half that period71 you would perceive that they go entirely round the celestial sphere1 or rather that it goes round with them1 and that at the end of twenty-four hours they return to their original positions4 ,but you can do this just as well by looking at them on two successive nights1 when you will find that at the same hour on the second night they are back again1 practically in the places where you saw them on the first night4 ,of course1 what happens on a ,july night happens on any other night of the year4 ,we have taken a particular date merely in order to make the description clearer4 ,it is only necessary to find the ,north ,star1 the ,great ,dipper1 and ,cassiopeia1 and you can observe the apparent revolution of the heavens at any time of the year4 ,these constellations1 being so near the ,north ,star that they never go entirely below the horizon in middle northern latitudes1 are always visible on one side or another of the ,north ,star4 ,now1 call upon your imagination to deal with what you have been observing1 and you will have no difficulty in explaining what all this apparent motion of the stars means4 ,you already know that the heavens form a sphere surrounding the earth4 ,you have simply to suppose the ,north ,star to be situated at1 or close to1 the north end1 or north pole1 of an imaginary axle1 or axis1 round which the celestial sphere seems to turn1 and instantly the whole series of phenomena will fall into order1 and the explanation will stare you in the face4 ,that explanation is that the motion of all the stars in concentric circles round the ,north ,star is due to an apparent revolution of the whole celestial sphere1 like a huge hollow ball1 about an axis1 the position of one of whose poles is graphically indicated in the sky by the ,north ,star4 ,the circles in which the stars seem to move are perpendicular to this axis1 and inclined to the horizon at an angle depending upon the altitude of the ,north ,star at the place on the earth where the observations are made4 ,another important fact demands our attention1 although the thoughtful reader will already have guessed it--the north pole of the celestial sphere1 whose position in the sky is closely indicated by the ,north ,star1 is situated directly over the north pole of the earth4 ,this follows from the fact that the apparent revolution of the celestial sphere is due to the real rotation of the earth4 ,you can see that the two poles1 that of the earth and that of the heavens1 must necessarily coincide1 by taking a school globe and imagining that you are an intelligent little being dwelling on its surface4 ,as the globe turned on its axis you would see the walls of the room revolving round you1 and the poles of the apparent axis round which the room turned1 would1 evidently1 be directly over the corresponding poles of the globe itself4 ,another thing which you could make clear by this experiment is that1 as the poles of the celestial sphere are over the earth's poles1 so the celestial equator1 or equator of the heavens1 must be directly over the equator of the earth4 ,we can determine the location of the poles of the heavens by watching the revolution of the stars around them1 and we can fix the position of the circle of the equator of the heavens1 by drawing an imaginary line round the celestial sphere1 half-way between the two poles4 ,we have spoken specifically only of the north pole1 but1 of course1 there is a corresponding south pole situated over the south pole of the earth1 but whose position is invisible from the northern hemisphere4 ,it happens that the place of the south celestial pole is not indicated to the eye1 like that of the northern1 by a conspicuous star4 ,illustration3 ,drawing of ,jupiter ,illustration3 ,drawing of ,jupiter ,note the change of details between the two drawings1 made at different times4 ,similar changes are continually occurring4 #f4 ,locating the ,stars on the ,celestial ,sphere4 ,having found the poles and the equator of the celestial sphere1 we begin to see how it is possible to make a map1 or globe1 of the heavens just as we do of the earth1 on which the objects that they contain may be represented in their proper positions4 ,when we wish to describe the location of an object on the earth1 a city for instance1 we have to refer to a system of imaginary circles1 drawn round the earth and based upon the equator and the poles4 ,these circles enable us to fix the place of any point on the earth with accuracy4 ,one set of circles called parallels of latitude are drawn east and west round the globe parallel to the equator1 and becoming smaller and smaller until the smallest runs close round their common central point1 which is one of the poles4 ,each pole of the earth is the centre of such a set of circles all parallel to the equator4 ,since each circle is unvarying in its distance from the equator1 all places which are situated anywhere on that circle have the same latitude1 or distance from the equator1 either north or south4 ,but to know the latitude of any place on the earth is not sufficient2 we must also know what is called its longitude1 or its angular distance east or west of some chosen point on the equator4 ,this knowledge is obtained with the aid of another set of circles drawn north-and-south round the earth1 and all meeting and crossing at the poles4 ,these are called meridians of longitude4 ,in order to make use of them we must1 as already intimated1 select some particular meridian whose crossing point on the equator will serve as a place of beginning4 ,by common consent of the civilised world1 the meridian which passes through the observatory at ,greenwich1 near ,london1 has been chosen for this purpose4 ,it is1 like all the meridians1 perpendicular to the equator1 and it is called the prime meridian of the earth4 ,in locating any place on the earth1 then1 we ascertain by means of the parallel of latitude passing through it how far in degrees1 it is north or south of the equator1 and by means of its meridian of longitude how far it is east or west of the prime meridian1 or meridian of ,greenwich4 ,these two things being known1 we have the exact location of the place on the earth4 ,let us now see how a similar system is applied to ascertain the location of a heavenly body on the celestial sphere4 ,we have observed that the poles of the heavens correspond in position1 or direction1 with those of the earth1 and that the equator of the heavens runs round the sky directly over the earth's equator4 ,it follows that we can divide the celestial sphere just as we do the surface of the earth by means of parallels and meridians1 corresponding to the similar circles of the earth4 ,on the earth1 distance from the equator is called latitude1 and distance from the prime meridian1 longitude4 ,in the heavens1 distance from the equator is called declination1 and distance from the prime meridian1 right ascension2 but they are essentially the same things as latitude and longitude1 and are measured virtually in the same way4 ,in place of parallels of latitude1 we have on the celestial sphere circles drawn parallel to the equator and centring about the celestial poles1 which are called parallels of declination1 and in place of meridians of longitude1 we have circles perpendicular to the equator1 and drawn through the celestial poles1 which are called hour circles4 ,the origin of this name will be explained in a moment4 ,for the present it is only necessary to fix firmly in the mind the fact that these two systems of circles1 one on the earth and the other in the heavens1 are fundamentally identical4 ,just as on the earth geographers have chosen a particular place1 viz4 ,greenwich1 to fix the location of the terrestrial prime meridian1 so astronomers have agreed upon a particular point in the heavens which serves to determine the location of the celestial prime meridian4 ,this point1 which lies on the celestial equator1 is known as the vernal equinox4 ,we shall explain its origin after having indicated its use4 ,the hour circle which passes through the vernal equinox is the prime meridian of the heavens1 and the vernal equinox itself is sometimes called the 8,greenwich of the ,sky40 ,if1 now1 we wish to ascertain the exact location of a star on the celestial sphere1 as we would that of ,new ,york1 ,london1 or ,paris1 on the earth1 we measure along the hour circle running through it1 its declination1 or distance from the celestial equator1 and then1 along its parallel of declination1 we measure its right ascension1 or distance from the vernal equinox4 ,having these two co-ordinates1 we possess all that is necessary to enable us to describe the position of the star1 so that someone else looking for it1 may find it in the sky1 as a navigator finds some lone island in the sea by knowing its latitude and longitude4 ,declination1 as we have seen1 is simply another name for latitude1 but right ascension1 which corresponds to longitude1 needs a little additional explanation4 ,it differs from longitude1 first1 in that1 instead of being reckoned both east and west from the prime meridian1 it is reckoned only toward the east1 the reckoning being continued uninterruptedly entirely round the circle of the equator2 and1 second1 in that it is usually counted not in degrees1 minutes1 and seconds of arc1 but in hours1 minutes1 and seconds of time4 ,the reason for this is that1 since the celestial sphere makes one complete revolution in twenty-four hours1 it is convenient to divide the circuit into twenty-four equal parts1 each corresponding to the distance through which the heavens appear to turn in one hour4 ,this explains the origin of the term hour circles applied to the celestial meridians1 which1 by intersecting the equator1 divide it into twenty-four equal parts1 each part corresponding to an hour of time4 ,in expressing right ascension in time1 the ,roman numerals--,i1 ,,ii1 ,,iii1 ,,iv1 ,v1 ,,vi1 ,,vii1 ,,viii1 ,,ix1 ,x1 ,,xi1 ,,xii1 ,,xiii1 ,,xiv1 ,,xv1 ,,xvi1 ,,xvii1 ,,xviii1 ,,xix1 ,,xx1 ,,xxi1 ,,xxii1 ,,xxiii1 ,,xxiv--are employed for the hours1 and the letters m and s respectively for the minutes and seconds4 ,since there are #cfj in every circle1 it is plain that one hour of right ascension corresponds to #ae4 ,so1 too1 one minute of right ascension corresponds to #ae1 and one second to #ae4 ,it will be found useful to memorise these relations4 ,illustration3 ,fig4 #c4 ,right ,ascension and ,declination4 ,the plane of the horizon1 with the north1 south1 east1 and west points1 and the zenith1 are represented as in ,fig4 #b4 ,p and ,p are the poles of the celestial sphere1 the dotted line connecting them representing the direction of the axis1 both of celestial sphere and the earth4 ,the circle ,eq ,eq is the equator4 ,v is the vernal equinox1 or the point on the equator whence right ascension is reckoned round toward the east4 ,the circle passing through s1 parallel to the equator1 is a declination circle4 ,the circle ,p s ,p is the hour circle of the star s4 ,the arc of this hour circle contained between s and the point where it meets the equator is the star's declination4 ,its right ascension is measured by the arc of the equator contained between ,v and the point where its hour circle meets the equator1 or by the angle ,v ,p s4 ,the hour circle ,p ,v ,p1 passing through the vernal equinox1 is the equinoctial colure4 ,when this has moved up to coincidence with the meridian1 ,n ,z ,s1 it will be astronomical noon4 #g4 ,effects ,produced by ,changing the ,observer's ,place on the ,earth4 ,the reader will recall that in ,sect4 #d we described another system of circles for determining the places of stars1 a system based on the horizon and the zenith4 ,this horizon-zenith system takes no account of the changes produced by the apparent motion of the heavens1 and consequently it is not applicable to determining the absolute positions of the stars on the celestial sphere4 ,it simply shows their positions in the visible half of the sky1 as seen at some particular time from some definite point on the earth4 ,in order to show the changing relations of this system to that which we have just been describing1 let us consider the effects produced by shifting our place of observation on the earth4 ,since the zenith is the point overhead and the nadir the point underfoot1 and the horizon is a great circle drawn exactly half-way between the zenith and the nadir1 it is evident1 upon a moment's consideration1 that every place on the earth has its own zenith and its own horizon4 ,it is also clear that every place must have its own meridian1 because the meridian is a north-and-south line running directly over the observer's head4 ,you can see how this is1 if you reflect that for an observer situated on the other side of the earth what is overhead for you will be underfoot for him1 and vice versa4 ,thus the direction of our zenith is the direction of the nadir for our antipodes1 and the direction of their zenith is the direction of our nadir4 ,they see the half of the sky which is invisible to us1 and we the half which is invisible to them4 ,now1 suppose that we should go to the north pole4 ,the celestial north pole would then be in our zenith1 and the equator would correspond with the horizon4 ,thus1 for an observer at the north pole the two systems of circles that we have described would fall into coincidence4 ,the zenith would correspond with the pole of the heavens2 the horizon would correspond with the celestial equator2 the vertical circles would correspond with the hour circles2 and the altitude circles would correspond with the circles of declination4 ,the ,north ,star1 being close to the pole of the heavens1 would appear directly overhead4 ,being at the zenith1 its altitude would be #ij 7see ,sect4 #d74 ,peary1 if he had visited the pole during the polar night1 would have seen the ,north ,star overhead1 and it would have enabled him with relatively little trouble to determine his exact place on the earth1 or1 in other words1 the exact location of the north terrestrial pole4 ,with the pole star in the zenith1 it is evident that the other stars would be seen revolving round it in circles parallel to the horizon4 ,all the stars situated north of the celestial equator would be simultaneously and continuously visible4 ,none of them would either rise or set1 but all1 in the course of twenty-four hours1 would appear to make a complete circuit horizontally round the sky4 ,this polar presentation of the celestial sphere is called the parallel sphere1 because the stars appear to move parallel to the horizon4 ,no man has yet beheld the nocturnal phenomena of the parallel sphere1 but if in the future some explorer should visit one of the earth's poles during the polar night1 he would behold the spectacle in all its strange splendour4 ,illustration3 ,jupiter ,photographed at the ,lick ,observatory4 ,observe on the left the ,great ,red ,spot1 which first appeared in #ahgh4 ,next1 suppose that you are somewhere on the earth's equator4 ,since the equator is everywhere #ij1 or one quarter of a circle1 from each pole1 it is evident that looking at the sky from the equator you would see the two poles 7if there was anything to mark their places7 lying on the horizon one exactly in the north and the other exactly in the south4 ,the celestial equator would correspond with the prime vertical1 passing east and west directly over your head1 and all the stars would rise and set perpendicularly to the horizon1 each describing a semicircle in the sky in the course of twelve hours4 ,during the other twelve hours1 the same stars would be below the horizon4 ,stars situated near either of the poles would describe little semi-circles near the north or the south point2 those farther away would describe larger semi-circles2 those close to the celestial equator would describe semi-circles passing overhead4 ,but all1 no matter where situated1 would describe their visible courses in the same period of time4 ,this equatorial presentation of the celestial sphere is called the right sphere1 because the stars rise and set at a right angle to the plane of the horizon4 ,comparing it with the system of circles on which right ascension and declination are based1 we see that1 as the prime vertical corresponds with the celestial equator1 so the horizon must represent an hour circle4 ,the meridian also represents an hour circle4 ,it may require a little thought to make this clear1 but it will be a good exercise4 ,finally1 if you are somewhere between the equator and one of the poles1 which is the actual situation of the vast majority of mankind1 you see either the north or the south pole of the heavens elevated to an altitude corresponding with your latitude1 and the stars apparently revolving round it in circles inclined to the horizon at an angle depending upon the latitude4 ,the nearer you are to the equator1 the steeper this angle will be4 ,this ordinary presentation of the celestial sphere is called the oblique sphere4 ,its horizon does not correspond with either the equator or the prime vertical1 and its zenith and nadir lie at points situated between the celestial poles and the celestial equator4 #h4 ,the ,astronomical ,clock and the ,ecliptic4 ,it will be remembered that the meridian of any place on the earth is a straight north and south line running through the zenith and perpendicular to the horizon4 ,more strictly speaking1 the meridian is a circle passing from north to south directly overhead and corresponding exactly with the meridian of longitude of the place of observation4 ,now1 let us consider the hour circles on the celestial sphere4 ,they are drawn in the same way as the meridians on the earth4 ,but the celestial sphere appears to revolve round the earth1 and as it does so it must carry the hour circles with it1 since they are fixed in position upon its surface4 ,fix your attention upon the first of these hour circles1 i4 e41 the one which runs through the vernal equinox4 ,its right ascension is called #j hours1 because it is the starting point4 ,suppose that at some time we find the vernal equinox exactly in the south2 then the #j hour circle1 or the prime meridian of the heavens1 will1 at that instant1 coincide with the meridian of the place of observation4 ,but one hour later1 in consequence of the motion of the heavens1 the vernal equinox1 together with the circle of #j hours1 will be #ae1 or one hour of right ascension1 west of the meridian1 and the hour circle marked ,i will have come up to1 and for an instant will be blended with1 the meridian4 ,an hour later still1 the circle of ,,ii hours right ascension will have taken its place on the meridian1 while the vernal equinox and the circle of #j hours will be ,,ii hours1 or #cj1 west of the meridian4 ,and so on1 throughout the entire circuit of the sky4 ,what has just been said makes it evident that the apparent motion of the heavens resembles the movement of a clock1 the vernal equinox1 or the circle of #j hours1 serving as a hand1 or pointer1 on the dial4 ,astronomers use it in exactly that way1 for astronomical clocks are made with dials divided into twenty-four hour spaces1 and the time reckoning runs continuously from #j hours to ,,xxiv hours4 ,the 8astronomical day0 begins when the vernal equinox is on the meridian4 ,at that instant the hands of the astronomical clock mark #j hours1 #j minutes1 #j seconds4 ,thus the clock follows the motion of the heavens1 and the astronomer can tell by simply glancing at the dial1 and without looking at the sky1 where the vernal equinox is1 and what is the right ascension of any body which may at that moment be on the meridian4 ,we must now explain a little more fully what the vernal equinox is1 and why it has been chosen as the 8,greenwich of the ,sky40 ,its position is not marked by any star1 but is determined by means of the intersecting circles that we have described4 ,there is one other such circle1 that we have not yet mentioned1 which bears a peculiar relation to the vernal equinox4 ,this is the ecliptic4 ,just as the daily1 or diurnal1 rotation of the earth on its axis causes the whole celestial sphere to appear to make one revolution every day1 so the yearly or annual revolution of the earth in its orbit about the sun causes the sun to appear to make one revolution through the sky every year4 ,as the earth moves onward in its orbit1 the sun seems to move in the opposite direction4 ,inasmuch as there are #cfj in a complete circle and #cfe days in a year1 the apparent motion of the sun amounts to nearly #a per day1 or #cj per month4 ,in twelve months1 then1 the sun comes back again to the place in the sky which it occupied at the beginning of the year4 ,since the motion of the earth in its orbit is from west to east 7the same as that of its rotation on its axis71 it follows that the direction of the sun's apparent annual motion in the sky is from east to west 7like its daily motion74 ,thus1 while in fact the earth pursues a path1 or orbit1 round the sun1 the sun seems to pursue a path round the earth4 ,this apparent path of the sun1 projected against the background of the sky1 is called the ecliptic4 ,the name arises from the fact that eclipses only occur when the moon is in or near the plane of the sun's apparent path4 ,as the apparent motion of the sun round the ecliptic is caused by the real motion of the earth round the sun1 we may regard the ecliptic as a circle marking the intersection of the plane of the earth's orbit with the celestial sphere4 ,in other words1 if we were situated on the sun instead of on the earth1 we would see the earth travelling round the sky in the circle of the ecliptic4 ,we must keep this fact1 that the ecliptic indicates the plane of the earth's orbit1 firmly in mind1 in order to understand what follows4 ,the ecliptic is not coincident with the celestial equator1 for the following reason3 ,the axis of the earth's daily rotation is not parallel to1 or does not point in the same direction as1 the axis of its yearly revolution round the sun4 ,as the axis of rotation is perpendicular to the equator1 so the axis of the yearly revolution is perpendicular to the ecliptic1 and since these two axes are inclined to one another1 it results that the equator and the ecliptic must lie in different planes4 ,the inclination of the plane of the ecliptic to that of the equator amounts to about #bc4 ,as it is very important to have a clear conception of this subject1 we may illustrate it in this way3 ,take a ball to represent the earth1 and around it draw a circle to represent the equator4 ,then1 through the centre of the ball1 and at right angles to its equator1 put a long pin to represent the axis4 ,set it afloat in a tub of water1 weighting it so that it will be half submerged1 and placing it in such a position that the pin will be not upright but inclined at a considerable angle from the vertical4 ,now1 imagine that the sun is situated in the centre of the tub1 and cause the ball to circle slowly round it1 while maintaining the pin always in the same position4 ,then the surface of the water will represent the plane of the ecliptic1 or plane of the earth's orbit1 and you will see that1 in consequence of the inclination of the pin1 the plane of the equator does not coincide with that of the ecliptic 7or the surface of the water71 but is tipped with regard to it in such a manner that one half of the equator is below and the other half above it4 ,instead of actually trying this experiment1 it will be a useful exercise of the imagination to represent it to the mind's eye just as if it were tried4 ,we have said that the inclination of the equator to the ecliptic amounts to #bc1 and this angle should be memorised4 ,now1 since both the ecliptic and the equator are great circles of the celestial sphere1 i4 e41 circles whose planes cut through the centre of the sphere1 they must intersect one another at two opposite points4 ,in the experiment just described1 these two points lie on opposite sides of the ball1 where the equator cuts the level of the water4 ,these points of intersection of the equator and the ecliptic on the celestial sphere are called the equinoxes1 or equinoctial points1 because when the sun appears at either of those points it is perpendicular over the equator1 and when it is in that position day and night are of equal length all over the earth4 7,equinox is from two ,latin words meaning 8equal night407 ,illustration3 ,saturn ,from a drawing by ,trouvelot4 ,illustration3 ,saturn ,photographed at the ,lick ,observatory4 ,we shall have more to say about the equinoxes later1 but for the present it is sufficient to remark that one of these points--that one where the sun is about the #bast of ,march1 which is the beginning of astronomical spring--is the 8,greenwich of the ,sky10 or the vernal equinox4 ,the other1 opposite1 point is called the autumnal equinox1 because the sun arrives there about the #bc;d of ,september1 the beginning of astronomical autumn4 ,the vernal equinox1 as we have already seen1 serves as a pointer on the dial of the sky4 ,when it crosses the meridian of any place it is astronomical noon at that place4 ,its position in the sky is not marked by any particular star1 but it is situated in the constellation ,pisces1 and lies exactly at the crossing point of the celestial equator and the ecliptic4 ,the hour circle1 running through this point1 and through its opposite1 the autumnal equinox1 is the prime meridian of the heavens1 called the equinoctial colure4 ,the hour circle at right angles to the equinoctial colure1 i4 e41 bearing to it the same relation that the prime vertical does to the meridian 7see ,sect4 #d71 is called the solstitial colure4 ,this latter circle cuts the ecliptic at two opposite points1 called the solstices1 which lie half-way between the equinoxes4 ,since the ecliptic is inclined #bc to the plane of the equator1 and since the solstices lie half-way between the two crossing points of the ecliptic and the equator1 it is evident that the solstices must be situated #bc from the equator1 one above and the other below1 or one north and the other south4 ,the northern one is called the summer solstice1 because the sun arrives there at the beginning of astronomical summer1 about the #bb;d of ,june1 and the southern one is called the winter solstice1 because the sun arrives there at the beginning of the astronomical winter1 about the #bb;d of ,december4 ,the name solstice comes from two ,latin words meaning 8the standing still of the sun10 because when it is at the solstitial points its apparent course through the sky is for several days nearly horizontal and its declination changes very slowly4 ,now1 just as there are two opposite points in the sky at equal distances from the equator1 which mark the poles of the imaginary axis about which the celestial sphere makes its diurnal revolution1 so there are two opposite points at equal distances from the ecliptic which mark the poles of the imaginary axis about which the yearly revolution of the sun takes place4 ,these are called the poles of the ecliptic1 and they are situated #bc from the celestial poles--a distance necessarily corresponding with the inclination of the ecliptic to the equator4 ,the northern pole of the ecliptic is in the constellation ,draco1 which you may see any night circling round the ,north ,star1 together with the ,great ,dipper and ,cassiopeia4 #i4 ,celestial ,latitude and ,longitude4 ,we have seen that the celestial sphere is marked with imaginary circles resembling the circles of latitude and longitude on the earth1 and that in both cases the circles are used for a similar purpose1 viz41 to determine the location of objects1 in one case on the globe of the earth and in the other on the sphere of the heavens4 ,it has also been explained that what corresponds to latitude on the celestial sphere is called declination1 and what corresponds to longitude is called right ascension4 ,it happens1 however1 that these same terms1 latitude and longitude1 are also employed in astronomy4 ,but1 unfortunately1 they are based upon a different set of circles from that which has been described1 and they do not correspond in the way that right ascension and declination do to terrestrial longitude and latitude4 ,a few words must therefore be devoted to celestial latitude and longitude1 as distinguished from declination and right ascension4 ,celestial latitude and longitude then1 instead of being based upon the equator and the poles1 are based upon the ecliptic and the poles of the ecliptic4 ,celestial latitude means distance north or south of the ecliptic 7not of the equator71 and celestial longitude means distance from the vernal equinox reckoned along the ecliptic 7not along the equator74 ,celestial longitude runs1 the same as right ascension1 from west toward east1 but it is reckoned in degrees instead of hours4 ,celestial latitude is measured the same as declination1 but along circles running through the poles of the ecliptic instead of the celestial poles1 and drawn perpendicular to the ecliptic instead of to the equator4 ,circles of celestial latitude are drawn parallel to the ecliptic and centring round the poles of the ecliptic1 and meridians of celestial longitude are drawn through the poles of the ecliptic and perpendicular to the ecliptic itself4 ,the meridian of celestial longitude that passes through the two equinoxes is the ecliptic prime meridian4 ,this intersects the equinoctial colure at the equinoctial points1 making with it an angle of #bc4 ,the solstitial colure1 which it will be remembered runs round the celestial sphere half-way between the equinoxes1 is perpendicular to the ecliptic as well as to the equator1 and so is common to the two systems of circles4 ,it passes alike through the celestial poles and the poles of the ecliptic4 ,it will also be observed that the vernal equinox is common to the two systems of co-ordinates1 because it lies at one of the intersections of the ecliptic and the equator4 ,in passing from one system to the other1 the astronomer employs the methods of spherical trigonometry4 ,illustration3 ,fig4 #d4 ,the ,ecliptic and ,celestial ,latitude and ,longitude4 ,c1 as in the other figures1 is the place of the observer and ,z is the zenith1 but to avoid complication of details the circle of the horizon is not drawn1 only the north-and-south line1 ,n ,c ,s1 being shown4 ,eq ,eq is the equator4 ,ec ,ec is the ecliptic4 ,p and ,p are the celestial poles4 p and p are the poles of the ecliptic4 ,na is the nadir4 ,v is the vernal equinox1 and ,a the autumnal equinox4 ,the circle through s1 parallel to the ecliptic1 is a latitude circle4 ,the circle p s p' is the ecliptic meridian of the star s4 ,the circle ,p ,v ,p ,a is the equinoctial colure4 ,the circle p ,v p ,a is the prime ecliptic meridian4 ,the arc of the ecliptic meridian contained between the ecliptic and s measures the star's latitude4 ,the arc of the ecliptic contained between ,v and the point where the ecliptic meridian p s p meets the ecliptic 7or the angle ,v p s7 measures the star's longitude east from ,v1 the vernal equinox4 #aj4 ,the ,zodiac and the ,precession of the ,equinoxes4 ,the next thing with which we must make acquaintance is the zodiac4 ,we have learned that the ecliptic is a great circle of the celestial sphere inclined at an angle of #bc to the equator1 and crossing the latter at two opposite points called the equinoxes1 and that the sun in its annual journey round the sky follows the circle of the ecliptic4 ,consequently1 the place which the sun occupies at any time must be somewhere on the course of the ecliptic4 ,the fact has been mentioned that as seen from the sun the earth would appear to travel round the ecliptic1 whence the ecliptic may be regarded as the projection of the earth's orbit1 or path1 against the background of the heavens4 ,but1 besides the earth there are seven other large planets1 ,mercury1 ,venus1 ,mars1 ,jupiter1 ,saturn1 ,uranus1 and ,neptune1 which1 like it1 revolve round the sun1 some nearer and some farther away4 ,now1 the orbits of all of these planets lie in planes nearly coincident with that of the earth's orbit4 ,none of them is inclined more than #g from the ecliptic and most of them are inclined only one or two degrees4 ,consequently1 as we watch these planets moving slowly round in their orbits we find that they are always quite close to the circle of the ecliptic4 ,this fact shows that the solar system1 i4 e41 the sun and its attendant planets1 occupies a disk-shaped area in space1 the outlines of which would be like those of a very thin round cheese1 with the sun in the centre4 ,the ecliptic indicates the median plane of this imaginary disk4 ,the moon1 too1 travels nearly in this common plane1 its orbit round the earth being inclined only a little more than #e to the ecliptic4 ,even the early astronomers noticed these facts1 and in ancient times they gave to the apparent road round the sky in which the sun and planets travel1 in tracks relatively as close together as the parallel marks of wheels on a highway1 the name zodiac4 ,they assigned to it a certain arbitrary width1 sufficient to include the orbits of all the planets known to them4 ,this width is #h on each side of the circle of the ecliptic1 or #af in all4 ,they also divided the ring of the zodiac into twelve equal parts1 corresponding with the number of months in a year1 and each part was called a sign of the zodiac4 ,since there are #cfj in a circle1 each sign of the zodiac has a length of just #cj4 ,to indicate the course of the zodiac to the eye1 its inventors observed the constellations lying along it1 assigning one constellation to each sign4 ,beginning at the vernal equinox1 and running round eastward1 they gave to these zodiacal constellations1 as well as to the corresponding signs1 names drawn from fancy resemblances of the figures formed by the stars to men1 animals1 or other objects4 ,the first sign and constellation were called ,aries1 the ,ram1 indicated by the symbol 2 the second1 ,taurus1 the ,bull1 2 the third1 ,gemini1 the ,twins1 2 the fourth1 ,cancer1 the ,crab1 2 the fifth1 ,leo1 the ,lion1 2 the sixth1 ,virgo1 the ,virgin1 2 the seventh1 ,libra1 the ,balance1 2 the eighth1 ,scorpio1 the ,scorpion1 2 the ninth1 ,sagittarius1 the ,archer1 2 the tenth1 ,capricornus1 the ,goat1 2 the eleventh1 ,aquarius1 the ,water-,bearer1 2 and the twelfth1 ,pisces1 the ,fishes1 4 ,the name zodiac comes from a ,greek word for animal1 since most of the imaginary figures formed by the stars of the zodiacal constellations are those of animals4 ,the signs and their corresponding constellations being supposed fixed in the sky1 the planets1 together with the sun and the moon1 were observed to run through them in succession from west to east4 ,when this system was invented1 the signs and their constellations coincided in position1 but in the course of time it was found that they were drifting apart1 the signs1 whose starting point remained the vernal equinox1 backing westward through the sky until they became disjoined from their proper constellations4 ,at present the sign ,aries is found in the constellation next west of its original position1 viz41 ,pisces1 and so on round the entire circle4 ,this motion1 as already intimated1 carries the equinoxes along with the signs1 so that the vernal equinox1 which was once at the beginning of the constellation ,aries 7as it still is at the beginning1 or 8first point10 of the sign ,aries71 is now found in the constellation ,pisces4 ,to explain the shifting of the signs of the zodiac on the face of the sky we must consider the phenomenon known as the precession of the equinoxes1 which is one of the most interesting things in astronomy4 ,let us refer again to the fact that the axis of the earth's daily rotation is inclined #bc from a perpendicular to the plane of its yearly revolution round the sun1 from which it results that the ecliptic is tipped at the same angle to the plane of the equator4 ,thus the sun1 moving in the ecliptic1 appears half the year above 7or north of7 the equator1 and half the year below 7or south of7 it1 the crossing points being the two equinoxes4 ,now1 this inclination of the earth's axis is the key to the explanation we are seeking4 ,the direction in which the axis lies in space is a fixed direction1 which can be changed only by some outside force interfering4 ,what we mean by this will become clearer if we think of the earth's axis as resembling the peg of a top1 or the axis of a gyroscope4 ,when a top is spinning smoothly1 with its peg vertical1 the peg will remain vertical as long as the spin is not diminished1 and no outside force interferes4 ,so1 too1 the axis of the spinning-wheel of a gyroscope keeps pointing in the same direction so persistently that the wheel is kept from falling4 ,if it is so mounted that it is free to move in any direction1 and if then you take the instrument in your hand and turn round with it1 the axis will adjust itself in such a manner as to retain its original direction in space4 ,this tendency of a rotating body to keep its axis of rotation fixed applies equally to the earth1 whose axis1 also1 maintains a constant direction in space1 except for a slow change produced by outside forces1 which change constitutes the phenomenon of the precession of the equinoxes4 ,we cannot too often recall the fact that the axis of the earth is coincident in direction with that of the celestial sphere1 so that the earth's poles are situated directly under the celestial poles4 ,but the poles of the ecliptic are #bc aside from the celestial poles4 ,if the direction of the earth's axis and with it that of the celestial sphere1 did not change at all1 then the celestial poles and the poles of the ecliptic would always retain the same relative positions in the sky2 but1 in fact1 an exterior force1 acting upon the earth1 causes a gradual change in the direction of its axis1 and in consequence of this change the celestial poles1 whose position depends upon that of the earth's poles1 have a slow motion of revolution about the poles of the ecliptic1 in a circle of #bc radius4 ,the force which produces this effect is the attraction of the sun and the moon upon the protuberant part of the earth round its equator4 ,if the earth were a perfect sphere1 this force could not act1 or would not exist1 but since the earth is an oblate spheroid1 slightly flattened at the poles1 and bulged round the equator1 the attraction acts upon the equatorial protuberance in such a way as to strive to pull the earth's axis into an upright position with respect to the plane of the ecliptic4 ,but1 in consequence of its spinning motion1 the earth resists this pull1 and tries1 so to speak1 to keep the inclination of its axis unchanged4 ,the result is that the axis swings slowly round while maintaining nearly the same inclination to the plane of the ecliptic4 ,here1 again1 we may employ the illustration of a top4 ,if the peg of the top is tipped a little aside1 so that the attraction of gravitation would cause the top to fall flat on the table if it were not spinning1 it will1 as long as it continues to spin1 swing round and round in a circle instead of falling4 ,we cannot enter into a mathematical explanation of this phenomenon here1 but the reader will find a clear popular account of the whole matter in ,prof4 ,john ,perry's little book on ,spinning ,tops4 ,it is sufficient here to say that the attraction of gravitation1 tending to make the top fall1 but really causing the peg to turn round and round1 resembles1 in its effect1 the attraction of the sun and the moon upon the equatorial protuberance of the earth1 which makes the earth's axis turn round in space4 ,illustration3 ,the ,milky ,way about ,chi ,cygni ,photographed at the ,lick ,observatory by ,e4 ,e4 ,barnard1 with the six-inch ,willard lens4 ,observe the cloud-like forms4 ,now1 as we have said1 this slow swinging round of the axis of the earth produces the so-called precession of the equinoxes4 ,in a period of about #be1hjj years1 the axis makes one complete swing round1 so that in that space of time the celestial poles describe a revolution about the poles of the ecliptic1 which remain fixed4 ,but since the equator is a circle situated half-way between the poles1 it is evident that it must turn also4 ,to illustrate this1 take a round flat disk of tin1 or pasteboard1 to represent the equator and its plane1 and perpendicularly through its centre run a straight rod to represent the axis4 ,put one end of the axis on the table1 and1 holding it at a fixed inclination1 turn the upper end round in a circle4 ,you will see that as the axis thus revolves1 the disk revolves with it1 and if you imagine a plane1 parallel to the surface of the table1 passing through the centre of the disk at the point where the rod pierces it1 you will perceive that the two opposite points1 where the edge of the disk intersects this imaginary plane1 revolve with the disk4 ,in one position of the axis1 for instance1 these points may lie in the direction of the north-and-south sides of the room4 ,when you have revolved the axis1 and with it the disk1 one quarter way round1 the points will lie toward the east and west sides of the room4 ,when you have produced a half revolution they will once more lie toward the north-and-south1 but now the direction of the slope of the disk will be the reverse of that which it had at the beginning4 ,finally1 when the revolution is completed1 the two points will again lie north-and-south and the slope of the disk will be in the same direction as at the start4 ,in this illustration the disk stands for the plane of the celestial equator1 the rod for the axis of the celestial sphere1 the imaginary plane parallel to the surface of the table for the plane of the ecliptic1 and the two opposite points where this plane is intersected by the edge of the disk for the equinoxes4 ,the motion of these points as the inclined disk revolves represents the precession of the equinoxes4 ,this term means that the direction of the motion of the equinoxes1 as they shift their place on the ecliptic1 is such that they seem to precess1 or move forward1 as if to meet the sun in its annual journey round the ecliptic4 ,the direction is from east to west1 and thus the zodiacal signs are carried farther and farther westward from the constellations originally associated with them2 for these signs1 as we have said1 are so arranged that they begin at the vernal equinox1 and if the equinox moves1 the whole system of signs must move with it4 ,the amount of the motion is about #ej4b per year1 and since there are #a1bif1jjj in a circle1 simple division shows that the time required for one complete revolution of the equinoxes must be1 as already stated in reference to the poles1 about #be1hjj years4 ,a little over #bjjj years ago the signs and the constellations were in accord2 it follows1 then1 that about #bc1hjj years in the future1 they will be in accord again4 ,in the meanwhile the signs will have backed entirely round the circle of the ecliptic4 ,the attentive reader will perceive that the precession of the equinoxes1 with its attendant revolution of the celestial poles round the poles of the ecliptic1 must affect the position of the ,north ,star4 ,we have already said that that star only happens to occupy its present commanding position in the sky4 ,the star itself is motionless1 or practically so1 with regard to the earth1 and it is the north pole that changes its place4 ,at the present time the pole is about #a #aj1 from the ,north ,star1 in the direction of the ,great ,dipper1 and it is slowly drawing nearer so that in about #bjj years it will be less than half a degree from the star4 ,after that the precessional motion will carry the pole in a circle departing farther and farther from the star1 until the latter will have entirely lost its importance as a guide to the position of the pole4 ,it happens1 however1 that several other conspicuous stars lie near this circle4 ,one of these is ,thuban1 or ,alpha ,draconis 7not now as bright as it once was71 and this star at the time when it served as an indicator of the place of the pole1 some #dfjj years ago1 was connected with a very romantic chapter in the history of astronomy4 ,in the great pyramid of ,cheops in ,egypt1 there is a long passage leading straight toward the north from a chamber cut deep in the rock under the centre of the pyramid1 and the upward slope of this passage is such that it is believed to have been employed by the ,egyptian astronomer-priests as a kind of telescope-tube for viewing the then pole star1 and observing the times of its passage over the meridian--for even the ,north ,star1 since it is not exactly at the pole1 revolves every twenty-four hours in a tiny circle about it1 and consequently crosses the meridian twice a day1 once above and once beneath the true pole4 ,about #aa1ejj years in the future1 the extremely brilliant star ,vega1 or ,alpha ,lyr1 will serve as a pole star1 although it will not be as near the pole as the ,north ,star now is4 ,at that time the ,north ,star will be nearly #ej from the pole4 ,in about #ba1jjj years the pole will have come round again to the neighbourhood of ,alpha ,draconis1 the star of the pyramid1 and in about #be1hjj years the ,north ,star will have been restored to its present prestige as the apparent hub of the heavens4 ,one curious irregularity in the motion of the earth's poles must be mentioned in connection with the precession of the equinoxes4 ,this is a kind of 8nodding10 known as nutation4 ,it arises from variation in the effect of the attraction of the sun and the moon1 due to the varying directions in which the attraction is exercised4 ,as far as the sun is concerned1 the precession is slower near the time of the equinoxes than in other parts of the year2 in other words1 it is most rapid in mid-summer and mid-winter when one or the other of the poles is turned sunward4 ,a similar1 but much larger1 change takes place in the effect of the moon's attraction owing to the inclination of her orbit to the ecliptic4 ,during about nine and a half years1 or half the period of revolution of her nodes 7see ,part ,,iii1 ,section #d71 the moon tends to hasten the precession1 and during the next nine and a half years to retard it4 ,the general effect of the combination of these irregularities is to cause the earth's poles to describe a slightly waving curve instead of a smooth circle round the poles of the ecliptic4 ,there are about #adjj of these 8waves10 or 8nods10 in the motion of the poles in the course of their #bf1jjj-year circuit4 ,in accurate observation the astronomer is compelled to take account of the effects of nutation upon the apparent places of the stars4 ,a very remarkable general consequence of the change in the direction of the earth's axis will be mentioned when we come to deal with the seasons4 ,illustration3 ,the ,great ,southern ,star-,cluster ,centauri ,photographed by ,s4 ,i4 ,bailey at the ,south ,american ,station of ,harvard ,observatory4 ,note the streaming of small stars around the cluster4 ,the cluster itself is globular and its stars are too numerous to be counted1 or even to be separately distinguished in the central part4 ---------------------------------------- -------------------------------- ,,part ,,ii4 ,,the ,,earth4 ---------------------------------------- -------------------------------- ,,part ,,ii4 ,,the ,,earth4 #a4 ,nature1 ,shape1 and ,size of the ,earth4 ,the situation of the earth in the universe has been briefly described in ,part ,i2 it remains now to see what the earth is in itself1 and what are some of the principal phenomena connected with it as a celestial body inhabited by observant and reasoning beings4 ,we know by ordinary experience that the earth is composed of rock1 sand1 soil1 etc41 and generally covered1 where there is no running or standing water in the form of rivers1 lakes1 or seas1 with vegetation1 such as trees and grass4 ,further experience teaches us that the earth is very large1 and that its surface is divided into wide areas of land and of water4 ,the largest bodies of water1 the oceans1 taken all together1 cover about #gb per cent41 or nearly three-quarters of the entire surface of the earth4 ,investigations carried as far down as we can go show that the interior of the earth consists of various kinds of rock1 in which are contained many different kinds of metals4 ,while there is reason for thinking that a high degree of temperature prevails deep in the earth1 yet it appears evident1 for other reasons1 that1 taken as a whole1 it is solid and very rigid throughout4 ,by methods1 the history and description of which we have not here sufficient space to give1 it has been proved that the earth is1 in form1 a globe1 or more strictly an ellipsoid1 slightly drawn in at the poles and swollen round the equator4 ,the polar diameter is #ghii miles1 and the equatorial diameter #gibf miles1 the difference amounting to only #bg miles4 ,thus1 for ordinary purposes1 we may regard the earth as being a true sphere4 ,the level of its surface1 however1 is varied by hills and mountains1 which1 though insignificant in comparison with the size of the whole earth1 are enormous when compared with the structures of human hands4 ,the loftiest known mountain on the earth1 ,mt4 ,everest in the ,himalayas1 has an elevation of #bi1jjj feet above sea-level1 and the deepest known depression of the ocean bottom1 near the island of ,guam in the ,pacific1 sinks #ca1fad feet below sea-level4 ,thus1 the apex of the highest mountain is about eleven and a half miles in vertical elevation above the bottom of the deepest pit of the sea--a distance very considerably less than half the difference between the equatorial and polar diameters of the earth4 ,it is believed that at the beginning of its history the earth was a molten mass1 or perhaps a mass of hot gases and vapours like the sun1 and that it assumed its present shape in obedience to mechanical laws1 as it cooled off4 ,the rotation caused it to swell round the equator and draw in at the poles4 ,the outer part of the earth is called its crust1 and geology shows that this has been subject to violent changes1 such as upheavals and subsidences1 and that in many places sea and land have interchanged places1 probably more than once4 ,geology also shows that the rocks of the earth's crust are filled with the remains1 or fossils1 of plants and animals differing from those now existing1 though related to them1 and that many of these must have lived millions of years ago4 ,thus we see that the earth bears marks of an immense antiquity1 and that it was probably inhabited during vast ages before the race of man had been developed4 ,the origin of life upon the earth is unknown4 #b4 ,the ,attraction of ,gravitation4 ,among the phenomena of life upon the earth1 which are so familiar that only thoughtful persons see anything to wonder at in them1 is what we call the 8weight0 of bodies4 ,every person feels that he is held down to the ground by his weight1 and he knows that if he drops a heavy body it will fall straight toward the ground4 ,but what is this weight which causes everything either to rest upon the earth or to fall back to it if lifted up and dropped8 ,the answer to this question involves a principle1 or 8law10 which affects the whole universe1 and makes it what we see it4 ,this principle is one of the great foundation stones of astronomy4 ,it is called the law of gravitation1 the word gravitation being derived from the ,latin gravis1 8heavy40 ,briefly stated1 the law is that every body1 or every particle of matter1 attracts1 or strives to draw to itself1 every other body1 or particle of matter4 ,this force is called the attraction of gravitation4 ,a large body possesses more attractive force than a small one1 in proportion to the mass1 or quantity of matter1 that it contains4 ,the earth1 being extremely large1 holds all bodies on its surface with a force proportionate to its great mass4 ,this explains why we possess what we call weight1 which is simply the effect of the attraction of the earth upon our bodies4 ,a large body is heavier1 or drawn with more force by the earth1 than a small one 7composed of the same kind of matter71 because it has a greater mass4 ,the body really attracts the earth as much as the earth attracts the body1 but the amount of motion caused by the attraction is proportional to the respective masses of the attracting bodies1 and since the mass of the earth is almost infinitely great in comparison with that of any body that we can handle1 the motion which the latter imparts to the earth is imperceptible1 and it is the small body only that is seen to move under the force of the attraction4 ,now we are going to see how vastly important in its effects is the fact that the earth is spherical in form4 ,sir ,isaac ,newton1 who first worked out mathematically the law of gravitation1 proved that a spherical body attracts1 and is attracted1 as if its entire mass were concentrated in a point at its centre4 ,from this it follows that the attraction of the earth is exercised just as if the whole attractive force emanated from a middle point1 and1 that being so1 the effect of the attraction is to draw bodies from all sides toward the centre of the earth4 ,this explains why people on the opposite side of the earth1 or under our feet1 as we say1 experience the same attractive force1 or have the same weight1 that we do4 ,all round the earth1 no matter where they may be situated1 objects are drawn toward the centre4 ,if at any point on the earth you suspend a plumb-line1 and then1 going one quarter way round1 suspend another plumb-line1 each of the lines will be vertical at the place where it hangs1 and yet1 the directions of the two lines will be at right angles to one another1 since both point toward the centre of the earth4 ,knowing the manner in which the earth attracts1 we have the means of determining its entire mass1 or1 as it is sometimes called1 the weight of the earth4 ,the principle on which this is done is easily understood1 ,suppose1 for instance1 that a small ball of lead1 of known weight1 is brought near a large ball1 and delicately suspended in such a way that1 by microscopic observation1 the movement imparted by the attraction of the large ball can be measured4 ,the force required to produce this movement can be compared with the force of the earth's attraction which produces the weight of the ball1 and thus the ratio of the mass of the earth to that of the ball is determined4 ,the total mass of the earth has been found to be equivalent to a 8weight0 of about #f1ejj1jjj1jjj1jjj1jjj1jjj1jjj tons4 ,the mean density of the earth compared with that of water is found to be about #e1 that is to say1 the earth weighs #e times as much as a globe of water of equal size4 ,newton did not stop with showing the manner of the earth's attraction upon bodies on or near its surface2 he proved that the earth attracted the moon also1 and thus retained it in its orbit4 ,to understand this we must notice another fact concerning the manner in which gravitation acts4 ,its force varies with distance4 ,experiment followed by mathematical demonstration1 has proved that the variation of the attraction is inversely proportional to the square of the distance4 ,this simply means that if the distance between the two bodies concerned is doubled1 the force of attraction will be diminished four times1 #d being the square of #b2 and that if the distance is halved1 the force will be increased fourfold4 ,increase the distance three times1 and the force diminishes nine times2 diminish the distance three times1 and the force increases nine times1 because #i is the square of #c1 and1 as we have said1 the force varies inversely1 or contrarily1 to the change of distance4 ,knowing this1 ,newton computed what the force of the earth's attraction must be on the moon1 and he found that it was just sufficient to keep the latter moving round and round the earth4 ,but why does not the moon fall directly to the earth8 ,because the moon had originally another motion across the direction of the earth's attraction4 ,how it got this motion is a question into which we cannot here enter1 but1 if it were not attracted by the earth 7or by the sun71 the moon would travel in a straight line through space1 like a stone escaping from a sling4 ,the force of the attraction is just sufficient to make the moon move in an orbital path about the earth4 ,illustration3 ,fig4 #e4 ,how the ,earth ,controls the ,moon4 ,let ,c be the centre of the earth and ,m that of the moon4 ,suppose the moon to be moving in a straight line at such a velocity that it will1 if not interfered with1 go to ,a in one day4 ,now suppose the attraction of the earth to act upon it4 ,that attraction will draw it to ,m4 ,again suppose that at ,m the moon were suddenly released from the earth's attraction2 it would then shoot straight ahead to ,b in the course of the next day4 ,but1 in fact1 the earth's attraction acts continually1 and in the second day the moon is drawn to ,m4 ,in other words the moon is all the time falling away from the straight line that it would pursue but for the earth's attraction1 and yet it does not get nearer the earth but simply travels in an endless curve round it4 ,the same principle was extended by ,newton to explain the motion of the earth around the sun4 ,the force of the sun's attraction1 calculated in the same way1 can be shown to be just sufficient to retain the earth in its orbit and prevent it from travelling away into space4 ,and so with all the other planets which revolve round the sun4 ,and this applies throughout the universe4 ,there are certain so-called double1 or binary1 stars1 which are so close together that their attraction upon one another causes them to revolve in orbits about their common centre4 ,in truth1 all the stars attract the earth and the sun1 but the force of this attraction is so slight on account of their immense distance that we cannot observe its effects4 ,the reader who wishes to pursue this subject of gravitational attraction should consult more extensive works1 such as ,prof4 ,young's ,general ,astronomy1 or ,sir ,george ,airy's ,gravitation4 ,illustration3 ,photograph of a ,group of ,sun-spots ,similar groups are frequently seen during periods of sun-spot maximum4 #c4 ,the ,tides4 ,the tides in the ocean are a direct result of the attraction of gravitation4 ,they also involve in an interesting way the principle that a spherical body1 like the earth1 attracts and is attracted as if its entire mass were concentrated at its centre4 ,the cause of the tides is the difference in the attraction of the sun and moon upon the body of the earth as a rigid sphere1 and upon the water of the oceans1 as a fluid envelope whose particles1 while not free to escape from the earth1 are free to move1 or slide1 among one another in obedience to varying forces4 ,the difference of the force of attraction arises from the difference of distance4 ,since the moon1 because of her relative nearness1 is the chief agent in producing tides we shall1 at first1 consider her tidal influence alone4 ,the diameter of the earth is1 in round numbers1 #hjjj miles2 therefore1 its radius is #djjj miles4 ,from this it follows that the centre of the earth is #djjj miles farther from the moon than that side of the earth which is toward her at any time1 and #djjj miles nearer than the side which is away from her4 ,consequently1 her attraction must be stronger upon the water of the ocean lying just under her than upon the centre of the earth1 and it must also be stronger upon the centre of the earth than upon the water of the ocean lying upon the side which is farthest from her4 ,the result of these differences in the force of the moon's attraction is that the water directly under her tends away from the centre of the earth1 while1 on the other hand1 the earth1 considered as a solid sphere1 tends away from the water on the side opposite to that where the moon is1 and these combined tendencies cause the water to rise1 with regard to its general level1 in two protuberances1 situated on opposite sides of the earth4 ,these we call tides4 ,illustration3 ,fig4 #f4 ,the ,tidal ,force of the ,moon4 ,the solid earth is represented surrounded by a shell of water4 ,the water on the side toward the moon is more attracted than the centre of the earth1 ,c2 the water on the opposite side is less attracted4 ,the lines of force from the moon to the parts of the water lying toward ,a and ,b are inclined to the direct line between the centres of the earth and the moon1 and the forces acting along these lines tend to draw the water in the directions shown by the arrow points4 ,these are resultants of the horizontal and vertical components of the moon's attraction at the corresponding points on the earth1 and the force acting along them tends to increase the weight of the water wherever the lines are inclined more toward the centre of the earth than toward the moon4 ,on the side opposite the moon the same effects are produced in reverse1 because on that side the general tendency is to draw the earth away from the water4 ,consequently if the earth did not rotate1 and if it were surrounded with a complete shell of water1 the latter would be drawn into an ellipsoidal shape1 with the highest points under and opposite to the moon1 and the lowest at the extremities of the diameter lying at right angles to the direction of the moon4 ,some persons1 when this statement is made1 inquire3 8,why1 then1 does not the moon take the water entirely away from the earth80 ,the answer is1 that the effect of the tidal force is simply to diminish very slightly the weight of the water1 or its tendency towards the earth's centre1 but not to destroy1 or overmaster1 the gravitational control of the earth4 ,the water retains nearly all its weight1 for the tidal force of the moon diminishes it less than one part in #h1jjj1jjj4 ,still1 this slight diminution is sufficient to cause the water to swell a little above its general level1 at the points where it feels the effect of the tidal force4 ,on the other hand1 around that part of the earth which is situated half-way between the two tides1 or along a diameter at right angles to the direction of the moon1 the latter's attraction increases the weight of the water1 i4 e41 its tendency toward the earth's centre 7see ,fig4 #f74 ,perhaps this can better be understood1 if we imagine the earth to be entirely liquid4 ,in that case the difference in the force of the moon's attraction with difference of distance would be manifested in varying degrees throughout the earth's whole frame1 and the result would be to draw the watery globe out into an ellipsoidal figure1 having its greatest diameter in the line of the moon's attraction1 and its smallest diameter at right angles to that line4 ,the proportions of the ellipsoid would be such that the forces would be in equilibrium4 ,owing to a variety of causes1 such as the rotation of the earth on its axis1 which carries the water rapidly round with it2 the inertia of the water1 preventing it from instantly responding to the tidal force2 the irregular shape of the oceans1 interrupted on all sides by great areas of land2 their varying depth1 producing differences of friction1 and so on1 the tidal waves do not appear directly under1 or directly opposite to1 the moon1 and the calculation of the course and height of the actual tides1 at particular points on the earth1 becomes one of the most difficult problems in astronomical physics4 ,we now turn to consider the effects of the sun's tidal force in connection with that of the moon4 ,this introduces further complications4 ,the solar tides are only about two-fifths as high as the lunar tides1 but they suffice to produce notable effects when they are either combined with1 or act in opposition to1 the others4 ,they are combined twice a month--once when the moon is between the earth and the sun1 at the time of new moon2 and again when the moon is in opposition to the sun1 at the time of full moon4 ,in these two positions the attractions of the sun and the moon must1 so to speak1 act together1 with the result that the tides produced by them blend into a single greater wave4 ,this combination produces what are called spring tides1 the highest of the month4 ,when1 on the other hand1 the moon is in a position at right angles to the direction of the sun1 which happens at the lunar phases named first and last quarters1 the solar and the lunar tides have their crests #ij apart1 and1 in a sense1 act against one another1 and then we have the neap tides1 which are the lowest of the month4 ,without entering into a demonstration1 it may here be stated as a fact to be memorised1 that the tidal force exerted by any celestial body varies inversely as the cube of the distance4 ,this is the reason why the sun1 although it exceeds the moon in mass more than #be1jjj1jjj times1 and is situated only about #djj times as far away from the earth1 exercises comparatively so slight a tidal force on the water of the ocean4 ,if the tidal force varied as the square of the distance1 like the ordinary effects of gravitation1 the tides produced by the sun would be more than #aej times as high as those produced by the moon1 and would sweep ,new ,york1 ,london1 and all the seaports of the world to destruction4 ,in that case it might be possible1 by delicate observations1 to detect a tidal effect produced upon the oceans of the earth by the planet ,jupiter4 #d4 ,the ,atmosphere4 ,the solid globe of the earth is enveloped in a mixture of gases1 principally oxygen and nitrogen1 which we call the air1 or the atmosphere1 and upon whose presence our life and most other forms of life depend4 ,the atmosphere is retained by the attraction of the earth1 and it rotates together with the earth4 ,if this were not so--if the atmosphere stood fast while the earth continued to spin within it--a terrific wind would constantly blow from the east1 having a velocity at the equator of more than a thousand miles an hour4 ,exactly how high the atmosphere extends we do not know--it may not have any definite limits--but we do know that its density rapidly diminishes with increase of height above the ground1 so that above an elevation of a few miles it becomes so rare that it would not support human life4 ,the phenomena of meteors1 set afire by the friction of their swift rush through the upper air1 prove1 however1 that there is a perceptible atmosphere at an elevation of more than a hundred miles4 ,from an astronomical point of view1 the most important effect of the presence of the atmosphere is its power of refracting light4 ,by refraction is meant the property possessed by every transparent medium of bending1 under particular circumstances1 the rays of light which enter it out of their original course4 ,the science of physics teaches us that if a ray of light passes from any transparent medium into another which is denser1 and if the path of this ray is not perpendicular to the surface of the second medium1 it will be turned from its original course in such a way as to make it more nearly perpendicular4 ,thus1 if a ray of light passes from air into water at a certain slope to the surface1 it will1 upon entering the water1 be so changed in direction that the slope will become steeper4 ,only if it falls perpendicularly upon the water will it continue on without change of direction4 ,conversely a ray passing from a denser into a rarer medium is bent away from a perpendicular to the surface of the first medium1 or its slope becomes less4 ,this explains why1 if we put a coin in a bowl1 with the eye in such a position that it cannot see the coin over the edge1 and then fill the bowl with water1 the coin seems to be lifted up into sight4 ,moreover1 if any transparent medium increases in density with depth1 the amount of refraction will increase as the ray goes deeper1 and the direction of the ray will be changed from a straight line into a curve1 tending to become more and more perpendicular4 ,now all this applies to the atmosphere4 ,if a star is seen in the zenith1 its light falls perpendicularly into the atmosphere and its course is not deviated1 or in other words there is no refraction4 ,but if the star is somewhere between the zenith and the horizon1 its light falls slopingly into the atmosphere1 and is subject to refraction1 the amount of bending increasing with approach to the horizon4 ,observation shows that the refraction of the atmosphere1 which is zero at the zenith1 increases to about half a degree 7and sometimes much more1 depending upon the state of the air71 near the horizon4 ,it follows that a celestial object seen near the horizon will ordinarily appear about half a degree above its true place4 ,since the apparent diameters of the sun and the moon are about half a degree1 when they are rising or setting they can be seen on the horizon before they have really risen above it1 or after they have really sunk below it4 ,tables of refraction at various altitudes have been prepared1 and they have to be consulted in all exact observations of the celestial bodies4 ,illustration3 ,fig4 #g4 ,refraction4 ,suppose an observer situated at ,o on the earth4 ,the sun1 at ,s1 has sunk below the level of his horizon1 ,o ,h1 but since the sun sends out rays in all directions there will be some1 such as ,s ,a ,b1 which will strike the atmosphere at ,a1 and the refraction1 tending to make the ray more nearly perpendicular to the surface of the atmosphere1 will1 instead of allowing it to go on straight over the observer's head to ,b1 bend it down along the dotted line ,a ,o1 and the observer will see the sun as if it lay in the direction of the dotted line ,o ,a ,s1 which places the sun apparently above the horizon4 #e4 ,dip of the ,horizon4 ,another correction which has to be applied in many observations depends upon the sphericity of the earth4 ,we have described the rational horizon1 and pointed out how it differs from the sensible horizon4 ,we have also said that at sea the sensible horizon nearly accords with the rational horizon 7see ,part ,i1 ,sect4 #c74 ,but the accord is not complete1 owing to what is called the dip of the horizon4 ,in fact1 the sea horizon lies below the rational horizon by an amount varying with the elevation of the eye above the surface4 ,geometry enables us to determine just what the dip of the horizon must be for any given elevation of the eye4 ,a rough and ready rule1 which may serve for many purposes1 is that the square root of the elevation of the eye in feet equals the dip of the horizon in minutes of arc1 or of angular measure4 ,the reader will readily see that the dip of the horizon is a necessary consequence of the rotundity of the earth4 ,it is because of this that1 as a ship recedes at sea her hull first disappears below the horizon1 and then her lower sails1 and finally her top-sails4 ,the use of a telescope does not help the matter1 because a telescope only sees straight1 and cannot bend the line of sight over the rim of the horizon4 ,atmospheric refraction1 however1 enables us to see an object which would be hidden by the horizon if there were no air4 ,in navigation1 which1 as a science1 is an outgrowth of astronomy1 these things have to be carefully taken into account4 ,illustration3 ,fig4 #h4 ,dip of the ,horizon4 ,it is to be remembered that it is the sensible horizon which dips1 and not the rational horizon4 ,the sensible horizon of the observer at the elevation ,a dips below the horizontal plane and he sees round the curved surface as far as a2 in other words his skyline is at a4 ,the observer at the elevation ,b has a sensible horizon still more inclined and he sees as far as b4 ,if the observation were made from an immense height the observer would see practically half round the earth just as we see half round the globe of the moon4 ,illustration3 ,polar ,streamers of the ,sun1 ,eclipse of #ahhi ,illustration3 ,the ,solar ,corona at the ,eclipse of #ahga ,from drawings4 #f4 ,aberration4 ,a few words must be said about the phenomenon known as aberration of light4 ,this is an apparent displacement of a celestial object due to the motion of the earth in its orbit4 ,it is customary to illustrate it by imagining oneself to be in a shower of rain1 whose drops are falling vertically4 ,in such a case1 if a person stands fast the rain will descend perpendicularly upon his head1 but if he advances rapidly in any direction he will feel the drops striking him in the face1 because his own forward motion is compounded with the downward motion of the rain so that the latter seems to be descending slantingly toward him4 ,the same thing happens with the light falling from the stars4 ,as the earth advances in its orbit it seems to meet the light rays1 and they appear to come from a direction ahead of the flying earth4 ,the result is that1 since we see a star in the direction from which its light seems to come1 the star appears in advance of its real position1 or of the position in which we would see it if the earth stood fast4 ,the amount by which the position of a star is shifted by aberration depends upon the ratio of the earth's velocity to the velocity of light4 ,in round numbers this ratio is as #a to #aj1jjj4 ,the motion of the earth being in a slightly eccentric ellipse1 the stars describe corresponding1 but very tiny1 ellipses once every year upon the background of the sky4 ,but the precise shape of the ellipse depends upon the position of the star on the celestial sphere4 ,if it is near one of the poles of the ecliptic1 it will describe an annual ellipse which will be almost a circle1 its greater diameter being #da of arc4 ,if it is near the plane of the ecliptic1 it will describe a very eccentric ellipse1 but the greater diameter will always be #da1 although the shorter diameter may be immeasurably small4 ,the effects of aberration have to be allowed for in all careful astronomical observation either of the sun or the stars4 ,this is done by reducing the apparent place of the object to the place it would have if it were seen at the centre of its annual ellipse4 #g4 ,time4 ,without astronomical observations we could have no accurate knowledge of time4 ,the basis of the measurement of time is furnished by the rotation of the earth on its axis4 ,we divide the period which the earth occupies in making one complete turn into twenty-four equal parts1 or hours4 ,the ascertainment of this period1 called a day1 depends upon observations of the stars4 ,suppose we see a certain star exactly on the meridian at some moment2 just twenty-four hours later that star will have gone entirely round the sky1 and will again appear on the meridian4 ,the revolving heavens constitute the great clock of clocks1 by whose movements all other clocks are regulated4 ,we know that it is not the heavens which revolve1 but the earth which rotates1 but for convenience we accept the appearance as a substitute for the fact4 ,the rotation of the earth is so regular that no measurable variation has been found in two thousand years4 ,we have reasons for thinking that there must be a very slow and gradual retardation1 owing principally to the braking action of the tides1 but it is so slight that we cannot detect it with any means at present within our command4 ,in ,part ,i it was shown how the passage across the meridian of the point in the sky called the vernal equinox serves to indicate the beginning of the astronomical 8day10 but the position of the vernal equinox itself has to be determined by observations on the stars4 ,by means of a telescope1 so mounted that it can only move up or down1 round a horizontal axis1 and with the axis pointing exactly east and west so that the up and down movements of the telescope tube follow the line of the meridian1 the moment of passage across the meridian of a star at any altitude can be observed4 ,observations of this nature are continually made at all great government observatories1 such as the observatory at ,washington or that at ,greenwich1 and at many others1 and by their means clocks and chronometers are corrected1 and a standard of time is furnished to the whole world4 ,there are1 however1 three different ways of reckoning time1 or1 as it is usually said1 three kinds of time4 ,one is sidereal time1 which is indicated by the passage of stars across the meridian1 and which measures the true period of the earth's rotation2 another is apparent solar time1 which is indicated by the passage of the sun across the meridian2 and a third is mean solar time1 which is indicated by a carefully regulated clock1 whose errors are corrected by star observations4 ,this last kind of time is that which is universally used in ordinary life 7the use of sidereal time being confined to astronomy71 so it is necessary to explain what it is and how it differs from apparent solar time4 ,illustration3 ,fig4 #i4 ,sidereal and ,solar ,time4 ,c is the centre of the earth1 and ,o the place of an observer on the earth's surface4 ,suppose the sun at ,a to be in conjunction with the star ,s4 ,then1 at the end of twenty-four sidereal hours1 when the earth has made one turn on its axis and the place ,o has again come into conjunction with the star1 the sun1 in consequence of its yearly motion in the ecliptic1 will have advanced to ,b1 and the earth will have to turn through the angle ,a ,c ,b before ,o will overtake the sun and complete a solar day2 wherefore the solar day is longer than the sidereal4 ,in the first place1 the reason why sidereal time is not universally and exclusively used is because1 although it measures the true period of the earth's rotation by the apparent motion of the stars1 it does not exactly accord with the apparent motion of the sun2 and1 naturally1 the sun1 since it is the source of light for the earth1 and the cause of the difference between day and night1 is taken for all ordinary purposes1 as the standard indicator of the progress of the hours4 ,the fact that it is mid-day1 or noon1 at any place when the sun crosses the meridian of that place1 is a fact of common knowledge1 which cannot be ignored4 ,on the other hand1 the vernal equinox1 which is the 8noon mark0 for sidereal time1 is independent of the alternation of day and night1 and may be on the meridian as well at midnight as at mid-day4 ,before clocks and watches were perfected1 the moment of the sun's passage over the meridian was determined by means of a gnomon1 which shows the instant of noon by the length of a shadow cast by an upright rod4 ,since the apparent course of the sun through the sky is a curve1 rising from the eastern horizon1 attaining its greatest elevation where it meets the meridian1 and thence declining to the western horizon1 it is evident that the length of the shadow must be least when the sun is on the meridian1 or at its maximum altitude4 ,the gnomon1 or the sun-dial1 gives us apparent solar time4 ,but this differs from sidereal time because1 as we saw in ,part ,i1 the sun1 in consequence of the earth's motion round it1 moves about one degree eastward every twenty-four hours1 and1 since one degree is equal to four minutes of time1 the sun rises about four minutes later1 with reference to the stars1 every morning4 ,consequently it comes four minutes later to the meridian day after day4 ,or1 to put it in another way1 suppose that the sun and a certain star are upon the meridian at the same instant4 ,the star is fixed in its place in the sky1 but the sun is not fixed2 on the contrary it moves about one degree eastward 7the same direction as that of the earth's rotation7 in twenty-four hours4 ,then1 when the rotation of the earth has brought the star back to the meridian at the end of twenty-four sidereal hours1 the sun1 in consequence of its motion1 will still be one degree east of the meridian1 and the earth must turn through the space of another degree1 which will take four minutes1 before it can have the sun again upon the meridian4 ,the true distance moved by the sun in twenty-four hours is a little less than one degree1 and the exact time required for the meridian to overtake it is #c min4 #ef4eee sec4 ,thus1 the sidereal day 7period of #bd hours7 is nearly four minutes shorter than the solar day4 ,it would seem1 then1 that by taking the sun for a guide1 and dividing the period between two of its successive passages over the meridian into twenty-four hours1 we should have a perfect measure of time1 without regard to the stars2 in other words1 that apparent solar time would be entirely satisfactory for ordinary use4 ,but1 unfortunately1 the apparent eastward motion of the sun is not regular4 ,it is sometimes greater than the average and sometimes less4 ,this variation is due almost entirely3 first1 to the fact that its orbit not being a perfect circle the earth moves faster when it is near perihelion1 and slower when it is near aphelion2 and1 second1 to the effects of the inclination of the ecliptic to the equator4 ,in consequence1 another measure of solar time is used1 called mean solar time1 in which1 by imagining a fictitious sun1 moving with perfect regularity through the ecliptic1 the discrepancies are avoided4 ,all ordinary clocks are set to follow this fictitious1 or mean1 sun4 ,the result is that clock time does not agree exactly with sun-dial time1 or1 what is the same thing1 apparent solar time4 ,the clock is ahead of the real sun at some times of the year1 and behind it at other times4 ,this difference is called the equation of time4 ,four times in the year the equation is zero1 i4e41 there is no difference between the clock and the sun4 ,these times are ,april #ae1 ,june #ad1 ,sept4 #a1 and ,dec4 #bd4 ,at four other times of the year the difference is at a maximum1 viz4 ,feb4 #aa1 sun #ad min4 #bg sec4 behind clock2 ,may #ad1 sun #c min4 #di sec4 ahead of clock2 ,july #bf1 sun #f min4 #af sec4 behind clock2 ,nov4 #b1 sun #af min4 #ah sec4 ahead of clock4 ,these dates and differences vary very slightly from year to year4 ,but1 whatever measures of time we may use1 it is observation of the stars that furnishes the means of correcting them4 ,illustration3 ,morehouse's ,comet1 ,october #ae1 #aijh ,photographed at the ,yerkes ,observatory by ,e4 ,e4 ,barnard with the ten-inch ,bruce telescope4 ,exposure one hour and a half4 ,note the detached portions which appeared to separate from the head and retreat up the line of the tail at enormous velocity4 ,illustration3 ,morehouse's ,comet1 ,november #ae1 #aijh ,photographed at the ,yerkes ,observatory by ,e4 ,e4 ,barnard1 with the ten-inch ,bruce telescope4 ,exposure forty minutes4 #h4 ,day and ,night4 ,the period of twenty-four hours required for one turn of the earth on its axis is called a day1 and in astronomical reckoning it is treated as an undivided whole1 the hours being counted uninterruptedly from #j to #bd2 but nature has divided the period into two very distinct portions1 one characterised by the presence and the other by the absence of the sun4 ,popularly we speak of the sunlighted portion as day and of the other as night1 and there are no two associated phenomena in nature more completely in contrast one to the other4 ,the cause of the contrast between day and night must have been evident to the earliest human beings who were capable of any thought at all4 ,they saw that day inevitably began whenever the sun rose above the horizon1 and as inevitably ceased whenever it sank beneath it4 ,in all literatures1 imaginative writers have pictured the despair of primeval man when he first saw the sun disappear and night come on1 and his joy when he first beheld the sun rise1 bringing day back with it4 ,even his uninstructed mind could not have been in doubt about the causal connection of the sun with daylight4 ,we now know that the cause of the alternate rising and setting of the sun1 and of its apparent motion through the sky1 is the rotation of the earth4 ,making in our minds a picture of the earth as a turning globe exposed to the sunbeams1 we are able to see that one half of it must necessarily be illuminated1 while the other half is in darkness4 ,we also see that its rotation causes these two halves gradually to interchange places so that daylight progresses completely round the earth once in the course of twenty-four hours4 ,if the earth were not surrounded by an atmosphere1 exactly one half of it would lie in the sunlight and exactly one half in darkness1 but the atmosphere causes the illuminated part slightly to exceed the unilluminated part4 ,the reason for this is twofold3 first1 because the atmosphere1 being transparent and extending to a considerable height above the solid globe1 receives rays from the sun after the latter has sunk below the horizon1 and these rays cause a faint illumination in the sky after the sun as viewed from the surface of the ground has disappeared2 and1 second1 because the air has the property of refracting the rays of light1 in consequence of which the sun appears above the horizon both a little time before it has actually risen and a little time after it has actually set4 ,the faint illumination at the beginning and the end of the day is called twilight4 ,its cause is the reflection of light from the air at a considerable elevation above the ground4 ,observation shows that evening twilight lasts until the sun has sunk about #ah below the western horizon1 while morning twilight begins when the sun is still #ah below the nearest horizon4 ,the length of time occupied by twilight1 or its duration1 depends upon the observer's place on the earth and increases with distance from the equator4 ,the length of twilight at any particular place also varies with the seasons4 ,it will probably have occurred to the reader that1 since day and night are ceaselessly chasing each other round the globe1 it must be necessary to choose some point of beginning1 in order to keep the regular succession of the days of the week4 ,the necessity for this is evident as soon as we reflect that what is sunrise at one place on the earth1 is sunset for a place situated half-way round1 on the other side4 ,to understand this it will be better1 perhaps1 to consider the phenomena of noon at various places4 ,it is noon at any place when the sun is on the meridian of that place4 ,but we have seen that every place has its own meridian2 consequently1 since the sun cannot be on the meridian of more than one place at a time1 each different place 7reckoning east and west1 for1 of course1 all places lying exactly north or south of one another have the same meridian71 must have its own local noontime4 ,since the sun appears to move round the earth from east to west1 it will arrive at the meridian of a place lying east of us sooner than at our meridian1 and it will arrive at our meridian sooner than at that of a place lying west of us4 ,thus1 when it is noon at ,greenwich1 it is about #g o'clock ,a4,m41 or five hours before noon1 at ,new ,york1 because the angular distance westward round the earth's surface from ,greenwich to ,new ,york is1 in round numbers1 #ge1 which corresponds with five hours of time1 there being #aej to every hour4 ,at the same moment it will be #e o'clock ,p4,m41 or five hours after noon1 at ,cashmere1 because ,cashmere lies #ge east of ,greenwich4 ,that is to say1 the sun crosses the meridian of ,cashmere five hours before it reaches the meridian of ,greenwich1 and it crosses the meridian of ,greenwich five hours before it reaches that of ,new ,york4 ,at a place half-way round the circumference of the globe1 i4e4 #ahj either east or west of ,greenwich1 it will be midnight at the same instant when it will be mid-day1 or noon1 at ,greenwich4 ,now let us consider this for a moment4 ,illustration3 ,the arrows show the direction in which the earth turns 7from west to east74 ,it is always noon at the place which is directly under the sun4 ,call it ,sunday noon at ,greenwich1 at the top of the circle2 then it is #aj ,a4,m4 ,sunday at a point #cj west and #b ,p4,m4 ,sunday at a point #cj east1 and so on4 ,exactly opposite to the noon point it is midnight4 ,by common consent we change the name of the day1 and the date1 at midnight2 consequently it is ,sunday midnight just east of the vertical line at the bottom of the circle and ,monday morning just west of it4 ,if we cross that line going westward we shall pass directly from ,sunday to ,monday1 and if we cross it going eastward we shall pass directly from ,monday to ,sunday4 ,since1 by convention1 this is a fixed line on the earth's surface1 the same change will take place no matter what the hour of the day may be4 ,it is customary to change the name of the day at midnight4 ,thus at the stroke of midnight1 anywhere1 ,sunday gives place to ,monday4 ,suppose1 then1 that the day when we see the sun on the meridian at ,greenwich happens to be ,sunday4 ,sunday will then be1 so to speak1 twelve hours old at ,greenwich1 because it began there at the preceding midnight4 ,sunday will be only seven hours old at ,new ,york1 where it also began at the preceding midnight4 ,in ,california1 #de1 or three hours1 still farther west than ,new ,york1 ,sunday will be only four hours old1 since the local time there is only four hours after midnight4 ,go on over the ,pacific ,ocean1 until we arrive at a point #ahj1 or twelve hours1 west of ,greenwich4 ,there1 evidently1 ,sunday will just have been born1 the preceding day1 ,saturday1 having expired at the stroke of midnight4 ,now if we just step over that line of #ahj in what day shall we be8 ,it cannot be ,sunday1 because ,sunday has just begun on the line itself4 ,it cannot be ,saturday1 because that would be counting backward4 ,evidently it can be no other than ,monday4 ,let us examine this a little more closely4 ,it is ,sunday noon at ,greenwich4 ,we now go round the earth eastward instead of westward4 ,at #ij1 or six hours1 east of ,greenwich1 we find that it is #f ,p4,m4 ,sunday and at #ahj1 or twelve hours1 east of ,greenwich we find that it is ,sunday midnight1 or in other words ,monday morning4 ,but the line of #ahj east of ,greenwich coincides with the line of #ahj west of ,greenwich1 which we formerly approached from the opposite direction4 ,so we see that we were right in concluding that in stepping over that line from the east to the west side1 we were passing from ,sunday into ,monday4 ,it is on that line that each day vanishes and its successor takes its place4 ,it is the 8date-line0 for the whole earth1 chosen by the common consent of every civilised nation1 just as we have seen that the meridian of ,greenwich is the common reference line for reckoning longitude4 ,it lies entirely in the ,pacific ,ocean1 hardly touching any island1 and it was chosen for this very reason1 because if it ran over inhabited lands1 like ,europe or ,america1 it would cause endless confusion4 ,situated as it is1 it causes no trouble except to sea captains1 and very little to them4 ,if a ship crosses the line going westward the captain jumps his log-book one day forward4 ,if it is1 for instance1 ,wednesday noon1 east of the line he calls it ,thursday noon1 as soon as he has passed over4 ,if he is going eastward he drops back a day on crossing the line1 as from ,thursday noon to ,wednesday noon4 ,the date-line theoretically follows the #ahjth meridian1 but1 in fact1 in order to avoid certain groups of islands1 it bends about a little1 while keeping its general direction from north to south4 #i4 ,the ,seasons4 ,we now recall again what was said in ,part ,i1 about the inclination of the ecliptic1 or the apparent path of the sun in the heavens1 to the equator4 ,because of this inclination1 the sun appears half the year above the equator and the other half below it4 ,when it is above the equator for people living in the northern hemisphere1 it is below the equator for those living in the southern hemisphere1 and vice versa4 ,this is because observers on opposite sides of the plane of the equator look at it from opposite points of view4 ,for the northern observer the celestial equator appears south of the zenith2 for the southern observer it appears north of the zenith1 its distance from the zenith1 in both cases1 increasing with the observer's distance from the equator of the earth4 ,if he is on the earth's equator1 the celestial equator passes directly through the zenith4 ,for convenience we shall suppose the observer to be somewhere in the northern hemisphere4 ,illustration3 ,head of the ,great ,comet of #ahfa ,from a drawing by ,warren ,de ,la ,rue4 ,illustration3 ,halley's ,comet1 ,may #e1 #aiaj ,photographed at the ,yerkes ,observatory by ,e ,e4 ,barnard1 with the ten-inch ,bruce telescope4 ,this was shortly before the passage of the comet between the earth and the sun1 when some think its tail was thrown over us4 ,let us begin with that time of the year when the sun arrives at the vernal equinox4 ,this occurs about the #bast of ,march4 ,the sun is then perpendicular over the equator1 daylight extends1 uninterrupted1 from pole to pole1 and day and night 7neglecting the effects of twilight and refraction7 are of equal length all over the earth4 ,everywhere there are about twelve hours of daylight and twelve hours of darkness4 ,this is the beginning of the astronomical spring4 ,as time goes on1 the motion of the sun in the ecliptic carries it eastward from the vernal equinox1 and1 at the same time1 owing to the inclination of the ecliptic1 it rises gradually higher above the equator1 increasing its northern declination slowly1 day after day4 ,immediately the equality of day and night ceases1 and in the northern hemisphere the day becomes gradually longer in duration than the night1 while in the southern hemisphere it becomes shorter4 ,moreover1 because the sun is now north of the equator1 daylight no longer extends from pole to pole on the earth1 but the south pole is in continual darkness1 while the north pole is illuminated4 ,you can illustrate this1 and explain to yourself why the relative length of day and night changes1 and why the sun leaves one pole in darkness while rising higher over the other1 by suspending a small terrestrial globe with its axis inclined about #bc from the perpendicular1 and passing a lamp around it in a horizontal plane4 ,at two points only in its circuit will the lamp be directly over the equator of the globe4 ,call one of these points the vernal equinox4 ,you will then see that1 when the lamp is directly over this point1 its light illuminates the globe from pole to pole1 but when it has passed round so as to be at a point higher than the equator1 its light no longer reaches the lower pole1 although it passes over the upper one4 ,illustration3 ,fig4 #aa4 ,the ,seasons4 ,the earth is represented at four successive points in its orbit about the sun4 ,since the axis of the earth is virtually unchangeable in its direction in space 7leaving out of account the slow effects of the precession of the equinoxes71 it results that at one time of the year1 the north pole is inclined toward the sun and at the opposite time of the year away from it4 ,it attains its greatest inclination sunward at the summer solstice1 then the line between day and night lies #bc beyond the north pole1 so that the whole area within the arctic circle is in perpetual daylight4 ,the days are longer than the nights throughout the northern hemisphere1 but the day becomes longer in proportion to the night as the arctic circle is approached1 and beyond that the sun is continually above the horizon4 ,in the southern hemisphere exactly the reverse occurs4 ,when the earth has advanced to the autumn equinox1 the axis is inclined neither toward nor away from the sun4 ,the latter is then perpendicular over the equator and day and night are of equal length all over the earth4 ,when the earth reaches the winter solstice the north pole is inclined away from the sun1 and now it is summer in the southern hemisphere4 ,at the vernal equinox again there is no inclination of the axis either toward or away from the sun1 and once more day and night are everywhere equal4 ,a little study of this diagram will show why on the equator day and night are always of equal length4 ,now1 with the lamp thus elevated above the equator1 set the globe in rotation about its axis4 ,you will perceive that all points in the upper hemisphere are longer in light than in darkness1 because the plane dividing the illuminated and the unilluminated halves of the globe is inclined to the globe's axis in such a way that it lies beyond the upper pole as seen from the direction of the lamp4 ,consequently1 the upper half of the globe above the equator1 as it goes round1 has more of its surface illuminated than unilluminated1 and1 as it turns on its axis1 any point in that upper half1 moving round parallel to the equator1 is longer in light than in darkness4 ,you will also observe that the ratio of length of the light to the darkness is greater the nearer the point lies to the pole1 and that when it is within a certain distance of the pole1 corresponding with the elevation of the lamp above the equator1 it lies in continual light--in other words1 within that distance from the pole night vanishes and daylight is unceasing4 ,at the same time you will perceive that round the lower pole there is a similar space within which day has vanished and night is unceasing1 and that in the whole of the lower hemisphere night is longer than day4 ,exactly on the equator1 day and night are always of equal length4 ,endeavour to represent all this clearly to your imagination1 before actually trying the experiment1 or consulting a diagram4 ,if you try the experiment you may1 instead of setting the axis of the globe at a slant1 place it upright1 and then gradually raise and lower the lamp as it is carried round the globe1 now above and now below the equator4 ,we return to our description of the actual movements of the sun4 ,as it rises higher from the equator1 not only does the day increase in length relatively to the night1 but the rays of sunlight descend more nearly perpendicular upon the northern hemisphere4 ,the consequence is that their heating effect upon the ground and the atmosphere increases and the temperature rises until1 when the sun reaches its greatest northern declination1 about the #bb;d of ,june 7when it is #bc north of the equator71 the astronomical summer begins4 ,this point in the sun's course through the circle of the ecliptic is called the summer solstice 7see ,part ,i1 ,sect4 #h74 ,having passed the solstice1 the sun begins to decline again toward the equator4 ,for a short time the declination diminishes slowly because the course of the ecliptic close to the solstice is nearly parallel to the equator1 and in the meantime the temperature in the northern hemisphere continues to increase1 the amount of heat radiated away during the night being less than that received from the sun during the day4 ,this condition continues for about six weeks1 the greatest heats of summer falling at the end of ,july or the beginning of ,august1 when the sun has already declined far toward the equator1 and the nights have begun notably to lengthen4 ,but the accumulation of heat during the earlier part of the summer is sufficient to counterbalance the loss caused by the declension of the sun4 ,about the #bc;d of ,september the sun again crosses the equator1 this time at the autumnal equinox1 the beginning of the astronomical autumn1 and after that it sinks lower and lower 7while appearing to rise in the southern hemisphere71 until about the #bb;d of ,december1 when it reaches its greatest southern declination1 #bc1 at the winter solstice1 which marks the beginning of the astronomical winter4 ,it is hardly necessary to point out that the southern winter corresponds in time with the northern summer1 and vice versa4 ,from the winter solstice the sun turns northward once more1 reaching the vernal equinox again on the #bast of ,march4 ,thus we see that we owe the succession of the seasons entirely to the inclination of the earth's axis out of a perpendicular to the plane of the ecliptic4 ,if there were no such inclination there would be climate but no seasons4 ,there would be no summer heat1 except in the neighbourhood of the equator1 while the middle latitudes would have a moderate temperature the year round4 ,owing to the effects of refraction1 perpetual day would prevail within a small region round each of the poles4 ,the sun would be always perpendicular over the equator4 ,two things remain to be pointed out with regard to the effect of the sun's annual motion in the ecliptic4 ,one of these is the circles called the tropics4 ,these are drawn round the earth parallel to the equator and at a distance of #bc from it1 one in the northern and the other in the southern hemisphere4 ,the northern one is called the tropic of ,cancer1 because its corresponding circle on the celestial sphere runs through the zodiacal sign ,cancer1 and the southern one is called the tropic of ,capricorn for a similar reason4 ,the tropics run through the two solstices1 and mark the apparent daily track of the sun in the sky when it is at either its greatest northern or its greatest southern declination4 ,the sun is then perpendicular over one or the other of the tropics4 ,that part of the earth lying between the tropics is called the torrid zone1 because the sun is always not far from perpendicular over it1 and the heat is very great4 ,illustration3 ,the ,six-,tailed ,comet of #agdd ,from a contemporary drawing4 ,the other thing to be mentioned is the polar circles4 ,these are situated #bc from each pole1 just as the tropics are situated a similar distance on each side of the equator4 ,the northern is called the arctic1 and the southern the antarctic circle4 ,those parts of the earth which lie between the tropics and the polar circles are called respectively the northern and the southern temperate zone4 ,the polar circles mark the limits of the region round each pole where the sun shines continuously when it is at one or the other of the solstices4 ,if the reader will recall the experiment with the globe and the lamp1 he will perceive that these circles correspond with the borders of the circular spaces at each pole of the globe which are alternately carried into and out of the full light as the lamp is elevated to its greatest height above the equator or depressed to its greatest distance below it4 ,at each pole1 in turn1 there are six months of continual day followed by six months of continual night1 and when the sun is at one of the solstices it just touches the horizon on the corresponding polar circle at the hour that marks midnight on the parts of the earth which lie outside the polar circles4 ,this is the celebrated phenomenon of the 8midnight sun40 ,at any point within the polar circle concerned1 the sun1 at the hour of midnight approaches the horizon but does not touch it1 its midnight elevation increasing with nearness to the pole1 while exactly at the pole itself the sun simply moves round the sky once in twenty-four hours in a circle practically parallel to the horizon4 ,it is by observations on the daily movement of the sun that an explorer seeking one of the earth's poles during the long polar day is able to determine when he has actually reached his goal4 ,the reader will have remarked in these descriptions how frequently the angle of #bc turns up1 and he should remember that it is1 in every case1 due to the same cause1 viz41 the inclination of the earth's axis from a perpendicular to the ecliptic4 ,a very remarkable fact must now be referred to4 ,although the angular distance that the sun has to travel in passing first from the vernal equinox to the autumnal equinox1 on the northern side of the equator1 and then back again from the autumnal equinox to the vernal equinox1 on the southern side of the equator1 is the same1 the time that it occupies in making these two half stages in its annual journey is not the same4 ,beginning from the #bast of ,march and counting the number of days to the #bc;d of ,september1 and then beginning from the #bc;d of ,september and counting the number of days to the next #bast of ,march1 you will find that in an ordinary year the first period is seven days longer than the second4 ,in other words1 the sun is a week longer above the equator than below it4 ,the reason for this difference is found in the fact that the orbit of the earth about the sun is not a perfect circle1 but is a slightly elongated ellipse1 and the sun1 instead of being situated in the centre1 is situated in one of the two foci of the ellipse1 #c1jjj1jjj miles nearer to one end of it than to the other4 ,now this elliptical orbit of the earth is so situated that the earth is nearest to the focus occupied by the sun1 or in perihelion1 about ,december #cast1 only a few days after the winter solstice1 and farthest from the sun1 or in aphelion1 about ,july #ast1 only a few days after the summer solstice4 ,thus the earth is nearer the sun during the winter half of the year1 when the sun appears south of the equator1 than during the summer half of the year1 when the sun appears north of the equator4 ,now the law of gravitation teaches that when the earth is nearer the sun it must move more rapidly in its orbit than when it is more distant1 from which it follows that the time occupied by the sun in its apparent passage from the vernal equinox to the autumnal equinox is longer than that occupied in the passage back from the autumnal to the vernal equinox4 ,but while the summer half of the year is longer than the winter half in the northern hemisphere1 the reverse is the case in the southern hemisphere4 ,there the winter is longer than the summer4 ,moreover1 the winter of the southern hemisphere occurs when the earth is farthest from the sun1 which accentuates the disadvantage4 ,it has been thought that the greater quantity of ice about the south pole may be due to this increased length and severity of the southern winter4 ,it is true that the southern summer1 although shorter1 is hotter than the northern1 but while1 theoretically1 this should restore the balance as a whole1 yet it would appear that the short hot summer does not1 in fact1 suffice to arrest the accumulation of ice4 ,however1 the present condition of things as between the two hemispheres will not continue1 but in the course of time will be reversed4 ,the reader will recall that the precession of the equinoxes causes the axis of the earth to turn slowly round in space4 ,at present the northern end of the earth's axis is inclined away from the aphelion and in the direction of the perihelion point of the orbit1 so that the northern summer occurs when the earth is in the more distant part of its orbit1 and the winter when it is in the nearer part4 ,but the precession swings the axis round westward from its present position at the rate of #ej4b per year1 while at the same time the position of the orbit itself is shifted 7by the effects of the attraction of the planets7 in such a manner that the aphelion and perihelion points1 which are called the apsides1 move round eastward at the rate of #aa4be per year4 ,the combination of the precession with the motion of the apsides produces a revolution at the rate of #fa4de per year1 which in the course of #aj1ejj years will completely reverse the existing inclination of the axis with regard to the major diameter of the orbit1 so that then the northern hemisphere will have its summer when the earth is near perihelion and its winter when it is near aphelion4 ,the winter1 then1 will1 for us1 be long and severe and the summer short though hot4 ,it has been thought possible that such a state of things may cause1 in our hemisphere1 a partial renewal of what is known in geology as a glacial period4 ,a glacial period in the southern hemisphere would probably always be less severe than in the northern1 because of the great preponderance of sea over land in the southern half of the globe4 ,an ocean climate is more equable than a land climate4 #aj4 ,the ,year1 the ,calendar1 and the ,month4 ,a year is the period of time required for the earth to make one revolution in its orbit about the sun4 ,but1 as there are three kinds1 or measures1 of time1 so there are three kinds1 or measures1 of the year4 ,the first of these is called the sidereal year1 but although1 like sidereal time1 it measures the true length of the period in question1 it is not suitable for ordinary use4 ,to understand what is meant by a sidereal year1 imagine yourself to be looking at the earth from the sun1 and suppose that at some instant you should see the earth exactly in conjunction with a star4 ,when1 having gone round the sun1 it had come back again to conjunction with the same star1 precisely one revolution would have been performed in its orbit1 and the period elapsed would be a sidereal year4 ,practically1 the length of the sidereal year is determined by observing when the sun1 in its apparent annual journey round the sky1 has come back to conjunction with some given star4 ,the second kind of year is called the tropical year1 and it is measured by the period taken by the sun to pass round the sky from one conjunction with the vernal equinox to the next4 ,this period differs slightly from the first1 because1 owing to the precession of the equinoxes1 the vernal equinox is slowly shifting westward1 as if to meet the sun in its annual course1 from which it results that the sun overtakes the equinox a little before it has completed a sidereal year4 ,the tropical year is about twenty minutes shorter than the sidereal year4 ,it is1 however1 more convenient for ordinary purposes1 because we naturally refer the progress of the year to that of the seasons1 and1 as we have seen1 the seasons depend upon the equinoxes4 ,but yet the tropical year is not entirely satisfactory as a measure of time1 because the number of days contained in it is not an even one4 ,its length is #cff days1 #e hours1 #dh minutes1 #df seconds4 ,accordingly1 as the irregularities of apparent solar time were avoided by the invention of mean solar time1 so the difficulty presented by the tropical year is gotten rid of1 as far as possible1 by means of what is called the civil year1 or the calendar year1 the average length of which is almost exactly equal to that of the tropical year4 ,this brings us to the consideration of the calendar1 which is as full of compromises as a political treaty--but there is no help for it since nature did not see fit to make the day an exact fraction of the year1 or1 in other words1 to make the day and the year commensurable quantities of time4 ,without going into a history of the reforms that the calendar has undergone1 which would demand a great deal of space1 we may simply say that the basis of the calendar we use to-day was established by ,julius ,csar1 with the aid of the ,greek astronomer ,sosigenes4 ,this is the ,julian calendar1 and the reformed shape in which it exists at present is called the ,gregorian calendar4 ,csar assumed #cfe days as the true length of the year1 and1 in order to get rid of the quarter day1 ordered that it should be left out of account for three years out of every four4 ,in the fourth year the four quarter days were added together to make one additional day1 which was added to that particular year4 ,thus the ordinary years were each #cfe days long and every fourth year was #cff days long4 ,this fourth year was called the bissextile year4 ,it was identical with our leap year4 ,the days of both the ordinary and the leap years were distributed among the twelve months very much as we distribute them now4 ,but ,csar's assumption of #cfe days as the length of the year was erroneous1 being about #aa min4 #ad sec4 longer than the real tropical year4 ,in the sixteenth century this error had accumulated to such a degree that the months were becoming seriously disjointed from the seasons with which they had been customarily associated4 ,in consequence1 ,pope ,gregory ,,xiii1 assisted by the astronomer ,clavius1 introduced a slight reform of the ,julian calendar4 ,the accumulated days were dropped1 and a new start taken1 and the rule for leap year was changed so as to read that 8all years1 whose date-number is divisible by four without a remainder are leap years1 unless they are century years 7such as #ahjj1 #aijj1 etc474 ,the century years are not leap years1 unless their date number is divisible by #djj1 in which case they are40 ,and this is the rule as it prevails to-day1 although there is now 7#aiab7 serious talk of undertaking a new revision4 ,but the ,gregorian calendar is so nearly correct that more than #cjjj years must elapse before the length of the year as determined by it will differ by one day from the true tropical year4 ,the subject of the reform of the calendar is a very interesting one1 but1 together with that of the rules for determining the date of ,easter1 its discussion must be sought in more extensive works4 ,there is one other measure of time1 depending upon the motion of a heavenly body1 which must be mentioned4 ,this is the month1 or the period required for the moon to make a revolution round the earth4 ,here we encounter again the same difficulty1 for the month also is incommensurable with the year4 ,then1 too1 the length of the month varies according to the way in which it is reckoned4 ,we have1 first1 a sidereal revolution of the moon1 which is measured by the time taken to pass round the earth from one conjunction with a star to the next4 ,this is1 on the average1 #bg days1 #g hours1 #dc minutes1 #ab seconds4 ,next we have a synodical revolution of the moon1 which is measured by the time it takes in passing from the phase of new moon round to the same phase again4 ,this seems the most natural measure of a month1 because the changing phases of the moon are its most conspicuous peculiarity4 7,these will be explained in ,part ,,iii47 ,the length of the month1 as thus measured1 is1 on the average1 #bi days1 #ab hours1 #dd minutes1 #c seconds4 ,the reason why the synodical month is so much longer than the sidereal month is because new moon can occur only when the moon is in conjunction with the sun1 i4e4 exactly between the earth and the sun1 and in the interval between two new moons the sun moves onward1 so that for the second conjunction the moon must go farther to overtake the sun4 ,it will be observed that both of the month measures are given in average figures4 ,this is because the moon's motion is not quite regular1 owing partly to the eccentricity of its orbit and partly to the disturbing effects of the sun's attraction4 ,the length of the sidereal revolution varies to the extent of three hours1 and that of the synodical revolution to the extent of thirteen hours4 ,but1 whichever measure of the month we take1 it is incommensurate with the year1 i4e4 there is not an even number of months in a year4 ,in ancient times ceaseless efforts were made to adjust the months to the measure of the year1 but we have practically given up the attempt1 and in our calendar the lunar months shift along as they will1 while the ordinary months are periods of a certain number of days1 having no relation to the movements of the moon4 ,it has been thought that the period called a week1 which has been used from time immemorial1 may have originated from the fact that the interval from new moon to the first quarter and from first quarter to full moon1 etc41 is very nearly seven days4 ,but the week is as incorrigible as all its sisters in the discordant family of time1 and there is no more difficult problem for human ingenuity than that of inventing a system of reckoning1 in which the days1 the weeks1 the months1 and the years shall be adjusted to the closest possible harmony4 ,illustration3 ,spiral ,nebula in ,ursa ,major 7,m #aja7 ,photographed at the ,lick ,observatory by ,j4 ,e4 ,keeler1 with the ,crossley reflector4 ,exposure four hours4 ,note the appearance of swift revolution1 as if the nebula were throwing itself to pieces like a spinning pin-wheel4 ,illustration3 ,the ,whirlpool ,nebula in ,canes ,venatici ,photographed at the ,lick ,observatory by ,j4 ,e4 ,keeler1 with the ,crossley reflector4 ,exposure four hours4 ,note the 8beading0 of the arms of the whirling nebula4 ---------------------------------------- -------------------------------- ,,part ,,iii4 ,,the ,,solar ,,system4 ---------------------------------------- -------------------------------- ,,part ,,iii4 ,,the ,,solar ,,system4 #a4 ,the ,sun4 ,by the term solar system is meant the sun together with the system of bodies 7planets1 asteroids1 comets and meteors7 revolving round it4 ,the sun1 being a star1 every other star1 for all that we can tell1 may be the ruler of a similar system4 ,in fact1 we know that a few stars have huge dark bodies revolving round them1 which may be likened to gigantic planets4 ,the reason why the sun is the common centre round which the other members of the solar system move1 is because it vastly exceeds all of them put together in mass1 or quantity of matter1 and the power of any body to set another body in motion by its attractive force depends upon mass4 ,if a great body and a small body attract each other1 both will move1 but the motion of the small body will be so much more than that of the great one that the latter will seem1 relatively1 to stand fast while the small one moves4 ,then1 if the small body had originally a motion across the direction in which the great body attracts it1 the result of the combination will be to cause the small body to revolve in an orbit 7more or less elliptical according to the direction and velocity of its original motion7 about the great body4 ,if the difference of mass is very great1 the large body will remain virtually immovable4 ,this is the case with the sun and its planets4 ,the sun has #ccb1jjj times as much mass 7or1 we may say1 is #ccb1jjj times as heavy7 as the earth4 ,it has a little more than a thousand times as much mass as its largest planet1 ,jupiter4 ,it has millions of times as much as the greatest comet4 ,the consequence is that all of these bodies revolve around the sun1 in orbits of various degrees of eccentricity1 while the sun itself remains practically immovable1 or just swaying a little this way and that1 like a huntsman holding his dogs in leash4 ,the distance of the sun from the earth--about #ic1jjj1jjj miles--has been determined by methods which will be briefly explained in the next section4 ,knowing its distance1 it is easy to calculate its size1 since the apparent diameter of all objects varies directly with their distance4 ,the diameter of the sun is thus found to be about #hff1djj miles1 or nearly #aaj times that of the earth4 ,in bulk it exceeds the earth about #a1cjj1jjj times1 but its mass1 or quantity of matter1 is only #ccb1jjj times the earth's1 because its average density is but one quarter that of the earth4 ,this arises from the fact that the earth is a solid1 compact body1 while the sun is a body composed of gases and vapours 7though in a very compressed state74 ,it is the high temperature of the sun which maintains it in this state4 ,its temperature has been calculated at about #af1jjj ,fahrenheit1 but various estimates differ rather widely4 ,at any rate1 it is so hot that the most refractory substances known to us would be reduced to the state of vapour1 if removed to the sun4 ,the quantity of heat received upon the earth from the sun can only be expressed in terms of the mechanical equivalent of heat4 ,the unit of heat in engineering is the calorie1 which means the amount of heat required to raise the temperature of one kilogram of water 7#b4b pounds7 one degree ,centigrade 7#a4h ,fahrenheit74 ,now observation shows that the sun furnishes #cj of these calories per minute upon every square metre 7about #a4b square yard7 of the earth's surface4 ,perhaps there is no better illustration of what this means than ,prof4 ,young's statement1 that 8the heat annually received on each square foot of the earth's surface1 if employed in a perfect heat engine1 would be able to hoist about a hundred tons to the height of a mile40 ,or take ,prof4 ,todd's illustration of the mechanical power of the sunbeams3 8,if we measure off a space five feet square1 the energy of the sun's rays when falling vertically upon it is equivalent to one horse power40 ,astronomers ordinarily reckon the solar constant in 8small calories10 which are but the thousandth part of the engineer's calorie1 and the latest results of the ,smithsonian ,institution observations indicate that the solar constant is about #a4ie of these small calories per square centimeter per second4 ,about #cj per cent4 must be deducted for atmospheric absorption4 ,heat1 like gravitation and like light1 varies inversely in intensity with the square of the distance2 hence1 if the earth were twice as near as it is to the sun it would receive four times as much heat and four times as much light1 and if it were twice as far away it would receive only one quarter as much4 ,this shows how important it is for a planet not to be too near1 or too far from1 the sun4 ,the earth would be vapourised if it were carried within a quarter of a million miles of the sun4 ,the sun rotates on an axis inclined about #g from a perpendicular to the plane of the ecliptic4 ,the average period of its rotation is about #be days--we say 8average0 because1 not being a solid body1 different parts of its surface turn at different rates4 ,it rotates faster at the equator than at latitudes north-and-south of the equator1 the velocity decreasing toward the poles4 ,the period of rotation at the equator is about #be days1 and at #dj north or south of the equator it is about #bg days4 ,the direction of rotation is the same as that of the earth's4 ,the surface of the sun1 when viewed with a telescope1 is often seen more or less spotted4 ,the spots are black1 or dusky1 and frequently of very irregular shapes1 although many of them are nearly circular4 ,generally they appear in groups drawn out in the direction of the solar rotation4 ,some of these groups cover areas of many millions of square miles1 although the sun is so immense that even then they appear to the naked eye 7guarded by a dark glass7 only as small dark spots on its surface4 ,the centres of sun-spots1 are the darkest parts4 ,generally around the borders of the spots the surface seems to be more or less heaped up4 ,often1 in large sun-spots1 immense promontories1 very brilliant1 project over the dark interior1 and many of these are prolonged into bridges of light1 apparently traversing the chasms beneath4 ,constant changes of shape and arrangement take place1 and there are few more astonishing telescopic objects than a great sun-spot4 ,illustration3 8,tress ,nebula0 7,n4 ,g4 ,c4 #fiib7 in ,cygnus ,photographed at the ,yerkes ,observatory by ,g4 ,w4 ,ritchey1 with the two-foot reflector4 ,observe the strangely twisted look of this long curved nebula2 also the curious curves composed of minute stars near it4 ,the spots are not always visible in equal numbers1 and in some years but few are seen1 and they are small4 ,it has been found that they occur in periods1 averaging about eleven years from maximum to minimum1 although the length of the period is very irregular4 ,it has also been observed that when the first spots of a new period appear1 they are generally seen some #cj from the equator1 either toward the north or toward the south1 and that as the period progresses the spots increase in size1 and seem to draw toward the equator1 the last spots of the period being seen quite close to the equator1 on one side or the other4 ,the duration of individual spots is variable2 some last but a day or two1 and others continue for weeks1 sometimes being carried out of view by the rotation of the sun and brought into view again from the other side4 ,the surface of the sun in the neighbourhood of groups of spots is frequently marked by large areas covered with crinkled bright lines and patches1 which are called facul4 ,these1 which are the brightest parts of the sun1 appear to be elevated above the general level4 ,as to the cause and nature of sun-spots much remains to be learned4 ,in #aijh1 ,prof4 ,george ,e4 ,hale1 by means of an instrument called the spectro-heliograph1 which selects out of the total radiation of the solar disk light peculiar to certain elements1 and thus permits the use of that light alone in photographing the sun1 demonstrated that sun-spots probably arise from vortices1 or whirling storms1 and that these vortices produce strong magnetic fields in the sun-spots4 ,the phenomenon may be regarded1 says ,prof4 ,hale1 as somewhat analogous to a tornado or waterspout on the earth4 ,the whirling trombe becomes wider at the top1 carrying the gases from below upward4 ,at the centre of the storm the rapid rotation produces an expansion which cools the gases and causes the appearance of a comparatively dark cloud1 which we see as the sun-spot4 ,the vortices whirl in opposite directions on opposite sides of the sun's equator1 thus obeying the same law that governs the rotation of cyclones on the earth4 ,it has long been a question whether the condition of the sun as manifested by the spots upon its surface has an influence upon the meteorology of the earth4 ,it is known that the sun-spot period coincides closely with periodical changes in the earth's magnetism1 and great outbursts on the sun have frequently been immediately followed by violent magnetic storms and brilliant displays of the aurora borealis on the earth4 ,the sun undoubtedly exercises other influences upon the earth than those familiar to us under the names of gravitation1 light1 and heat2 but the nature of these other influences is not yet fully understood4 ,the brilliant white surface of the sun is called the photosphere4 ,it has been likened to a shell of intensely hot clouds1 consisting of substances which are entirely vaporous within the body of the sun4 ,above the photosphere lies an envelope1 estimated to be from #ejjj to #aj1jjj miles thick1 known as the chromosphere4 ,it consists mainly of hydrogen and helium1 and when seen during a total eclipse1 when the globe of the sun is concealed behind the moon1 it presents a brilliant scarlet colour4 ,above this are frequently seen splendid red flame-like objects1 named prominences4 ,they are of two varieties--one cloud-like in appearance1 and the other resembling spikes1 or trees with spreading tops1--but often their forms are infinitely varied4 ,the latter1 the so-called eruptive prominences1 exhibit rapid motion away from the sun's surface1 as if they consisted of matter which has been ejected by explosion4 ,occasionally these objects have been seen to grow to a height of several hundred thousand miles1 with velocities of two or three hundred miles per second4 ,the sun has still another envelope1 of changing form1--the corona4 ,this apparently consists of rare gaseous matter1 whose characteristic constituent is an element unknown on the earth1 called coronium4 ,the corona appears in the form of a luminous halo1 surrounding the hidden sun during a total eclipse1 and it often extends outward several million miles4 ,its shape varies in accordance with the sun-spot period4 ,it has a different appearance and outline at a time of maximum sun-spots from those which it presents at a minimum4 ,there are many things about the corona which suggest the play of electric and magnetic forces4 ,the corona1 although evidently always existing1 is never seen except during the few minutes of complete obscuration of the sun that occurs in a total eclipse4 ,this is because its light is not sufficiently intense to render it visible1 when the atmosphere around the observer is illuminated by the direct rays of sunlight4 #b4 ,parallax4 ,we now return to the question of the sun's distance from the earth1 which we treat in a separate section1 because thus it is possible to present1 at a single view1 the entire subject of the measurement of the distances of the heavenly bodies4 ,the common basis of all such measurements is furnished by what is called parallax1 which may be defined as the difference of direction of an object when viewed alternately from two separate points4 ,the simplest example of parallax is found in looking at an object first with one eye and then with the other without1 in the meantime1 altering the position of the head4 ,suppose you sit in front of a window through which you can see the wall of a house on the opposite side of the street4 ,choose one of the vertical bars of the window-sash1 and1 closing the left eye1 look at the bar with the right and note where it seems to be projected against the wall4 ,then close the right eye and open the left1 and you will observe that the place of projection of the bar has shifted toward the right4 ,this change of direction is due to parallax and its amount depends both upon the distance between the eyes and upon the distance of the window from the observer4 ,to see how this principle is applied by the astronomer1 let us suppose that we wish to ascertain the distance of the moon4 ,the moon is so far away that the distance between the eyes is infinitesimal in comparison1 so that no parallactic shift in its direction is apparent on viewing it alternately with the two eyes4 ,but by making the observations from widely separated points on the earth we can produce a parallactic shifting of the moon's position which will be easily measurable4 ,let one of the points of observation be in the northern hemisphere and the other in the southern1 thousands of miles apart4 ,the two observers might then be compared to the eyes of an enormous head1 each of which sees the moon in a measurably different direction4 ,if the northern observer carefully ascertains the angular distance of the moon from his zenith1 and the southern observer does the same with regard to his zenith1 as indicated in ,fig4 #ab1 they can1 by a combination of their measurements1 construct a quadrilateral ,a ,c ,b ,m1 of which all the angles may be ascertained from the two measurements1 while the length of the sides ,a ,c and ,b ,c is already known1 since they are each equal to the radius of the earth4 ,with these data it is easy1 by the rules of plane trigonometry1 to calculate the length of the other sides1 and also the length of the straight line from the centre of the earth to the moon4 ,in all such cases the distance between the points of observation is called the base-line1 whose length is known to start with1 while the angles formed by the lines of direction at the opposite ends of the base-line are ascertained by measurement4 ,illustration3 ,fig4 #ab4 ,parallax of the ,moon4 ,let ,c be the centre of the earth1 ,a and ,b the stations of two observers1 one in the northern1 the other in the southern hemisphere1 and ,m the moon4 ,the lines ,c ,a ,z and ,c ,b ,z indicate the direction of the zenith at ,a and ,b respectively4 ,subtracting the measured angles at ,a and ,b each from #ahj gives the inside angles at those points4 ,the angle at ,c is equal to the sum of the latitudes of ,a and ,b since they are on opposite sides of the equator4 ,with three angles known1 the fourth1 at ,m1 is found by simply subtracting their sum from #cfj4 ,illustration3 ,the ,great ,andromeda ,nebula ,photographed at the ,yerkes ,observatory by ,g4 ,w4 ,ritchey1 with the two-foot reflector4 ,observe the vast spiral1 or elliptic1 rings surrounding the central condensation and the appearance of breaking up and re-shaping into smaller masses which some of the rings present4 ,in the case of the sun the distance concerned is so great 7about #djj times that of the moon7 that the parallax produced by viewing it from different points on the earth is too small to be certainly measured1 and a modification of the method has to be employed4 ,one such modification1 which has been much used1 depends upon the fact that the planet ,venus1 being nearer the sun than the earth is1 appears1 at certain times1 passing directly over the face of the sun4 ,this is called a transit of ,venus4 ,during a transit1 ,venus is between three and four times nearer the earth than the sun is1 and consequently its parallactic displacement1 when viewed from widely separated points on the earth1 is much greater than that of the sun4 ,one of the ways in which the astronomer takes advantage of this fact is shown in ,fig4 #ac4 ,let ,a and ,b be two points on opposite sides of the earth1 but both somewhere near the equator4 ,as ,venus swings along in its orbit to pass between the earth and the sun1 it will manifestly be seen just touching the sun's edge sooner from ,a than from ,b4 ,the observer at ,a notes with extreme accuracy the exact moment when he sees ,venus apparently touch the sun4 ,several minutes later1 the observer at ,b will see the same phenomenon1 and he also notes accurately the time of the apparent contact4 ,now1 since we know from ordinary observation the time that ,venus requires to make one complete circuit of its orbit1 we can1 by simple proportion1 calculate1 from the time that it takes to pass from v to v#a1 the angular distance between the lines ,a ,s and ,b ,s1 or in other words the size of the angle at ,s1 which is equal to the parallactic displacement of the sun1 as seen from opposite ends of the earth's diameter4 ,knowing1 to begin with1 the distance between ,a and ,b1 we have the means of determining the length of all the other lines in the triangle1 and hence the distance of the sun4 ,this process is known as ,delisle's method4 ,there is another method1 called ,halley's1 but in a brief treatise of this kind we cannot enter into a description of it4 ,it suffices to say that both depend upon the same fundamental principles4 ,illustration3 ,fig4 #ac4 ,parallax of the ,sun from ,transit of ,venus4 7,for description see text47 ,it must be added1 however1 that other ways of measuring the sun's distance than are afforded by transits of ,venus have been developed4 ,one of these depends upon observation of the asteroid ,eros1 which periodically approaches much nearer to the earth than ,venus ever does4 ,by observing the parallax of ,eros1 when it is nearest the earth1 its distance can be ascertained1 and that being known the distance of the sun is immediately deducible from it1 because1 by the third law of ,kepler 7to be explained later71 the relative distances of all the planets from the sun are proportional to their periods of revolution1 so that if we know any one of the distances in miles we can calculate all the others4 ,it is important here to state the angular amount of the sun's parallax1 since it is a quantity which is continually referred to in books on astronomy4 ,according to the latest determination1 based on observations of ,eros1 the solar parallax is #h4hjg1 which corresponds1 in round numbers1 to a distance of #ib1hjj1jjj miles4 ,a mean parallax of #h4gif is given by ,mr4 ,c4 ,g4 ,abbot1 based on a combination of results from a number of different methods1 and this corresponds to a distance of #ib1icj1jjj miles4 ,to the astronomer1 who seeks extreme exactness1 the slightest difference is important4 ,it should be noted that the figures #h4hjg or #h4gif represent the parallactic displacement of the sun1 as seen not from the opposite ends of the earth's entire diameter1 but from opposite ends of its radius1 or semi-diameter4 ,accordingly it is equal to half of the angle at ,s in ,fig4 #ac4 ,it is for convenience of calculation that1 in such cases1 the astronomer employs the semi-diameter1 instead of the whole diameter for his base-line4 ,the case of the stars must next be considered1 and now we find that the distances involved are so enormous that the diameter1 or semi-diameter1 of the earth is altogether too insignificant a quantity to afford an available base-line for the measurement4 ,we should have remained forever ignorant of star distances but for the effects produced by the earth's change of place due to its annual revolution round the sun4 ,the mean diameter of the earth's orbit is about #ahf1jjj1jjj miles1 and we are able to make use of this immense distance as a base-line for ascertaining the parallax of a star4 ,suppose1 for instance1 that the direction of a star in the sky is observed on the #ast of ,january1 and again on the #ast of ,july4 ,in the meantime1 the earth will have passed from one end of the base-line just described to the other1 and unless the star observed is extremely remote1 a careful comparison of the two measurements of direction will reveal a perceptible parallax1 from which the actual distance of the star in question can be deduced4 ,it is to be observed that if all the stars were equally distant this method would fail1 because then there would be no 8background0 against which the shift of place could be observed2 all of the stars would shift together4 ,but1 in fact1 the vast majority of the stars are so remote that even a base-line of #ahf1jjj1jjj miles is insufficient to produce a measurable shift in their direction4 ,it is only the distances of the nearer stars which we can measure1 and for them the multitude of more remote ones serves1 like the wall of the house in the experiment with the window-bar1 as a background on which the shift of place can be noted4 ,just as in calculations of the sun's parallax the semi-diameter of the earth is chosen for a base-line1 so in the case of the stars the semi-diameter of the earth's orbit1 amounting to #ic1jjj1jjj miles1 forms the basis4 ,measured in this way the parallaxes of the nearest stars come out in tenths1 or hundredths1 of a second of arc1 or angular measurement4 ,thus the parallax of ,alpha ,centauri1 the nearest known star1 is about #j4ge1 corresponding to a distance of about #bf1jjj1jjj1jjj1jjj miles4 ,now #j4ge is a quantity inappreciable to the naked eye1 and only to be measured with delicate instruments1 and yet this almost invisible shift of direction is all that is produced by viewing the nearest star in the sky from the opposite ends of a base-line #ic1jjj1jjj miles long6 #c4 ,spectroscopic ,analysis4 ,we have next to deal with the constitution of the sun1 or the nature of the substances of which it consists1 and for this purpose we must first understand the operation of the spectroscope1 in many respects the most wonderful instrument that man has invented4 ,it has given birth to the 8chemistry of the sun0 and the 8chemistry of the stars10 for by its aid we can be as certain of the nature of many of the substances of which they are made as we could be by actually visiting them4 ,illustration3 ,fig4 #ad4 ,spectrum ,analysis4 ,the red is least turned by the prism from its original course and the violet most4 ,if between the prism and the screen on which the spectrum falls there were interposed a gas of any kind that gas would absorb from the coloured rays passing through it the exact waves of light with which it would itself shine if it were made luminous by heat4 ,it would not take out an entire section1 or colour1 from the spectrum1 but only a small part of one or more of the colours1 and the absence of these parts would be indicated on the screen by narrow black lines situated in various places2 and these lines1 in number and in situation1 would differ with every different kind of gas that was interposed4 ,if several kinds were interposed simultaneously they would all pick out their own peculiar rays from the light1 and thus the spectrum would be crossed by a large number of dark lines1 by the aid of which the nature of the various gases that produced them could be told4 ,the effect would be the same if the gases were interposed in the path of the white light before it enters the prism2--and this1 in fact1 is what happens when the spectrum of the sun1 or a star1 is examined--the absorption has already occurred at the surface of the luminous body before the light comes to the earth4 ,fundamentally1 spectroscopic analysis depends upon the principle of refraction1 of which we have spoken in connection with the atmosphere4 ,although the most powerful spectroscopes are now made on a different plan1 the working of the instrument can best be comprehended by considering it in the form in which it was first invented1 and in which it is still most often used4 ,in its simplest form the spectroscope consists of a three-angle prism of glass1 through which a ray of light is sent from the sun1 star1 or other luminous object to be examined4 ,glass1 like air or water1 has the property of refracting1 or bending1 all rays of light that enter it in an inclined direction4 ,in passing through two of the opposite-sloping sides of a prism1 the ray is twice bent1 once on entering and again on leaving1 in accordance with the principle that we have already mentioned 7see ,part ,,ii1 ,sect4 #d74 ,still1 merely bending the ray out of its original course would have no important result but for another associated phenomenon1 known as dispersion4 ,to explain dispersion we must recall the familiar fact that white light consists of a number of coloured components which1 when united1 make white4 ,it is usual to speak of these primary1 or prismatic1 colours1 as seven in number4 ,these are red1 orange1 yellow1 green1 blue1 indigo1 and violet4 ,physicists now assign a different list of primary colours1 but these1 being generally familiar1 will best serve our purpose4 ,without going into an explanation of the reasons1 it will suffice to say that the waves of light producing these fundamental colours are not all equally affected by refraction4 ,the red is least1 and the violet most1 bent out of its course in passing through the prism1 the other colours being bent more and more in proportion to their distance from the red4 ,it follows that the ray1 or beam1 of light1 which was white when it entered the prism1 becomes divided or dispersed during its passage into a brush of seven different hues4 ,thus the prism may be said to analyse the light into its fundamental colours1 making them separately visible4 ,this1 as a scientific fact1 dates from the time of ,newton4 ,but ,newton did not dream of the further magic that lay in the prism4 ,it was noticed as early as #ahja that1 when the light of the sun was dispersed in the way we have described1 not only did the seven primary colours make their appearance1 but across the ribbon-like band1 called the spectrum1 that was thus formed1 ran a number of thin black lines1 like narrow gaps in the band4 ,the position of these lines was carefully studied by a ,german astronomer1 ,fraunhofer1 in #ahad1 and they still bear the name of ,fraunhofer lines4 ,but the full explanation of them did not come until #aheh when1 with their aid1 ,kirschoff laid the foundations of spectrum analysis4 ,this analysis is based upon the fact that the ,fraunhofer lines are visual indications of the existence of certain substances in the sun4 ,to explain this we must know three fundamental facts3 #ast3 ,every incandescent body that is either solid or liquid 7or1 if it consists of gases1 is under high pressure7 shines with compound white light1 which1 when dispersed by prisms1 gives a continuous coloured band1 or spectrum4 #b;d3 ,every elementary substance when in the gaseous state1 and under low pressure1 if brought to incandescence by heat1 shines with light which1 when dispersed1 gives a discontinuous spectrum1 made up of separate bright lines2 and each different element possesses its own peculiar spectral lines1 never coinciding in position with the lines of any other element4 #c;d3 ,if the light from a body giving a continuous spectrum is caused to pass through a gas which is at a lower temperature1 the gas will absorb precisely those light waves1 of which its own spectrum is composed and will leave in the spectrum of the body a series of dark lines1 or gaps1 whose number and position indicate the nature of the gas whose absorptive action has produced them4 ,now1 to apply these principles to the sun we have only to remember that it is a globe of gaseous substances1 which are under great pressure1 owing to the immense force of the sun's gravitation4 ,consequently it gives a continuous spectrum4 ,but1 at the same time1 it is surrounded with gaseous envelopes1 which are not as much compressed as the internal gases are1 and which are at a lower temperature because they come in contact with the cold of surrounding space4 ,the light from the body of the sun must necessarily pass through these envelopes1 and each of the gases of which they consist absorbs from the passing sunlight its own peculiar rays1 with the result that the spectrum of the sun is seen crossed with a great number of black lines--the ,fraunhofer lines4 ,it will be remarked that the evidence which the ,fraunhofer lines afford concerning the composition of the sun applies1 strictly1 only to the outer portion1 or to the envelopes of gaseous matter that surround the interior globe4 ,but since there is every reason to believe that the entire body of the sun is in a gaseous state1 notwithstanding the internal pressure1 and since we see that there is a continual circulation going on between the inner and outer portions1 it is logical to conclude that essentially the same elements exist under varying conditions in all parts of the sun4 ,in this way1 then1 we have learned the composition of the sun1 and we find that it consists of virtually the same elementary substances found upon the earth1 but existing there in a gaseous or vaporous state4 ,among the elements which have been positively identified in the sun by means of their characteristic spectral lines are iron1 calcium1 sodium1 aluminum1 copper1 zinc1 silver1 lead1 potassium1 nickel1 tin1 silicon1 manganese1 magnesium1 cobalt1 hydrogen1 and at least twenty others which are likewise found upon the earth4 ,some elementary substances known on the earth1 such as gold and oxygen1 have not yet been certainly found in the sun1 but there is every reason to believe that they all exist there1 though perhaps under conditions which render their detection difficult or impossible4 ,helium was recognised as an element in the sun1 by giving spectral lines different from any known substance1 and it received its name 8sun-metal10 long before it was discovered on the earth4 ,we have seen that there is at least one element in the sun1 coronium1 which1 as far as we know1 does not exist at all upon the earth1 and it is not improbable that there may be others which have no counterparts on the earth4 ,the same kind of analysis applies to the stars1 no matter how far away they may be1 so long as they give sufficient light to form a spectrum4 ,and in this way it has been found that the stars differ somewhat from the sun and from one another in their composition1 and thus a classification of the stars has been made1 and it has been possible to draw conclusions concerning their relative age1 which show that some stars are comparatively younger than the sun1 others older1 and others so far advanced in age1 or evolution1 that they are drawing near extinction4 ,many dark bodies also exist among the stars1 which appear to be completely extinguished suns4 ,it only remains to add on this subject that1 according to prevailing theories1 the earth itself was once an incandescent body1 shining with its own light1 and at that time it1 too1 would have yielded a spectrum showing of what substances it consisted4 #d4 ,the ,moon4 ,the earth is a satellite of the sun1 and the moon is a satellite of the earth4 ,the mean1 or average1 distance of the sun from the earth is about #ic1jjj1jjj miles2 the mean distance of the moon is a little less than #bci1jjj miles4 ,this distance is variable to the extent of about #ca1jjj miles1 owing to the eccentricity of the moon's orbit about the earth4 ,that is1 the moon is sometimes nearly #bec1jjj miles away1 and sometimes only about #bba1fjj4 ,the diameter of the moon is #bafc miles4 ,its bulk is one-forty-ninth that of the earth1 but its mass is only one-eightieth1 because its mean density is only about six-tenths as great as the earth's4 ,the moon appears to travel in an orbit round the earth1 but in fact the orbit is always concave toward the sun1 and the disturbing attraction of the earth1 as the two move together round the sun1 causes it to appear now on one side and now on the other4 ,but we may treat the moon's orbit as if the earth were the true centre of force1 the attraction of the sun being regarded as the disturbing element4 ,according to a mathematical theory1 which has been largely accepted as probably true1 but into which we cannot enter here 7see ,prof4 ,george ,darwin's ,the ,tides1 or ,prof4 ,r4 ,ball's ,time and ,tide71 the moon was thrown off from the earth many ages ago1 as a consequence of tidal 8friction40 ,as it moves round in its orbit the moon keeps the same face toward the earth4 ,this fact is also ascribed to tidal influence4 ,illustration3 ,spiral ,nebula in ,cepheus 7,h ,,iv #gf7 ,photographed at the ,lick ,observatory by ,j4 ,e4 ,keeler1 with the ,crossley reflector4 ,exposure four hours4 ,observe that the central portion is only of stellar magnitude4 ,illustration3 ,nebulous ,groundwork in ,taurus ,photographed at the ,yerkes ,observatory by ,e4 ,e4 ,barnard with #aj-;inch ,bruce telescope4 ,exposure six hours twenty-eight minutes4 ,prof4 ,barnard has suggested that some of these dark lanes in rich regions of stars are non-luminous nebul4 ,apparently the moon has no atmosphere1 or if it has any it is too rare to be certainly detected4 ,on its surface1 there is no appearance of water4 ,consequently we cannot suppose it to be inhabited1 at least by any forms of life familiar to us on the earth4 ,but when the moon is viewed with a telescope large relatively flat areas are seen1 which some think may have been the beds of seas in ancient times4 ,they are still called maria1 or 8seas10 and are visible to the naked eye in the form of great irregular dusky regions4 ,nearly two-thirds of the surface of the moon1 as we see it1 consists of bright regions1 which are very broken and mountainous4 ,most of the mountains of the moon are roughly circular1 surrounding enormous depressions1 which look like gigantic pits4 ,for this reason they are called lunar volcanoes1 but1 to say nothing of their immense size--for many are fifty or sixty miles across--they differ in many ways from the volcanoes of the earth4 ,it suffices to point out that what resemble volcanic craters are not situated1 as is the case on the earth1 at the summits of mountains1 but are vast sink-holes1 descending thousands of feet below the general surface of the moon4 ,their real origin is unknown1 but it is possible that volcanic forces may have produced them4 7,for a description1 with photographs1 of these gigantic formations in the lunar world1 see the present author's ,the ,moon47 ,in addition to the circular mountains1 or craters1 there are several long and lofty chains of lunar mountains much resembling terrestrial mountain ranges4 ,as to the absence of air and water from the moon1 some have supposed that they once existed1 but1 in the course of ages1 have disappeared1 either by absorption1 partly mechanical and partly chemical1 into the interior rocks1 or by escaping into space on account of the slight force of gravity on the moon1 which appears to be insufficient to enable it to retain1 permanently1 such volatile gases as oxygen1 hydrogen1 and nitrogen4 ,this leads us to consider the force of the moon's attraction at its surface4 ,we have seen that spherical bodies attract as if their whole mass were collected at their centres4 ,we also know that the force of attraction varies directly as the mass of the attracting body and inversely as the square of the distance from its centre4 ,now the mass of the moon is one-eightieth that of the earth1 so that1 upon bodies situated at an equal distance from the centres of both1 the moon's attraction would be only one-eightieth of the earth's4 ,but the diameter of the moon is not very much more than one quarter that of the earth1 and for the sake of round numbers let us call it one quarter4 ,it follows that an object on the surface of the moon is four times nearer the centre of attraction than is an object on the surface of the earth1 and since the force varies inversely as the square of the distance the moon's attraction upon bodies on its surface is relatively sixteen times as great as the earth's4 ,but the total force of the earth's attraction is eighty times greater than the moon's4 ,in order1 then1 to find the real relative attraction of the moon at its surface we must divide #hj by #af1 the quotient1 #e1 showing the ratio of the earth's force of attraction at its surface to that of the moon at its surface4 ,in other words1 this calculation shows that the moon draws bodies on its surface with only one-fifth the force with which the same bodies would be drawn on the earth's surface4 ,the weight of bodies of equal mass would1 therefore1 be only one-fifth as great on the moon as on the earth4 ,but the real difference is greater than this1 for we have used round numbers1 which exaggerated the size of the earth as compared with that of the moon4 ,if we employ the fractional numbers which show the actual ratio of the moon's radius 7half-diameter7 to that of the earth1 we shall find that the weight of the same body would be only about one-sixth as great on the moon as on the earth4 ,it has been thought that this relative lack of weight on the moon may account for the gigantic proportions assumed by its craters1 since the same elective force would throw volcanic matter to a much greater height and distance there than on our planet4 ,the connection of the slight force of gravity on the moon with its ability to retain an atmosphere is shown by the following considerations4 ,it is possible to calculate for any planet of known mass the velocity with which a particle would have to move in order to escape from the control of that planet4 ,in the case of the earth this critical velocity1 as it is called1 amounts to about #g miles per second1 and in the case of the moon to only #a miles per second4 ,now the kinetic theory of gases informs us that their molecules are continually flying in all directions with velocities varying with the nature and the temperature of the gas4 ,the maximum velocity of the molecules of oxygen is #a4h miles per second1 of hydrogen #g4d miles1 of nitrogen #b miles1 of water vapour #b4e miles4 ,it is evident1 then1 that the force of the earth's attraction is sufficient permanently to retain all these gases except hydrogen1 and in fact there is no gaseous hydrogen in the atmosphere1 that element being found on the earth only in combination with other substances4 ,but oxygen and nitrogen1 which constitute the bulk of the atmosphere1 have maximum molecular velocities much less than the critical velocity above described4 ,in the case of the moon1 however1 the critical velocity is less than those of the molecules of oxygen1 nitrogen1 and water vapour1 to say nothing of hydrogen2 therefore the moon cannot permanently retain them4 ,we say 8permanently10 because they might be retained for a time for the reason that the molecules of a gas fly in all directions1 and continual collisions occur among them in the interior of the gaseous mass1 so that it would be only those at the exterior of the atmosphere which would escape2 but gradually all that remained free from combination would get away4 ,illustration3 ,fig4 #ae4 ,the ,phases of the ,moon4 ,as the moon goes round the earth in the direction indicated by the arrows1 the sun remaining always on the left-hand side1 it is evident that the illuminated half of the moon will be turned away from the earth at new moon1 and toward it at full moon1 while between these positions more or less will be seen according to the direction of the moon with regard to the sun4 ,as the moon travels round the earth it shows itself in different forms1 gradually changing from one into another1 which are known as phases4 ,if the moon shone with light of its own its outline would always be circular1 like the sun's4 ,the apparent change of form is due1 first1 to its being an opaque globe1 reflecting the sunlight that falls upon it1 and necessarily illuminated on only one side at a time2 and second1 to the fact that as it travels round the earth the half illuminated by the sun is sometimes turned directly toward us1 at other times only partly toward us1 and at still other times directly away from us4 ,when it is in that part of its orbit which passes between the sun and the earth1 the moon1 so to speak1 has its back turned to us1 the illuminated side being1 of course1 toward the sun4 ,it is then invisible1 and this unseen phase is the true 8new moon40 ,it is customary1 however1 to give the name new moon to the narrow1 sickle-shaped figure1 which it shows in the west1 after sunset1 a few days after the date of the real new moon4 ,the sickle gradually enlarges into a half circle as the moon passes away from the sun1 and the half circle phase1 which occurs when the moon arrives at a position in the sky at right angles to the direction of the sun1 is called first quarter4 ,after first quarter the moon begins to move round behind the earth1 with respect to the sun1 and when it has arrived just behind the earth1 its whole illuminated face is turned toward the earth1 because the sun1 which causes the illumination1 is on that same side4 ,this phase is called full moon4 ,afterward the moon returns round the other part of its orbit toward its original position between the earth and the sun1 and as it does so1 it again assumes1 first1 the form of a half circle1 which in this case is called third1 or last1 quarter1 then that of a sickle1 known as 8old moon10 and finally disappears once more to become new moon again4 ,a perfectly evident explanation of these changes of form1 clearer than any description1 can be graphically obtained in this way4 ,take a billiard ball1 a croquet ball1 or a perfectly round1 smooth1 and tightly rolled ball of white yarn1 and1 placing yourself not too near a brightly burning lamp and sitting on a piano stool 7in order to turn more easily71 hold the ball up in the light1 and cause it to revolve round you by turning upon the stool4 ,as it passes from a position between you and the lamp to one on the opposite side from the lamp1 and so on round to its original position1 you will see its illuminated half go through all the changes of form exhibited by the moon1 and you will need no further explanation of the lunar phases4 ,illustration3 ,nebula in ,sagittarius 7,m #h7 ,photographed at the ,lick ,observatory by ,j4 ,e4 ,keeler1 with the ,crossley reflector4 ,exposure three hours4 ,note the clustering of stars over the whole field1 the intricate forms of the nebula1 and particularly the curious black spots1 or 8holes10 resembling drops of ink4 ,the ,harvest ,moon and the ,hunter's ,moon1 which are popularly celebrated not only on account of their romantic associations1 but also because in some parts of the world they afford a useful prolongation of light after sunset1 occur only near the time of the autumnal equinox1 and they are always full moons4 ,the full moon nearest the date of the equinox1 ,september #bc;d1 is the ,harvest ,moon1 and the full moon next following is the ,hunter's ,moon4 ,their peculiarity is that they rise1 for several successive evenings1 almost at the same hour1 immediately after sunset4 ,this is due to the fact that at that time of the year the ecliptic1 from which the moon's path does not very widely depart1 is1 in high latitudes1 nearly parallel with the horizon4 ,the full moon in winter runs higher in the sky1 and consequently gives a brighter light1 than in summer4 ,the reason is because1 since the full moon must always be opposite to the sun1 and since toe sun in winter runs low1 being south of the equator1 the full moon rides proportionally high4 #e4 ,eclipses4 ,we have mentioned the connection of the moon with the tides1 but there is another phenomenon in which the moon plays the most conspicuous part--that of eclipses4 ,there are two kinds of eclipses--solar and lunar4 ,in the former it is the moon that causes the eclipse1 by hiding the sun from view2 and in the latter it is the moon that suffers the eclipse1 by passing through the shadow which the earth casts into space on the side away from the sun4 ,in both cases1 in order that there may be an eclipse it is necessary that the three bodies1 the moon1 the sun1 and the earth1 shall be nearly on a straight line1 drawn through their centres4 ,since the moon occupies about a month in going round the earth there would be two eclipses in every such period 7one of the sun and the other of the moon71 if the moon's orbit lay exactly in the plane of the ecliptic1 or of the earth's orbit4 ,but1 in fact1 the orbit of the moon is inclined to that plane at an angle of something over #e4 ,even so1 there would be eclipses every month if the two opposite points1 called nodes1 where the moon crosses the plane of the ecliptic1 always lay in a direct line with the earth and the sun2 but they do not lie thus4 ,if1 then1 the moon comes between the earth and the sun when she is in a part of her orbit several degrees above or below the plane of the ecliptic1 it is evident that she will pass either above or below the straight line joining the centres of the earth and the sun1 and consequently cannot hide the latter4 ,but1 since eclipses do occur in some months and do not occur in others1 we must conclude that the situation of the nodes changes1 and such is the fact4 ,in consequence of the conflicting attractions of the sun and the earth1 the orbit of the moon1 although1 like that of the earth1 it always retains nearly the same shape and the same inclination1 swings round in space1 so that the nodes1 or crossing points on the ecliptic1 continually change their position1 revolving round the earth4 ,this motion may be compared to that of the precession of the equinoxes1 but it is much more rapid1 a complete revolution occurring in a period of about nineteen years4 ,from this it follows that sometimes the moon in passing its nodes will be in a line with the sun1 and sometimes will not4 ,but1 owing to the fact that the sun and moon are not mere points1 but on the contrary present to our view circular disks1 each about half a degree in diameter1 an eclipse may occur even if the moon is not in an exact line with the centres of the sun and the earth4 ,the edge of the moon will overlap the sun1 and there will be a partial eclipse1 if the centres of the two bodies are within one degree apart4 ,now1 the inclination of the moon's orbit to the ecliptic being only a little over #e1 it is apparent that in approaching one of its nodes1 along so gentle a slope1 it will come within less than a degree of the ecliptic while still quite far from the node4 ,thus1 eclipses occur for a considerable time before and after the moon passes a node4 ,the distances on each side of the node1 within which an eclipse of the sun may occur1 are called the solar ecliptic limits1 and they amount to #ah in either direction1 or #cf in sum4 ,within these limits the sun may be wholly or partially eclipsed according as the moon is nearer to1 or farther from1 the node4 ,if she is exactly at1 or very close to1 the node the eclipse will be total4 ,solar eclipses vary in another way4 ,what would be a total eclipse1 under other circumstances1 may be only an annular eclipse if the moon happens to be near her greatest distance from the earth4 ,we have described the variations in her distance due to the eccentricity of her orbit1 and we have said that the orbit itself swings round the earth in such a way as to cause the nodes continually to change their places on the ecliptic4 ,the motion of the orbit also causes the lunar apsides1 or the points where she is at her greatest and least distances from the earth1 to change their places1 but their revolution is opposite in direction to that of the nodes1 as the revolution of the apsides of the earth's orbit is opposite to that of the equinoxes4 ,the moon's apsides sometimes move eastward and sometimes westward1 but upon the whole the eastward motion prevails and the apsides complete one revolution in that direction once in about nine and one-half years4 ,in consequence of the combined effects of the revolution of the nodes and that of the apsides1 the moon is sometimes at her greatest distance from the earth at the moment when she passes centrally over the sun1 and sometimes at her least distance1 or she may be at any intervening distance4 ,if she is in the nearer part of her orbit1 her disk just covers that of the sun1 and the eclipse is total2 if she is in the farther part 7since the apparent size of bodies diminishes with increase of distance71 her disk does not entirely cover the sun1 and a rim of the latter is visible all around the moon4 ,this is called an annular eclipse1 because of the ring shape of the part of the sun remaining visible4 ,the length of the shadow which the moon casts toward the earth during a solar eclipse also plays an important part in these phenomena4 ,this length varies with the distance from the sun4 ,since the moon accompanies the earth1 it follows that when the latter is in aphelion1 or at its greatest distance from the sun1 the moon is also at its greatest mean distance from the sun1 and the length of the lunar shadow may1 in such circumstances1 be as much as #bcf1jjj miles4 ,when the earth1 attended by the moon1 is in perihelion1 the length of the moon's shadow may be only about #bbh1jjj miles4 ,the average length of the shadow is about #bcb1jjj miles4 ,this is nearly #gjjj miles less than the average distance of the moon from the earth1 so it is evident that generally the shadow is too short to reach the earth1 and it would never reach it1 and there would never be a total eclipse of the sun1 but for the varying distance of the moon from the earth4 ,when the moon is nearest the earth1 or in perigee1 its distance may be as small as #bba1fjj miles1 and in all cases when near perigee it is near enough for the shadow to reach the earth4 ,inasmuch1 as the moon's shadow1 even under the most favourable circumstances1 is diminished almost to a point before touching the earth1 it hardly need be said that it can cover but a very small area on the earth's surface4 ,its greatest possible diameter cannot exceed about #afg miles1 but ordinarily it is much smaller4 ,if both the earth and the moon were motionless1 this shadow would be a round or oblong dot on the earth1 its shape varying according as it fell square or sloping to the surface2 but since the moon is continually advancing in its orbit1 and the earth is continually rotating on its axis1 the shadow moves across the earth1 in a general west to east direction4 ,but the precise direction varies with circumstances1 as does also the speed4 ,the latter can never be less than about a thousand miles per hour1 and that1 only in the neighbourhood of the equator4 ,the moon advances eastward about #bajj miles per hour1 and the earth's surface turns in the same direction with a velocity diminishing from about a thousand miles an hour at the equator to #j at the poles4 ,it is the difference between the velocity of the earth's rotation and that of the moon's orbital revolution which determines the speed of the shadow4 ,the greatest time1 which the shadow can occupy in passing a particular point on the earth is only eight minutes1 but ordinarily this is reduced to one1 two1 or three minutes4 ,the true shadow only lasts during the time that the moon covers the whole face of the sun1 but before and after this total obscuration of the solar disk the sun is seen partially covered by the moon1 and these partial phases of the eclipse may be seen from places far aside from the track which the central shadow pursues4 ,it is only during a total eclipse1 and only from points situated within the shadow track1 that the solar corona is visible4 ,in a lunar eclipse it is the earth that is the intervening body1 and its shadow falls upon the moon4 ,a solar eclipse can only occur at the time of new moon1 and a lunar eclipse only at the time of full moon4 ,the shadow of the earth is much longer and broader than that of the moon1 and it never fails to reach the moon1 so that it is not necessary here to consider its varying length4 ,the width1 or diameter1 of the shadow at the average distance of the moon from the earth is about #egjj miles4 ,the moon may pass through the centre of the shadow1 or to one side of the centre1 or merely dip into the edge of it4 ,when it goes deep enough into the shadow to be entirely covered1 the eclipse is total2 otherwise it is partial4 ,since in a total lunar eclipse the entire moon is covered by the shadow1 it is evident that such an eclipse1 unlike a solar one1 may be visible simultaneously from all parts of the earth which1 at the time1 lie on the side facing the moon4 ,in other words1 the earth's shadow does not make merely a narrow track across the face of the moon1 but completely buries it4 ,when the moon passes centrally through the shadow1 she may remain totally obscured for about two hours4 ,but the moon does not completely disappear at such times1 because the refraction of the earth's atmosphere bends a little sunlight round its edges and casts it into the shadow4 ,if the atmosphere round the edges of the earth happens to be thickly charged with clouds1 but little light is thus refracted into the shadow1 and the moon appears very faint1 or almost entirely disappears4 ,but this is rare1 and ordinarily the eclipsed moon shines with a pale copperish light4 ,the occurrence of a lunar eclipse is governed by similar circumstances to those affecting solar eclipses4 ,the lunar ecliptic limits1 or the distance on each side of the node within which an eclipse may occur1 vary from #i to #ab in either direction4 ,taking all the various circumstances into account1 it is found that there may be1 though rarely1 seven eclipses in a year1 two being of the moon and five of the sun1 and that the least possible number of eclipses in a year is two1 in which case both will be of the sun4 ,taking into account also all the various positions which the sun and moon occupy with regard to the earth1 it is found that there exists a period of #ah years1 #aa days1 #h hours1 at the return of which eclipses of both kinds begin to recur again in the same order that they occur in the next preceding period4 ,this is called the saros1 and it was known to the ,chaldeans #bfjj years ago4 #f4 ,the ,planets4 ,we have several times mentioned the fact that1 beside the earth1 there are seven other principal planets revolving round the sun1 in the same direction as the earth1 but at various distances4 ,we shall consider each of these in the order of its distance from the sun4 ,but first it is desirable to explain briefly certain so-called 8laws0 which govern the motions of all the planets4 ,these are known as ,kepler's laws of planetary motion1 and are three in number4 ,the demonstration of their truth would carry us beyond the scope of this book1 and consequently we shall merely state them as they are recognised by astronomers4 #ast ,law3 ,the orbit of every planet is an ellipse1 having the sun situated in one of the foci4 #b;d ,law3 ,the radius vector of a planet describes equal areas in equal times4 ,by the radius vector is meant the straight line joining the planet to the sun1 and the law declares that as the planet moves round the sun1 the area of space swept over by this line in any given time1 say one day1 is equal to the area which it will sweep over in any other equal length of time4 ,if the orbit were a circle it is evident at a glance that the law must be true1 because then the sun would be situated in the centre of the circle1 the length of the radius vector1 no matter where the planet might be in the orbit1 would never vary1 and the area swept over by it in one day would be equal to the area swept over in any other day1 because all these areas would be precisely similar and equal triangles4 ,but ,kepler discovered that the same thing is true when the orbit is an ellipse1 and when1 in consequence of the eccentricity of the orbit1 the planet is sometimes farther from the sun than at other times4 ,as the triangular area swept over in a given time increases in length with the planet's recession from the sun1 it diminishes in breadth just enough to make up the difference which would otherwise exist between the different areas4 ,this law grows out of the fact that the force of gravitation varies inversely with the square of the distance4 #c;d ,law3 ,the squares of the periods 7i4 e4 times of revolution in their orbits7 of the different planets are proportional to the cubes of their mean 7average7 distances from the sun4 ,the meaning of this will be best explained by an example4 ,suppose one planet1 whose distance we know1 has a period only one-eighth as long as that of another planet1 whose distance we do not know4 ,then ,kepler's third law enables us to calculate the distance of the second planet4 ,call the period of the first planet #a1 and that of the second #h1 and also call the distance of the first #a1 since all we really need to know is the relative distance of the second1 from which its distance in miles is readily deduced by comparison with the distance of the first4 ,then1 by the law1 #ab 3 #hb 3 #ac 3 x#c 78x0 representing the unknown quantity74 ,now1 this is simply a problem in proportion where the product of the means is equal to the product of the extremes4 ,but #ab #a1 and also #ac #a2 therefore x#c #hb1 and x 7#hb7 7the cube root of the square of #h71 which is #d4 ,thus we see that the distance of the second planet must be four times that of the first4 ,this third law of ,kepler is applied to ascertain the distances of newly discovered planets1 whose periods are easily ascertained by simple observation4 ,if we know the distance of any one planet by measurement1 we can calculate the distances of all the others after observing their periods4 ,the law also works conversely1 i4 e4 from the distances the periods can be calculated4 99 99 99 99 99 ,we now take up the various planets singly4 ,the nearest to the sun1 as far as known1 is ,mercury1 its average distance being only #cf1jjj1jjj miles4 ,but its orbit is so eccentric that the distance varies from #bh1ejj1jjj miles at perihelion to #dc1ejj1jjj at aphelion4 ,in consequence its speed in its orbit is very variable1 and likewise the amount of heat and light received by it from the sun4 ,on the average it gets more than #f times as much solar light and heat as the earth gets4 ,but at perihelion it gets #b times as much as at aphelion1 and the time which it occupies in passing from perihelion to aphelion is only six weeks1 its entire year being equal to #hh of our days4 ,being situated so much nearer the sun than the earth is1 ,mercury is never visible to us except in the morning or the evening sky1 and then not very far from the sun4 ,its diameter is about #cjjj miles1 but its mass is not certainly known from lack of knowledge of its mean density4 ,this lack of knowledge is due to the fact that ,mercury has no satellite4 ,when a planet has a satellite it is easy to calculate its density from its measured diameter combined with the orbital speed of its satellite4 ,certain considerations have led some to believe that the mean density of ,mercury may be very great1 perhaps as great as that of lead1 or of the metal mercury itself4 ,not knowing the mass1 we cannot say exactly what the weight of bodies on ,mercury is4 ,we are also virtually ignorant of the condition of the surface of this planet1 the telescope revealing very little detail1 but it is generally thought that it bears a considerable resemblance to the surface of the moon4 ,there is another way in which ,mercury is remarkably like the moon4 ,the latter1 as we have seen1 always keeps the same side turned toward the earth1 which is the same thing as saying that it turns once on its axis1 while going once around the earth4 ,so ,mercury keeps always the same side toward the sun1 making one rotation on its axis in the course of one revolution in its orbit4 ,consequently1 one side of ,mercury is continually in the sunlight1 while the opposite side is continually buried in night4 ,there must1 however1 be regions along the border between these two sides1 where the sun does rise and set once in the course of one of ,mercury's years4 ,this arises from the eccentricity of the orbit1 and the consequent variations in the orbital velocity of the planet1 which cause now a little of one edge and now a little of the other edge of the dark hemisphere to come within the line of sunlight4 7,the same thing occurs with the moon1 though to a less degree owing to the smaller eccentricity of the moon's orbit1 which1 however1 is sufficient to enable us to see at one time a short distance round one side of the moon and at another time a short distance round the opposite side47 ,this phenomenon is known as libration4 ,mercury apparently possesses an atmosphere1 but we know nothing certain concerning its density4 99 99 99 99 99 ,the next planet1 in the order of distance from the sun1 is ,venus1 whose average distance is #fg1bjj1jjj miles4 ,the orbit of ,venus is remarkable for its small eccentricity1 so that the difference between its greatest and least distances from the sun is less than a million miles4 ,the period1 or year1 of ,venus is #bbe of our days4 ,owing to her situation closer to the sun1 she gets nearly twice as much light and heat as the earth gets4 ,in size ,venus is remarkably like the earth1 her diameter being #ggac miles1 which differs by only #bje miles from the mean diameter of the earth4 ,her axis is nearly perpendicular to the plane of her orbit4 ,her globe is a more perfect sphere than that of the earth1 being very little flattened at the poles or swollen at the equator4 ,although ,venus1 like ,mercury1 has no satellite1 her mean density has been calculated by other means1 and is found to be #j4hi that of the earth4 ,from this1 in connection with her measured diameter1 it is easy to deduce her mass1 and the force of gravity on her surface4 ,the latter comes out at about #j4he that of the earth1 i4 e4 a body weighing #ajj pounds on the earth would weigh #he pounds if removed to ,venus4 ,she possesses an atmosphere denser and more extensive than would theoretically have been expected--indicating1 perhaps1 a difference of constitution4 ,her atmosphere has been estimated to be twice as dense as ours1 a great advantage1 it may be remarked1 from the point of view of aronautics4 ,but this dense and abundant atmosphere renders ,venus a very difficult object for the telescope on account of the brilliance of its reflection4 ,in consequence1 we know but little of the surface of the planet4 ,one important result of this is that the question remains undecided whether ,venus rotates on her axis at a rate closely corresponding with that of the earth1 as some observers think1 or whether1 as others think1 she1 like ,mercury1 turns only once on her axis in going once round the sun4 ,the importance of the question in its bearing on the habitability of ,venus is apparent1 for if she keeps one face always sunward1 then on one side there is perpetual day and on the other perpetual night4 ,on the other hand1 if she has days and nights approximately equal in length to those of the earth1 it may well be thought that she is habitable by beings not altogether unlike ourselves1 because the force of gravity on her surface is not much less than on the earth1 and her dense atmosphere1 filled with clouds1 might tend to shield her inhabitants from the effects of the greater amount of heat poured upon her by the sun4 ,as her orbit is inside that of the earth1 ,venus1 like ,mercury1 is only visible either in the evening or in the morning sky1 but owing to her greater actual distance from the sun1 her apparent distance from it in the sky is greater than that of ,mercury4 ,illustration3 ,the ,great ,nebula in ,orion ,photographed at the ,lick ,observatory by ,j4 ,e4 ,keeler1 with the ,crossley reflector4 ,exposure one hour4 ,both of these planets1 in consequence of passing alternately between the sun and the earth and round the opposite side of the sun1 present phases resembling those of the moon4 ,the reader can explain these to himself by means of the experiment1 before mentioned1 with a billiard ball and a lamp4 ,in this case let the observer remain seated in his chair while another person carries the ball round the lamp in such a manner that it shall alternately pass between the lamp and the observer and round the other side of the lamp4 ,when ,venus comes nearly in line between the earth and the sun1 she becomes an exceedingly brilliant object in either the evening or the morning sky1 although at such times we see1 in the form of a crescent1 only a part of that half of her surface which is illuminated4 ,her increase of brightness at such times is due to her greater nearness to the earth4 ,when between the earth and the sun she may be only about #bf1jjj1jjj miles away1 while when she is on the other side of the sun she may be over #afj1jjj1jjj miles away4 ,both ,venus and ,mercury when passing exactly between the sun and the earth are seen1 in the form of small black circles1 moving slowly across the sun's disk4 ,these occurrences are called transits1 and in the case of ,venus have been before referred to4 ,they are more frequent with ,mercury than with ,venus1 but ,mercury's transits are not utilisable for parallax observations4 ,the latest transit of ,venus occurred in #ahhb1 and there will not be another until #bjjd4 ,the latest transit of ,mercury occurred in #aijg1 and there will be another in #aiad4 99 99 99 99 99 ,the earth is the third planet in order of distance1 and then comes ,mars1 whose average distance from the sun is #ada1ejj1jjj miles4 ,the orbit of ,mars is so eccentric that the distance varies between #adh1jjj1jjj and #ace1jjj1jjj miles4 ,its period or year is about #fhg of our days4 ,in consequence of its distance1 ,mars gets1 on the average1 a little less than half as much light and heat as the earth gets4 ,when it is on the same side of the sun with the earth1 and nearly in line with them1 it is said to be in opposition4 ,at such times it is manifestly as near the earth as it can come1 and thus an opposition of ,mars offers a good opportunity for the telescopic study of its surface4 ,these oppositions occur once in about #ghj days1 but they are not all of equal importance1 because the distance between the two planets is not the same at different oppositions4 ,the cause of the difference of distance is the eccentricity of the orbit4 ,if an opposition occurs when ,mars is in aphelion its distance from the earth will be about #fa1jjj1jjj miles1 but if the opposition occurs when ,mars is in perihelion the distance will be only about #ce1jjj1jjj miles4 ,the average distance at an opposition is about #dh1ejj1jjj miles4 ,the most favourable oppositions always occur in ,august or ,september1 and are repeated at an interval of from fifteen to seventeen years4 ,but at some of the intervening oppositions the distance of the planet is not too great to afford good views of its surface4 ,the diameter of ,mars is about #dccj miles1 with a similar polar flattening to that of the earth4 ,its density is #j4ga that of the earth1 and the force of gravity on its surface #j4ch4 ,a body weighing #ajj pounds on the earth would weigh #ch pounds on ,mars4 ,the evidence in regard to its atmosphere is conflicting1 but the probability is that it has an atmosphere not denser than that existing on our highest mountain peaks4 ,opinions concerning the existence of water vapour on ,mars are also conflicting4 ,one fact tending to show that its atmosphere must be very rare and cloudless is that its surface features are very plainly discernible with telescopes4 ,illustration3 ,fig4 #af4 ,orbits of ,mars and the ,earth4 ,inspection shows at once why the oppositions of ,mars which occur in ,august and ,september are the most favourable because ,mars being then near the perihelion point of its elongated orbit is comparatively near the earth1 while oppositions which occur in ,february and ,march are very unfavourable because then ,mars is near the aphelion point of its orbit1 and its distance from the earth is much greater4 ,the oppositions occur along the more favourable part of the orbit about two years and two months apart4 ,thus the figure shows that the opposition of ,september #bd1 #aiji was followed by one on ,november #be1 #aiaa4 ,about each pole1 as it happens to be turned earthward1 is to be seen a round white patch 7supposed to be snow71 and this gradually disappears as the summer advances in that hemisphere of the planet--for ,mars has seasons very closely resembling our seasons1 except that they are about twice as long4 ,the inclination of the axis of ,mars to the plane of its orbit is about #bd #ej1 which is not very different from the inclination of the earth's axis4 ,moreover1 ,mars rotates in a period of #bd hours1 #cg min41 #bb sec41 so that the length of day and night upon its surface is very nearly the same as upon the earth4 ,the surface of the planet is marked by broad irregular areas of contrasting colour1 or tone1 some of them being of a slightly reddish1 or yellowish1 hue1 and others of a neutral dusky tint4 ,the general resemblance to a globe of the earth1 with differently shaped seas and oceans1 is striking4 ,on account of the many likenesses between ,mars and the earth1 some astronomers are disposed to think that ,mars may be a habitable planet4 ,the terms 8seas0 and 8continents0 were formerly applied to the contrasted areas just spoken of1 but now it is believed that there are no large bodies of water on ,mars4 ,crossing the light1 or reddish-coloured1 areas there are sometimes seen great numbers of intersecting lines1 very narrow and faint1 which have received the name of 8canals40 ,some speculative minds find in these ground for believing that they are of artificial origin1 and a theory has been built up1 according to which the so-called canals are 8irrigated bands10 the result of the labours of the inhabitants4 ,the argument of the advocates of this theory is put about as follows3 ,mars is evidently a nearly dried-up planet1 and most of the water left upon it is periodically locked up in the polar snows4 ,as these snows melt away in the summer time1 now in one hemisphere and now in the other1 the water thus formed is conducted off toward the tropical and equatorial zones by innumerable canals1 too small to be seen from the earth4 ,the lands irrigated by these canals are narrow strips1 whose situation is determined by local circumstances1 and which cross one another in all directions4 ,within these bands1 which enlarge into rounded 8oases0 where many of them intersect1 vegetation pushes1 and its colour causes them to appear as dark lines and patches on the surface of the planet4 ,the fact that the lines make their appearance gradually1 after the polar caps begin to disappear1 is regarded as strongly corroborative of the theory4 ,in answer to the objection that works so extensive as this theory of irrigation calls for would be practically impossible1 it is replied that the relatively small force of gravity on ,mars not only immensely diminishes the weight of all bodies there1 but also renders it possible for animal forms to attain a greater size1 with corresponding increase of muscular power4 ,it is likewise argued that ,mars may have been longer inhabited than the earth1 and that its inhabitants may consequently have developed a more complete mastery over the powers of nature than we as yet possess4 ,many astronomers reject these speculations1 and even aver that the lines called 8canals0 7and it must be admitted that many powerful telescopes show few or none of them7 have no real existence1 what is seen1 or imagined to be seen1 being due to some peculiarity of the soil1 rocks1 or atmosphere4 ,mars has two small satellites1 revolving round it with great speed at close quarters4 ,the more distant satellite1 ,deimos1 is #ad1fjj miles from the centre of ,mars and goes round it in #cj hours1 #ah min4 ,the nearer one1 ,phobos1 is only #ehjj miles from the planet's centre1 and its period of revolution is only #g hours1 #ci min41 so that it makes more than three circuits while the planet is rotating once on its axis4 ,both of the satellites are minute in size1 probably under ten miles in diameter4 99 99 99 99 99 ,beyond ,mars1 at an average distance of about #bdf1jjj1jjj miles from the sun1 is a system of little planets called asteroids4 ,more than #fjj are now known1 and new ones are discovered every year1 principally by means of photography4 ,only four of these bodies are of any considerable size1 and they were1 naturally1 the first to be discovered4 ,they are ,ceres1 diameter #dgg miles2 ,pallas1 #cjd miles2 ,vesta1 #bci miles2 and ,juno1 #abj miles4 ,many of the others have a diameter of only about ten1 or even1 perhaps1 as little as five1 miles4 ,their orbits are more eccentric than those of any of the large planets1 and one of them1 ,eros1 has a mean distance of #ace1jjj1jjj miles1 and a least distance of only #aje1jjj1jjj1 so that it is nearer to the sun than ,mars is4 ,eros may1 under favourable circumstances1 approach within #ad1jjj1jjj miles of the earth4 ,this fact1 as already mentioned1 has been taken advantage of for measuring its distance from the earth1 from which the distance of the sun may be calculated with increased accuracy4 ,eros and some others of the asteroids seem to be of an irregular or fragmentary form1 and this has been used to support a theory1 which is not1 however1 generally accepted1 that the asteroids are the result of an explosion1 by which a larger planet was blown to pieces4 99 99 99 99 99 ,sixth in order of distance from the sun 7counting the asteroids as representing a single body7 is the greatest of all the planets1 ,jupiter4 ,his average distance from the sun is #dhc1jjj1jjj miles1 but the eccentricity of his orbit causes him to approach within #dgb1ejj1jjj miles at perihelion1 and to recede to #dic1ejj1jjj miles at aphelion4 ,when in opposition1 ,jupiter's mean distance from the earth is #cij1jjj1jjj miles4 ,this gigantic planet has a mean diameter of #hg1chj miles1 but is so flattened at the poles and bulged round the equator that the polar diameter is only #hd1egj miles1 while the equatorial diameter is #ij1aij miles1 a difference of #efhj miles4 ,this peculiar form is doubtless due to the planet's swift rotation4 ,the axis1 like that of ,venus1 is nearly perpendicular to the plane of the orbit4 ,he makes a complete turn on his axis in a mean period of #i hours1 #ee minutes4 ,the reason for saying 8a mean period0 will appear in a moment4 ,jupiter's year is equal to #aa4hf of our years1 but it comes into opposition to the sun1 as seen from the earth1 once in every #cii days4 ,the volume of ,jupiter is about #acjj times that of the earth1 i4e4 it would take #acjj earths rolled into one to equal ,jupiter in size4 ,but its mean density is slightly less than one quarter of the earth's1 so that its mass is only #caf times greater than the earth's4 ,the force of gravity on its surface is #b4fd times the earth's4 ,a body weighing #ajj pounds on the earth would weigh #bfd pounds on ,jupiter4 ,it will be observed that ,jupiter's mean density is very nearly the same as that of the sun1 and we conclude that it cannot be a solid1 rigid globe like the earth4 ,this conclusion is made certain by the fact that its period of rotation on its axis is variable1 another resemblance to the sun4 ,the equatorial parts go round in a shorter period than parts situated some distance north or south of the equator4 ,it may be supposed that there is a solid nucleus within1 but if so1 no direct evidence of its existence has been found4 ,nevertheless1 although ,jupiter appears to be in a cloud-like state1 it does not shine with light of its own1 so that its temperature1 while no doubt higher than that of the earth1 cannot approach anywhere near that of the sun4 ,we do not know of what materials ,jupiter is composed1 for spectroscopic analysis applies especially to bodies which shine with their own light4 ,when they shine only by reflected light received from the sun1 their spectra resemble the regular solar spectrum1 except for the presence of faint bands due to absorption in the planet's atmosphere4 ,it may be that there are no elements of great atomic density1 such as iron or lead1 in the globe of ,jupiter4 ,yet in the course of long ages the planet may become smaller and more condensed1 in consequence of the escape of its internal heat4 ,in this way ,jupiter may be regarded as representing an intermediate stage of evolution between an altogether vaporous and very hot body like the sun1 and a cool and solid one like the earth4 ,jupiter presents a magnificent appearance in a good telescope4 ,its oblong disk is seen crossed in an east and west direction1 and parallel to its equator1 by broad1 vari-coloured bands1 called belts4 ,these frequently change in form and1 to some extent1 in situation1 as well as in number4 ,but there are always at least two wide belts1 one on each side of the equator4 ,in #ahgh a very remarkable feature was noticed just south of the principal south belt of ,jupiter1 which has become celebrated under the name of the ,great ,red ,spot4 ,in a few years after its discovery its colour faded1 but it still remains visible1 with varying degrees of distinctness1 as an oblong marking1 about #cj1jjj miles long and #gjjj miles broad4 ,the outer border of the great south belt bends away from the spot1 as if some force of repulsion acted between them1 or as if the spot were an elevation round which the clouds of the belt flowed like a river round a projecting headland4 ,the nature of this curious spot is unknown4 ,other smaller spots1 sometimes white1 sometimes dusky1 occasionally make their appearance1 but they do not exhibit the durability of the ,great ,red ,spot4 ,jupiter has eight satellites1 four of which1 known since the time of ,galileo1 are conspicuous objects in the smallest telescope4 ,all but one of these four are larger than our moon1 while the other four are extremely insignificant in size4 ,the four principal satellites are designated by ,roman numerals1 ,i1 ,,ii1 ,,iii1 ,,iv1 arranged in the order of distance from the planet4 ,they also have names which are seldom used4 ,satellite ,i 7,io7 has a diameter of #bdeb miles1 and revolves in a period of #a day1 #ah hours1 #bg min41 #ce4e sec41 at a mean distance of #bfa1jjj miles2 ,,ii 7,europa7 is #bjde miles in diameter1 and revolves in #c days1 #ac hours1 #ac min41 #db4a sec41 at a mean distance of #dae1jjj miles2 ,,iii 7,ganymede7 has a diameter of #ceeh miles1 a period of seven days1 #c hours1 #db min41 #cc4d sec41 and a mean distance of #ffd1jjj miles2 ,,iv 7,callisto7 is #ccde miles in diameter1 has a period of #af days1 #af hours1 #cb min41 #aa4b sec41 and a mean distance of #a1afg1jjj miles4 ,the object of giving the periods with extreme accuracy will appear when we speak of the use made of observations of ,jupiter's satellites4 ,the first of the four small satellites1 discovered by ,barnard in #ahib1 is probably less than #ajj miles in diameter1 and has a mean distance of #aab1ejj miles1 and a period of only #aa hours1 #eg min41 #bb4f sec4 ,the other small satellites are much more distant than any of the large ones1 the latest to be discovered1 the eighth1 being situated at a mean distance of about #ae1jjj1jjj miles1 but travelling in an orbit so eccentric that the distance ranges between #aj1jjj1jjj and #bj1jjj1jjj miles4 ,the period is about two and a fifth years4 ,but the most remarkable fact is that this satellite revolves round ,jupiter from east to west1 a direction contrary to that pursued by all the others1 and contrary to the direction which is almost universal among the rotating and revolving bodies of the solar system4 ,the large satellites are very interesting objects for the telescope4 ,when they come between the sun and ,jupiter their round black shadows can be plainly seen moving across his disk1 and when they pass round into his shadow they are suddenly eclipsed1 emerging after a time out of the other side of the shadow4 ,these phenomena are known as transits and eclipses1 and their times of occurrence are carefully predicted in the ,american ,ephemeris and ,nautical ,almanac1 published at ,washington for the benefit of astronomers and navigators1 because these eclipses can be employed in comparing local time with standard meridian time4 ,they were formerly utilised to determine the velocity of light1 in this way3 ,as the earth goes round its orbit inside that of ,jupiter the latter is seen in opposition to the sun at intervals of #cii days4 ,when it is thus seen the earth must be between the sun and ,jupiter1 and the distance between the two planets is the least possible4 ,but when the earth has passed round to the other side of the sun from ,jupiter this distance becomes the greatest possible4 ,the increase of distance between the two planets1 as the earth goes from the nearest to the farthest side of its orbit1 is about #ahf1jjj1jjj miles4 ,now it was noticed by the ,danish astronomer1 ,roemer1 that as the earth moved farther and farther from ,jupiter the times of occurrence of the eclipses kept getting later and later1 until when the earth arrived at its greatest distance the eclipses were about #af minutes behind time4 ,he correctly inferred that the retardation of the time was due to the increase of the distance1 and that the #af minutes by which the eclipses were behindhand when the distance was greatest represented the time taken by light to cross the #ahf1jjj1jjj miles of space by which the earth had increased its distance from ,jupiter4 ,in other words1 light must travel #ahf1jjj1jjj miles in about sixteen minutes1 from which it was easy to calculate its speed per second--which we now know to be #ahf1ccj miles4 ,our knowledge of the velocity of light furnishes one of the means of calculating the distance of the sun4 ,we come next to the beautiful planet ,saturn1 whose mean distance from the sun is #hhf1jjj1jjj miles4 ,the distance varies between #iaa1jjj1jjj and #hfa1jjj1jjj miles4 ,saturn's year is equal to #bi4df of our years4 ,it comes into opposition every #cgh days4 ,the most surprising feature of ,saturn is the system of immense rings surrounding it above the equator4 ,the globe of the planet is #gf1dgj miles in equatorial diameter1 and #fi1ghj miles in polar diameter1 a difference of #ffij miles1 so that ,saturn is even more compressed at the poles and swollen at the equator than ,jupiter4 ,the axis of rotation is inclined #bg from a perpendicular4 ,the rings are three in number1 very thin in proportion to their vast size1 and placed one within another in the same plane4 ,the outer diameter of the outer ring1 called ,ring ,a1 is about #afh1jjj miles4 ,its breadth is about #aj1jjj miles4 ,then comes a gap1 about #afjj miles across1 separating it from ,ring ,b1 the brightest of the set4 ,this is about #af1ejj miles broad1 and at its inner edge it gradually fades out1 blending with ,ring ,c1 which is called the crape1 or gauze1 ring1 because it has a dusky appearance1 and is so translucent that the globe of the planet can be seen through it4 ,this ring is about #aj1jjj miles broad1 and its inner edge comes within a distance of between #ijjj and #aj1jjj miles of the surface of the planet4 ,ring ,a apparently has a very narrow gap running round at about a third of its breadth from the outer edge4 ,this1 known as ,encke's ,division1 is not equally plain at all times4 ,occasionally observers report the temporary appearance of other thin gaps4 ,the mean density of ,saturn is less than that of any other planet1 being but #j4ac that of the earth1 or #j4gb that of water4 ,it follows that this great planet would float in water4 ,the weight of bodies at its surface would be a little less than three-quarters of their weight on the surface of the earth4 ,the globe of ,saturn1 like that of ,jupiter1 is marked by belts parallel with the equator1 but they are less definite in outline and less conspicuous than the belts of ,jupiter4 ,the equatorial zone often shows a beautiful pale salmon tint1 while the regions round the poles are faintly bluish4 ,light spots are occasionally seen upon the planet1 and it appears to rotate more rapidly at the equator than in the higher latitudes4 ,there seems to be every reason to think that ,saturn1 also1 is of a vaporous constitution1 although it may have a relatively condensed nucleus4 ,but while the globe of the planet appears to be vaporous1 the same is not true of the rings4 ,we have already mentioned the fact that they are exceedingly thin in proportion to their great size and width4 ,the thickness has not been determined with exactness1 but it probably does not exceed1 on the average1 one hundred miles4 ,there appear to be portions of the rings which are thicker than the average1 as if the matter of which they are composed were heaped up there4 ,this matter evidently consists of an innumerable multitude of small bodies4 ,in other words1 the rings are composed of swarms of what may be called meteors4 ,that their composition must be of this nature1 although the telescope does not reveal it1 has been proved in two ways3 first1 by mathematical calculation1 which shows that if the rings were all of a piece1 whether solid or liquid1 they would be destroyed by the contending forces of attraction to which they are subject2 and1 second1 by spectroscopic observation1 which proves1 in a way that will be shown when we come to deal with the stars1 that the rings rotate with velocities proportional to the distances of their various parts from the centre of the planet4 ,hence it is inferred that they must consist of a vast number of small bodies or particles4 ,saturn has ten satellites1 all revolving outside the rings4 ,the names of nine of these in the order of increasing distance are3 ,mimas1 distance #aag1jjj miles2 ,enceladus1 distance #aeg1jjj miles2 ,tethys1 distance #ahf1jjj miles2 ,dione1 distance #bch1jjj miles2 ,rhea1 distance #ccb1jjj miles2 ,titan1 distance #gga1jjj miles2 ,hyperion1 distance #icd1jjj miles2 ,japetus1 distance #b1bbe1jjj miles2 and ,phbe1 distance #h1jjj1jjj miles4 ,the last1 like the eighth satellite of ,jupiter1 revolves in a retrograde direction4 ,only ,titan and ,japetus are conspicuous objects4 ,the period of ,mimas is only about #bb hours2 that of ,titan is #ae days1 #bb hours1 #da min41 and that of ,japetus about #gi days1 #h hours4 ,barnard's measurements indicate for ,titan a diameter of #bgbj miles4 ,japetus is probably about two-thirds as great in diameter as ,titan4 ,illustration3 ,photographs of ,mars ,made at the ,yerkes ,observatory by ,e4 ,e4 ,barnard1 with the forty-inch refractor1 ,september #bh1 #aiji4 ,beyond ,saturn1 in the order named1 are ,uranus and ,neptune4 ,the mean distance of the former from the sun is #a1ghb1jjj1jjj miles1 and that of the latter #b1gia1ejj1jjj miles4 ,the orbit of ,uranus is more eccentric than that of ,neptune4 ,the diameter of ,uranus is about #cb1jjj miles and that of ,neptune about #ce1jjj miles4 ,the year of ,uranus is equal to #hd of our years1 and that of ,neptune to #afd4gh4 ,these planets are so remote1 and so poorly illuminated by the sun1 that the telescope reveals very little detail on their surfaces4 ,their density is somewhat less than that of ,jupiter4 ,uranus has four satellites1 ,ariel1 ,umbriel1 ,titania1 and ,oberon1 situated at the respective distances of #abj1jjj1 #afg1jjj1 #bgc1jjj1 and #cfe1jjj miles4 ,neptune has one1 nameless1 satellite1 at a distance of #bbe1jjj miles4 ,the most remarkable thing about these two planets is that their axes of rotation1 as compared with those of all the other planets1 are tipped over into a different plane1 so that they rotate in a retrograde or backward direction1 and their satellites1 in like manner1 revolve from east to west4 ,the axis of ,uranus is not far from upright to the plane of the ecliptic1 so that the motion of its satellites carries them alternately far northward and far southward of that plane1 but the axis of ,neptune is tipped so far over that the retrograde1 or east to west1 motion is very pronounced4 ,neptune is celebrated for having been discovered by means of mathematical calculations1 based on its disturbing attraction on ,uranus4 ,these calculations showed where it ought to be at a certain time1 and when telescopes were pointed at the indicated spot the planet was found4 ,similar disturbances of the motions of ,neptune lead some astronomers to think that there is another1 yet undiscovered1 planet still more distant4 #g4 ,comets4 ,comets are the most extraordinary in appearance of all celestial objects visible to the naked eye4 ,great comets have been regarded with terror and superstitious dread in all ages of the world1 wherever ignorance of their nature has prevailed4 ,they have been taken for prognosticators of wars1 famines1 plagues1 the death of rulers1 the outbreak of revolutions1 and the subversion of empires4 ,one reason for this1 aside from their strange and menacing appearance1 is1 no doubt1 the rarity of very great and conspicuous comets4 ,it was not until ,newton had demonstrated the law of gravitation that the fact began to be recognised that comets are controlled in their motions by the sun4 ,we now know that they travel in orbits1 frequently1 and perhaps always1 elliptical1 having the sun in one of the foci4 ,comets are habitually divided into two classes3 first1 periodical comets1 meaning those which have been observed at more than one return to perihelion2 and1 second1 non-periodical comets1 meaning those which have been seen but once1 but which1 nevertheless1 may return to perihelion in a period so long that a second return has not been observed4 ,a better division is into comets of short period1 and comets of long1 or unknown1 periods4 ,illustration3 ,fig4 #ag4 ,ellipse1 ,parabola1 and ,hyperbola4 ,the figure shows graphically why it is so difficult to tell exactly the form of a comet's orbit4 ,the three kinds of curves are nearly of the same form near the focus 7the ,sun71 and it is only in that part of its orbit that the comet can be seen4 ,moreover a comet is1 at best1 a misty and indefinite object1 which renders it so much the more difficult to obtain good observations of its precise position and movement4 ,still1 many astronomers are disposed to think that the majority of comets do not travel in elliptical but in parabolic1 and a few in hyperbolic1 orbits4 ,this calls for a few words of explanation4 ,ellipses1 parabolas1 and hyperbolas are all conic-section curves1 but the ellipse alone returns into itself1 or forms a closed circuit4 ,in each case the sun is situated at the focus where the perihelion1 or nearest approach1 of the comet occurs1 but only comets travelling in elliptical orbits return again after having once been seen4 ,a comet moving in a parabola would go back into the depths of space nearly in the direction from which it had come1 and would never be seen again2 and if it moved in a hyperbola it would go off toward another quarter of the celestial sphere1 and likewise would never return4 ,now it is true that the forms calculated for the orbits of the majority of comets that have been observed appear to be parabolic 7a very few seem to be hyperbolic71 and if this is the fact such comets cannot be permanent members of the solar system1 but must enter it from far-off regions of space1 and having visited the sun must return to such regions without any tendency to come back again4 ,in that case they may pay similar visits to other suns4 ,but it is quite possible that what appear to be parabolic orbits may1 in reality1 be ellipses of very great eccentricity4 ,the difficulty in determining the precise shape of a comet's orbit arises from the fact that all three of the curves just mentioned closely approximate to one another in the neighbourhood of their common focus1 the sun1 and it is only in that part of their orbits that comets are visible4 ,the whole question is yet in abeyance1 but1 as we have said1 it seems likely that all comets really move in elliptical orbits1 and consequently never get entirely beyond the control of the sun's attraction4 ,but in all cases the orbits of comets are much more eccentric than those of the large planets4 ,the famous comet of ,halley1 for instance1 which has the longest period of any of the known periodical class1 about seventy-five years1 is #c1bic1jjj1jjj miles from the sun when in aphelion1 and only #ed1ggj1jjj miles when in perihelion4 ,comets1 when near the sun1 are greatly affected by the disturbing attraction of large planets1 and especially of the most massive of them all1 ,jupiter4 ,the effect of this disturbance is to change the form of their orbits1 with the not infrequent result that the latter are altered from apparent parabolas into unquestionable ellipses1 and thus the comets concerned are said to be 8captured10 or made prisoners to the sun1 by the influence of the disturbing planet4 ,about twenty small comets are known as 8,jupiter's ,comet ,family10 because they appear to have been 8captured0 in this way by him4 ,a few others are believed to have been similarly captured by ,saturn1 ,uranus1 and ,neptune4 ,the orbits of comets differ from those of the planets in other ways beside their greater eccentricity4 ,the planets all move round the sun from west to east1 but comets move in both directions4 ,the orbits of the planets1 with the exception of some of the asteroids1 all lie near one common plane1 but those of comets are inclined at all angles to this plane1 some of them coming down from the north side of the ecliptic and others up from the south side4 ,a comet consists of two distinct portions3 first1 the head1 or nucleus2 and1 second1 the tail4 ,the latter only makes its appearance when the comet is drawing near the sun1 and1 as a whole1 it is always directed away from the sun1 but usually more or less curved backward along the comet's course1 as if the head tended to run away from it4 ,the appearance of a comet's tail at once suggests that it is produced by some repulsive force emanating from the sun4 ,recently there has been a tendency to explain this on the principle of what is known as the pressure of light4 ,this demands a brief explanation4 ,light is believed to be a disturbance of the universal ether in the form of waves which proceed from the luminous body4 ,these waves possess a certain mechanical energy tending to drive away bodies upon which they impinge4 ,the energy is relatively slight1 and in ordinary circumstances produces no perceptible effect1 but when the body acted upon by the light is extremely small the pressure may become so great relatively to gravitation as to prevail over the latter4 ,to illustrate this1 let us recall two facts--first1 that gravitation acts upon the mass1 i4e4 all the particles of a body throughout its entire volume2 and1 second1 that pressure acts only upon the exterior surface4 ,consequently gravitation is proportional to the volume1 while the pressure of light is proportional to the surface of the body acted upon4 ,now the mass1 or volume1 of any body varies as the cube of its diameter1 and the surface only as the square4 ,if1 then1 we have two bodies1 one of which has twice the diameter of the other1 the mass of the second will be eight times less than that of the first1 but the surface will be only four times less4 ,if the second has only one-third the diameter of the first1 then its mass will be twenty-seven times less1 but its surface only nine times less4 ,thus we see that as we diminish the size of the body1 the mass falls off more rapidly than the area of the surface1 and consequently the pressure gains relatively to the gravitation4 ,experiment has corroborated the conclusions of mathematics on this subject1 and has shown that when a particle of matter is only about one one-hundred-thousandth of an inch in diameter the pressure of light upon it becomes greater than the force of gravitation1 and such a particle1 situated in open space1 would be driven away from the sun by the light waves4 ,this critical size would vary with the density of the matter composing the particle1 but what we have said will serve to convey an idea of its minuteness4 ,now in applying this to comets' tails it is only necessary to remark that they are composed of either gaseous or dusty particles1 or both1 rising from the nucleus1 probably under the influence of the heat or the electrical action of the sun1 and these particles1 being below the critical size1 are driven away from the sun1 and appear in the form of a tail following the comet4 ,it may be added that the same principle has been evoked to explain the corona of the sun1 which may be composed of clouds of gas or dust kept in suspension by the pressure of light4 ,the nuclei of comets contain nearly their whole mass4 ,the actual mass of no comet is known1 but it can in no case be very great4 ,moreover1 it is probable that the nucleus of a comet does not consist of a single body1 either solid or liquid1 but is composed of a large number of separate small bodies1 like a flock of meteors1 crowded together and constantly impinging upon one another4 ,as the comet approaches the sun the nucleus becomes violently agitated1 and then the tail begins to make its appearance4 ,the possibility exists of an encounter between the earth and the head of a comet1 but no such occurrence is known4 ,two or three times1 however1 the earth is believed to have gone through the tail of a comet1 the last time in #aiaj1 when ,halley's comet passed between the earth and the sun1 but no certain effects have been observed from such encounters4 ,the spectroscope shows that comets contain various hydrocarbons1 sodium1 nitrogen1 magnesium1 and possibly iron1 but we know1 as yet1 very little about their composition4 ,the presence of cyanogen gas was reported in ,halley's comet at its last appearance4 ,we are still more ignorant of the origin of comets4 ,we do know1 however1 that they tend to go to pieces1 especially those which approach very close to the sun4 ,the great comet of #ahhb1 which almost grazed the sun1 was afterward seen retreating into space scattered into several parts1 each provided with a tail4 ,in at least one case1 several comets have been found travelling in the same track1 an indication that one large original comet has been separated into three or four smaller ones4 ,this appears to be true of the comets of #ahdc1 #ahhj1 and #ahhb1--;and perhaps the comet of #aegf should be added4 ,but the most remarkable case of disruption is that of ,biela's ,comet1 which first divided into two parts in #ahdf and then apparently became scattered into a swarm of meteors which was encountered by the earth in #ahgb1 when it passed near the old track of the comet4 ,this leads us to our next subject4 #h4 ,meteors4 ,everybody must1 at some time1 have beheld the phenomenon known as a falling1 or shooting1 star4 ,a few of these objects can be seen darting across the sky on almost any clear night in the course of an hour or two of watching4 ,sometimes they appear more numerously1 and at intervals they are seen in 8showers40 ,they are called meteors1 and it is believed that they are minute solid bodies1 perhaps averaging but a small fraction of an ounce in weight1 which plunge into the atmosphere with velocities varying from twenty to thirty or more miles per second1 and are set afire and consumed by the heat of friction developed by their rush through the air4 ,anybody who has seen a bullet melted by the heat suddenly developed when it strikes a steel target has had a graphic illustration of the transformation of motion into heat4 ,but if we could make the bullet move fast enough it would melt in the air1 the heat being developed by the constant friction4 ,the connection of meteors with comets is very interesting4 ,in the year #ahcc1 a magnificent and imposing display of meteors1 which1 for hours1 on the night between the #acth and #adth of ,november1 filled the sky with fire-balls and flaming streaks1 astonished all beholders and filled many with terror4 ,it was found that these meteors travelled in an orbit intersecting that of the earth at the point where the latter arrived in the middle of ,november1 and also that they had a period of revolution about the sun of #cc years1 and were so far scattered along their orbit that they required nearly three years to pass the point of intersection with the orbit of the earth4 ,thus it was concluded that for three years in succession1 in mid-,november1 there should be a display of the meteors plunging into the earth's atmosphere4 ,but only in the year when the thickest part of the swarm was encountered by the earth would the display be very imposing4 ,upon this it was predicted that there would be a recurrence of the phenomenon of #ahcc in the year #ahff4 ,it happened as predicted1 except that the number of meteors was not quite so great as before4 ,in the meantime1 it had been discovered that these meteors followed in the track of a comet known as ,temple's ,comet1 and also that certain other meteors1 which appear every year in considerable numbers about the #ajth of ,august1 followed the track of another comet called ,tuttle's ,comet4 ,then in #ahgb came the display1 mentioned in the last section1 of meteors which were evidently the debris of the vanished comet of ,biela4 ,the inference from so many similar cases was irresistible that the meteors must be fragments of destroyed or partially destroyed comets4 ,several other cases of identity of orbits between meteors and comets have been discovered4 ,it has been said that the ,august meteors appear every year4 ,the explanation of this is that they have1 in the course of many ages1 been scattered around the whole circuit of their orbit1 so that each year1 about the #ajth of ,august1 when the earth crosses their track1 some of the meteors are encountered4 ,they are like an endless railroad train travelling upon a circular track4 ,the ,november meteors also appear1 in small numbers1 every year1 a fact indicating that some of them1 too1 have been scattered all around their orbit1 although the great mass of them is still concentrated in an elongated swarm1 and a notable display can only occur when this swarm is at the crossing simultaneously with the earth4 ,these meteors were eagerly awaited in #ahii1 when it was hoped that the splendid displays of #ahcc and #ahff might be repeated1 but1 unfortunately1 in the meantime the planets ,jupiter and ,saturn1 by their disturbing attractions1 had so altered the position of the path of the meteors in space that the principal swarm missed the connection4 ,there are many other periodical meteor showers1 generally less brilliant than those already mentioned1 and some astronomers think that all of them had their origin from comets4 ,it is not known that any meteor from any of these swarms has ever reached the surface of the earth4 ,the meteors appear to be so small that they are entirely burnt up before they can get through the atmosphere1 which thus acts as a shield against these little missiles from outer space4 ,but there is another class of meteoric bodies1 variously known as meteorites1 arolites1 uranoliths1 or bolides1 which consists of larger masses1 and these sometimes fall upon the earth1 after a fiery passage through the air4 ,specimens of them may be seen in many museums4 ,they are divided into two principal classes1 according to their composition3 first1 stony meteorites1 which are by far the most numerous2 and1 second1 iron meteorites1 which consist of almost pure iron1 generally alloyed with a little nickel4 ,the stony meteorites1 which usually contain some compound of iron1 consist of a great variety of substances1 including between twenty and thirty different chemical elements4 ,although they resemble in many ways minerals of volcanic origin on the earth1 they also possess certain characteristics by which they can be recognised even when they have not been seen to fall4 ,when a meteorite passes through the air it makes a brilliant display of light1 and frequently bursts asunder1 with a tremendous noise1 scattering its fragments about4 ,the largest fragment of a meteorite actually seen to fall1 weighs about a quarter of a ton4 ,upon striking the ground the meteorite sometimes penetrates to a depth of several feet1 and some have been picked up which were yet hot on the surface1 although very cold within4 ,it is not known that meteorites have any connection with comets1 and their origin can only be conjectured4 ,among the various suggestions that have been made the following may be mentioned3 7#a7 that they have been shot out of the sun--particularly the iron meteorites2 7#b7 that they were cast into space by lunar volcanoes when the moon was still subject to volcanic action2 7#c7 that they are the products of explosion in the stars4 ,but some astronomers are disposed to think that they originated in a similar manner to other members of the solar system1 although it is difficult1 on this hypothesis1 to account for their great density4 ,the opinion that the iron meteorites have come from the sun1 or some other star1 is enforced by the fact that they contain hydrogen1 carbon1 and helium1 in forms suggesting that these gases were absorbed while the bodies were immersed in a hot1 dense atmosphere4 ---------------------------------------- -------------------------------- ,,part ,,iv4 ,,the ,,fixed ,,stars4 ---------------------------------------- -------------------------------- ,,part ,,iv4 ,,the ,,fixed ,,stars4 #a4 ,the ,stars4 ,the stars are distant suns1 varying greatly in remoteness1 in magnitude1 and in condition4 ,many of them are much smaller than our sun1 and many others are as much larger4 ,they vary1 likewise in age1 or state of development4 ,some are relatively young1 others in a middle stage1 and still others in a condition that may be called solar decrepitude4 ,these proofs of evolution among the stars1 the knowledge of which we owe mainly to spectroscopic analysis1 serve to establish more firmly the conclusion1 to which the simple aspect of the heavens first leads us1 that the universe is a connected system1 governed everywhere by similar laws and consisting of like materials4 ,the number of stars visible to the naked eye is about six thousand1 but telescopes show tens of millions4 ,it is customary to divide the stars into classes1 called magnitudes1 according to their apparent brightness4 ,by a system of photometry1 or light-measurement1 they are grouped into stars of the first1 second1 third1 etc41 magnitude4 ,with the naked eye no stars fainter than the sixth magnitude are visible1 but very powerful telescopes may show them down to the eighteenth magnitude4 ,each magnitude is about two and a half times brighter than the next magnitude below in the scale4 ,a first-magnitude star is about one hundred times brighter than one of the sixth magnitude4 ,but1 in reality1 the variation of brightness is gradual1 and for very accurate estimates fractions of a magnitude have to be employed4 ,there are about twenty first-magnitude stars1 but they are not all of equal brightness4 ,a more accurate photometry assumes a zero magnitude1 very nearly1 represented by the star ,arcturus1 and makes the ratio #b4eab4 ,thus a star1 nearly represented by ,aldebaran or ,altair1 which is #b4eab times fainter than the zero magnitude1 is of the first magnitude1 and a star1 nearly represented by the ,north ,star1 which is #b4eab times fainter than the first magnitude1 is of the second magnitude4 ,counting in the other direction1 a star1 like ,sirius1 which is brighter than the zero magnitude1 is said to be of a negative magnitude4 ,the magnitude of ,sirius is--#a4f4 ,there is only one other star of negative magnitude1 ,canopus1 whose magnitude is--#j4i4 ,but for ordinary purposes one need not trouble himself with these refinements4 ,illustration3 ,schiaparelli's ,chart of ,martian 8,canals40 ,the stars are divided into five principal types1 according to their spectra4 ,these are3 ,i4 ,white stars1 having a bluish tinge1 in which the spectrum is characterised by broad dark bands1 due apparently to an extensive atmosphere of hydrogen1 while there are but few lines indicating the presence of metallic vapours4 ,about half the stars whose spectra have been studied belong to ,type ,i4 ,,ii4 ,yellowish-white stars1 resembling the sun in having their spectra crossed with a great number of lines produced by metallic vapours1 while the hydrogen lines are less conspicuous4 ,these are often called solar stars1 and they1 too1 are very numerous4 ,,iii4 ,orange and slightly reddish stars1 whose spectra contain mostly broad bands instead of narrow lines1 the bands being situated toward the blue end of the spectrum1 whence the prevailing colour1 since the blue light is thus cut off4 ,only a few hundred of these stars are known1 but they include most of the well-known variable stars4 ,,iv4 ,small deep-red stars having dark bands absorbing the light of the red end of the spectrum4 ,less than a hundred of these stars are known4 ,v4 ,stars whose spectra are characterised by bright instead of dark lines1 although they also show dark bands4 ,the bright lines indicate that the atmospheric vapours producing them are at a higher temperature than the body of the star4 ,stars of this type are sometimes called ,wolf-,rayet stars and they are few in number4 ,various modifications of these main types exist1 but we cannot here enter into an account of them4 ,in a general way1 although there are exceptions depending upon the precise nature of each spectrum1 the white stars are thought to be younger than the yellowish ones1 and the red stars older4 ,in speaking of the 8size0 of the stars we really mean their luminosity1 or the amount of light radiated from them4 ,when a star is said to be a thousand times greater than the sun1 the meaning is that the amount of light that it gives would1 if both were viewed from the same distance1 be equal to a thousand times the amount given by the sun4 ,we have no direct knowledge of the actual size of the stars as globes1 because the most powerful telescope is unable to reveal the real disk of a star4 ,in comparing the luminosity of a star with that of the sun its distance must be taken into account4 ,most of the stars are so far away that we really know nothing of their distances1 but there are fifty or more which lie within a distance not too great to enable us to obtain an approximate idea of what it is4 ,the nearest star in the northern sky is so far from being the brightest that it can barely be seen with the naked eye4 ,it must be very much less luminous than the sun4 ,on the other hand1 some very bright stars lie at a distance so immense that it can hardly be estimated1 and they must exceed the sun in luminosity hundreds and even thousands of times4 ,the question of the distance of the stars has already been treated in the section on ,parallax4 ,in employing our knowledge of star distances for the purpose of comparing their luminosity with that of the sun1 we must first ascertain1 as accurately as possible1 the actual amount of light that the star sends to the earth as compared with the actual amount of light that the sun sends4 ,the star ,arcturus gives to our eyes about one forty-billionth as much light as the sun does4 ,knowing this1 we must remember that the intensity of light varies1 like gravitation1 inversely as the square of the distance4 ,thus1 if the sun were twice as far away as it is1 the amount of its light received on the earth would be reduced to one fourth1 and if its distance were increased three times1 the amount would be reduced to one ninth4 ,if the sun were #bjj1jjj times as far away1 its light would be reduced to one forty-billionth1 or the same as that of ,arcturus4 ,at this point the actual distance of ,arcturus enters into the calculation4 ,if that distance were #bjj1jjj times the sun's distance1 we should have to conclude that ,arcturus was exactly equal to the sun in luminosity1 since the sun1 if removed to the same distance1 would give us the same amount of light4 ,but1 in fact1 we find that the distance of ,arcturus1 instead of being #bjj1jjj times that of the sun1 is about #aj1jjj1jjj times4 ,in other words1 it is fifty times as far away as the sun would have to be in order that it should appear to our eyes no brighter than ,arcturus4 ,from this it follows that the real luminosity of ,arcturus must be the square of #ej1 or #bejj1 times that of the sun4 ,in the same manner we find that ,sirius1 which to the eye appears to be the brightest star in the sky 7much brighter than ,arcturus because much nearer71 is about thirty times as luminous as the sun4 ,many of the stars are changeable in brightness1 and those in which the changes occur to a notable extent1 and periodically1 are known as variable stars4 ,it is probable that all the stars1 including the sun1 are variable to a slight degree4 ,among the most remarkable variables are ,mira1 or ,omicron ,ceti1 in the constellation ,cetus1 which in the course of about #cca days rises from the ninth to the third magnitude and then falls back again 7the maxima of brightness are irregular72 and ,algol1 or ,beta ,persei1 in the constellation ,perseus1 which1 in a period of #b days1 #bj hours1 #di minutes1 changes from the third to the second magnitude and back again4 ,in the case of ,mira the cause of the changes is believed to lie in the star itself1 and they may be connected with its gradual extinction4 ,the majority of the variable stars belong to this class4 ,as to ,algol1 the variability is apparently due to a huge dark body circling close around the star with great speed1 and periodically producing partial eclipses of its light4 ,there are a few other stars with short periods of variability which belong to the class of ,algol4 ,when examined with telescopes many of the stars are found to be double1 triple1 or multiple4 ,often this arises simply from the fact that two or more happen to lie in nearly the same line of sight from the earth1 but in many other cases it is found that there is a real connection1 and that the stars concerned revolve1 under the influence of their mutual gravitation1 round a common centre of force4 ,when two stars are thus connected they are called a binary4 ,the periods of revolution range from fifty to several hundred years4 ,among the most celebrated binary stars are ,alpha ,centauri1 in the southern hemisphere1 the nearest known star to the solar system1 whose components revolve in a period of about eighty years2 ,gamma ,virginis1 in the constellation ,virgo1 period about one hundred and seventy years2 and ,sirius1 period about fifty-three years4 ,in the case of ,sirius1 one of the components1 although perhaps half as massive as its companion1 is ten thousand times less bright4 ,there is another class of binary stars1 in which one of the companions is invisible1 its presence being indicated by the effects of its gravitational pull upon the other4 ,algol may be regarded as an example of this kind of stellar association4 ,but there are stars of this class1 where the companion causes no eclipses1 either because it is not dark1 or because it never passes over the other1 as seen from the earth1 but where its existence is proved1 in a very interesting way1 by the spectroscope4 ,in these stars1 called spectroscopic binaries1 two bright components are so close together that no telescope is able to make them separately visible1 but when their plane of revolution lies nearly in our line of sight the lines in their combined spectrum are seen periodically split asunder4 ,to understand this1 we must recall the principles underlying spectroscopic analysis and add something to what was said before on that subject4 ,light consists of waves in the ether of different lengths and making upon the eye different impressions of colour according to the length of the waves4 ,the longest waves are at the red end of the spectrum and the shortest at the blue1 or violet1 end4 ,but since they all move onward with the same speed1 it is clear that the short blue waves must fall in quicker succession on the retina of the eye than the long red waves4 ,now suppose that the source of light from which the waves come is approaching very swiftly2 it is easy to see that all the waves will strike the eye with greater rapidity1 and that the whole spectrum will be shifted toward the blue1 or short-wave1 end4 ,the ,fraunhofer lines will share in this shifting of position4 ,next suppose that the source of the light is retreating from the eye4 ,the same effect will occur in a reversed sense1 for now there will be a general shift toward the red end of the spectrum4 ,a sufficiently clear illustration1 by analogy1 is furnished by the waves of sound4 ,we know that low-pitched sounds are produced by long waves1 and high-pitched ones by short waves2 then if the source of the sound1 such as a locomotive whistle1 rapidly approaches the ear the waves are crowded together1 or shifted as a whole toward the short end of the gamut1 whereupon the sound rises to a shrill scream4 ,if1 on the contrary1 the source of sound is retreating1 the shift is in the other direction1 and the sound drops to a lower pitch4 ,this is precisely what happens in the spectrum of a star which is either approaching or receding from the eye4 ,if it is approaching1 the ,fraunhofer lines are seen shifted out of their normal position toward the blue1 and if it is receding they are shifted toward the red4 ,the amount of shifting will depend upon the speed of the star's motion4 ,if that motion is across the line of sight there will be no shifting1 because then the source of light is neither approaching nor receding4 ,now take the case of a binary star whose components are too close to be separated by a telescope4 ,if they happen to be revolving round their common centre in a plane nearly coinciding with the line of sight from the earth1 one of them must be approaching the eye at the same time that the other is receding from it1 and the consequence is that the spectral lines of the first will be shifted toward the blue1 while those of the second are shifted toward the red4 ,the colours of the two intermingled spectra blend into each other too gradually to enable this effect to be detected by their means1 but the ,fraunhofer lines are sharply defined1 and in them the shift is clearly seen2 and since there is a simultaneous shifting in opposite directions the lines appear split4 ,but when the two stars are in that part of their orbit where their common motion is across the line of sight the lines close up again1 because then there is no shift4 ,this phenomenon is beautifully exhibited by one of the first spectroscopic binaries to be discovered1 ,beta ,aurig4 ,in #ahhi1 ,prof4 ,e4 ,c4 ,pickering noticed that the spectral lines of this star appeared split every second night1 from which he inferred that it consisted of two stars revolving round a common centre in a period of four days4 ,this spectroscopic method has been applied to determine the speed with which certain single stars are approaching or receding from the solar system4 ,it has also served to show1 what we have before remarked1 that the inner parts of ,saturn's rings travel faster than the outer parts4 ,moreover1 it has been used in measuring the rate of the sun's rotation on its axis1 for it is plain that one edge of the sun approaches us while the opposite edge is receding4 ,even the effect of the rotation of ,jupiter has been revealed in this way1 and the same method will probably settle the question whether ,venus rotates rapidly1 or keeps the same face always toward the sun4 ,not only do many stars revolve in orbits about near-by companions1 but all the stars1 without exception1 are independently in motion4 ,they appear to be travelling through space in many different directions1 each following its own chosen way without regard to the others1 and each moving at its own gait4 ,these movements of the stars are called proper motions4 ,the direction of the sun's proper motion is1 roughly speaking1 northward1 and it travels at the rate of twelve or fourteen miles per second1 carrying the earth and the other planets along with it4 ,some stars have a much greater speed than the sun1 and some a less speed4 ,as we have said1 these motions are in many different directions1 and no attempt to discover any common law underlying them has been entirely successful1 although it has been found that in some parts of the sky a certain number of stars appear to be travelling along nearly parallel paths1 like flocks of migrating birds4 ,in recent years some indications have been found of the possible existence of two great general currents of movement1 almost directly opposed to each other1 part of the stars following one current and part the other4 ,but no indication has been discovered of the existence of any common centre of motion4 ,several relatively near-by stars appear to be moving in the same direction as the sun4 ,stars that are closely grouped together1 like the cluster of the ,pleiades1 seem to share a common motion of translation through space4 ,we have already remarked that when stars are found to be moving toward or away from the sun1 spectroscopic observation of the shifting of their lines gives a means of calculating their velocity4 ,in other cases1 the velocity across the line of sight can be calculated if we know the distance of the stars concerned4 ,one interesting result of the fact that the earth goes along with the sun in its flight is that the orbit of the earth cannot be a closed curve1 but must have the form of a spiral in space4 ,in consequence of this we are continually advancing1 at the rate of at least #djj1jjj1jjj miles per year1 toward the northern quarter of the sky4 ,the path pursued by the sun appears to be straight1 although it may1 in fact1 be a curve so large that we are unable in the course of a lifetime1 or many lifetimes1 to detect its departure from a direct line4 ,at any rate we know that1 as the earth accompanies the sun1 we are continually moving into new regions of space4 ,it has been stated that many millions of stars are visible with telescopes--perhaps a hundred millions1 or even more4 ,the great majority of these are found in a broad irregular band1 extending entirely round the sky1 and called the ,milky ,way1 or the ,galaxy4 ,to the naked eye the ,milky ,way appears as a softly shining baldric encircling the heavens1 but the telescope shows that it consists of multitudes of faint stars1 whose minuteness is probably mainly due to the immensity of their distance1 although it may be partly a result of their relative lack of actual size1 or luminosity4 ,in many parts of the ,milky ,way the stars appear so crowded that they present the appearance of sparkling clouds4 ,the photographs of these aggregations of stars in the ,milky ,way1 made by ,barnard1 are marvellous beyond description4 ,in the ,milky ,way1 and sometimes outside it1 there exist globular star-clusters1 in which the stars seem so crowded toward the centre that it is impossible to separate them with a telescope1 and the effect is that of a glistering ball made up of thousands of silvery particles1 like a heap of microscopic thermometer bulbs in the sunshine4 ,a famous cluster of this kind is found in the constellation ,hercules4 ,the ,milky ,way evidently has the form of a vast wreath1 made up of many interlaced branches1 some of which extend considerably beyond its mean borders4 ,within1 this starry wreath space is relatively empty of stars1 although some thousands do exist there1 of which the sun is one4 ,we are at present situated not very far from the centre of the opening within the ring or wreath1 but the proper motion of the sun is carrying us across this comparatively open space1 and in the course of time1 if the direction of our motion does not change1 we shall arrive at a point not far from its northern border4 ,the ,milky ,way probably indicates the general plan on which the visible universe is constructed1 or what has been called the architecture of the heavens1 but we still know too little of this plan to be able to say exactly what it is4 ,the number of stars in existence at any time varies to a slight degree1 for occasionally a star disappears1 or a new one makes its appearance4 ,these1 however1 are rare phenomena1 and new stars usually disappear or fade away after a short time1 for which reason they are often called temporary stars4 ,the greatest of these phenomena ever beheld was ,tycho ,brahe's star1 which suddenly burst into view in the constellation ,cassiopeia in #aegb1 and disappeared after a couple of years1 although at first it was the brightest star in the heavens4 ,another temporary star1 nearly as brilliant1 appeared in the constellation ,perseus1 in #aija1 and this1 as it faded1 gradually turned into a nebula1 or a star surrounded by a nebula4 ,it is generally thought that outbursts of this kind are caused by the collision of two or more massive bodies1 which were invisible before their disastrous encounter in space4 ,the heat developed by such a collision would be sufficient to vaporise them1 and thus to produce the appearance of a new blazing star4 ,it is possible that space contains an enormous number of great obscure bodies1--extinguished suns1 perhaps--which are moving in all directions as rapidly as the visible stars4 #b4 ,the ,nebul4 ,these objects1 which get their name from their cloud-like appearance1 are among the most puzzling phenomena of the heavens1 although they seem to suggest a means of explaining the origin of stars4 ,many thousands of nebul are known1 but there are only two or three bright enough to be visible to the naked eye4 ,one of these is in the 8sword0 of the imaginary giant figure marking the constellation ,orion1 and another is in the constellation ,andromeda4 ,they look to the unaided eye like misty specks1 and require considerable attention to be seen at all4 ,but in telescopes their appearance is marvellous4 ,the ,orion nebula is a broad1 irregular cloud1 with many brighter points1 and a considerable number of stars intermingled with it1 while the ,andromeda nebula has a long spindle shape1 with a brighter spot in the centre4 ,it is covered and surrounded with multitudes of faint stars4 ,it was only after astronomical photography had been perfected that the real shapes of the nebul were clearly revealed4 ,thousands of nebul have been discovered by photography1 which are barely if at all visible to the eye1 even when aided by powerful telescopes4 ,this arises from the fact that the sensitive photographic plate accumulates the impression that the light makes upon it1 showing more and more the longer it is exposed4 ,plates placed in the focus of telescopes1 arranged to utilise specially the 8photographic rays10 are often exposed for many hours on end in order to picture faint nebul and faint stars1 so that they reveal things that the eye1 which sees all it can see at a glance1 is unable to perceive4 ,nebul are generally divided into two classes--the 8white0 nebul and the 8green0 nebul4 ,the first1 of which the ,andromeda nebula is a striking example1 give a continuous spectrum without dark lines1 as if they consisted either of gas under high pressure1 or of something in a solid or liquid state4 ,the second1 conspicuously represented by the ,orion nebula1 give a spectrum consisting of a few bright lines1 characteristic of such gases as hydrogen and helium1 together with other substances not yet recognised4 ,but there is no continuous spectrum like that shown by the white nebul1 from which it is inferred that the green nebul1 at least1 are wholly gaseous in their constitution4 ,the precise constitution of the white nebul remains to be determined4 ,it is only in relatively recent years that the fact has become known that the majority of nebul have a spiral form4 ,there is almost invariably a central condensed mass from which great spiral arms wind away on all sides1 giving to many of them the appearance of spinning pin-wheels1 flinging off streams of fire and sparks on all sides4 ,the spirals look as if they were gaseous1 but along and in them are arrayed many condensed knots1 and frequently curving rows of faint stars are seen apparently in continuation of the nebulous spirals4 ,the suggestion conveyed is that the stars have been formed by condensation from the spirals4 ,these nebul generally give the spectra of the white class1 but there are also sometimes seen bright lines due to glowing gases4 ,the ,andromeda nebula is sometimes described as spiral1 but its aspect is rather that of a great central mass surrounded with immense elliptical rings1 some of which have broken up and are condensing into separate masses4 ,the ,orion nebula is a chaotic cloud1 filled with partial vacancies and ribbed with many curving1 wave-like forms4 ,there are other nebul which have the form of elliptical rings1 occasionally with one or more stars near the centre4 ,a famous example of this kind is found in the constellation ,lyra4 ,still others have been compared in shape to the planet ,saturn with its rings1 and some are altogether bizarre in form1 occasionally looking like glowing tresses floating among the stars4 ,the apparent association of nebul with stars led to the so-called nebular hypothesis1 according to which stars are formed1 as already suggested1 by the condensation of nebulous matter4 ,in the celebrated form which ,laplace gave to this hypothesis1 it was concerned specially with the origin of our solar system4 ,he assumed that the sun was once enormously expanded1 in a nebulous state1 or surrounded with a nebulous cloud1 and that as it contracted rings were left off around the periphery of the vast rotating mass4 ,these rings subsequently breaking and condensing into globes1 were supposed to have given rise to the planets4 ,it is still believed that the sun and the other stars may have originated from the condensation of nebul1 but many objections have been found to the form in which ,laplace put his hypothesis1 and the discovery of the spiral nebul has led to other conjectures concerning the way in which the transformation is brought about4 ,but we have not here the space to enter into this discussion1 although it is of fascinating interest4 ,a word more should be said about the use of photography in astronomy4 ,it is hardly going too far to aver that the photographic plate has taken the place of the human retina in recording celestial phenomena1 especially among the stars and nebul4 ,not only are the forms of such objects now exclusively recorded by photography1 but the spectra of all kinds of celestial objects--sun1 stars1 nebul1 etc4--are photographed and afterward studied at leisure4 ,in this way many of the most important discoveries of recent years have been made1 including those of variable stars and new stars4 ,photographic charts of the heavens exist1 and by comparing these with others made later1 changes which would escape the eye can be detected4 ,comets are sometimes1 and new asteroids almost invariably1 discovered by photography4 ,the changes in the spectra of comets and new stars are thus recorded with an accuracy that would be otherwise unattainable4 ,photographs of the moon excel in accuracy all that can be done by manual drawing1 and while photographs of the planets still fail to show many of the fine details visible with telescopes1 continual improvements are being made4 ,many of the great telescopes now in use or in course of construction are intended specially for photographic work4 #c4 ,the ,constellations4 ,the division of the stars into constellations constitutes the uranography or the 8geography of the heavens40 ,the majority of the constellations are very ancient1 and their precise origin is unknown1 but those which are invisible from the northern hemisphere have all been named since the great exploring expeditions to the south seas4 ,there are more than sixty constellations now generally recognised4 ,twelve of these belong to the zodiac1 and bear the same names as the zodiacal signs1 although the precession of the equinoxes has drifted them out of their original relation to the signs4 ,many of the constellations are memorials of prehistoric myths1 and a large number are connected with the story of the ,argonautic expedition and with other famous ,greek legends4 ,thus the constellations form a pictorial scroll of legendary history and mythology1 and possess a deep interest independent of the science of astronomy4 ,for their history and for the legends connected with them1 the reader who desires a not too detailed rsum1 may consult ,astronomy with the ,naked ,eye1 and for guidance in finding the constellations1 ,astronomy with an ,opera-glass1 or ,round the ,year with the ,stars4 ,the quickest way to learn the constellations is to engage the aid of some one who knows them already1 and can point them out in the sky4 ,the next best way is to use star charts1 or a star-finder or planisphere4 ,a considerable number of the brighter and more important stars are known by individual names1 such as ,sirius1 ,canopus1 ,achernar1 ,arcturus1 ,vega1 ,rigel1 ,betelgeuse1 ,procyon1 ,spica1 ,aldebaran1 ,regulus1 ,altair1 and ,fomalhaut4 ,astronomers usually designate the principal stars of each constellation by the letters of the ,greek alphabet1 1 1 1 etc41 the brightest star in the constellation bearing the name of the first letter1 the next brightest that of the second letter1 and so on4 ,the constellations are very irregular in outline1 and their borders are only fixed with sufficient definiteness to avoid the inclusion of stars catalogued as belonging to one1 within the limits of another4 ,in all cases the names come from some fancied resemblance of the figures formed by the principal stars of the constellation to a man1 woman1 animal1 or other object4 ,in only a few cases are these resemblances very striking4 ,the most useful constellations for the beginner are those surrounding the north celestial pole1 and we give a little circular chart showing their characteristic stars4 ,the names of the months running round the circle indicate the times of the year when these constellations are to be seen on or near the meridian in the north4 ,turn the chart so that the particular month is at the bottom1 and suppose yourself to be facing northward4 ,the hour when the observation is supposed to be made is1 in every case1 about #i o'clock in the evening1 and the date is about the first of the month4 ,the top of the chart represents the sky a little below the zenith in the north1 and the bottom represents the horizon in the north4 ,illustration3 ,fig4 #ah4 ,the ,north ,circumpolar ,stars4 ,the apparent yearly revolution of the heavens1 resulting from the motion of the earth in its orbit1 causes the constellations to move westward in a circle round the pole1 at the rate of about #cj per month4 ,but the daily rotation of the earth on its axis causes a similar westward motion of the heavens1 at the rate of about #cj for every two hours4 ,from this it results that on the same night1 after an interval of two hours1 you will see the constellations occupying the place that they will have1 at the original hour of observation1 one month later4 ,thus1 if you observe their positions at #i ,p4,m4 on the first of ,january1 and then turn the chart so as to bring ,february at the bottom1 you will see the constellations around the north pole of the heavens placed as they will be at #aa ,p4,m4 on the first of ,january4 ,illustration3 ,fig4 #ai4 ,key to ,north ,circumpolar ,stars4 ,only the conspicuous stars have been represented in the chart1 just enough being included to enable the learner to recognise the constellations by their characteristic star groups1 from which they have received their names4 ,the chart extends to a distance of #dj from the pole1 so that1 for observers situated in the mean latitude of the ,united ,states1 none of the constellations represented ever descends below the horizon1 those that are at the border of the chart just skimming the horizon when they are below the pole4 ,on the key to the chart the ,greek-letter names of the principal stars have been attached1 but some of them have other names which are more picturesque4 ,these are as follows3 ,in ,ursa ,major 7the ,great ,bear1 which includes the ,great ,dipper71 is called ,dubhe1 ,merak1 ,phaed1 ,megrez1 ,alioth1 ,mizar1 and ,benetnash4 ,the little star close by ,mizar is ,alcor4 ,in ,cassiopeia1 is called ,schedar1 ,caph1 and ,ruchbar4 ,in ,ursa ,minor1 the ,little ,bear1 is called ,polaris1 or the ,north ,star1 and ,kochab4 ,in ,draco1 is called ,thuban1 and ,eltanin4 ,in ,cepheus1 is called ,alderamin1 and ,alfirk4 ,these names are nearly all of ,arabic origin4 ,it will be observed that ,merak and ,dubhe are the famous 8,pointers10 which serve to indicate the position of the ,north ,star1 while ,thuban is the 8star of the pyramid10 before mentioned4 ,the north celestial pole is situated almost exactly on a straight line drawn from ,mizar through the ,north ,star to ,ruchbar1 and a little more than a degree from the ,north ,star in the direction of ,ruchbar4 ,this furnishes a ready means for ascertaining the position of the meridian4 ,for instance1 about the middle of ,october1 ,mizar is very close to the meridian below the pole1 and ,ruchbar equally close to it above the pole1 and then1 since the ,north ,star is in line with these two1 it also must be practically on the meridian1 and its direction indicates very nearly true north4 ,the same method is applicable whenever1 at any other time of the year or of the night1 ,mizar and ,ruchbar are observed to lie upon a vertical line1 no matter which is above and which below4 ,it is also possible to make a very good guess at the time of night by knowing the varying position of the line joining these stars4 ,the star ,caph is an important landmark because it lies almost on the great circle of the equinoctial colure1 which passes through the vernal and autumnal equinoxes4 ,on the key1 the location of the ,north ,pole of the ,ecliptic is shown1 and the greater part of the circle described by the north celestial pole in the period of #be1hjj years4 ,while the reader who wishes to pursue the study of the constellations in detail must be referred to some of the works before mentioned1 or others of like character1 it is possible here to aid him in making a preliminary acquaintance with other constellations beside those included in our little chart1 by taking each of the months in turn1 and describing the constellations which he will see on or near the meridian south of the border of the chart at the same time that the polar constellations corresponding to the month selected are on or near the meridian in the north4 ,thus1 at #i ,p4,m4 about the first of ,january1 the constellation ,perseus1 lying in a rich part of the ,milky ,way1 is nearly overhead and directly south of the ,north ,star4 ,this constellation is marked by a curved row of stars1 the brightest of which1 of the second magnitude1 is ,algenib1 or ,persei4 ,a few degrees south-west of ,algenib is the wonderful variable ,algol4 ,east of ,perseus is seen the very brilliant white star ,capella in the constellation ,auriga4 ,this is one of the brightest stars in the sky4 ,almost directly south of ,perseus1 the eye will be caught by the glimmering cluster of the ,pleiades in the constellation ,taurus4 ,a short distance south-east of the ,pleiades is the group of the ,hyades in ,taurus1 shaped like the letter ,v1 with the beautiful reddish star ,aldebaran in the upper end of the southern branch of the letter4 ,the ecliptic runs between the ,pleiades and the ,hyades4 ,still lower in the south will be seen a part of the long-winding constellation ,eridanus1 the ,river ,po4 ,its stars are not bright but they appear in significant rows and streams4 ,about the first of ,february the constellation ,auriga is on the meridian not far from overhead1 ,capella lying toward the west4 ,directly under ,auriga1 two rather conspicuous stars mark the tips of the horns of ,taurus1 imagined as a gigantic bull1 and south of these1 with its centre on the equator1 scintillates the magnificent constellation ,orion1 the most splendid in all the sky1 with two great first-magnitude stars1 one1 in the shoulder of the imaginary giant1 of an orange hue1 called ,betelguese1 and the other in the foot1 of a blue-white radiance1 called ,rigel4 ,between these is stretched the straight line of the 8belt10 consisting of three beautiful second-magnitude stars1 about a degree and a half apart4 ,their names1 beginning with the western one1 are ,mintaka1 ,alnilam1 and ,alnitah4 ,directly under the belt1 in the midst of a short row of faint stars called the 8sword10 is the great ,orion nebula4 ,it will be observed that the three stars of the belt point1 though not exactly1 toward the brightest of all stars1 ,sirius1 in the constellation ,canis ,major1 the ,great ,dog1 which is seen advancing from the east4 ,under ,orion is a little constellation named ,lepus1 the ,hare4 ,the first of ,march the region overhead is occupied by the very faint constellation ,lynx4 ,south of it1 and astride the ecliptic1 appear the constellations ,gemini1 the ,twins1 and ,cancer1 the ,crab4 ,these1 like ,taurus1 belong to the zodiac4 ,the ,twins are westward from ,cancer1 and are marked by two nearly equal stars1 about five degrees apart4 ,the more westerly and northerly one is ,castor and the other is ,pollux4 ,cancer is marked by a small cluster of faint stars called ,prsepe1 the ,manger 7also sometimes the ,beehive74 ,directly south of the ,twins1 is the bright lone star ,procyon1 in the constellation ,canis ,minor1 the ,little ,dog4 ,sirius and the other stars of ,canis ,major1 which make a striking figure1 are seen south-west of ,procyon4 ,the first of ,april the zodiac constellation ,leo is near the meridian1 recognisable by a sickle-shaped figure marking the head and breast of the imaginary ,lion4 ,the bright star at the end of the handle of the sickle is ,regulus4 ,above ,leo1 between it and the ,great ,dipper1 appears a group of stars belonging to the small constellation ,leo ,minor1 the ,little ,lion4 ,farther south is a winding ribbon of stars indicating the constellation ,hydra1 the ,water ,serpent4 ,its chief star1 ,alphard1 of a slightly reddish tint1 is seen west of the meridian and a few degrees south of the equator4 ,at the beginning of ,may1 when the ,great ,dipper is nearly overhead1 the small constellation ,canes ,venatici1 the ,hunting ,dogs1 is seen directly under the handle of the ,dipper1 and south of that a cobwebby spot1 consisting of minute stars1 indicates the position of the constellation ,coma ,berenices1 ,berenice's ,hair4 ,still farther south1 where the ecliptic and the equator cross1 at the autumnal equinox1 is the large constellation ,virgo1 the ,virgin1 also one of the zodiacal band4 ,its chief star ,spica1 a pure white gem1 is seen some #bj east of the meridian4 ,below and westward from ,virgo1 and south of the equator1 are the constellations ,crater1 the ,cup1 and ,corvus1 the ,crow4 ,the stars of ,hydra continue to run eastward below these constellations4 ,the westernmost1 ,crater1 consists of small stars forming a rude semicircle open toward the east1 while ,corvus1 which possesses brighter stars1 has the form of a quadrilateral4 ,the first of ,june the great golden star ,arcturus1 whose position may be found by running the eye along the curve of the handle of the ,great ,dipper1 and continuing onward a distance equal to the whole length of the ,dipper1 is seen approaching the meridian from the east and high overhead4 ,this superb star is the leader of the constellation ,botes1 the ,bear-,driver4 ,spica in ,virgo is now a little west of the meridian4 ,the first of ,july1 when the centre of ,draco is on the meridian north of the zenith1 the exquisite circlet of stars called ,corona ,borealis1 the ,northern ,crown1 is nearly overhead4 ,a short distance north-east of it appears a double-quadrilateral figure1 marking out the constellation ,hercules1 while directly south of the ,crown a crooked line of stars trending eastward indicates the constellation ,serpens1 the ,serpent4 ,south-west of ,serpens1 two widely separated but nearly equal stars of the second magnitude distinguish the zodiacal constellation ,libra1 the ,balance2 while lower down toward the south-east appears the brilliant red star ,antares1 in the constellation ,scorpio1 likewise belonging to the zodiac4 ,on the first of ,august the head of ,draco is on the meridian near the zenith1 and south of it is seen ,hercules1 toward the west1 and the exceedingly brilliant star ,vega1 in the constellation ,lyra1 the ,lyre1 toward the east4 ,vega1 or ,alpha ,lyr1 has few rivals for beauty4 ,its light has a decided bluish-white tone1 which is greatly accentuated when it is viewed with a telescope4 ,south of ,hercules two or three rows of rather large1 widely separated stars mark the constellation ,ophiuchus1 the ,serpent-,bearer4 ,this extends across the equator4 ,below it1 in a rich part of the ,milky ,way1 is ,scorpio1 whose winding line1 beginning with ,antares west of the meridian1 terminates a considerable distance east of the meridian in a pair of stars representing the uplifted sting of the imaginary monster4 ,the first of ,september the ,milky ,way runs directly overhead1 and in the midst of it shines the large and striking figure called the ,northern ,cross1 in the constellation ,cygnus1 the ,swan4 ,the bright star at the head of the ,cross is named ,denib4 ,below the ,cross and in the eastern edge of the ,milky ,way is the constellation ,aquila1 the ,eagle1 marked by a bright star1 ,altair1 with a smaller one on each side and not far away4 ,low in the south1 a little west of the meridian and partly immersed in the brightest portion of the ,milky ,way1 is the zodiacal constellation ,sagittarius1 the ,archer4 ,it is distinguished by a group of stars several of which form the figure of the upturned bowl of a dipper1 sometimes called the ,milk ,dipper4 ,east of ,cygnus and ,aquila a diamond-shaped figure marks the small constellation ,delphinus1 the ,dolphin4 ,at the opening of ,october1 when ,denib is near the meridian1 the sky directly in the south is not very brilliant4 ,low down1 south of the equator1 is seen the zodiacal constellation ,capricornus1 the ,goat1 with a noticeable pair of stars in the head of the imaginary animal4 ,on the first of ,november1 when ,cassiopeia is approaching the meridian overhead1 the ,great ,square1 in the constellation ,pegasus1 is on the meridian south of the zenith1 while south-west of ,pegasus the zodiacal constellation ,aquarius1 the ,water-,bearer1 appears on the ecliptic4 ,a curious scrawling ,y-shaped figure in the upper part of ,aquarius serves as a mark to identify the constellation4 ,thirty degrees south of this shines the bright star ,fomalhaut1 in the constellation ,piscis ,australis1 the ,southern ,fish4 ,the two stars forming the eastern side of the ,great ,square of ,pegasus are interesting because1 like ,caph in ,cassiopeia1 they lie close to the line of the equinoctial colure4 ,the northern one is called ,alpheratz and the southern ,gamma ,pegasi4 ,alpheratz is a star claimed by two constellations1 since it not only marks one corner of the square of ,pegasus1 but it also serves to indicate the head of the maiden in the celebrated constellation of ,andromeda4 ,the first of ,december1 ,andromeda is seen nearly overhead1 south of ,cassiopeia4 ,the constellation is marked by a row of three second-magnitude stars1 beginning on the east with ,alpheratz and terminating near ,perseus with ,almaack4 ,the central star is named ,mirach4 ,a few degrees north-west of ,mirach glimmers the great ,andromeda nebula4 ,below ,andromeda1 west of the meridian1 appears the zodiacal constellation ,aries1 the ,ram1 indicated by a group of three stars1 forming a triangle1 the brightest of which is called ,hamal4 ,south-westerly from ,aries is the zodiacal constellation ,pisces1 the ,fishes1 which consists mainly of faint stars arranged in pairs and running far toward the west along the course of the ecliptic1 which crosses the equator at the vernal equinox1 near the western end of the constellation4 ,south of ,pisces and ,aries is the broad constellation ,cetus1 the ,whale1 marked by a number of large quadrilateral and pentagonal figures1 formed by its stars4 ,near the centre of this constellation1 but not ordinarily visible to the naked eye1 is the celebrated variable ,mira1 also known as ,omicron ,ceti4 ,with a little application any person can learn to recognise these constellations1 even with the slight aid here offered1 and if he does1 he will find the knowledge thus acquired as delightful as it is useful4 ---------------------------------------- -------------------------------- ,,index ,aberration1 #hh ,alpha ,centauri1 #ade ,alpha ,draconis1 #fb ,altitude1 #ac1 #ad ,andromeda1 nebula in1 #bcf ,antares1 #bd ,aphelion1 #h ,april1 aspect of sky in1 #bea ,arcturus1 #bbd ,asteroids1 the1 #ahg ,atmosphere1 the1 #hb ,august1 aspect of sky in1 #bec ,azimuth1 #ac1 #ad ,beta ,aurig1 #bcj ,binary 7and multiple7 stars1 #bbf ,binaries1 spectroscopic1 #bbg ,calendar1 the1 #aag ,calorie1 measure of sun's heat1 #abi ,cassiopeia1 #bb ,cheops1 pyramid of1 #fb ,chromosphere1 of sun1 #ace ,circles1 vertical1 #ae2 altitude1 #ad2 division of1 #af ,circumpolar stars1 #bbd ,clock1 the astronomical1 #da1 #ij ,comets1 #bja1 #bjc ,constellations1 the1 #bda ,corona1 of the sun1 #ace ,coronium1 #aeb ,corona ,borealis1 #bd ,day1 change of1 #ii1 #aja ,day and night1 #if ,december1 aspect of sky in1 #bef ,declination1 #ca1 #ce ,dipper1 the ,great1 #ba2 the ,little1 #bc ,earth1 description of the1 #fg2 weight of1 #gc ,eclipses1 #afc ,ecliptic1 #dc ,elements1 chemical1 in the sun1 #aea ,equator1 #ch ,equinoxes1 #de ,eros1 the asteroid1 #adb ,february1 aspect of sky in1 #bdi ,galaxy1 the1 #bcc ,gravitation1 laws of1 #gj 8,greenwich of the ,sky10 #cb ,heavens1 apparent motion of1 #ai ,helium1 #aeb ,horizon1 #aj1 #ab2 dip of1 #hf ,hour ,circles1 #ca ,january1 aspect of sky in1 #bdh ,july1 aspect of sky in1 #beb ,june1 aspect of sky in1 #beb ,jupiter1 the planet1 #ahi ,kepler1 laws of1 #agc ,latitude1 terrestrial1 #cj2 celestial1 #di1 #ea ,light1 pressure of1 #bjf ,longitude1 terrestrial1 #cj2 celestial1 #di1 #ea ,magnitudes1 stellar1 #bbj ,march1 aspect of sky in1 #bej ,mars1 the planet1 #aha ,may1 aspect of sky in1 #bea ,mercury1 the planet1 #age ,meteors1 #baj ,meteorites1 #bad ,milky ,way1 the1 #bcc ,molecules1 escape from planetary atmospheres1 #aeh ,moon1 description of1 #aec2 how earth controls1 #ge ,motion1 proper1 of solar system1 #bcb ,nadir1 #aa ,nebul1 #bcf ,nebular ,hypothesis1 #bci ,neptune1 the planet1 #aii ,noon-line1 #ab ,north ,point1 #bj ,north ,pole1 #bg1 #cg ,north ,star1 #bj1 #bg1 #fa ,november1 aspect of sky in1 #bee ,nutation1 #fc ,oblique sphere1 #ci ,october1 aspect of sky in1 #bed ,oppositions1 of ,mars1 #ahc ,orbits of planets1 #g1 #eb ,orion1 nebula in1 #bcf ,parallax1 #acf1 #aci ,parallel sphere1 #ch ,perihelion1 #h ,phases of the moon1 #afj ,photography1 in astronomy1 #bdj ,photometry1 of stars1 #bbj ,photosphere of sun1 #acd ,planets1 description of the1 #agb ,polar circles1 #aaa ,precession of the ,equinoxes1 #ee ,refraction1 #hc1 #he ,right ,ascension1 #ca1 #ce ,right sphere1 #ci ,rotation1 effect of earth's1 #e ,saturn1 description of1 #aie ,seasons1 the1 #ajd1 #ajg2 secular change of1 #aae ,september1 aspect of sky in1 #bed ,signs of ,zodiac1 #ed ,spectroscopic analysis1 #ade1 #adg2 shifting of lines1 #bbg ,sphere1 celestial1 #i ,solstices1 the1 #dg ,stars1 the fixed1 #bai2 daily revolution of1 #be2 how to locate1 #bi2 luminosity of1 #bbb2 spectra of1 #bba2 variable1 #bbe2 temporary1 #bce2 double and multiple1 #bbf ,sun1 the description of1 #abg ,sun-spots1 #aca ,temperature1 of sun1 #acj ,temporary stars1 #bce ,tides1 the1 #gf1 #gi ,time1 #hi2 sidereal and solar1 #ic ,transits1 of ,venus1 #adj1 #ada ,tropics1 the1 #aaa ,universe1 appearance of1 #h ,uranus1 description of1 #aii ,ursa ,major1 #ba ,variable stars1 #bbe ,vega1 #fc ,venus1 the planet1 #agh ,vernal ,equinox1 #cb1 #db1 #df ,zenith1 #aj ,zodiac1 #ej ---------------------------------------- -------------------------------- ,transcriber's ,notes3 ,new original cover art included with this e,book is granted to the public domain4 ,missing or obscured punctuation was silently corrected4 ,typographical errors were silently corrected4 ,inconsistent spelling and hyphenation were made consistent only when a predominant form was found in this book4 ,text that3 was in italics is enclosed by underscores 7italics72 was in bold by is enclosed by 8equal0 signs 7bold74 ,the use of a caret 77 before a letter1 or letters1 shows that the following letter or letters was intended to be a superscript1 as in ,st ,bartholomew or #ajth ,century4 ,superscripts are used to indicate numbers raised to a power4 ,in this plain text document1 they are represented by characters like this3 8,p#c0 or 8#ajah01 i4e4 ,p cubed or #aj to the #ahth power4 ,variables in formul sometimes use subscripts1 which look like this3 8,a#j04 ,this would be read 8,a sub #j04