John Swett 
 
Cambriirge Courst of 
 
 ELEMENTS 
 
 OF 
 
 ASTRONOMY 
 
 BY 
 
 W. J. ROLFE AND J. A. GILLET, 
 
 TEACHERS IN THE HIGH SCHOOL, CAMBRIDGE, MASS. 
 
 SECOND EDITION, 
 
 REVISED AND ENLARGED. 
 
 BOSTON: 
 CROSBY AND AINSWORTH. 
 
 NEW YORK: O. S. FELT. 
 1868. 
 
< I 
 
 .' . . . 
 
 QB4-3 
 
 P L& 
 
 Entered according to Act of Congress, in the year 1868, by 
 
 W. J. ROLFE AND J. A. GILLET, 
 in the Clerk's Office of the District Court of the District of Massachusetts. 
 
 fij^ O Cw >. J " < JiNi 
 EDUCATION DEPT, 
 
 UKIVERSITY PRESS : WELCH, BIGELOW, & Ca, 
 CAMBRIDGE. 
 
PREFACE 
 
 TO THE SECOND EDITION. 
 
 THE method of treatment in this ASTRONOMY agrees 
 with that adopted in other parts of the Course, so far as 
 the nature of the subject will admit. The aim throughout 
 has been to show the scholar from what facts of observa- 
 tion, and by what processes of reasoning, astronomers 
 have reached their present knowledge of the structure of 
 the universe. 
 
 The authors believe that the principles which lie at the 
 bottom of the explanation of most astronomical phenom- 
 ena are really simple, and, if rightly presented, capable 
 of being understood by high-school scholars of ordinary 
 ability. They do not assume, however, that the explana- 
 tions given in this book are in all cases full enough to 
 enable the teacher to dispense with oral instruction. 
 
 The first part of the book treats of the motions and dis- 
 tances of the heavenly bodies ; the second, of their physi- 
 cal features ; and the third, of gravity, or the force by 
 which they act upon one another. In this edition a fourth 
 part, treating of the origin, transmutation, and conserva- 
 tion of energy, has been added, since it forms a fitting 
 conclusion to the Astronomy, and also to the whole 
 Course. 
 
 In no portion of the book is there assumed, on the part 
 of the pupil, any knowledge of mathematics beyond that 
 of the elements of plane geometry, and an ability to prove 
 that in plane triangles the sines of the angles are propor- 
 
 541830 
 
iv PREFACE. 
 
 tional to their opposite sides. That it may not be neces- 
 sary for scholars to study trigonometry before taking up 
 this book, this last proposition is .demonstrated in an 
 Appendix. 
 
 In the Appendix, the principal constellations have been 
 described, and illustrated by seventeen star-maps. These 
 maps have been reduced by photography from the excel- 
 lent charts in Argelander's Uranometria Nova. In order, 
 however, that the maps in this reduced form might not be 
 too crowded, all stars below the fourth magnitude have 
 been omitted, as well as the circles of right ascension and 
 declination. The dotted lines have been added by the 
 authors to assist in tracing the leading stars in each con- 
 stellation. 
 
 The Appendix also contains an outline of the history 
 and mythology of the constellations ; an account of the 
 metric system and the calendar ; and various astronomical 
 tables, 
 
 In the preparation of the first and third parts of this 
 book the authors have made free use of Airy's " Popular 
 Astronomy" (London, 1866). In many instances material 
 has been taken from this source with little alteration, ex- 
 cept that it has been condensed and the language sim- 
 plified. Yet the method of treatment which we have em- 
 ployed is quite different from that adopted by Airy. 
 
 The material of the second part of the volume has been 
 drawn largely from the English translation of Guille- 
 min's " Heavens " (London, 1866), Hind's " Solar System " 
 (London, 1851), and Hind's "Astronomy" (London, 1863.) 
 
 The division of labor in preparing the book has been 
 the same as was explained in the Preface to Part First. 
 
 CAMBRIDGE, March 5, 1868. 
 
TABLE OF CONTENTS. 
 
 PAGE 
 MOTIONS AND DISTANCES OF THE HEAVENLY 
 
 BODIES i 
 
 THE SHAPE OF THE HEAVENLY BODIES ... 3 
 
 THE APPARENT MOTIONS OF THE STARS .... 5 
 
 THE APPARENT MOTIONS OF THE SUN . . . 21 
 
 TWILIGHT .' . . . .- . ... . 29 
 
 THE APPARENT MOTION OF THE MOON . . . 32 
 
 THE APPARENT MOTIONS OF THE PLANETS ... 34 
 
 THE PTOLEMAIC SYSTEM ; . " .. . '.. . . 35 
 
 THE SYSTEM OF TYCHO DE BRAKE . . . ', - . 38 
 
 THE COPERNICAN SYSTEM . . ' . . . . . 39 
 
 THE SYSTEM OF KEPLER ,)> . .' . . . . 40 
 
 SUMMARY. .' . .' ..:. . . . . ' . . 42 
 
 HOW TO FIND THE PERIODIC TIMES OF THE PLANETS . 45 
 
 SUMMARY. .' . . ."".' . . i " . 48 
 HOW TO FIND THE DISTANCE OF THE PLANETS FROM 
 
 THE SUN . . . -, : . . . . . . . 49 
 
 SUMMARY . , ......... . 66 
 
 HOW TO FIND THE DISTANCE OF THE MOON ... 67 
 
 SUMMARY .'.'.. 74 
 
 A GENERAL SURVEY OF THE ORBITS OF THE PLANETS . 75 
 
 HOW TO FIND THE DISTANCE OF THE FlXED STARS 76 
 
 SUMMARY U- : ' '. . ' . '- * ' . . v . .- . 88 
 
 SYSTEMS OF SATELLITES AND SUNS . . ... 89 
 
 SUMMARY '. , ' . . ' .. '',. " . , * . . . 96 
 
 PHYSICAL FEATURES OF THE HEAVENLY BODIES 97 
 
 THE SUN ' . . * . ' . ~ . " -. ; . . '' . 99 
 
 THE NATURE OF SUN-SPOTS . ', . . . . .. 113 
 
 SUMMARY . ' . '. ,: ' . .' . " ' . ' .- ... . 118 
 
 MERCURY ' . ' . . . . ' , .... 120 
 
 VENUS . ' . ' . " , ; " . ' . ' \ ' .. . . . 124 
 
 THE ZODIACAL LIGHT . ' . " . : i' ' .' . . 127 
 
VI TABLE OF CONTEXTS. 
 
 THE EA*TH . .... ... 09 
 
 THE MOON ..... . . . 129 
 
 BUUMJ& ...... - .. . . .142 
 
 SODCAKT or THE Moon AKD Jfimnu * . 152 
 
 '57 
 
 OF THE INNE* GROCP OF PLANETS . . 160 
 
 MDKML PLANETS 161 
 
 OF THE MINOT PLANETS 166 
 
 JUPTTE* 167 
 
 IT* 
 
 t - - i?S 
 
 ITS 
 
 OF THE Ovm GEOCP OF PLANETS . . i So 
 
 181 
 
 1*4 
 
 THE Frrm STAIS 185 
 
 SUMMARY 197 
 
 GRAVITY. OR THE FORCE BY WHICH THE HEAV- 
 ENLY BODIES ACT UPON ONE ANOTHER 199 
 
 THE LAWS OF MOTION 201 
 
 THE PENDCLUM ........ 210 
 
 SnOCAKY OF THE PEXDCT.UM 215 
 
 GRAVITY ACTS aajmij^x THE EAETH AND THE Mooar 216 
 GEATTTY ACTS BETWEES THE SUN AND PLANETS, AXD 
 
 ^^L PLANETS AND THEZE MOONS . . . 21$ 
 
 GlATITY ACTS !LllJm THE SUN AND COMTTS . . 225 
 
 GULYTTY ACTS AMDNG AH. THE HEAVENLY BODIES . 226 
 
 GXATTTY ACTS UPON THE PAKTICI-ES OF \LATTEX . 257 
 
 SnOLUtT .......... ^ 
 
 HOW TO FIND THE WEIGHT OF THE HEAVENLY BODIES 247 
 
 SrXXATT .......... 3 ^ 1 
 
 GENTXJLL SnotAiY ........ 262 
 
 ORIGIN, TRANSMUTATION, AND CONSERYATION 
 
 OF ENERGY ......... 271 
 
 SnotAiY . ....... . 299 
 
 AWESDLX .......... 301 
 
 aaaauoL ........ 307 
 
 METUC SYSTEM . . . . . . . .512 
 
 ASTMKOMJCAL TAMLES ..... - . . jxS 
 
CAMJI M 
 
 APPENDIX 
 THE 
 
 CoacsnuuiTioxs TISBLE EACH MOCTH . 331 
 
 STAXS or THE Futsr MACXFTUBC . 332 
 
 THE HMBUM or THE CossrELunoffs . . . 332 
 
 THE MTTHOLOGT or IBB C0nu4XMMi . . 334 
 
 QugiMiM* PBK. ggjnnr ASP FYUfmanag - - 343 
 
 INDEX ........... 335 
 
I. 
 
 MOTIONS AND DISTANCES OF 
 THE HEAVENLY BODIES. 
 
MOTIONS AND DISTANCES OF THE 
 HEAVENLY BODIES. 
 
 1. AT the beginning of our study of Physics we came to 
 the conclusion that matter is made up of insensible masses 
 called molecules, and that these molecules are separated by 
 spaces, which, though probably thousands of times greater 
 than their own bulk, are yet insensibly small. We have 
 also learned that many, and probably all, of these mole- 
 cules are made up of yet smaller parts, called atoms. 
 
 Hitherto we have been mainly occupied with the con- 
 sideration of the forces which act upon these atoms and 
 molecules through insensible distances. 
 
 We now pass to the study of the earth and the heavenly 
 bodies, and the forces which act upon them through the 
 spaces by which they are separated. 
 
 THE SHAPE OF THE HEAVENLY BODIES. 
 
 2. The Shape of the Earth. For several thousand 
 years men supposed that the earth was a large platform, 
 and that, if one went far enough, he would everywhere 
 come to the edge, as one does at the sea-shore. As soon, 
 however, as they began to make long voyages at sea, it 
 was seen that the sea is not flat, but rounded like a low 
 hill ; for wherever we go at sea, we always see the masts 
 of ships a long way off before we can see the hull or body 
 of the ship, though, so far as size goes, the latter would be 
 
' 4 , - , ." ASTRONOMY. 
 
 much easier to be seen. The sea cuts off the view just 
 like a hill rising between the two ships. It was also found 
 that the distance at which ships of the same height begin 
 to be seen is everywhere the same, and as light is known 
 to come in straight lines, the hill of sea between the two 
 ships must be everywhere the same. This can be so only 
 on a globe, that is, on a body whose surface is rounded 
 equally in every direction. 
 
 We see, then, that the surface of the ocean is spherical, 
 and when we remember that about three fourths of the 
 surface of the earth is covered with water, it seems prob- 
 able that the whole surface of the earth is spherical. 
 
 Again, in an eclipse of the moon, we always see a 
 shadow with a round edge moving across its disc. This 
 shadow has never any other shape, whether the eclipse be 
 great or small, and whatever part of the earth be facing 
 the moon at the time. Now this shadow is known to be 
 the shadow of the earth, and a body which casts a round 
 shadow in every position must be a sphere. 
 
 The earth, therefore, must be a globe, or sphere. 
 
 3. The Sun, Moon, and Planets are Globes, The disc 
 of the sun is always circular. The same is true of that 
 of the moon, though at times we see only a part of its disc. 
 The same is true of all the planets, which bodies always 
 present sensible discs when viewed with the telescope. 
 Now it is well known that these bodies do not always 
 present the same side to the earth ; and, as a sphere is 
 the only body that presents a circular outline from what- 
 ever position it is looked at, we see that the sun, moon, 
 and planets are also globes. 
 
 The fixed stars present no sensible disc when viewed 
 with the most powerful telescope, therefore we know noth- 
 ing about the shape of these bodies. 
 
ASTRONOMY. 
 
 THE APPARENT MOTIONS OF THE STARS. 
 
 4. If, on a clear night, we watch the eastern horizon 
 through its whole extent from north to south, we see stars 
 continually rising; and if we watch the western horizon 
 through its whole extent from north to south, we see 
 stars continually setting. We see, also, that the stars do 
 not rise perpendicularly, but obliquely. Those which rise 
 near to the north or near to the south rise very slantingly 
 indeed. Those nearest to the east rise less obliquely. 
 The same is true of their setting. Those near to the 
 north or to the south set very obliquely ; those which set 
 nearest to the west set with a sharp incline. If we trace 
 the whole path of any one of these stars, we find that it 
 rises somewhere in the east in the sloping direction al- 
 ready described ; that it continues to rise with a path 
 becoming more and more horizontal, till it reaches a cer- 
 tain height in the south, when its course is exactly hori- 
 zontal ; and that it then declines by similar degrees, and 
 sets at a place in the west just as far from the north point 
 as the place where it rose in the east. 
 
 If we select a star that has risen near to the north, it 
 takes it a long time to rise to its greatest height, which 
 is very high in the south, and then an equally long time 
 to set. Lastly, if we look to the north and observe 
 those stars which are fairly above the horizon, we find 
 them going around the Polar Star and describing a com- 
 plete circle. These stars are called circumpolar. 
 
 The Polar Star to an ordinary observer does not appear 
 to change its place during the whole night. Whenever he 
 looks out, he finds it in the same place. Careful observa- 
 tion, however, shows that it does change its place and 
 moves in a small circle. The stars 'of the Great Bear and 
 of Cassiopeia turn in a circle considerably larger than the 
 i* 
 
6 ASTRONOMY. 
 
 Polar Star, but they go completely round in it without 
 descending below the horizon. Capella and Vega de- 
 scribe still longer circles, of which the Pole Star is the 
 centre. These stars pass below the horizon in the north, 
 and pass nearly overhead when farthest to the south. 
 
 Thus, if we fix a straight rod in a certain standard direc- 
 tion, pointing nearly, but not exactly, to the Polar Star, we 
 find that the stars which are close in the direction of this 
 rod, as seen by viewing along it, describe a very small cir- 
 cle ; the stars farther from it describe a larger circle ; oth- 
 ers just touch the northern horizon ; whilst, in regard to 
 others, if they do describe a whole circle at all, part of that 
 circle is below the horizon ; they are seen to come up in 
 the east, to pass the south, and to go down in the 1 west, 
 and they are lost below the horizon from that place till 
 they rise again in the east. 
 
 5. Are the Movements of the Stars such that they appear 
 to describe accurate Circles about a Point of the Sky near the 
 Polar Star as a Centre ? To answer this question we must 
 use an instrument called the Equatorial. One form of this 
 instrument is represented in Figure i. It turns round an 
 axis A J3, which is placed in the direction which leads 
 to the point of the sky around which the stars appear to 
 turn, and which is not far from the Polar Star. This axis 
 carries the telescope CD. As the instrument turns on 
 its axis the telescope retains the same inclination to this 
 axis unless another motion is given it at the same time. 
 The telescope is, however, so arranged that another mo- 
 tion may be given to it, so as to place it in different posi- 
 tions, as C' D\ C"D" . It can thus be directed to stars in 
 different parts of the heavens. If now the telescope is 
 directed to any one star, it is found, by turning the instru- 
 ment on its axis, that the telescope, without any alteration 
 of its inclination to the axis, will follow that star from its 
 rising to its setting. It is the same wherever the star may 
 
ASTRONOMY. 
 
 Fig. 2. 
 
 be, whether near the Polar Star or far from it. The tel- 
 escope will follow the star by merely turning the instru- 
 ment on its axis. 
 
 The movement of the stars, then, is of such a kind that 
 they appear to describe accurate circles about a point of 
 the sky near the Pole Star as a centre ; for it is evident 
 that the telescope, when the instrument is turned on its 
 axis, describes such a circle, and, as seen, the telescope 
 always points to the star to which it was directed. 
 
 6. The Stars move at a uniform Rate, and all describe their 
 Circles in the same Time. The best equatorials are fur- 
 nished with a toothed wheel attached to the axis, in which 
 works an endless screw or worm, as seen in Figure i. 
 By turning this worm the whole instrument is made to 
 revolve. The worm is turned by an apparatus constructed 
 especially for producing uniform movement. The one 
 usually adopted, with some modification, is represented 
 in Figure 2. The lower drum is turned by a falling 
 weight, and its motion is regulated by the centrifugal balls 
 A B, similar to those which are used to regulate the mo- 
 
8 ASTRONOMY. 
 
 tion of a steam-engine. It is well known that whirling 
 the balls, by the rotation of the axis to which they are 
 attached, causes them to spread out, and the more rapidly 
 they are whirled the more they spread. 
 
 When the speed has reached a certain limit, the spread- 
 ing out of the balls causes their arms to rub against the 
 fixed part, S H. This friction prevents further accelera- 
 tion, and thus a uniform speed is produced with very great 
 nicety. The spindle KL from this apparatus is attached 
 to the screw which carries the equatorial. It causes the 
 telescope of the equatorial to revolve around its axis uni- 
 formly, and thus gives us the means of ascertaining with 
 the utmost exactness whether or not the stars move with 
 uniform speed. When the machinery is in operation the 
 telescope is pointed to a star. Whether this star be near 
 the pole or at a distance from the pole, it is found that it 
 is constantly seen in the field of view of the telescope ; 
 that is, the telescope turns just as fast as the star moves. 
 Now as the telescope is moving with a uniform speed, it 
 follows that all the stars are describing their orbits in the 
 same time, and that each star moves with the same speed 
 in every part of its orbit. The stars then move as though 
 they were attached to a shell, which rotates at a uniform 
 rate from east to west about an axis passing from a point 
 of the sky near the Polar Star through the centre of the 
 earth. This axis is therefore called the celestial axis, and 
 the point of the sky near the Polar Star is called the north 
 celestial pole. 
 
 7. Refraction. When a telescope of considerable power 
 is attached to the equatorial, so that we can see a small 
 departure from the centre of the telescope in the position 
 of the star we are looking at, and when we trace the 
 course of the star down to the horizon, we find it to be a 
 universal fact that the star is not quite so near the horizon 
 as we should be led to expect. This is due to refraction. 
 
ASTRONOMY. 
 
 We have already learned that a ray of light in passing 
 from a rarer into a denser medium is always bent toward 
 a perpendicular to the surface of this medium. The earth 
 is surrounded by an atmosphere, and we will suppose, at 
 first, that this atmosphere has a definite boundary and a 
 uniform density. Let Figure 3 represent a part of the earth 
 covered by the atmosphere. Suppose a beam of light is 
 coming from a star in the direction A B, and that it meets 
 the atmosphere at B. In passing into this denser medi- 
 um it is bent toward a line 
 perpendicular to the sur- 
 face of the atmosphere, 
 and takes the direction 
 B C. Consequently the 
 star would be seen in 
 the direction CB. This 
 would be the case if the 
 atmosphere had a defi- 
 nite boundary and a uni- 
 form density. But if the atmosphere has not a definite 
 boundary and varies in density from stratum to stratum, 
 becoming more and more dense as we near the earth, the 
 ray of light would be bent as described above in passing 
 from one stratum to the next. This condition of things 
 is shown in Figure 4. The star would be seen in the 
 position f, instead of its real position A. The effect of 
 refraction is, then, to cause 
 all the stars to appear nearer 
 the zenith (the point directly 
 overhead) than they really 
 are. If a star were exactly 
 in the zenith, its position 
 would not be changed by 
 refraction, since the ray of 
 light coming from the star 
 
IO ASTRONOMY. 
 
 would meet each stratum of air perpendicularly. The far- 
 ther a star is from the zenith, the more is it displaced by 
 refraction, since the light coming from it would meet each 
 stratum more obliquely, and the more obliquely the ray of 
 light meets the surface of the denser medium, the more is 
 its direction bent. 
 
 8. Does the Celestial Sphere really rotate about the Earth 
 from East to West? It was for a long time supposed 
 that the starry heavens turned round the earth daily, and 
 that the apparent motion of the stars was real. But when 
 it was discovered that the earth is round, it was at once 
 seen that the visible motion of the heavenly bodies could 
 be explained as well by supposing that the earth rotates 
 from west to east about an axis which has the same direc- 
 tion as the axis about which the celestial sphere appears 
 to rotate from east to west, as by supposing that this 
 sphere does really rotate. The supposition that the earth 
 rotates instead of the heavens is the simpler of the two, 
 and the fact that the earth does thus rotate is capable of 
 the following direct proof. It is found that when a heavy 
 ball is suspended by a long and flexible string, at the 
 equator, and made to vibrate, its vibrations appear to take 
 place always in the same direction ; that is, if it is set vi- 
 brating in a north and south direction, it will continue to 
 vibrate in that direction; while if a ball similarly sus- 
 pended is set to vibrating anywhere north of the equator, 
 the direction in which it vibrates appears to be continually 
 changing. Now we know that a body when once put in 
 motion tends always to move in the same absolute direc- 
 tion, and it is reasonable to suppose that the heavy ball, 
 when once set swinging, will always vibrate in the same 
 absolute direction, provided that nothing interferes with 
 its motion. If the point from which the ball is suspended 
 is twirled while the ball is swinging, its direction of vibra- 
 tion does not change ; and if the point is moved forward 
 
ASTRONOMY. 1 1 
 
 in a straight line, or in the circumference of a circle, its 
 directions of vibration are always parallel to one another. 
 Suppose now that the earth be rotating from west to east, 
 and that a ball be suspended at the equator ; the motion 
 of the earth would carry the point of suspension around in 
 a circle, and the same would be true were the ball sus- 
 pended north of the equator. Suppose now that a ball 
 at the equator, and one some way north of the equator, 
 were both set swinging in a north and south direction; 
 what would be the apparent direction of the vibration of 
 the ball in each case, on the supposition that the earth 
 rotates ? In each case, as we have seen, the vibrations of 
 the ball would be parallel to one another. On the sup- 
 position that the earth rotates on its axis from west to east, 
 are the directions which at different times we call north 
 and south parallel to one another, or not ? We must first 
 see what we mean by north and south. 
 
 Suppose that two straight rods are fastened to a terres- 
 trial globe, one at the equator and the other some way 
 north of the equator, close by the brass meridian and par- 
 allel to it. These rods, of course, would point north and 
 south to observers at these two points on the globe. Now 
 rotate the globe, and the rod fastened at the equator is 
 seen to remain parallel to the brass meridian, while the 
 rod north of the equator begins to deviate at once from a 
 direction parallel to the meridian, and deviates more and 
 more till the globe has rotated through 90, when it be- 
 gins again to approach this direction, and when the globe 
 has rotated through 180 it is again parallel to the brass 
 meridian. At the equator, then, on the supposition that 
 the earth is rotating, the directions which an observer at 
 a given place would at different times call north and south 
 are parallel with one another; while at a place north or 
 south of the equator the directions which an observer at 
 different times calls north and south are continually chan- 
 ging, although they appear to be always the same. 
 
1 2 ASTRONOMY. 
 
 If, then, the vibrations of the ball suspended as described 
 above are always in the same absolute direction, and the 
 ball be set swinging from north to south, its vibrations at 
 the equator ought to appear to be always in the same di- 
 rection while at a point north of the equator its plane of 
 vibration ought to appear continually shifting in a direc- 
 tion contrary to that in which the north and south direc- 
 tion is really shifting. This is just what is found to be 
 true on trial. The experiment was first made by Foucault 
 at Paris in 1851, and has been often repeated with the 
 same results. It was tried in this country some years 
 ago, in the Bunker Hill Monument. 
 
 The supposition, then, that the earth rotates on its axis 
 from west to east must be true, and the starry heavens 
 are really at rest. That the earth appears to be at rest 
 and the heavens rotating, is not surprising when we re- 
 member that, on looking out at the window of a railway 
 car while the train is in rapid motion, we seem to be at 
 rest, and the fences and trees to be shooting past us in the 
 opposite direction. 
 
 9. The Direction of the Circles described by the Apparent 
 Motion of the Stars is different in different Parts of the Earth. 
 The circles described by the stars in their apparent 
 daily motion are always perpendicular to the axis of the 
 earth. In our latitude they are oblique to the horizon, 
 sloping from the south. They are oblique to the horizon 
 because the horizon here is inclined to the earth's axis.* 
 At the equator the horizon is parallel to this axis, and 
 the circles described by the stars are consequently per- 
 pendicular to the horizon. South of the equator the hori- 
 zon is inclined to the axis in a direction opposite to that 
 in which it is inclined north of the equator, and the circles 
 described by the stars are again oblique to the horizon, 
 but sloping from the north. At the poles the horizon is 
 perpendicular to the earth's axis, and the circles described 
 * See Appendix, II. 
 
ASTRONOMY. 
 
 Fig. 
 
 by the stars are consequently parallel to the horizon. 
 Those stars which are nearer to the elevated pole than 
 the horizon is, are always in view; while those nearer 
 the depressed pole than the horizon is, are always out of 
 sight. At any point north of the equator, the north pole 
 of the heavens is elevated above the horizon, and the south 
 pole depressed below it. Hence north of the equator the 
 north pole is the elevated pole, and the south pole the 
 depressed pole. South of the equator, of course, it is 
 just the reverse. 
 
 10. The Fixed Stars appear in the same Position in the 
 Sky, from whatever Part of the Earth they are observed. 
 It is necessary to find some way of describing the position 
 of a star, as seen in the sky, in order to ascertain whether it 
 is seen in the same position from different parts of the earth. 
 
 I wish to describe the position of a speck, D (see Fig- 
 ure 5), on a wall, so that any 
 person could mark the posi- 
 tion of the speck on a similar 
 wall elsewhere. I could de- 
 scribe the position of the 
 speck by giving the horizon- 
 tal distance, A C, from one 
 end of the wall, and the ver- 
 tical distance, CD, from the floor, or by giving the meas- 
 ure of the distance A D from the corner A, and of the 
 distance E D from the corner E. I might also give the 
 measure of the distance A C, and of the inclination of 
 the line A D to the horizon. 
 
 It is thus seen that there are several ways of describing 
 the position of the speck, but that in every case two meas- 
 ures are necessary. The two measures which are neces- 
 sary for defining the position of any point on a surface are 
 called the co-ordinates of the point. Thus the distances 
 A C and CD are co-ordinates of the point D. So also the 
 
 2 
 
14 ASTRONOMY. 
 
 distances A D and E Z>, and the distance A C and the 
 angle D A C are co-ordinates of the point D. 
 
 Suppose we wish to define the position of a point on a 
 celestial globe. We could do it most conveniently by 
 giving its distance from the pole of the globe measured in 
 degrees, and the distance that the globe must rotate from 
 a certain point before this point comes under the brass 
 meridian. These two distances, both measured in degrees, 
 would be the co-ordinates of the point. 
 
 Suppose, for instance, there is a fixed point marked on 
 every celestial globe, and I wish to tell some one at a dis- 
 tance the position of a second mark, which I have found 
 on my globe. I find that I must rotate the globe 23 to 
 the westward from the fixed point to bring the mark under 
 the brass meridian, and that the mark is 36 from the north 
 pole of the globe. I send these co-ordinates to the dis- 
 tant person, and he sets his globe so that the fixed point 
 is under the brass meridian, and rotates it 23 westward. 
 He now knows that the point is under the meridian. He 
 next measures along the meridian 36 from the given pole, 
 and he knows the exact position of the point. If the 
 globe were stationary and the brass meridian movable, we 
 could describe the position of the point equally well by 
 giving its angular distance from one of the poles of the 
 globe, and the angular distance through which the meridian 
 must be turned from a fixed point, in order to bring the 
 point under it. 
 
 If now we suppose an imaginary arc of a great circle 
 passing directly over our heads and through the celestial 
 poles, and fixed to the earth in such a manner as to be 
 carried around with it in its rotation from west to east, 
 we can evidently describe the position of a star in the 
 sky by ascertaining how far this imaginary meridian must 
 sweep from a fixed point to bring the star under it, and 
 by ascertaining its angular distance from one of the celes- 
 
ASTRONOMY. 15 
 
 tial poles when under this meridian. The angular distance 
 of a star from a celestial pole, and the angular distance that 
 an imaginary meridian must sweep over from a fixed point 
 in order to bring the star under it, are the most convenient 
 co-ordinates of a star. 
 
 ii. The Measurement of the, Angular Distance that the 
 Meridian must sweep over in order to bring the Star under it. 
 The measurement of the angular space over which the 
 meridian must sweep from a fixed point to bring the star 
 under it is effected by means of a Transit Instrument. 
 This instrument is- represented in Figure 6. It consists 
 
 Fig. 6. 
 
 of a telescope mounted on an axis, A JB, in such a way 
 that when it turns around on this axis the line C D E 
 prolonged to the sky will describe the imaginary meridian 
 
1 6 ASTRONOMY. 
 
 just spoken of. This curve must be perpendicular to the 
 horizon, must divide the visible heavens into two equal 
 parts, and must pass through the poles of the heavens. 
 
 To meet the first condition, it is necessary that the axis 
 A B be exactly horizontal. To meet the second condi- 
 tion, it is necessary that the telescope CD be exactly 
 square with its axis A B. The astronomer ascertains 
 whether the telescope be exactly square with its axis or 
 not, by looking at a distant mark, first, with the pivots 
 A and B of the instrument resting on the piers a and , 
 and then with the axis turned over so that the pivots A 
 and B rest on the piers b and a. If the telescope points 
 equally well to the mark in both positions of the axis, it 
 is exactly square with its axis. 
 
 The astronomer ascertains whether the instrument is so 
 adjusted that the curve described by the line C D E pro- 
 longed shall pass through the celestial pole, by means of 
 the Polar Star. This star, as has already been stated, 
 describes a small circle about the celestial pole as a 
 centre. Let FGHIKL represent this circle. Sup- 
 pose that in turning the transit instrument about its axis, 
 the line CDE prolonged, traces the line G I or FK, as 
 the case may be. The Polar Star in its revolution passes 
 that line twice ; and if the line passes through the celes- 
 tial pole, which is the centre of the circle, the arcs FHK 
 and KL F must be equal, and as the motion of the star 
 is uniform, it will take it just as long to pass from F to K y 
 as from K to F. If these arcs are described in equal 
 times, the instrument is properly adjusted. 
 
 By means of the transit instrument objects can be 
 viewed only when they come under the meridian. Some 
 bright star, as Altair, is selected, and the time when it 
 comes under the meridian accurately observed by means 
 of the transit instrument and the clock. The time when 
 it next comes under the meridian is also carefully ob- 
 
ASTRONOMY. 1 7 
 
 served, and the interval between these two transits of the 
 star across the meridian is called a sidereal day. This 
 day is divided into twenty-four equal parts called sidereal 
 hours. The clock used in the observatory is called a 
 sidereal clock, and is so constructed that it would de- 
 scribe just twenty^four hours between two successive tran- 
 sits of the same star, if its movements were perfectly 
 accurate. In practice it is found impossible to construct 
 a perfectly accurate clock. The rate at whicrr the clock 
 gains or loses time is ascertained by observing the suc- 
 cessive transits of the same star, and, this being known, 
 it becomes easy to reduce every observation to true si- 
 dereal time. The sidereal clock should beat seconds, and 
 the beats should be very distinctly given. 
 
 To facilitate the determination of the exact time when a 
 star or planet comes under the meridian, a number of cob- 
 web threads are strung across the focus of the telescope 
 at equal distances, parallel to one another and to the mo- 
 tion of the telescope as it is turned on its axis. These are 
 called cross-wires. The observer notices a star approaching 
 the meridian. He directs the telescope so as to observe 
 the star when it actually crosses the meridian, and looks 
 into the telescope. Just before the star begins to cross 
 the wires, he looks at the face of the clock for the hours 
 and minutes; he then listens to the beats of the clock, 
 and thus finds the hour, minute, second, and fraction of a 
 second when the star crosses each wire ; then, by taking 
 the mean of these times, he finds the time at which the 
 star passes the meridian. The same observations are made 
 with star after star, as they approach the meridian, and 
 when these observations have been corrected for the 
 error of the clock, the interval of time which elapses be- 
 tween the transit of a given star and the other stars ob- 
 served becomes known. And as the apparent rotation of 
 the celestial sphere is uniform, we thus find one of the 
 
 2* 
 
i8 
 
 ASTRONOMY. 
 
 co-ordinates by which the position of a star is defined, 
 that is, the distance that the imaginary meridian must 
 turn from a given point in order to bring the star under 
 it. Suppose the bright star Vega to be taken as the 
 starting-point, and suppose we find that a given star is 
 under the meridian two hours afterward. The meridian 
 must then turn through 30 from Vega in order to bring 
 the star under it. 
 
 12. The Mural Circle. The next thing is to ascertain 
 the angular distance of the star from the pole of the 
 heavens when it is under the meridian. This is ascer- 
 tained by means of the Mural Circle. One form of this 
 
 Fig. 7. 
 
 instrument is represented in Figure 7. A is a stone pier 
 which supports the axis of the instrument, and to which 
 microscopes, a, b, c, d, e, and / are attached. The face 
 of the pier which carries the microscopes fronts either 
 the east or the west. The axis carries the circle B C 
 
ASTRONOMY. 19 
 
 and the telescope F G. The telescope is fastened to the 
 circle, so that both must move together. This circle is 
 graduated on its outside into degrees, minutes, and other 
 subdivisions. The microscopes serve as pointers for ob- 
 serving the exact position of the circle, and by their aid 
 the space between the divisions can be subdivided with 
 great exactness. 
 
 We wish to know in any observation how far the tele- 
 scope points above the horizon. This can be easily 
 ascertained, if we know what is the reading of the circle 
 when the telescope points horizontally. For example, 
 if the reading of the circle is 5 15' when the telescope 
 points horizontally, and 27 16' 25" when the telescope 
 is pointing to the star, the telescope must point 27 16' 
 25" 5 15' = 22 i' 25" above the horizon. The read- 
 ing of the circle when the telescope points horizontally 
 is ascertained as follows. It is well known that a star 
 seen by reflection from the surface of water or quick- 
 silver appears just as far below the horizon as it is above 
 it. The trough o is filled with quicksilver, and the tele- 
 scope first directed to a star, S (see Figure 8), on the me- 
 
 Fig. 8. 
 
 S, 
 
20 ASTRONOMY. 
 
 ridian, and the reading of the circle observed ; the tele- 
 scope is then turned so as to observe the star as reflected 
 by the quicksilver, and the reading of the circle again ob- 
 served. The horizontal reading of the circle is evidently 
 midway between these two readings. 
 
 The elevation of the north celestial pole must next be 
 ascertained. This is done by observing the Pole Star. 
 This star, as has already been stated, describes a small 
 circle about the celestial pole as its centre. With the 
 mural circle the angular elevation of this star above the 
 horizon is observed at its highest and lowest points. 
 These observations are corrected for refraction, and their 
 mean gives the angular elevation of the pole above the 
 horizon. The angular elevation of any body above the 
 horizon is called its altitude, and its altitude when on the 
 meridian is called its meridian altitude. 
 
 13. Polar Distance. By observing now the altitude 
 of any star when under the meridian, we can easily as- 
 certain its angular distance from the pole. This angular 
 distance is called t\\e polar distance. If the star be north 
 of the zenith, its polar distance is equal to the difference 
 between its meridian altitude and the altitude of the pole. 
 If the star is south of the zenith, its polar distance will 
 be 1 80 minus the sum of the altitude of the pole and 
 of the meridian altitude of the star. This is at once seen 
 by a reference to Figure 9. Let A Z B represent the 
 
 arc of the meridian above 
 the horizon. It contains, 
 of course, 180. Let P 
 represent the position of 
 the pole whose altitude 
 we will suppose to be 
 42. Let S be a star 
 north of the zenith, 
 whose meridian altitude is 75 : its polar distance P S = 
 
ASTRONOMY. 2 1 
 
 75 42 = 33. Let s be a star south of the zenith, 
 whose meridian altitude H s is 45: its polar distance P s 
 
 = 180 -(42 + 45) = 93. 
 
 It is often found more convenient to refer the position 
 of the pole and of the star to the zenith rather than to 
 the horizon. The angular distance of the pole or of a 
 star from the zenith is evidently equal to 90 minus the 
 altitude of the pole or star. 
 
 14. Summary. By means, then, of the transit instru- 
 ment and the mural circle, we can determine the two 
 co-ordinates necessary for describing the position of a 
 star or planet on the surface of the sky. These co-ordi- 
 nates for the fixed stars are found to be precisely the 
 same, whether they are measured at Washington, Green- 
 wich, or the Cape of Good Hope. This shows that the 
 stars are seen in exactly the same position, from what- 
 ever part of the earth they are observed. 
 
 We have now learned that the starry heavens appear 
 to rotate, all in a piece, from west to east, once in twenty- 
 four hours, about an axis which passes through the centre 
 of the earth to a point near the Pole Star ; and that the 
 fixed stars, whether viewed from one part of the earth or 
 another, always appear in the same parts of the heavens. 
 
 THE APPARENT MOTIONS OF THE SUN. 
 
 15. The Sidereal and the Solar Day and Year. We 
 have already defined a sidereal day as> the interval of 
 time between two successive transits of the same star 
 across the meridian. The solar or ordinary day is the 
 interval between two successive transits of the sun across 
 the meridian. This interval is ascertained by means of 
 the transit instrument, in the same way as the interval 
 between the successive transits of a given star. This 
 interval is found to be a little longer than a sidereal day. 
 
2 2 ASTRONOMY. 
 
 If a bright star which can be seen with the telescope of 
 the transit instrument at noonday comes under the me- 
 ridian at precisely the same instant as the sun, when 
 this star comes under the meridian the next day, the sun 
 will be about a degree eastward of the meridian ; and the 
 next day, when the star comes under the meridian, the 
 sun will be about two degrees eastward ; and so on. In 
 about 360 days after both came under the meridian to- 
 gether, they will come under the meridian together a 
 second time. When the sun and a given star come under 
 the meridian together, they are said to come into con- 
 junction. The interval between two successive conjunc- 
 tions of the sun and a given fixed star is called a sidereal 
 year. This year is about 2oJ- minutes longer than the 
 ordinary year. The sun, then, appears to move entirely 
 around the heavens, from west to east in a period of about 
 one year. The fact that the sun is apparently moving 
 eastward among the stars is evident without the use of 
 the transit instrument. If we notice the position of the 
 constellations above the western horizon night after night 
 at the same time after sunset, we shall find that they 
 come nearer and nearer the horizon, until many of them 
 have disappeared below it, and we shall find, in _ about a 
 year from the first observation, that these constellations 
 occupy the same position in the heavens as at first. 
 
 One of the co-ordinates of the sun's position in the sky 
 is daily changing. This co-ordinate is the angular space 
 over which the meridian must sweep, from a fixed point, 
 in order to bring the sun on the meridian. 
 
 1 6. The Solar Days are of Unequal Length. Careful 
 observation with the transit instrument shows that the 
 sun is not only apparently moving around the heavens 
 eastward, but that it is moving at unequal rates from day 
 to day. The interval, therefore, between two successive 
 passages of the sun across the meridian varies in length. 
 
ASTRONOMY. 23 
 
 The solar days are therefore of unequal length. The 
 solar day, like the sidereal, is divided into twenty-four 
 equal parts called hours. The solar hours are a little 
 longer than sidereal hours, and of unequal length. An 
 hour of ordinary clock time is the average length of all 
 the solar hours; and the ordinary civil day, consisting of 
 twenty-four hours of clock time, is the average length of 
 the solar days. Hence ordinary clock time is called 
 mean solar time. 
 
 17. The Polar Distance of the Sun is continually chang- 
 ing. In midwinter the sun appears low in the south, 
 and from that time till midsummer its meridian altitude 
 gradually increases. It then begins to diminish, and goes 
 on diminishing till midwinter again. Now, since at a 
 given place on the earth's surface the altitude of the ce- 
 lestial pole 1 remains the same, we must conclude that the 
 second co-ordinate of the sun's position in the heavens, 
 its polar distance, is continually changing. By means of 
 the mural circle the least polar distance of the sun, which 
 occurs in midsummer, is found to be about 66 1, and its 
 greatest polar distance in midwinter is 113^. The circle 
 described by the sun in its apparent journey round the 
 earth, then, is not perpendicular to the earth's axis, but 
 is inclined to that axis at an angle of about 66 J. The 
 plane of the sun's orbit passes through the centre of the 
 earth, and the circle formed by the intersection of this 
 plane with the celestial sphere is called the ecliptic. 
 
 When the polar distance of the sun is 90, it is directly 
 overhead at midday at the equator of the earth. When 
 its polar distance is 66 1, it is directly overhead at mid- 
 day at any place 23 J north of the equator ; and when 
 its polar distance is 113!, it will be directly overhead at 
 midday at any place 23^ south of the equator. At 
 every place, then, situated within about 23^ of the 
 equator either north or south, that is, between the tropic 
 
24 ASTRONOMY. 
 
 of Cancer and the tropic of Capricorn, the sun comes 
 directly overhead at least once a year. This belt of the 
 earth is called the Torrid Zane, ..'^ f 
 
 1 8. The Relative Length of Day and Night, and the 
 Changes of the Seasons. The sun, of course, always il- 
 lumines just one half of the earth ; and when the sun is 
 just over the equator, the illumined part just reaches the 
 north and the south poles. When the sun is directly over 
 the tropic of Cancer, of course the illumined part of the 
 earth reaches 23^ beyond the north pole, and only to 
 within 23 J of the south pole. Hence an observer situated 
 within 23^ of the north pole would see the sun during 
 the entire rotation of the earth, while an observer within 
 2 3i f t ne south pole would not see the sun at all. 
 When the sun is directly over the tropic of Capricorn, the 
 illumined part of the earth reaches 23 J beyond the south 
 pole, and only to within 23^ of the north pole. Hence 
 a person situated anywhere within 23^ of the north pole 
 would not see the sun at all during twenty-four hours, 
 while any person situated anywhere within 23 J of the 
 south pole would see the sun the whole 24 hours. At 
 every place, then, which is situated within 23^ of the 
 north or south pole, that is, north of the arctic Or south 
 of the antarctic circle, there is at least one day in the 
 year in which the sun does not come above the horizon 
 at all, and one day in which the sun does not sink below 
 the horizon at all. The belts of the earth betwen these 
 circles and the poles are called the Frigid Zones. Just 
 at the arctic and antarctic circles there is only one day 
 in the year in which the sun does not rise above or sink 
 below the horizon. But as you go nearer the poles, the 
 number of days when the sun does not rise above or 
 sink below the horizon increases. Between the arctic 
 and antarctic circles and the tropics there is no place 
 where the sun comes directly overhead, or where it does 
 
ASTRONOMY. 25 
 
 not rise and set every day. These belts of the earth are 
 called the Temperate Zones. 
 
 A moment's reflection will make it clear that, when 
 the sun is directly over the equator, every place on the 
 surface of the earth is illumined twelve hours and is in 
 darkness twelve hours ; and as the sun is directly over 
 the equator twice a year, the days and nights are equal 
 in every part of the earth twice a year. When the sun 
 is directly overhead at any place north of the equator, 
 every part of the earth south of the equator is in the sun- 
 shine a shorter time than it is out of it, while every place 
 north of the equator is in the sunshine longer than it is 
 out ; that is, in this position of the sun the days south of 
 the equator are shorter than the nights, while north of 
 the equator the days are longer than the nights. The 
 farther a place is south of the equator, the shorter the 
 day and the longer the night ; while the farther north of 
 the equator a place is, the longer the day and the shorter 
 the night. When the sun is directly over any place south 
 of the equator, the relative length of the day and night 
 is the reverse of that just described ; that is, the day 
 north of the equator is shorter than the night, while 
 south of the equator it is longer than the night. . 
 
 When the sun's north polar distance is less than 90, 
 it is summer in the northern hemisphere and winter in 
 the southern, since the northern hemisphere then receives 
 more heat from the sun than the southern. When the 
 north polar distance of the sun is more' than 90, it is 
 winter in the northern hemisphere and summer in the 
 southern, since the latter then receives more heat from 
 the sun than the former. 
 
 The variation of the sun's polar distance, then, gives 
 rise to the change of seasons and the varying length of 
 day and night. If the axis of the earth were perpendic- 
 ular to the plane of the sun's path among the stars, there 
 3 
 
26 ASTRONOMY. 
 
 would be no change of seasons and no variation in the 
 relative length of day and night.* 
 
 19. Declination and Right Ascension. It is often 'con- 
 venient to refer the position of the sun and stars to the 
 celestial equator rather than to the celestial poles. The 
 celestial equator is an imaginary circle perpendicular to 
 the earth's axis, and dividing the celestial sphere into two 
 equal parts. ' The angular distance of the sun or other 
 heavenly body from the equator, is the difference between 
 90 and its polar distance. This angular distance is called 
 decimation ; north declination when it is north of the equa- 
 tor, and south declination when it is south of the equator. 
 When the polar distance of the sun is 66J, its declination 
 is 23^ north; when its polar distance is 1132? its decli- 
 nation is 23^ south. 
 
 The plane of the sun's apparent orbit is evidently in- 
 clined about 23 -i to the equator, which it bisects. 
 Twice a year the sun's declination is o. The points at 
 which the plane of the sun's orbit cuts the equator are 
 called equinoctial points, since, as we have already seen, 
 the days and nights are equal in every part of the earth 
 when the sun is at these points. The sun is at one of 
 these points on the 2ist of March, and at the other on 
 the 2ist of September. The first point is called the spring 
 or vernal equinox, and the second the autumnal equinox. 
 The Spring equinox is not far from Algenib, a bright star 
 in the constellation Pegasus ; and the autumnal equinox is 
 not far from Denebola, the bright star in the tail of Leo. 
 The Spring equinox is usually taken as the fixed point on 
 the celestial sphere from which the imaginary meridian is 
 supposed to start in sweeping over the heavens, so as to 
 bring a given star under it ; and the angular distance which 
 
 * The change of seasons and of the relative length of day and night 
 can be more clearly illustrated by means of one of the little globes 
 made for that purpose than by any description or figures. 
 
,? 
 
 
 ASTRONOMY. 
 
 the meridian must sweep over from this point to bring a 
 star or planet under it is called right ascension. Right as- 
 cension is, therefore, always measured eastward. 
 
 20. The Precession of the Equinoxes. It is found that 
 the path of the sun does not always cross the equator at 
 exactly the same place from year to year. The equinoctial 
 point shifts along the equator westward 50.1" yearly. This 
 yearly shifting of the equinoctial point is called ti\t preces- 
 sion of the equinoxes. < . 
 
 21. The Tropical Year. The interval between two suc- 
 cessive conjunctions of the sun with the same fixed star is 
 called, as we have seen, a sidereal year. The interval be- 
 tween two successive appearances of the sun at the same 
 equinoctial point is evidently a little shorter than the si- 
 dereal year, since this point is continually shifting west- 
 ward. This interval is called a tropical year. It is 20 J- 
 minutes shorter than the sidereal year. The seasons are 
 evidently completed in a tropical year, since they depend 
 on the declination of the sun. Hence the tropical year 
 is the year of common life, which is regulated by the 
 change of the seasons. 
 
 22. Solstitial Points. When the sun has reached his 
 greatest northern or southern declination, his declination 
 scarcely changes for two or three days. He seems to halt 
 a little in his journey toward the poles before he turns 
 back toward the equator. These two points in his path 
 are called solstices (sun-stands'). The one north of the 
 equator, where the sun appears in midsummer, is called 
 the summer solstice; and the one south of the equator, 
 where the sun appears at midwinter, is called the winter 
 solstice. 
 
 23. The Variation of the Sun's apparent Diameter. The 
 angular diameter of the sun is about 32', but this diameter 
 is continually changing. From a certain point it goes on 
 gradually increasing for six months. It then begins to 
 
28 ASTRONOMY. 
 
 diminish, and continues to diminish for the next six 
 months, when it becomes the same as at first. We must, 
 therefore, conclude that the sun's distance from the earth 
 is continually changing. It is obviously at the greatest 
 distance from the earth when its diameter is least, and 
 nearest to the earth when its diameter is greatest. It is a 
 well-known fact that the angle subtended by any object di- 
 minishes in the same proportion as its distance increases. 
 If its distance is doubled, the angle which it subtends is 
 diminished one half. Hence, by measuring the angular 
 diameter of the sun from time to time we find out the 
 relative distance of the sun from the earth at those times. 
 24. The Form of the Sun's apparent Path among the 
 Stars. If we draw a straight line, E A, to represent the 
 direction and distance of the sun at any time, and observe 
 the sun's angular diameter and his right ascension at this 
 time, we can, by observing his right ascension and angular 
 diameter at any other time, find the length and direction 
 of another line, E JB, which shall represent the direction 
 and distance of the sun at the time of the second observa- 
 tion. For the length of the line E B will be to the length 
 of the line E A in the inverse ratio of the observed angu- 
 lar diameters of the sun, and the angle which the line E B 
 makes with E A will evidently be the difference of the ob- 
 served right ascensions. 
 In the same way the 
 length and direction of 
 the lines E C, E D, E F, 
 E G, and E H, are de- 
 termined at different times 
 in the course of a year. 
 Now if a curve be drawn 
 through the ends of these 
 lines, it will evidently 
 represent the form of the 
 
ASTRONOMY. 2Q 
 
 sun's path among the stars during a year. This curve is 
 found to be, not a circle, but an ellipse. The earth is sit- 
 uated at one of the foci of this ellipse. The nearer the 
 sun is to the earth, the more rapid is his motion in right 
 ascension. 
 
 25. Summary. We find, then, that the sun is con- 
 tinually changing his position with reference to the fixed 
 stars ; that he is travelling eastward among them at the 
 rate of about a degree a day, thus making an entire cir- 
 cuit of the heavens in a year. We find that the axis of 
 the earth is not perpendicular to this path, but inclined 
 to it at an angle of about 66 J ; and that the sun travels 
 at unequal rates in different parts of his path. 
 
 The plane of the sun's path passes through the earth's 
 centre, and its intersection with the celestial sphere is 
 called the ecliptic. 
 
 The inclination of the earth's axis to the plane of the 
 ecliptic gives rise to the change of seasons and the change 
 in the relative length of day and night. 
 
 TWILIGHT. 
 
 26. Darkness does not come on at once after sunset. 
 Full daylight gradually fades away into the darkness of 
 night, and in the morning the darkness gradually melts 
 away into full daylight again. This gradual transition from 
 daylight to darkness in the evening, and from darkness to 
 full daylight in the morning, is called twitight. 
 
 27. Cause of Twilight. After the sun sinks below the 
 horizon, it still shines upon the particles of air above the 
 earth, and these reflect the light to the earth again. At 
 first there is a large number of these illumined particles 
 above the horizon, but as the sun sinks lower and lower 
 they become fewer and fewer, and the light which they > re- 
 flect to the earth feebler and feebler, until it becomes im- 
 
 3* 
 
30 ASTRONOMY. 
 
 perceptible when the sun has sunk 18 below the horizon. 
 And again in the morning, when the sun has come within 
 1 8 of the horizon, it begins to shine- on the particles of 
 air above the horizon, and they begin to reflect a feeble 
 light to the earth. As the sun comes nearer and nearer 
 to the horizon, more and more particles above the horizon 
 become illumined, and the light which they reflect to the 
 earth becomes more and more intense, till full daylight 
 bursts forth at the rising of the sun. 
 
 28. Duration of Twilight. Twilight, then, lasts at night 
 till the sun is 18 below the horizon, and begins in the 
 morning when the sun has come within 18 of the hori- 
 zon. Is twilight of the same length in different parts of 
 the earth, and in the same parts of the earth at different 
 seasons of the year? This is equivalent to inquiring 
 whether the sun gets 18 below the horizon in the same 
 time in different parts of the earth, or in the same part of 
 the earth at different seasons. When we say that the sun 
 is 18 below the horizon, we mean 18 measured on a ver- 
 tical circle, that is, a circle perpendicular to the horizon 
 and passing through the zenith. We will suppose the time 
 to be the 2ist of March, and the place to be the equator 
 of the earth. Here the circle described by the sun in his 
 apparent daily motion is perpendicular to the horizon and 
 passes through the zenith, that is, it is a vertical circle ; 
 and when the earth has rotated through 18 after the sun 
 has reached the horizon, he will be 18 below it, and twi- 
 light will end. We will next suppose the time to be the 
 same, but the observer to be either north or south of the 
 equator. The circle described by the sun in his apparent 
 daily motion is still a great circle, but it is inclined to the 
 horizon, and so is not a vertical circle. The sun here will 
 evidently not be 18 below the horizon when the earth has 
 rotated 18 after the sun has reached the horizon. For 
 the sun has gone down obliquely below the horizon, and 
 
ASTRONOMY. 3 1 
 
 he must descend more than 18 degrees in this oblique 
 path in order to get 18 below the horizon; just as one in 
 walking obliquely from a wall must ^walk more than ten 
 feet to get ten feet from the wall. Hence when the sun is 
 on the equator, twilight is shorter at the equator than at 
 places north or south of the equator. The farther north 
 or south of the equator, the more obliquely does the sun 
 rise and set, and of course the longer the twilight. 
 
 We will next suppose that the sun is at the summer or 
 winter solstice, and that the observer is at the equator. 
 The diurnal path of the sun is still perpendicular to the 
 horizon, but does not pass through the zenith. It is not 
 a great circle, but a small circle. When, therefore, the 
 earth has rotated 18 after the sun has reached the hori- 
 zon, the sun is not 18 below the horizon, since an arc of 
 1 8 on a small circle is shorter than an arc of 18 on a 
 vertical circle, which is a great circle. Hence twilight at 
 the equator grows longer as the sun passes north or south 
 of the equator. 
 
 Suppose now that an observer is north of the equator, 
 and the sun is at one of the solstices. The plane of the 
 horizon is now inclined to the axis of the earth's rotation, 
 and is carried around that axis with a wabbling motion. 
 This motion may be illustrated by passing a wire through 
 the centre of a piece of cardboard, and fastening the card 
 so that it will be inclined to the wire, and then rotating 
 the wire. 
 
 Let us first see what would be true of twilight, provided 
 the horizon were rotating on an axis which coincided with 
 its own plane. When the sun is either north or south of 
 the equator, its daily motion is in a small circle, and as 
 these small circles are all equally inclined to the 'plane of 
 the horizon, twilight would grow longer as these circles 
 become smaller ; that is, as the sun moves north and south 
 from the equator. But by referring to the illustration of 
 
32 ASTRONOMY. 
 
 the wabbling motion of the plane of the horizon in conse- 
 quence of its being inclined to the axis of the earth's rota- 
 tion, it will be seen that to a person. north of the equator 
 the portion of the heavens south of the east and west 
 points is carried, as it rotates, bodily away from the stars as 
 they sink below it ; while the portion north of those points 
 is carried bodily towards the stars as they sink below it. 
 Thus this wabbling motion of the horizon tends to increase 
 the length of twilight in summer, and to shorten it in win- 
 ter ; while the fact that the sun is moving in small circles 
 at each of these times tends to increase the length of twi- 
 light as well in winter as in summer. The tendency of 
 this wabbling motion of the horizon to diminish the length 
 of twilight in winter, in our latitude, almost exactly balan- 
 ces the effect of the sun's moving in a small circle. The 
 length of twilight varies but a few minutes from the au- 
 tumnal to the vernal equinox ; while in midsummer in our 
 latitude, twilight is half an hour longer than at the equi- 
 noxes. At the poles the sun never sinks more than 23^ 
 below the horizon, hence the twilight there lasts about two 
 thirds of the long winter night. 
 
 29. Summary. The twilight at the equator is shortest 
 when the sun is on the equator, and longest when the 
 sun is farthest north or south of the equator. The short- 
 est twilight at any time is at the equator. 
 
 As you go from the equator either north or south, the 
 twilight lengthens, and it is longer in summer than in win- 
 ter. The shortest twilight at the equator is about one 
 hour and twelve minutes ; in our latitude it is about an 
 hour and a half. 
 
 THE* APPARENT MOTION OF THE MOON. 
 
 30. The Lunar Month. The new moon is always seen 
 near the western horizon soon after sunset. It is farther 
 
ASTRONOMY. 33 
 
 and farther from the horizon at sunset, night after night, 
 until about a fortnight from new moon, when the moon 
 becomes full and rises just as the sun sets. It then lags 
 farther and farther behind the sun until it does not rise till 
 just before sunrise. 
 
 We see, then, that the moon is also moving eastward 
 among the stars, and that it is moving more rapidly than 
 the sun. When the moon and sun both rise or set to- 
 gether, they are said to be in conjunction; and when the 
 moon rises just as the sun sets, it is said to be in opposi- 
 tion. The moon passes from conjunction to conjunction, 
 or from opposition to opposition, in 29 J days. This period 
 is the ordinary lunar month. 
 
 The moon, like the sun, in her eastward journey among 
 the stars, changes not only her right ascension from day to 
 day, but also her declination. The points at which the 
 moon's path cuts the ecliptic are called the nodes (knots). 
 The point where its path cuts it from south to north is 
 called the ascending node, while the other is called the 
 descending node. 
 
 3 1. The Lunar Day. The interval between two succes- 
 sive passages of the moon across the meridian is sometimes 
 called a lunar day. This interval is nearly an hour longer 
 than the solar day. The lunar days are found to be even 
 more unequal in length than the solar days. 
 
 32. The Moon's Orbit is an Ellipse. By a method sim- 
 ilar to that used in the case of the sun, the orbit of the 
 moon is found to be an ellipse, which hasthe earth at one 
 of its foci. When the moon is in that part of her orbit 
 which is nearest to the earth, she is said to be in perigee 
 (near the earth), and when in that part of her orbit farthest 
 from the earth, she is said to be in apogee (away from the 
 earth). The line joining these points of the moon's orbit 
 is the major axis of an ellipse, and is called the line of 
 apsides. The moon moves faster at perigee than at apogee. 
 
34 ASTRONOMY. 
 
 THE APPARENT MOTIONS OF THE PLANETS. 
 
 33. Venus. There is a conspicuous star sometimes seen 
 in the west in the early evening, and sometimes in the east 
 before sunrise. This star is familiarly known as the morn- 
 ing and evening star. If it be watched for some time it 
 will be seen, after it has ceased to be a morning star, close 
 to the horizon in the west soon after sunset. Then night 
 after night it will be seen to have moved farther and far- 
 ther to the eastward from the sun, until its angular dis- 
 tance from him is about 47. Venus, at this point, is said 
 to be at its greatest eastern elongation from the sun. It 
 then begins to approach the sun, and finally passes him 
 and appears again on his western side as a morning star. 
 It separates farther and farther from him to the westward, 
 until its angular distance from him is again about 47, 
 when it is said to be at its greatest western elongation 
 from the sun. It then approaches the sun again, and 
 passes by him to the eastward. The interval between two 
 successive appearances of Venus at its greatest eastern or 
 its greatest western elongation is about nineteen months. 
 We see, then, that Venus is apparently carried on with the 
 sun in his eastward journey among the stars, sometimes 
 falling behind him an angular distance of 47, and again 
 overtaking and passing beyond him a like distance. 
 
 34. Mercury. The movements of Mercury are similar 
 to those of Venus, but his greatest elongation from the sun 
 never exceeds 29, so that he sinks below the horizon too 
 soon after sunset, and rises too short a time before the 
 sun, to be often visible to the naked eye. 
 
 Stars, like Mercury and Venus, which are thus continu- 
 ally changing their position in the sky, are called planets 
 (wanderers), to distinguish them from the fixed stars, which 
 
ASTRONOMY. 35 
 
 we have seen do not sensibly change their position in the 
 sky. 
 
 35. Movements of the other Planets among the Stars. 
 Besides the two planets, Mercury and Venus, there are 
 three other planets, Mars, Jupiter, and Saturn, which are 
 conspicuous to the naked eye ; and two large planets, Ura- 
 nus and Neptune, which are so distant that they cannot be 
 seen except with the telescope ; and a large number of 
 smaller ones, called asteroids, which, though nearer, can 
 be seen only with a telescope. 
 
 If one of the most conspicuous of these planets, as Ju- 
 piter, be watched for a series of years, it will be found to 
 work its way gradually to the eastward among the stars, 
 and to complete the circuit of the heavens in a longer or 
 shorter time. This time is found to be always the same 
 for the same planet ; but different for different planets. 
 But this eastward motion of the planet is not regular and 
 uniform. The planet advances quite rapidly at times, then 
 halts and remains stationary, then actually goes backward 
 or retrogrades, then halts and remains stationary again, 
 
 and again advances. 
 
 Fig. n. 
 
 Figure n represents the apparent motion of Jupiter 
 among the stars during the year 1866. 
 
 THE PTOLEMAIC SYSTEM. 
 
 36. We have now seen that the sun appears to revolve 
 about the earth from west to east once in a year in an 
 orbit whose exact form is an ellipse ; that the moon ap- 
 pears to revolve about the earth in the same direction 
 and in an orbit of the same form once in a month-; that 
 
36 ASTRONOMY. 
 
 Mercury and Venus appear to swing backward and for- 
 ward across the sun, while they are at the same time car- 
 ried onward with him in his eastward motion ; and that 
 the other planets also appear to move about the earth in 
 longer or shorter periods and in very irregular paths. It 
 seems improbable that any planet should really move in so 
 irregular a path as Jupiter appears to move in. 
 
 The ancient astronomers assumed that the planets all 
 moved in circular orbits, and attempted to account for 
 their apparent irregular motions by the combination of 
 various circular motions. They supposed that the earth is 
 fixed, and that the sun moves. They supposed that a bar, 
 or something equivalent, was connected at one end with 
 the earth, and that on some part it carried the sun ; and as 
 they saw that the planet Venus is apparently sometimes 
 on one side of the sun and sometimes on the other, they 
 said that the planet Venus moves in a circle whose centre 
 is on the same bar. Then if we suppose that Venus is re- 
 volving around this centre at the same time that the bar 
 is moving about the earth, we get a perfect representa- 
 tion of the apparent motion of Venus and the sun as seen 
 from the .earth. This is illustrated by Figure 12. Sup- 
 
 Fig. 12. 
 
 pose E to be the fixed earth ; E v S m n, a bar turning in 
 a circle, having one end fixed at E ; S the sun carried by 
 it ; v y the centre of the orbit in which Venus revolves ; 
 
ASTRONOMY. 37 
 
 V, the planet Venus, connected with v by a bar (real or 
 imaginary), and thus describing a circle round v, while v 
 itself is carried on the bar round the earth. 
 
 It was supposed that Mercury revolved in another cir- 
 cle, whose centre was also on the same bar, but perhaps 
 beyond the sun, as at m. They did not pretend to say 
 exactly where these centres were : all that they were cer- 
 tain about was this; that the centre of motion of each 
 planet was on the same bar that supported the sun. Now 
 it is easy to be seen, on these suppositions, that both 
 Mercury and Venus would appear, when viewed from the 
 earth, at one time on the right and again on the left of 
 the sun, and at the same time they would appear to be 
 carried around the earth with him. 
 
 With regard to Mars, they found out that its motion 
 could be represented pretty well by supposing that this 
 same bar carried another centre at n, around which Mars 
 revolved as at Ma, carried by an arm long enough to 
 project beyond the earth, so that its orbit completely sur- 
 rounded the earth as well as the sun. In the same way 
 the apparent motions of Jupiter and Saturn were ac- 
 counted for. 
 
 The motion of the planet Mars, however, still pre- 
 sented some discordances, and there were some smaller 
 discordances with regard to all the other planets. These 
 led to the invention of those things known as epicycles, 
 deferents, etc., the nature of which may be thus ex- 
 plained. By the contrivance which we have already de- 
 scribed, they found that the movement of the point Ma 
 at the end of the rod n Ma would nearly, but not ex- 
 actly, represent the motion of Mars. To make it repre- 
 sent the motion more exactly, they supposed that another 
 small rod, Ma N, was carried by the longer rod, jointed at 
 Ma, and turning around in a different time. To make it 
 still more exact, they supposed another shorter rod car- 
 4 
 
38 ASTRONOMY. 
 
 ried at JV, and that its extremity carried the planet Mars. 
 The same complications were necessary for all the other 
 planets. It will be thus seen that a combination of no 
 less than five circular motions was necessary to account 
 for the apparent irregularities in the motion of a single 
 planet. Thus the joint n moved in a circle about E ; the 
 joint 'Ma in a circle about n; the joint JV about Ma ; and 
 the planet Mars about N. Of all the complicated sys- 
 tems that man ever devised, there never was one like 
 this Ptolemaic system. The celebrated king of Castile, 
 Alfonso, the greatest patron of astronomy in his age, 
 alluding to this theory of epicycles, said that " if he had 
 been consulted at the creation, he could have done the 
 thing better." 
 
 THE SYSTEM OF TYCHO DE BRAHE. 
 
 37. If we suppose the earth fixed as at E (Figure 13), 
 and Venus to be revolving around a centre situated 
 
 somewhere in the line E , 
 we may remove that cen- 
 tre as far from the earth as 
 we please, and yet get the 
 same appearance, provided 
 we enlarge the dimensions 
 of the orbit of Venus in the 
 same . proportion. For in- 
 stance, suppose E to be the 
 earth, the smaller circle to be the orbit of Venus, and the 
 sun to be at S ; then, in revolving in her orbit, Venus will 
 appear to go to a certain distance to the right and to the 
 left of the sun. But we may take any other point on the 
 bar, even the point S itself, as the centre of the orbit of 
 Venus, provided we give Venus a larger circle to revolve 
 in. If the larger circle in the figure represents the orbit 
 
ASTRONOMY. 
 
 39 
 
 of Venus, she will appear to move just as far to the right 
 and to the left of the sun as when she moved in the small 
 orbit. We may then fix the centre of the orbit of Venus 
 where we please ; and so with the centres of the orbits 
 of Mercury, Mars, and of each of the other planets, pro- 
 vided we give proper dimensions to their orbits. By hav- 
 ing all their centres at the 
 centre of the sun, we have 
 all the planets revolving 
 about the sun, while the 
 sun revolves about the 
 earth, as shown in Figure 
 14. This system is much 
 less complex than the 
 Ptolemaic system, though 
 the theory of epicycles 
 and deferents is still re- 
 tained. This modification 
 of the Ptolemaic system 
 
 was adopted by the great Danish astronomer, Tycho de 
 Brahe. 
 
 THE COPERNICAN SYSTEM. 
 
 38. Now, instead of supposing the sun to be travelling, 
 and by some imaginary power causing the planets to re- 
 volve about himself as their travelling centre, suppose we 
 say that the earth revolves about the sun, and that the 
 sun is a fixed, or nearly fixed, body, and that all the 
 planets, including the earth, go around the sun ; that is, 
 in Figure 14, instead of supposing S with the whole sys- 
 tem of orbits to be travelling around , suppose Me, V, 
 E. and Ma to travel in separate orbits about S, and the 
 appearances of the planets, as viewed from the earth, will 
 be represented exactly as well as before. 
 
40 ASTRONOMY. 
 
 This great step of assuming the sun to be the centre 
 of motion of all the planets, including the earth, was 
 taken by Copernicus. But he could- not get rid of the 
 epicycles to account for the apparent irregularities in the 
 motion of the planets. 
 
 THE SYSTEM OF KEPLER. 
 
 39. Tycho de Brahe had employed a good part of his 
 life in observing and recording the position of the heav- 
 enly bodies. His pupil, Kepler, by examining carefully 
 the observations which Brahe had made of the planets, 
 and especially of the planet Mars, and comparing them 
 with his own, ascertained that the whole could be repre- 
 sented with the utmost accuracy by supposing that Mars 
 moves in an ellipse, one of whose foci is occupied by the 
 sun. It is difficult to explain in a few words how Kepler 
 came to this conclusion ; generally speaking, it was by 
 the method of trial and error. The number of supposi- 
 tions he made to account for the motion of the planets 
 is beyond belief: that the planets turned round centres 
 at a little distance from the sun ; that their epicycles and 
 deferents turned on points at a little distance from the 
 ends of the bar to which they were jointed ; and the 
 like. After trying every device he could think of with 
 epicycles, eccentrics, and deferents, and computing the 
 apparent place of Mars from these different assumptions, 
 and comparing them with the places really observed by 
 Brahe, he found that he could not bring them nearer to 
 Brahe's observations than eight minutes of a degree. He 
 then said boldly that so good an observer as Brahe could 
 not be wrong by eight minutes, and added, " Out of these 
 eight minutes we will construct a new theory that will 
 explain the motion of all the planets." The theory thus 
 constructed was, that all the planets move in ellipses 
 
ASTRONOMY. 41 
 
 which have the sun at one of their foci. This theory 
 has been found to explain accurately all the seeming ir- 
 regularities in the motion of the planets. 
 
 The planets appear to advance and retrograde because 
 they are seen from the earth, which is itself revolving 
 about the sun. If they were seen from the sun, their 
 advance would be steady and regular. 
 
 To construct an ellipse, stick two pins into a board a 
 little way apart; fasten to the pins the ends of a string 
 somewhat longer than the distance between the pins ; then, 
 keeping the string stretched by the point of a pencil, 
 carry the pencil round. The curve described will be an 
 ellipse, and the points where the pins are stuck into the 
 board will be the foci of the ellipse. 
 
 If the ellipse in Figure 15 be the orbit of a planet, 6* 
 will be the place of the sun. The sun 
 is at the focus of the ellipse described 
 by every planet. Every planet describes 
 a different ellipse. The degree of flat- 
 ness of the ellipse is different for every 
 planet, and the direction of the long 
 diameter of the ellipse is different for 
 every planet. There is, in fact, the 
 greatest variety among the ellipses de- 
 scribed by the different planets. 
 
 40. Kepler's First Law. The first great fact, then, 
 that Kepler made out with regard to the motion of the 
 planets is, that they all move in ellipses, which have the 
 sun at one focus. This fact is usually called Kepler's 
 first law. 
 
 41. Kepler's Second Law. The second fact made out 
 by this astronomer is, that the planets move at unequal 
 rates in different parts of their orbits. He found that 
 each planet, when in its perihelion, that is, the part of its 
 orbit which is nearest the sun, travels quickly, and when 
 
 4* 
 
4 2 ASTRONOMY. 
 
 in its aphelion, or the part of its orbit which is farthest 
 from the sun, travels slowly. 
 
 Kepler expressed this law of motion in this way : if in 
 one part of the planet's orbit the lines S K and SL (see 
 Figure 15) enclose a certain portion of the area of the 
 ellipse, and in another part the two lines s k and s I en- 
 close a space equal to that enclosed by S K and S L, the 
 planet will be just as long in moving over the short arc 
 k I as over the large arc K L ; that is, the planets describe 
 equal areas in equal times. 
 
 42. Kepler's Third Law. Kepler made out another 
 very important fact with regard to the motions of the 
 planets compared with their distances from the sun ; 
 namely, that the squares of the periodic times of the plan- 
 ets are to each other as the cubes of their mean distances from 
 the sun. 
 
 SUMMARY. 
 
 The earth, sun, moon, and planets are globes. The 
 shape of the fixed stars is unknown. (2, 3.) 
 
 The starry heavens appear to rotate in a piece from 
 east to west about an axis which passes through the 
 centre of the earth and a point near the Polar Star. 
 This rotation is completed in twenty-four hours. (6.) 
 
 The earth rotates from west to east once in twenty- 
 four hours about an axis which passes through the cen- 
 tre of the earth and a point near the Polar Star. This 
 rotation of the earth causes the heavens to appear to 
 rotate in the opposite direction. (8.) 
 
 The stars describe accurate circles, though their paths 
 are somewhat disturbed by refraction. (5, 7.) 
 
 The circles described by the stars are differently in- 
 clined to the plane of the horizon in different parts of 
 the earth. (9.) 
 
ASTRONOMY. 43 
 
 The co-ordinates of a heavenly body are the angular 
 distance of the body from the celestial pole, and the 
 angular distance that the meridian must sweep over from 
 a fixed point to bring the body under it. (10.) 
 
 The latter of these co-ordinates is measured by means 
 of the Transit Instrument ; the former, by means of the 
 Mural Circle, (n, 12.) 
 
 The co-ordinates of the fixed stars are always the 
 same wherever they are measured. (14.) 
 
 The co-ordinates of the sun ^.re found to change daily. 
 He travels eastward among the stars and completes the 
 circuit of the heavens once a year. 
 
 The plane of his orbit passes through the centre of 
 the earth, and is inclined to the earth's axis at an angle 
 of 661. (15, 17.) 
 
 The sun in his eastward journey describes an ellipse 
 with the earth at one of its foci. (24.) 
 
 The moon travels eastward among the stars more rap- 
 idly than the sun. She completes a circuit of the heav- 
 ens in a month, and describes an ellipse with the earth 
 at its focus. (30, 32.) 
 
 Venus and Mercury are seen to vibrate to and fro 
 across the sun. At their greatest elongations, Venus is 
 47, and Mercury 29, from the sun. (33, 34.) 
 
 The other planets describe very circuitous paths among 
 the stars. They advance to the eastward for a time, then 
 halt, and then even go backward. (35-) 
 
 The ancient astronomers assumed that' the planets all 
 moved in circular orbits, and attempted to account for 
 their apparent irregular motion by the combination of 
 various circular motions. They constructed a system of 
 cycles, epicycles, and deferents. (36.) 
 
 Tycho de Brahe simplified the Ptolemaic system by 
 placing the centres of all the cycles at the centre of the 
 sun. (37.) 
 
44 ASTRONOMY. 
 
 Copernicus simplified it further by making the earth 
 revolve about the sun. (38.) 
 
 Kepler was the first who did away with the complex 
 system of cycles and epicycles by showing that all the 
 planets move in ellipses, all of which have the sun at one 
 focus. (39, 40.) 
 
 He further showed that the planets describe equal areas 
 in equal times, and that the squares of the periodic times 
 of the planets are to each other as the cubes of their mean 
 distances from the sun. (4% 42.) 
 
 A sidereal day is the interval between two successive 
 transits of a star across the meridian. 
 
 The solar day is the interval between two successive 
 transits of the sun across the meridian. (15.) 
 
 The solar days are of unequal length. The ordinary 
 civil day is the average length of these. (16.) 
 
 The variation of the sun's polar distance gives rise 
 to the change of seasons and the varying length of day 
 and night. (18.) 
 
 The circle formed by the intersection of the plane of the 
 sun's? orbit with the celestial sphere is called the ecliptic. 
 
 The celestial equator is a circle which is perpendicular 
 to the earth's axis and which divides the celestial sphere 
 into two equal parts. 
 
 The points where the sun's orbit cuts the celestial 
 equator are called the equinoxes. 
 
 Angular distance measured north or south from the 
 celestial equator is called declination. 
 
 Angular distance measured from the vernal equinox 
 eastward is called right ascension. (19.) 
 
 The equinoxes slowly shift along the equator to the 
 westward. This shifting is called the precession of the 
 equinoxes. (20.) 
 
 The interval between two successive conjunctions of 
 the sun with the same fixed star is a sidereal year. 
 
ASTRONOMY. 45 
 
 The interval between two successive appearances of 
 the sun at the same equinox is a tropical year. (21.) 
 
 The points in the sun's path at which he gains his 
 greatest northern or southern declination are called the 
 solstices. (22.) 
 
 Twilight is caused by the reflection of the sun-light 
 from the clouds and the particles of air. 
 
 It continues while the sun is within 18 of the hori- 
 zon. It is shortest at the equator and longest at the 
 poles. In our latitude it is longer in the summer than 
 in the winter. (27.) 
 
 HOW TO FIND THE PERIODIC TIMES OF 
 THE PLANETS. 
 
 43. The Periodic time of the Earth determined by direct 
 Observation. We have seen that the real motion of the 
 earth about the sun causes the sun to appear to revolve 
 about the earth. It is evident that the time that it takes 
 the earth to revolve about the sun is the same as that 
 which it takes the sun to make an apparent revolution 
 around the earth. The periodic time of the earth is 
 found by observing the interval between two successive 
 appearances of the sun at the same equinox, or two suc- 
 cessive conjunctions with the same star. 
 
 44. Synodic Period of a Planet determined by direct Ob- 
 servation. 'The planets Venus and Mercury, as we have 
 already seen, never appear in the part of the heavens 
 opposite to the sun. Hence the orbits of these planets 
 must lie wholly inside the orbit of the earth. When 
 these planets come between the earth and the sun they 
 are said to be in inferior conjunction, and when the sun is 
 between them and the earth they are said to be in supe- 
 rior conjunction. The planets whose orbits lie wholly 
 
46 ASTRONOMY. 
 
 within the earth's orbit are called inferior planets. Those 
 whose orbits lie wholly without the earth's orbit are called 
 superior planets. When a superior planet appears in the 
 same part of the heavens as the sun, that is, when the 
 sun is between the earth and planet, it is said to be in 
 conjunction. When the planet appears in the opposite 
 part of the heavens to that of the sun, that is, when the 
 earth is between the planet and the sun, it is said to be 
 in opposition. 
 
 The interval between two successive oppositions of a 
 planet, or between two successive conjunctions of the 
 same kind, is called the synodic revolution of the planet. 
 This interval is determined by direct observation. 
 
 45. Hoiv to find the Sidereal Period of an inferior Planet. 
 The sidereal period of a planet is the time it takes to 
 make a complete revolution about the sun. This time 
 can be easily computed when we know the sidereal period 
 of the earth and the synodic period of the planet. 
 
 Let P be the sidereal period of the earth, S the sy- 
 nodic period of Venus, and / the sidereal period of Venus. 
 P and S are known by direct observation, and / is re- 
 quired. 
 
 We will suppose that Venus is 
 at inferior conjunction ; then , 
 V, and S will represent the re- 
 spective places of the earth, Ve- 
 nus, and the sun. If the earth 
 were stationary as well as the sun, 
 then Venus would come again into 
 conjunction when it had just com- 
 pleted a revolution about the sun ; but the earth is mov- 
 ing in the same direction as Venus, hence Venus must 
 make a complete revolution and then overtake the earth 
 before it comes into inferior conjunction again. If two 
 persons start together at some point on the circumference 
 
ASTRONOMY. 47 
 
 of a circle, and the first walks faster than the other, he 
 must gain the whole length of the circumference before 
 he comes up to the- second again. In the same way, 
 after Venus has come into inferior conjunction, it must 
 gain 360 upon the earth before it can come into inferior 
 conjunction again. 
 
 =~L. the angular space passed over by the earth in 
 
 one day. ^-r- angular space passed over by Venus 
 in one day. 
 
 ^-T- ^p- =. the angular gain of Venus upon the earth 
 in one day. But Venus gains 360 in S days, hence 
 = daily gain of Venus. 
 
 Hence 36 36 36 
 
 JLJLCllV^C ~ ~ ~ 
 
 'Divide by 360, and we have 
 
 i _ __ _ 
 / P~~ S' 
 PSpS= 
 
 . 
 
 = 
 
 46. To find the Sidereal Period of a Superior Planet. 
 The sidereal period of a superior planet can be found by 
 a similar method. In this case the earth gains upon 
 the planet. 
 
 Let/ and -S" represent the sidereal and synodical period 
 of a superior planet. Then ^ --- ^-^- = daily gain of 
 the earth upon the planet: 
 
 360 _ 360 _ 360 
 P ' ' S ' 
 
48 ASTRONOMY. 
 
 47. Synodical and Sidereal Periods of the Planets. The 
 following table gives the synodical and sidereal periods 
 of the principal planets : 
 
 
 Synodical Period. 
 
 Sidereal Period. 
 
 Mercury 
 
 115.877 days 
 
 87.969 days or 3 months 
 
 Venus 
 
 583.921 
 
 224.701 " 7! " 
 
 Earth 
 
 
 365.256 " i year 
 
 Mars 
 
 779.936 
 
 686.980 " 2 years 
 
 Jupiter 
 
 398.884 
 
 4332.585 " 12 " 
 
 Satlirn 
 
 378.092 " 
 
 10759.220 " 29 " 
 
 Uranus 
 
 369.656 " 
 
 30686.821 " 84 " 
 
 Neptune 
 
 367.489 
 
 60126.722 " 164 " 
 
 SUMMARY. 
 
 The sidereal period of the earth is found by observing 
 the interval between two successive appearances of the 
 sun at the same equinox, or two successive conjunctions 
 of the sun with the same star. (43.) 
 
 An inferior planet is one whose orbit lies wholly with- 
 in the earth's orbit. 
 
 A superior planet is one whose orbit lies wholly with- 
 out the earth's orbit. 
 
 A planet is in inferior conjunction when it lies in the 
 same part of the heavens as the sun, and is between the 
 earth and sun. 
 
 A planet is in superior conjunction when it lies in the 
 same part of the heavens as the sun, and is beyond the 
 sun. 
 
 A planet is in opposition when it lies in the opposite 
 part of the heavens from the sun. 
 
 The superior planets are never in inferior conjunction, 
 and the inferior planets are never in opposition. 
 
 The synodical period of a planet, is the interval between 
 
ASTRONOMY. 
 
 49 
 
 two successive oppositions of the planet, or between two 
 successive conjunctions of the same kind. 
 
 The synodical period is ascertained by direct observa- 
 tion. (44.) 
 
 The sidereal period of a planet is the time it takes the 
 planet to make a complete revolution about the sun. 
 
 The sidereal period of a planet can be computed when 
 the sidereal period of the earth and the synodical period 
 of the planet are known. (45, 46.) 
 
 Fig. 17. 
 
 HOW TO FIND THE DISTANCE OF THE 
 PLANETS FROM THE SUN. 
 
 48. To find the relative Distances of the Inferior Planets 
 from the Sun. We have now seen how to find the peri- 
 odic times of the planets, which must have been known to 
 Kepler before he could discover the simple relation which 
 the periodic times of the planets bear to their mean dis- 
 tances from the sun. We must next see how we can find 
 the relative distances of the planets from the sun. We will 
 begin with the inferior planets. 
 
 Let ^ in Figure 17, represent the 
 position of Venus at its greatest elon- 
 gation from the sun ; S, the position of 
 the sun ; and E that of the earth. The 
 line E Fwill evidently be tangent to a 
 circle described about the sun with a 
 radius equal to the distance of Venus 
 from the sun at the time of this great- 
 est elongation. Draw the radius S V 
 and the line S E. Since S V is a ra- 
 dius, the angle at V is a right angle. 
 The angle at E is known by measure- 
 ment, and the angle at S = 90 the 
 angle E. In the right-angled triangle 
 
50 ASTRONOMY. 
 
 E V S, we then know the three angles, and we wish to 
 find the ratio of the side S V to the side S E. 
 
 The ratio of these two sides may be found by construc- 
 tion as follows : 
 
 Draw any line, as A B (see Figure 18), and from the 
 Fig ig point A draw the line A D 
 
 at right angles to the line 
 A B. From the point B 
 
 G draw the line B C, making 
 
 ^""^JD with the line B A an angle 
 equal to the angle at ,5 in 
 
 Figure 17. These lines will intersect at some point, as 
 E, and E A B will be a right-angled triangle similar to 
 E V S, and the side A B will have the same ratio to BE 
 as V S has to S E. Measure now the two lines A B and 
 BE by means of the scale and dividers, and the ratio 
 of AB to BE, and consequently of V S to E S, be- 
 comes known. 
 
 The ratio of these lines may be found with greater ac- 
 curacy by trigonometrical computation, as follows : 
 
 VS \E S = sin SE F:(sin S VE= i).* 
 Substitute the value of the sine of E V, and we have 
 VS-.E =.723 : i. 
 
 Hence the relative distances of Venus and of the earth 
 from the sun are .723 and i. 
 
 As Venus moves in an ellipse, and its greatest elonga- 
 tion takes place in different parts of its orbit, the angle 
 S E V will not always be the same. In order to get the 
 mean distance of Venus from the sun, we must know the 
 average value of its greatest elongation from the sun. 
 This is obtained by observing a large number of such 
 elongations. 
 
 * See Appendix, T. i and 3. 
 
ASTRONOMY. 
 
 49. To find the relative Distances of the Superior Plan- 
 ets from the Sun. Let S, e, and m, in Figure 19, repre- 
 sent the relative positions of the sun, the earth, and 
 
 Fig. 19. 
 
 Mars, when the latter planet is in opposition. Let E 
 and M represent the relative positions of the earth and 
 Mars the day after opposition. At the first observation 
 Mars will be seen in the direction e m A, and at the 
 second observation, in the direction E M A. 
 
 But the fixed stars are so distant that, if a line, e A, 
 were drawn to a fixed star at the first observation, and a 
 line, E B^ drawn from the earth to the same fixed star 
 at the second observation, these two lines would be sen- 
 sibly parallel ; that is, the fixed star would be seen in 
 the direction of the line e A at the first observation, and 
 in the direction of the line E B, parallel to e A, at the 
 second observation. But if Mars were seen in the direc- 
 tion of the fixed star at the first observation, it would ap- 
 pear back, or west, of that star at the second observation 
 by the angular distance B E A ; that is, the planet would 
 have retrograded that angular distance. Now this retro- 
 gression of Mars during one day at the time of opposi- 
 tion can be measured directly by observation. This 
 measurement gives us the value of the angle B E A. 
 But we know the rate at which both the earth and Mars 
 are moving in their orbits, and from this we can easily 
 
52 ASTRONOMY. 
 
 find the angular distance passed over by each in one 
 day. This gives us the angles ESA and MSA. We 
 can now find the relative length of 'the lines MS and 
 E S (which represent the distance of Mars and of the 
 earth from the sun) both by construction and by trigono- 
 metrical computation. The relative length of these lines 
 can be found by construction, as follows. Draw any line, 
 
 Fig. 20. 
 
 A B, then through the point A draw two lines, A C and 
 A D, making with A B angles respectively equal to the 
 angles MSA and J5SA, as found above. Through 
 any point on the line A D draw the line E G, parallel to 
 the line A B ; and draw E F> making with E G an angle 
 equal to the angle B E A, as found by observation. The 
 triangle A E F will evidently be similar to the triangle 
 E S M, and the side FA will bear to EA the same 
 ratio as MS bears to E S. This ratio can be found by 
 measurement of the two lines A F and A E. 
 
 This ratio can be determined with much greater accu- 
 racy by the following trigonometrical calculation. 
 
 Since E B and e A are parallel, the angle E A S is 
 equal to B E A. 
 
 S E A = 180 (E S A + E A S). 
 ESMESA MSA. 
 
 We have then 
 
 MS : E S = sin S E A : sin E MS. 
 
ASTRONOMY. 53 
 
 Substituting the values of the sines, and reducing the 
 ratio to its lowest terms, we have 
 
 MS : E S = 1.524 : i. 
 
 Thus we find that the relative distances of Mars and 
 the earth from the sun are 1.524 and i. By the simple 
 observation of its greatest elongation we are able to de- 
 termine the relative distance of an inferior planet and 
 the earth from the sun ; and by the equally simple obser- 
 vation of the daily retrogression of a superior planet we 
 can find the relative distance of such a planet and the 
 earth from the sun. 
 
 50. The Relative Distances of the Planets from the Sun. 
 In this way the relative distances of the principal plan- 
 ets have been found to be as follows : 
 
 Mercury 0-387 
 
 Venus 0.723 
 
 Earth i.oo 
 
 Mars 1-524 
 
 Jupiter 5- 2 3 
 
 Saturn 9.539 
 
 Uranus' 19-183 
 
 Neptune 30.037 
 
 Knowing the periodic times of the planets and their 
 relative distances from the sun, Kepler found the ratio 
 which these bear to each other by the method of trial 
 and error, which he had previously used in ascertaining 
 the form of the orbits of the planets. 
 
 51. To find the Distance of the Earth from the Sun. 
 We have now found the relative distances of all the 
 planets, including the earth, from the sun. If now we 
 can find the distance of the earth from the sun in miles, 
 we can easily find the distances of all the planets from 
 the sun in miles. 
 
 Now it is evident that, when two straight lines cross 
 5* 
 
54 
 
 ASTRONOMY. 
 
 each other, the distances between these two lines at any 
 two points are proportionate to the distance of these 
 points from the intersection of the two lines. 
 
 Thus, suppose the two straight lines A B and CD 
 (Figure 21) cross each other at , and suppose the point 
 
 Fig. 21. 
 
 G be twice as far from E as F is from the same point ; 
 the distance between the two lines will be twice as great 
 at G as at F. 
 
 Now it occasionally happens that Venus, at inferior 
 conjunction, passes directly across the disc of the sun. 
 
 In Figure 22 let V represent the position of Venus at 
 
 Fig. 22. 
 
 inferior conjunction, A B the position of the earth, and 
 CD that of the sun. 
 
 An observer at A would see Venus crossing the sun in 
 the line CD, and an observer at B would see it cross 
 the sun in the line E F. These two chords will be par- 
 allel to each other, and the distance between them will 
 
ASTRONOMY. 
 
 55 
 
 be equal to the distance between the two lines A H and 
 B G at the distance If from their intersection at V. This 
 distance bears to the distance between the two lines at 
 A the same ratio that the distance V H bears to the 
 distance V A. 
 
 But we have already found that the distance AH bears 
 to the distance V H the ratio of i to .723. But V A = 
 A H V H. Hence VA bears to VH the ratio 277 
 to 723. Then G H \ A B = 723 : 277. 
 
 Hence, if we know the distance between the two ob- 
 servers at A and B in a straight line in miles, we can 
 find the distance G H in miles. 
 
 Since Venus revolves about the sun from west to east, 
 it will appear to us to be moving westward when it 
 crosses the sun, while the sun is apparently moving east- 
 ward. We however know the rate at which both the 
 sun and Venus are moving. Hence, if we know the time 
 that it takes Venus to cross the sun's disc, we can find 
 what angular distance both have passed over in this time. 
 And as they are moving in opposite directions, the sum 
 of these distances will give the angular measure of the 
 chord described by Venus across the sun's disc. 
 
 Each observer, then, thus notices carefully the time 
 that it takes Venus to cross the sun's disc. From this 
 observed time each is able to find the angular value of 
 the chord described by the planet. 
 
 Let A B and CD (Figure 23) 
 represent the chords described on 
 the sun's disc by the passage of 
 Venus. Draw the radii E F, E B, 
 and E D. The radius E F is 
 drawn perpendicular to the two 
 chords, and therefore bisects them. 
 The angular diameter of the sun 
 can be found directly by observa- 
 
 Fig. 23. 
 
56 ASTRONOMY. 
 
 tion. Hence the angular value of each of the radii E B 
 and E D is known ; also the angular values of G B and 
 H D, the halves of A B and CD.. Hence in each of 
 the right-angled triangles E G B and E H D the angu- 
 lar values of the hypothenuse and of one side are known, 
 and the* angular value of the other side can be easily 
 
 found. For ^~B* ^ 2 = ~G 2 and ~D 2 JT& 
 ~ But G H= G E HE. 
 
 The angular value of G If is then known, and also its 
 linear value. Dividing the linear value by the number 
 of seconds in its angular value, we find how long a line 
 will subtend an angle of i" at the distance of the sun. 
 Knowing this, we know how large an angle will be sub- 
 tended by the earth's radius at the distance of the sun. 
 
 In Figure 24, let S 
 
 Flg-24 " represent the place 
 
 of the sun, and C 
 the centre of the 
 earth. Draw the 
 line S A tangent 
 to the surface of 
 the earth, and draw 
 the radius A C. The triangle SAC will be right- 
 angled at A. The comparative length of the lines A C 
 and C S can now be determined either by construction, 
 as in section 45, or by the following computation : 
 
 C S : C A = i : sin C S A. 
 Substituting the value of sin C S A, we find 
 
 C S : C A = 23,750 (in round numbers) : i. 
 
 Hence the distance of the sun from the earth is, in 
 round numbers, 23,750 times the length of the earth's 
 radius in miles. 
 
 Now if we can find the length of the earth's radius in 
 
ASTRONOMY. 57 
 
 miles, and the distance in a straight line between the 
 points A and B (Figure 22), we can find the distance of 
 the earth and of each of the planets from the sun in 
 miles. 
 
 52. To find the Length of the Radius of the Earth in 
 Miles. We know that the circumference of a .circle is 
 3.1416 times as long as its diameter. Now, if the earth 
 is an exact sphere, every meridian of the earth will evi- 
 dently be an exact circle ; and if we can measure any 
 known fraction of one of these meridians, we can easily 
 find its whole length ; and from this the length of the 
 diameter of the earth, which is of course the diameter of 
 every great circle of the earth. 
 
 53. How to measure a known Fraction of a Meridian. 
 Suppose two places, A and B (Figure 25), to be situ- 
 
 Fig. 25. 
 
 ated, the one, for instance, at Shanklin Down, in the 
 Isle of Wight, and the other on the little island of Balta, 
 in the Shetland Isles. We wish to know, first, what 
 fraction of a whole meridian is the arc included between 
 these two places ; and second, how long this arc is in 
 miles. 
 
 Any line which is perpendicular to a tangent to a 
 circle at the point of contact is said to be vertical to 
 the circle ; and, if two verticals be prolonged within the 
 circumference of the circle, they will meet at the centre 
 of the circle. The fraction of the circumference included 
 between the two verticals depends upon their inclination 
 to each other. If they are inclined to each other at an 
 
ASTRONOMY. 
 
 angle of i, the arc included between them is ^^ of the 
 whole circumference, and, if they are inclined to each 
 other at an angle of 12, the arc included between them 
 is -3*3- of the whole circumference. 
 
 But a plumb-line is always vertical to a great circle 
 of the earth ; hence, if we can find the inclination of a 
 plumb line at A to one at B, we know what fraction of 
 the whole meridian the arc included between A and B 
 is. The angle which the directions of the plumb-lines 
 at the two stations make with each other can be ascer- 
 tained by means of the Zenith Sector. 
 
 This instrument is shown in Figure 26. It consists of 
 a telescope swinging upon pivots A B, 
 Fig. 26. an( j having attached to it an arc CD , 
 
 graduated into degrees and minutes. There 
 is a plumb-line, B F, connected with the 
 upper end of the telescope, or with one of 
 the pivots. This plumb-line is a very fine 
 silver wire supporting a weight, and kept' 
 steady by hanging in water. It gives us 
 the direction of the vertical. 
 
 The zenith sector is taken to one of 
 the stations, and the telescope directed 
 to a bright star upon the meridian near 
 the zenith. The number of degrees and 
 minutes which the plumb-line hangs from 
 the zero point at the centre of the telescope on the grad- 
 uated arc is observed. The sector is now taken to the 
 other station, and the same star is again observed when 
 upon the meridian, and the number of degrees and min- 
 utes that the plumb-line hangs from the zero point on 
 the arc is again observed. Now, since the directions of 
 the telescope at the two stations are sensibly parallel, 
 the difference of the degrees and minutes that the plumb- 
 line at the two stations hangs away from the telescope 
 
ASTRONOMY. 59 
 
 must be the amount by which the verticals at the two 
 places are inclined .to each other. Suppose that this dif- 
 ference amounts to 12, then the arc A B is equal to -fa 
 of the whole circumference of the meridian. 
 
 As these two stations are 700 or 800 miles apart, we 
 cannot of course measure the distance between them by 
 using only a yard-stick, though the distance between 
 these stations must be calculated by means of a distance 
 first measured by a yard-stick. 
 
 54. Triangulation. Such measurements are effected 
 by means of a system of triangulation. Suppose that we 
 have three places, , F, and G (Figure 27); the two 
 nearest, E and F, on a plain, 
 
 and perhaps six or eight miles 
 apart ; a third, G, at a consid- 
 erable distance, perhaps inac- 
 cessible from E and F, at least 
 in a straight line. The dis- 
 tance of G from either E or F, which cannot well be 
 measured, can be readily found by measuring the line 
 F Fj and the angle which this line makes with lines 
 drawn from E and F to the point G. For we may draw 
 any line, E F, and from its extremities draw the lines 
 E G and F G, making with the first line the angle de- 
 termined by measurement, and by means of the scale 
 and dividers the lines F G and F G can be measured. 
 We can also find the length of the line by trigonometri- 
 cal computation.* 
 
 55. The Measurement of a Base Line. For every system 
 of triangulation one line must be measured. This line is 
 called a base line. In extensive systems of triangulation, 
 where great accuracy is required, the measurement of the 
 base line is a very troublesome operation. It seems at 
 first thought extremely easy to measure a straight line, 
 
 * See Appendix, I. 5. 
 
60 ASTRONOMY. 
 
 but, in fact, there is nothing more difficult. In the first 
 place what are we to measure it with? If we use bars 
 of metal, they, as we have seen, expand when warmed 
 and contract when cooled, and consequently are not al- 
 ways of the same length. The line must be measured 
 by the yard. But the yard is a certain definite length, 
 and cannot therefore be the length of any rod whose 
 length changes with the temperature to which it is ex- 
 p3sed. A rod can be a yard long only at a particular 
 temperature. Many base lines have been measured with 
 rods and chains of iron or brass, but every precaution 
 has been used in every part of the operation to screen 
 them from changes of temperature, by covering them 
 with tents ; putting perhaps half a dozen bars at a time 
 in a row, with several thicknesses of tent over them, so 
 as to protect them effectually from the sun and wind. 
 Having taken this precaution to shield them from the 
 effects of changes of temperature, thermometers are placed 
 by the side of the bars, and their temperature thus as- 
 certained. Knowing, then, their length at a given tem- 
 perature, and how much they expand for a given rise of 
 temperature or contract for a given fall of temperature, 
 the length represented by the bars when used can be 
 ascertained. Figure 28 represents another contrivance 
 
 which has been 
 used with great 
 
 JE? success. It con- 
 
 """VJA""" '"' KZB^F 
 
 ^m^^^^^^^^^m^^f^ sists of a combina- 
 tion of two bars ; 
 
 one, A B C, of brass, and the other, D E F, of iron. 
 These bars are connected at the middle, E B, and they 
 have projecting tongues, ADG and C F H. These 
 tongues turn easily on pivots at A, D, C, and F. The 
 length G D, is just | of G A, and H F just % of If C. 
 Now brass expands more than iron for the same rise of 
 
ASTRONOMY. 6 1 
 
 temperature. Suppose the rod A B C to remain of the 
 same length, and the rod D E F to expand ; the points 
 G and H would evidently be carried farther apart. But 
 suppose the rod D E F to remain of the same length, 
 and the rod A B C to expand ; the points G and .//"will 
 come nearer together. Suppose now that both rods ex- 
 pand together, but that the rod ABC expands just as 
 much more rapidly than the other rod as the distance 
 A G is greater than the distance D G ; the points .//and 
 G will evidently remain at the same distance from each 
 other. Now we know that brass expands if times as 
 fast as iron, and the distance A G is i times the dis- 
 tance D G. 
 
 A number of combined bars like these are placed one 
 after another, with a small interval between each two ; 
 and then the question is, how is the interval between 
 them to be measured ? It will not do to make one bar 
 touch the other, because expansions may be going on in 
 one of the series of bars, and it would jostle the others 
 throughout the whole extent. This small distance is 
 sometimes measured by means of microscopes mounted 
 on the same principle as the bars, so that the measure 
 which they give is not affected by temperature. In some 
 cases, glass wedges have been dropped between the suc- 
 cessive bars, in others sliding tongues have been used. 
 The result of all this has been, that a distance of eight 
 or ten miles has been measured to within a very small 
 fraction of an inch. 
 
 We have been thus minute in our account of the meas- 
 urement of a base line, to give an illustration of the ex- 
 treme care that must be taken in measuring lines and 
 angles which are to be used in the computation of 
 celestial distances. And we see the necessity of this 
 great carefulness when we remember that this base line, 
 which does not exceed eight or ten miles, is to be used, 
 6 
 
62 
 
 ASTRONOMY. 
 
 Fig. 29. 
 
 first, in the computation of the radius of the earth, which 
 is some 4,000 miles long ; then in computing the distance 
 of the sun, which is some 24,000 times the length of the 
 earth's radius ; then also in computing the distance of 
 Neptune from the sun, which is some thirty times the 
 distance of the earth from the sun ; and finally, as we 
 shall see, in computing the distance of the fixed stars, 
 which are thousands of times more remote than Neptune 
 from the sun. It is like measur- 
 ing a length of a hundredth of an 
 inch on the wall in hair-breadths as 
 a basis for computing the dimen- 
 sions of a house in hair-breadths. 
 A slight mistake in the measure 
 of the first length would lead to 
 an enormous error in the final 
 result. 
 
 56. But the point B (Figure 25) 
 is too distant to be seen from the 
 extremities of our base line, one 
 end of which may be at A. We 
 must, therefore, approach it step 
 by step with our triangles. 
 
 The method by which this is 
 accomplished, and the distance 
 between the points finally deter- 
 mined, is illustrated by Figure 29. 
 Suppose we are to find the dis- 
 tance between the points A and 
 B. First measure the base line 
 AC. The angle which this line 
 makes with a north and south line 
 is then ascertained. To do this, a 
 transit instrument is set up at A, 
 and its telescope so adjusted that 
 
ASTRONOMY. 63 
 
 it will point exactly to the north celestial pole. It is 
 then turned down Jo the horizon, and a mark is set up 
 at a distance in the direction of the north as thus found. 
 A theodolite is then set up at A. This instrument consists 
 of a telescope attached to a graduated circle which is ar- 
 ranged so as to turn horizontally. When, therefore, the 
 telescope of the instrument is turned horizontally, the 
 graduate:! circle carried around with it shows how many 
 degrees it has been turned. The telescope is first di- 
 rected to the mark, and then turned around till it points 
 to the station C. The number of degrees that the tele- 
 scope has been turned, as indicated by the graduated 
 circle, shows the angle which the line A C makes with 
 the north and south line. A third station, D, is then 
 chosen, which can be distinctly seen from both A and C, 
 and a signal erected at this point. The telescope of the 
 theodolite is again turned to C and then to D, and the 
 number of degrees that the telescope is turned in passing 
 from C to D gives the angle CAD. The line A D is 
 then drawn so as to make this angle with A C. The the- 
 odolite is next carried to C and pointed to A, and then 
 turned till it points to D. The number of degrees it has 
 to be turned gives the angle D C A. The line D C is 
 then drawn, making this angle with C A. 
 
 A fourth station, E, is now selected, which can be 
 readily seen at C and D. Then E C D and E D C are 
 measured by means of the theodolite, as before, and the 
 lines C E and D E are drawn, making die angles at C 
 and D equal to those measured. Thus we go on step 
 by step, measuring the angles and drawing the triangles, 
 till we reach the point B. The distance B A can then 
 be measured by means of the scale and dividers, and 
 compared with the length of the base line A C. The 
 distance of the stations D, E, F, etc. from the preceding 
 station, and the distance of B from A, can be more accu- 
 
64 ASTRONOMY. 
 
 rately determined by trigonometrical computation. In 
 the first triangle, the side C A and 1^ie angles at C and 
 A are known by measurement ; hence the other parts of 
 the triangle can be readily computed. Then, in the sec- 
 ond triangle, the side CD and the angles at C and D 
 become known, and the other part of this triangle can 
 be computed ; and so on to the end. Then, by drawing 
 the dotted lines, a series of right-angled triangles is 
 formed, in each of which the hypothenuse is known, and 
 one of the acute angles can be readily found. For in 
 the right-angled triangle A N D the angle N A D =. 
 D A C N A C. In the right-angled triangle F M D, 
 
 This may be shown by drawing a line through D par- 
 allel to N S. The sum of all the angles at the point D 
 will then be 180. But the angle formed by FD with 
 the line supposed to be drawn will be equal to MFD, 
 and the angle formed by A D with the same line will be 
 equal to D A N. In a similar manner the angles F H L 
 and H B K can be found. Hence the parts of these 
 right-angled triangles can be computed, and the lengths 
 of the sides AN, M F, L K, and KB can be found. 
 But the sum of these sides is evidently equal to^the 
 length of the line A B. 
 
 57. In this way it has been ascertained, that, if the 
 two plumb-lines at A and B (Figure 25) are inclined to 
 each other at an angle of 12, the length of the arc be- 
 tween them in miles is about 830 miles. From this we 
 conclude that we must pass over an arc 69^ miles long 
 in order to find the distance of two places whose verti- 
 cals are inclined one degree. 
 
 69^ X 360, then, gives the circumference of the earth, 
 and this divided by 3.1416 gives the diameter of the earth, 
 one half of which is the radius, which is thus found to 
 be about 4,000 miles long. 
 
ASTRONOMY. 65 
 
 58. The Earth not a perfect Sphere. By measuring arcs 
 of meridian in different parts of the earth, we find that 
 the arcs included between two places whose verticals are 
 inclined to each other one degree are not always of the 
 same length in miles. It has been found that towards 
 the poles two places must be farther apart than near the 
 equator, to have their verticals inclined to each other one 
 degree. The earth, then, cannot be an exact sphere. 
 Since the arc between two places whose verticals are in- 
 clined one degree is longer near the poles than at the 
 equator, the curvature of the earth at the poles must be 
 that of a larger circle than the curvature at the equator, 
 and since the larger the circle the less rapidly does it 
 curve, we see that the earth is slightly flattened at the 
 poles. The polar diameter of the earth has been found 
 to bear to the equatorial the ratio of 299 to 300. 
 
 59. Knowing the exact size and form of the earth, 
 the distance between the two stations A and B (Figure 
 22) in a straight line can be computed. 
 
 The transits of Venus, by which the sun's distance 
 from the earth can be determined, occur in pairs at in- 
 tervals of eight years separated by more than one hun- 
 dred years. The last pair occurred in 1761 and 1769, 
 and the next will be in 1874 and 1882. 
 
 It is now supposed by many that there was an error 
 in one of the observations of the last transit of Venus, 
 so that the distance of the sun as computed from these 
 observations is some 3,000,000 of miles 'greater than it 
 really is. Hence the next transits of Venus are looked 
 forward to with great interest. 
 
 60. The Mean Distances of the Planets. The follow- 
 ing is a table of the mean distances of the most impor- 
 tant planets from the sun, as computed from the last 
 transit of Venus : 
 
 6* 
 
66 ASTRONOMY. 
 
 Mercury 37,000,000 miles 
 
 Venus 69,000,000 " 
 
 Earth 95,000,000 " 
 
 Mars 145,000,000 " 
 
 Jupiter 436,000,000 " 
 
 Saturn 909,000,000 " 
 
 Uranus 1,828,000,000 " 
 
 Neptune 2,862,000,000 " 
 
 SUMMARY. 
 
 The distance of a planet from the sun compared with 
 the earth's distance from the same is called its relative dis- 
 tance from the sun. 
 
 To find the relative distance of an inferior planet from 
 the sun, its greatest elongation must be measured ; and the 
 right-angled triangle which the earth, the planet, and the 
 sun then form must be computed. (48.) 
 
 To find the relative distance of a superior planet from 
 the sun, the retrogression of the planet during one day, 
 when it is in opposition, must be measured ; and the tri- 
 angle which the earth, the planet, and the sun then form 
 must be computed. (49.) 
 
 The distance of the earth from the sun is found by 
 means of the transits of Venus. 
 
 To find this distance, we must determine the angle sub- 
 tended by the diameter of the sun, and by two chords 
 which Venus, as seen by two observers, one north and the 
 other south of the equator, describes across the sun's disc ; 
 the relative distance of Venus and of the earth from the 
 sun ; and the size and shape of the earth. 
 
 The angle subtended by the diameter of the sun is 
 ascertained by direct measurement. 
 
 The angle subtended by the chords described by Venus 
 
 is ascertained by observing the transit of Venus. (51.) 
 
 i 
 
ASTRONOMY. 67 
 
 The size and shape- of the earth are found by meas- 
 uring known arcs of meridians on different parts of the 
 earth. (53-56.) 
 
 The actual distance of any planet from the sun can be 
 found by multiplying its relative distance by the distance 
 of the earth from the sun. 
 
 HOW TO FIND THE DISTANCE OF THE MOON. 
 
 6 1. We have already ascertained the actual distance 
 of the earth, as well as of all the other planets, from 
 the sun, but as yet we do not know the distance of the 
 moon from the earth. We have also seen that all the 
 planets, though they appear to revolve about the earth, 
 really revolve about the sun, but the moon's motion 
 among the stars can be explained only on the supposition 
 that she revolves about the earth. 
 
 The ancients ascertained the distance of the moon with 
 considerable accuracy by the observation of her eclipses. 
 They knew that these phenomena were caused by the 
 passage of the moon through the earth's shadow. Now 
 the earth's shadow is not very much narrower at the dis- 
 tance of the moon than at the surface of the earth, and 
 the average length of time the moon takes to pass through 
 that shadow is about four hours. The moon passes 
 over a part of her orbit equal to the diameter of the 
 earth in about four hours, and consequently she passes 
 over a length of her orbit equal to six diameters of the 
 earth in a day, and, as she completes a revolution in 
 about thirty days, her whole orbit must be about one 
 hundred and eighty times as long as the diameter of the 
 earth. Consequently the diameter of the moon's orbit 
 is about sixty times the diameter of the earth, and the 
 distance of the moon about thirty times the diameter of 
 the earth. 
 
68 
 
 ASTRONOMY. 
 
 62. Parallax. The distance of the moon can now 
 be measured by means si parallax. 
 
 The following illustration shows that this is really the 
 method by which we commonly estimate distance. If 
 you place your head in a corner of a room or against a 
 high-backed chair, and close one eye, and allow another 
 person to put a lighted candle on a table before you, 
 and if you then try to snuff the candle, with one eye still 
 shut, you will find that you cannot do it : you will prob- 
 ably fail nine times out of ten. But if you open the 
 other eye, the charm is broken ; or if, without opening 
 the other eye, you move your head sensibly, you are 
 enabled to judge of the distance. 
 
 In Figure 30 let A and B be the two eyes, and C an 
 object which is first viewed with the eye A alone. This 
 
 Fig. 30. 
 
 eye alone has no means of judging of the distance of C. 
 All that it can tell is that this object is in the direction 
 of A C, but there is nothing by which it can judge of 
 its distance in that line. Suppose now the other eye, , 
 is opened and turned to C, then there is a circumstance 
 introduced which is affected by the distance, namely, the 
 difference of direction of the two eyes. While the object 
 is at C, the two eyes are turned inward but very little to 
 see it ; but if the object is brought quite close, .as at Z>, 
 
ASTRONOMY. 69 
 
 then the two eyes have to be turned inward considerably 
 to see it ; and from this effort of turning the eyes we 
 acquire some notion of the distance. We cannot lay 
 down any accurate rule for the estimation of the distance ; 
 but we see clearly enough in this explanation, and we 
 feel distinctly enough when we make the experiment, that 
 the estimation of distance does depend upon this differ- 
 ence of direction of the eyes. Now, this difference of 
 direction of the two eyes is a veritable parallax ; and this 
 is what we mean by parallax, that it is the difference of 
 direction of an object as seen in two different places. 
 The two places in the above experiment are the two 
 eyes in the head. The distance of the moon is found by 
 precisely the same method. The two eyes in the head 
 will be two telescopes, one in the observatory at Green- 
 wich, and the other in the observatory at the Cape of 
 Good Hope ; and the difference of direction of the eyes 
 becomes the difference of direction of these two tele- 
 scopes when ppinted at the moon. When this difference 
 of direction becomes known the distance of the moon is 
 easily computed. 
 
 63. How to find the Difference of the Direction of the 
 two Telescopes when turned to the Moon. The difference 
 of direction of the two telescopes when pointed at the 
 moon is found by means of the mural circle. By means 
 of this the zenith distances of the north celestial pole 
 and of the moon are observed at Greenwich, and the sum 
 of these distances gives the north polar 'distance of the 
 moon as seen at Greenwich. 
 
 By means of this same instrument the zenith distances 
 of the south celestial pole and of the moon are also 
 observed at the Cape of Good Hope at the same time 
 that the observations were made at Greenwich. The 
 sum of these zenith distances gives the south polar dis- 
 tance of the moon. It is found, for instance, that the 
 
ASTRONOMY. 
 
 north polar distance of the moon as obtained at Green- 
 wich is 1 08, and that the south polar distance as ob- 
 served at the Cape of Good Hope is 73^. The sum of 
 these two polar distances is then i8i|. 
 
 Suppose now that G and C in Figure 31 represent the 
 position of the observatories at Greenwich and at the 
 
 Fig. 31 
 
 Cape of Good Hope, and that G P and C P 1 represent 
 the direction of the north and south poles of the heavens 
 respectively from each of these stations. The line G P 
 has of course a direction just opposite to that of the line 
 C P'. The line G M represents the direction of the tele- 
 scope at Greenwich when turned toward the moon, and 
 the line C M represents the direction of the telescope at 
 the Cape of Good Hope when turned toward the moon. 
 Suppose now that the telescope at each observatory be 
 turned toward the same fixed star. G S will be the di- 
 rection of the telescope at Greenwich, and C S' the di- 
 rection of the telescope at the Cape of Good Hope. 
 Now when the north polar distance of any fixed star is 
 measured at Greenwich, and the south polar distance of 
 the same star is measured at the Cape of Good Hope, 
 
ASTRONOMY. 7 1 
 
 the sum of these polar distances always equals 180; that 
 is, the angle S G P + S C P' = 180. Hence S G 
 and S C must be parallel. For S G P + S G P' = 
 180. Therefore S' CP' SGP' ; that is, S G and S* C 
 are parallel. 
 
 We have found that M G P + M C P' = i8ij. The 
 two lines M G and J/ C must then be inclined to each 
 other at an angle of ij, for if these two lines were par- 
 allel the two angles M G P + M C P' would be equal 
 to 1 80. 
 
 We have now found the difference of direction of the 
 two telescopes when turned toward the moon. Now 
 since the exact size and form of the earth are known, 
 the length of the line G C and the angle M G C can be 
 computed, and the distance M G can then be found by 
 construction or by computation. 
 
 64. The Moon's Parallax. This gives the distance of 
 the moon from each of the observatories G and C. It 
 is convenient, however, to make all our calculations of 
 the moon's place with reference to the centre of the earth. 
 By reference to the above figure it will be seen that the 
 direction of the moon is not the same when seen from 
 the centre of the earth E as when seen from its surface 
 at G or C. The difference of the directions of the moon 
 as seen at Greenwich and as seen from the centre of the 
 earth is called the moon's parallax at Greenwich. Thus 
 the angle G ME is the moon's parallax at Greenwich, 
 and the angle C M E is her parallax at the Cape of 
 Good Hope. 
 
 The sum of the moon's parallaxes at Greenwich and 
 at the Cape of Good Hope is evidently equal to the 
 angle G M C. The method by which the moon's dis- 
 tance is actually found is as follows. From a knowledge 
 of the earth's dimensions, the length of G is known 
 with considerable accuracy. And though the plumb-line 
 
72 ASTRONOMY. 
 
 at G is not directed actually to the earth's centre, E, but 
 in a slightly different direction, H' G J?, yet from know- 
 ing the form of the earth, we can calculate accurately 
 how much it is inclined to the line H , which is di- 
 rected to the earth's centre. Then we know the angle 
 H' G H y and we have observed the angle H' G M with 
 the mural circle, and their difference is the angle H G M, 
 which is therefore known. The difference between 180 
 and the angle H G M gives the angle E G M. Then 
 we assume, for trial, a value of the distance E M. With 
 the length E M, the length G E, and the angle E G M, 
 it is easy to compute the angle G M E* The same 
 process is used to calculate the angle C M E. We then 
 add these two calculated angles together, and rind whether 
 their sum is equal to the angle G M C, which we have 
 found from observation. If their sum is not equal to 
 this angle found from observation, we must try another 
 assumption for the length of E M, and go through the 
 calculation again ; and so on till the numbers agree. 
 
 We supposed at first that the observations were made 
 at the same instant at Greenwich and at the Cape of 
 Good Hope. This is not strictly correct; but the dif- 
 ference of time is known, and the moon's motion is well 
 enough known to enable us to compute how much the 
 angle P' C M changes in that time ; and thus we know 
 what would have been the direction of the line C M, if 
 the observations had been made at exactly the same in- 
 stant as the observation at G. 
 
 When now we wish to know the position of the moon 
 at any observation as seen from the centre of the earth, 
 its parallax must be computed and applied. By correct- 
 ing the observed place of the moon for parallax, it has 
 been found that the plane of the moon's orbit passes 
 through the centre of the earth in the same way as the 
 
 * See Appendix, I. 6. 
 
ASTRONOMY. 73 
 
 orbits of the earth and of the other planets pass through 
 the centre of the sun. 
 
 65. Another Method of finding the Difference in the Di- 
 rection of the two Telescopes pointed at the Moon. The 
 method given above for ascertaining the difference of the 
 direction of the two telescopes when turned towards the 
 moon, is liable to only one error. Since the inclination 
 of these lines is determined by observations made with 
 the mural circle, it is necessary that every observation 
 should be corrected for refraction, which, as we have 
 seen, causes objects in every part of the heavens to ap- 
 pear higher than they really are. Now this correction 
 is very troublesome, since the amount of refraction 
 changes with the altitude of the object and with the dif- 
 ferent conditions of the atmosphere. Prof. Airy, the As- 
 tronomer Royal of England, says that refraction is the 
 very abomination of astronomers. It changes with the 
 condition of the atmosphere in so irregular a manner 
 that every correction made for it is liable to a slight 
 error. 
 
 There is another way of ascertaining the difference of 
 direction of the lines G M and C M, which is liable to 
 error from refraction to a much less extent. 
 
 We have already seen that, if the telescopes at the 
 two observatories are pointed to the same fixed star, their 
 direction will be precisely the same. If, then, a fixed 
 star, S, be chosen, which is quite near the moon, and 
 which comes upon the meridian at nearly the same time, 
 and the telescope of the mural circle at each station be 
 first directed to this star, and then turned to the moon, 
 we shall get the inclination of each of the directions 
 G M and C M to the direction G S. The difference of 
 their inclinations to this direction will evidently be their 
 inclination to each other. Suppose, for instance, that at 
 G the moon is seen two degrees below the star, and at 
 7 
 
74 ASTRONOMY. 
 
 C half a degree below it; the two lines G M and C J/ 
 will evidently be inclined to each other ij. As the 
 moon and star must be observed at- very nearly the same 
 altitude, and under almost precisely the same conditions 
 of the atmosphere, refraction can make no appreciable 
 difference in their angular distance from each other. 
 
 SUMMARY. 
 
 The ancients ascertained the distance of the moon 
 with considerable accuracy by the observation of her 
 eclipses. (61.) 
 
 The distance of the moon is now found by means of 
 parallax. (62.) 
 
 Parallax is the difference of direction of any body as 
 seen from two different places. 
 
 We really determine the distance of ordinary bodies 
 by means of parallax. 
 
 When a telescope at Greenwich and another at the 
 Cape of Good Hope are pointed at the moon, their dif- 
 ference of direction can be ascertained, either by meas- 
 uring the polar distance of the moon at both observa- 
 tories (63), or by measuring at both observatories the 
 angular distance of the moon from a fixed star near her. 
 
 (65.) 
 
 The parallax of the moon is the difference of her direc- 
 tion as seen from the centre and from the surface of 
 the earth. 
 
 When the difference of direction of two telescopes 
 which have been pointed at the moon from the observa- 
 tories at Greenwich and the Cape of Good Hope has 
 been ascertained, the parallax of the moon is found by 
 the method of trial and error. (64.) 
 
ASTRONOMY. 75 
 
 A GENERAL SURVEY OF THE ORBITS OF 
 THE PLANETS. 
 
 66. The Inclination of the Orbits of the Planets to the Plane 
 of the Ecliptic. We have now learned that the earth 
 and all the planets revolve about the sun from west to 
 east ; that each describes a curve called an ellipse, one of 
 whose foci is occupied by the sun; and that the plane 
 of this orbit always passes through the centre of the 
 sun. Also that each planet moves at such a rate in dif- 
 ferent parts of its orbit that a line joining the planet 
 with the sun always sweeps over equal areas in equal 
 times; consequently the planets all move faster in their 
 orbits at perihelion than at aphelion. We have found, 
 also, that the different planets move at such rates that 
 the squares of their periodic times bear the same ratio as 
 the cubes of their mean distances from the sun. We 
 have learned, too, that these ellipses differ in form, some 
 being .flatter than others ; also in the direction of their 
 major axes, and in their inclination to the ecliptic. 
 
 The orbits of the larger planets are, however, but 
 slightly inclined to the ecliptic, as Figure 32 shows. E 
 
 represents the plane of the ecliptic ; y t the plane of Ju- 
 piter's orbit ; JV t Neptune's; V, Venus's ; M y Mercury's. 
 P is the plane of the orbit of Pallas, one of the minor 
 planets. 
 
 67. Nodes. As the orbits of all the planets are some- 
 
76 ASTRONOMY. 
 
 what inclined to the ecliptic, they must all intersect it. 
 The points at which they intersect the ecliptic are called 
 the nodes of their orbits. 
 
 68. Transits of Venus. The considerable inclination 
 of the orbit of Venus to the ecliptic explains why the 
 transits of Venus occur so seldom. This will be made 
 clear by Figure 33. S represents the position of the sun ; 
 
 Fig. 33- 
 
 V V V", the orbit of Venus ; and E E' E", the orbit 
 of the earth, that is, the plane of the ecliptic. Now it is 
 evident from inspection of the figure that Venus will not 
 be seen from the earth to cross the disc of the sun, unless 
 the earth be very near one of the nodes of Venus's orbit, 
 as at E' ', at the time of inferior conjunction. 
 
 HOW TO FIND THE DISTANCE OF THE 
 FIXED STARS. 
 
 69. We have already seen that two telescopes so far 
 apart as those at the observatories at Greenwich and at 
 the Cape of Good Hope do not sensibly differ in direc- 
 tion when each is turned to the same fixed star ; so that 
 we cannot estimate the distance of the stars by the method 
 employed in finding the distance of the moon. 
 
 It will be remembered that, in our first illustration of 
 parallax (62), we were enabled to estimate the distance 
 of the candle, either by turning both of the eyes upon it at 
 the same time and so becoming aware of their difference 
 of direction, or by using only one eye and moving the 
 head, and so becoming aware of the amount by which 
 
ASTRONOMY. 77 
 
 the eye must change its direction for a given movement 
 of the head, to be still turned toward the candle. The 
 first method of estimating the distance of the candle was 
 imitated in ascertaining the distance of the moon. Can 
 we ascertain the distance of the fixed stars by imitating 
 the second? In sweeping round the sun the earth, as 
 we have seen, describes an ellipse, whose mean diameter 
 is some 190,000,000 of miles. Can we, by using the tel- 
 escope of the observatory at Greenwich as a single eye, 
 estimate the distance of a fixed star by observing how 
 much the direction of the telescope must be changed in 
 order always to point to that star when on the meridian 
 throughout an entire revolution of the earth ? Suppose 
 that the north polar distance of a fixed star be measured 
 by means of the mural circle at Greenwich, and six months 
 from this time, when that observatory has moved away 
 from its former position 190,000,000 miles, its north polar 
 distance be measured again. If the polar distances of 
 the star thus measured differ, their difference must be 
 the diiference of direction of the telescope at the two 
 observations. 
 
 70. Does the Earth's Axis always point in the same Di- 
 rection? But since these observations are made at long 
 intervals, it becomes necessary to know whether the pole 
 of the heavens from which the angular distance of the 
 star is measured remains unchanged during the year. It 
 must be borne in mind that the pole of the heavens is 
 that part of the heavens to which the axis of the earth 
 points. Now we must ascertain whether the axis of the 
 earth always points to exactly the same part of the heav- 
 ens, or not ; that is, whether the axis of the earth always 
 points in exactly the same direction. That the axis of 
 the earth always points in very nearly the same direction 
 is evident from the fact that the pole of the heavens does 
 not sensibly change its position from year to year. But 
 
78 ASTRONOMY. 
 
 we have already noticed the fact (20) that the points 
 where the equator cuts the ecliptic are slowly shifting 
 along the ecliptic to the westward at the rate of 50" an- 
 nually. It is also found by observation that the incli- 
 nation of the celestial equator to the ecliptic does not 
 change. Let us suppose that a top, with its upper sur- 
 face perfectly flat, be spinning upon a perfectly level 
 surface. After a time, the end of the handle of the top 
 will be seen to describe a small circle, and the upper 
 surface of the top will then be seen to be inclined at a 
 certain angle to the floor. Suppose now that the top 
 keep on spinning for a time, and that the inclination of 
 the upper surface of the top to the floor remain the same. 
 Conceive a plane parallel with the floor passing through 
 the point of contact of the handle with the top. This 
 plane may represent the ecliptic ; the upper surface of 
 the top may represent the plane of the earth's equator ; 
 and the points where the circumference of the upper sur- 
 face of the top cuts this plane may be considered as 
 the equinoctial points. Now as the top goes on spin- 
 ning, the direction of its inclination to the floor is con- 
 stantly shifting, though its amount remain unchanged. 
 It is evident, then, that the points where the circumfer- 
 ence of this surface cuts our imaginary ecliptic are con- 
 tinually shifting, and that they will pass entirely around 
 while the end of the top handle is describing a circle. 
 In this experiment the top handle represents the axis of 
 the earth. In Figure 34 let a b represent the ecliptic, 
 and efh represent the position of the equator at one 
 time ; then g k I must represent its position after the 
 equinoxes have shifted from h to / and from e to g. The 
 shifting of the equinoctial points, then, seems to be due 
 to a shifting of the direction of the inclination of the 
 earth's equator similar to that of the upper surface of 
 the top in the above experiment. If this is really so, 
 
ASTRONOMY. 
 
 79 
 
 the end of the axis of the earth, C f, ought to describe 
 in the mean time an arc, Pf, and eventually to describe 
 
 a complete circle like the end of the top handle. Now 
 observation reveals the fact that the pole of the heavens 
 is actually describing a circle in the heavens whose ra- 
 dius is an arc of 23^, and that it is describing this circle 
 at the rate of 50" annually. It therefore describes a 
 complete circle in about 26,000 years. The earth, then, 
 as it spins on its axis in its journey around the sun, wab- 
 bles like a spinning top, not several times a minute, but 
 once in 26,000 years. 
 
 Careful observation has also shown that the earth's 
 axis, while describing this circle in 26,000 years, has a 
 slight tremulous movement, swinging back and forth 
 through a space of 18" in nineteen years. The effect 
 of both these movements is to cause the 
 pole of the heavens to describe in 26,000 
 years such a curve as is represented in 
 'Figure 35. The effect of the first move- 
 ment of the axis is called precession ; that 
 of the second, nutation. 
 
 The polar distance of a star is not in 
 any case changed more than 21" by pre- 
 
8o ASTRONOMY. 
 
 cession and nutation. But these are quantities so large 
 that we must be perfectly acquainted with their laws and 
 magnitude when we are dealing - with changes in the 
 places of the stars not exceeding one or two seconds. 
 
 71. The Aberration of Light. In observing, then, the 
 polar distance of our fixed star at an interval of six 
 months, we must allow for precession and nutation. This 
 can, however, be done with the greatest accuracy. Is 
 there anything else that would make the star appear in a 
 different direction at the end of the six months, except 
 the change of position of the observer? On a rainy 
 day, when the drops are large and there is no wind, if 
 one goes out and stands still, he will see the drops of 
 rain falling directly downwards. If he then walks for- 
 ward, he will see the drops fall towards him ; and if he 
 walks backward, he will see them fall away from him. 
 Again, in Figure 36, let A be a gun of a battery, from 
 which a shot is fired at a ship, 
 D E, that is passing. Let A 
 B C be the course of the shot. 
 The shot enters the ship's side at 
 B, and passes out at the other 
 side at C. But in the mean time 
 the ship has moved from E to e, 
 and the part B where the shot 
 entered has been carried to b. 
 If a person on board the ship 
 could see the ball as it crossed 
 
 the ship, he would see it cross in the diagonal line b C. 
 And he would at once say that the cannon was in the 
 direction of C b. If the ship were moving in the oppo- 
 site direction, he would say that the cannon was just as 
 far the other side of its true position. 
 
 Now we see a star in the direction in which the light 
 coming from the star appears to be moving. When we 
 
 e 
 
ASTRONOMY. 8 1 
 
 examine a star with a telescope we are in the same con- 
 dition as the person who on shipboard saw the cannon 
 ball cross the ship. The telescope is carried along by 
 the earth at the rate of eighteen miles a second, hence 
 the light will appear to pass through the tube in a slightly 
 different direction from that in which it is really moving ; 
 just as the cannon ball appears to pass through the ship 
 in a different direction from that in which it is really 
 moving. As light moves with enormous velocity, it passes 
 through the tube so quickly that it is apparently changed 
 from its true direction only by a very slight angle, but it 
 is sufficient to displace the star. This apparent change 
 in the direction of light caused by the motion of the 
 earth is called aberration of light. Now as it is at once 
 seen that the earth is moving in opposite directions at 
 the beginning and the end of six months, it is clear that 
 the observations must be corrected for aberration as well 
 as for precession and nutation. This correction can, how- 
 ever, be made with great accuracy, since we can compute 
 the exact effect of this disturbance. There however re-- 
 mains the correction for refraction, which in this case is 
 more troublesome than usual, since stars which are on 
 the meridian at twelve at night are, six months from that 
 time, on the meridian during the day, and the atmospheric 
 conditions which affect refraction are widely different by 
 day and by night. 
 
 72. By this method the inclination of the directions 
 of a telescope, when turned to a bright star in the con- 
 stellation of the Centaur (Alpha Centauri) in the South- 
 ern Hemisphere, has been found to be an angle of about 
 two seconds (Airy). This inclination would make the 
 distance of this star some 100,000 times the radius of 
 the earth's orbit, which, as we know, is about 95,000,000 
 miles. 
 
 An angle of two seconds is that which a circle of T 6 <j of 
 
8 1 ASTRONOMY. 
 
 an inch in diameter would subtend at the distance of a 
 mile. Yet this is the greatest parallax that any star is 
 found to have, when seen at opposite parts of the earth's 
 orbit. The parallax of Vega, in the constellation Lyra, 
 is not more than J of a second ; and there are compar- 
 atively few of the stars whose parallax is above T V of a 
 second. But considering the uncertainty of refraction, 
 Airy, the Astronomer Royal of England, says that the 
 determination of a parallax of T 2 - of a second by the 
 above method is more than he can undertake to answer 
 for. 
 
 73. Another Method of finding the Parallax of a Fixed 
 Star. In consequence of this uncertainty another method 
 has been devised, admitting of far greater accuracy ; 
 namely, by comparing two stars whose declinations are 
 very nearly the same. This method is very similar to 
 that which is used for measuring the distance of the 
 moon. 
 
 Suppose that two stars have very nearly the same dec- 
 lination, and that from observation by the first method 
 we have reason to suppose that one of the stars is at 
 such an enormous distance that it will have no sensible 
 parallax, while from the same observation we have reason 
 to believe that the other is very much nearer. If now 
 we measure the angular distance between the two stars 
 at opposite points of the earth's orbit, the difference of 
 these angular measurements will be the parallax of the 
 nearer of the two stars. 
 
 By this method, since we compare stars which are 
 seen very nearly in the same direction, we get rid of the 
 uncertainty of refraction, and also of precession, nuta- 
 tion, and aberration ; because these produce the same 
 effect on both stars. This is the method which the cel- 
 ebrated Bessel, of Konigsberg, used for determining 
 the distance of the small star known as 61 Cygni. He 
 
^ASTRONOMY. 83 
 
 thus found the parallax of this star as seen from opposite 
 parts of the earth's orbit to be T %- of a second ; and this 
 corresponds to a distance of 660,000 times the radius of 
 the earth's orbit, or 63,000,000,000,000 miles. " Enor- 
 mous as this distance is," says Airy, "I state it as my 
 deliberate opinion, founded upon a careful examination 
 of the whole process of observation and calculation, that 
 it is ascertained with what may be called in such a prob- ' 
 lem considerable accuracy." The distance of those stars 
 whose parallax is estimated at T V of a second is about 
 2,000,000 times the distance of the earth from the sun. 
 
 74. The Immensity of these Distances. We have no 
 appreciation of distances so vast. The moon has been 
 found to be distant from the earth about 240,000 miles. 
 If a locomotive were travelling at the rate of 1000 miles 
 a day it would take it eight months to reach the moon ; 
 travelling at the same rate it would reach the sun in 
 260 years, and the star 61 Cygni in 171,600,000 years, 
 a period of which we can form no conception whatever. 
 
 Light, it will be remembered, travels at the rate of 
 about *i 90,000 miles a second. It would accordingly 
 take light about yj years to reach us from 61 Cygni. If 
 this star were suddenly annihilated, it would be over 
 seven years before we should become aware of it. Yet 
 this is one of the nearer fixed stars. It has been esti- 
 mated from tolerably accurate measurements that it 
 would take light fourteen years to reach Us from Sirius, 
 twenty years from Vega, and twenty-five years from Arc- 
 turus ; and Sir John Herschel has estimated that light 
 requires at least 2000 years to reach us from the smaller 
 stars with which the Milky Way is crowded. 
 
 75. Nebula. Nor is this all. Near the belt of An- 
 dromeda there may be seen with the naked eye a faint 
 glimmer of light oh a very clear night. Figure 37 shows 
 this object as it appeared in Sir John Herschel's tele- 
 
scope, and Figure 38 as it appears in the powerful re- 
 fractor of the Observatory at Cambridge, Mass. Such 
 an object is called a nebula. Nebulae are really very nu- 
 
 Fig. 38- 
 
ASTRONOMY. 
 
 merous, though very few of them are bright enough to 
 be seen with the unaided eye. 
 
 In Figure 39 is represented the celebrated nebula in 
 the constellation of Vulpecula, as it appeared to Sir 
 
 John Herschel. Figure 40 shows the same nebula as it 
 appears in the great reflecting telescope of Lord Rosse. 
 8 
 
86 
 
 ASTRONOMY. 
 
 ITig. 41. 
 
 Figure 41 represents the Crab nebula in Taurus, as de- 
 lineated by Lord Rosse ; and Figure 42, the great nebula 
 of Orion, as figured by Professor G. P. Bond of the Cam- 
 bridge Observatory. Another celebrated nebula, known 
 as the Ring nebula in Cygnus, is shown in Figure 43. 
 
 About five thousand nebulae have been observed. It is 
 seen from the above figures that they differ greatly in form. 
 It will be noticed in the case of the Dumb-bell nebula 
 (Figure 39), and also in the Crab nebula, that these neb- 
 ulae often have the appearance of clusters of minute stars 
 when viewed with very powerful telescopes. This has led 
 astronomers generally to believe that many of the neb- 
 ulae are vast systems of stars like our own, seen at im- 
 mense distances. Figure 44 is a representation of what 
 Sir John Herschel conceived would be the appearance 
 
ASTRONOMY. 
 
 Fi- 
 
 Fig. 43- 
 
 cf our system of stars including the Milky Way, when 
 seen at the distance of one of the nebulae. According to 
 this theory, our system of stars, which is to us so great 
 that we can have no appreciation of its vast dimensions, 
 is really but one of countless systems which are scattered 
 throughout space at such distances, that, when viewed 
 from one another with the most 
 powerful telescopes, they appear 
 as small faintly luminous spots. 
 We now begin to see that the 
 supposition which we made a 
 long time ago (Part First, Sec- 
 tion 4) of beings small enough 
 to dwell on a molecule of a 
 stone as we dwell upon the 
 earth, is after all not so very 
 
unreasonable. For as we gain some faint conception of 
 the dimensions of the universe as a whole, we feel that we 
 are such minute beings, dwelling, not upon a molecule, 
 but upon one of the smallest atoms of which a single mole- 
 cule of the universe is made up. But the greatest wonder 
 of all is that we, after measuring but a small fraction of the 
 distance around our atom, and making a few simple obser- 
 vations of the position of the heavenly bodies, can then, 
 by simple geometric and trigonometric computation, meas- 
 ure the dimensions of the universe. 
 
 76. The Nebulce are not all Systems of Stars. It is not 
 at all clear as yet that the nebulae are all systems of stars. 
 While it seems quite certain that some of them are such 
 systems at immense distances, there are strong reasons 
 for believing that others are but thin clouds of luminous 
 gases which may be much nearer the earth than the 
 nearest fixed star. 
 
 SUMMARY. 
 
 A telescope at the Cape of Good Hope, when pointed 
 at a fixed star, does not cliifer appreciably in direction 
 from a telescope at Greenwich pointed at the same star. 
 
ASTRONOMY. 89 
 
 If a telescope is turned to the same fixed star at op- 
 posite points of the earth's orbit, the difference of its 
 direction, if appreciable, can be found by measuring the 
 star's polar distance. (69.) 
 
 The earth's axis has a slight wabbling motion, which 
 causes the celestial pole to describe a circle with a ra- 
 dius of 23! in about 26,000 years. 
 
 This movement of the pole is called precession. 
 
 In addition to its regular wabble, the earth's axis has 
 a tremulous motion. The effect of this motion is called 
 nutation. 
 
 In an exact measurement of the polar distances of a 
 star, a correction must be made for the effect of preces- 
 sion and nutation. (70.) 
 
 Aberration of light is the apparent change in the di- 
 rection of light caused by the motion of the earth in its 
 orbit. The observation of a star's polar distance must 
 also be corrected for aberration. (71.) 
 
 The parallax of a fixed star may often be best deter- 
 mined by measuring, at opposite points of the earth's 
 orbit, its angular distance from another star near it. (73.) 
 
 It takes light about seven years to come to us from the 
 nearest fixed stars of our system, and probably several 
 thousand to come from the most remote. (74.) 
 
 Many of the nebulcz are supposed to be outlying sys- 
 tems of stars, so distant that they appear no larger than 
 a man's fist, yet so large that it takes light several thou- 
 sand years to cross them. (75.) 
 
 SYSTEMS OF SATELLITES AND SUNS. 
 
 77. Satellites. We have already seen that the earth 
 in its revolution about the sun is attended by a moon, 
 which revolves about it as a centre. Such an attendant 
 
 is called a satellite. 
 
 8* 
 
90 ASTRONOMY. 
 
 The telescope shows that Jupiter is accompanied by a 
 system of four satellites revolving about him as a centre, 
 and that Saturn is accompanied by a system of eight sat- 
 ellites, Uranus by a system of four (perhaps six), and 
 Neptune by one satellite. 
 
 In our solar system, then, we have satellites revolving 
 about planets, and these planets with their systems of 
 satellites revolving about the sun. Is there now any 
 evidence that the sun, with this complex system of plan- 
 ets and satellites, revolves about some other sun? 
 
 78. The Motio?i of our Solar System through Space. 
 We have heretofore spoken of the stars as fixed. But 
 upon comparing the places of stars as we observe them 
 in different years, and applying the corrections for pre- 
 cession, nutation, and aberration, so as to reduce every 
 observation of every star to what it ought to exhibit on 
 the first day in the year, agreeably to the common prac- 
 tice of astronomers, we find that the vast majority of the 
 stars which have been well observed seem to have a mo- 
 tion of their own. This motion is known as the proper 
 motion of the stars. In all good catalogues of stars, the 
 direction in which the stars appear to be moving, and 
 the amount of their motion in a year, are given. This 
 proper motion has been discovered only after many years' 
 observations ; it is in every case a small quantity ; yet 
 in most instances this quantity has been correctly as- 
 certained. The proper motions of Sirius and Arcturus 
 are pretty large ; but the largest observed are those of 
 two small stars known to astronomers as 61 Cygtii and 
 Groombridge 1830. The motion of the former is about 
 five seconds a year, and of the latter nearly seven seconds. 
 The proper motions of many of the stars are very irregular 
 in direction and magnitude, but with regard to others there 
 is a certain approach to regularity. 
 
 If you are walking through a forest, and keep your at- 
 
ASTRONOMY. 91 
 
 tention on the objects directly in front of you, they do not 
 appear to change their place ; but i-f you look at the ob- 
 jects to the right or to the left, they appear to be spreading 
 away to the right or to the left. Even if you did not know 
 that you were moving yourself, yet by seeing these ob- 
 jects spreading away you could infer with tolerable cer- 
 tainty that you were moving in a certain direction. Now 
 if it should appear that, taking the stars generally, we can 
 fix on any direction and see that the stars in that direc- 
 tion do not appear to be moving, but that the stars right 
 and left appear to be moving away from that point, then 
 there is good reason to infer that we are travelling toward 
 that point. This speculation was first started by Sir 
 William Herschel. He found a point in the heavens, 
 in the constellation Hercules, such that the great ma- 
 jority of the stars about the point have no sensible 
 proper motion, while the stars to the right and left of it 
 have apparently a motion to the right and left respec- 
 tively. He inferred from this that the solar system is 
 travelling in a body towards this point. Every astrono- 
 mer who has examined this subject carefully has come to 
 a conclusion very nearly the same as that reached by Sir 
 William Herschel ; namely, that the whole solar system 
 is moving toward that point in the constellation Her- 
 cules. 
 
 It is probable, then, that our sun, with his complex 
 system of planets and satellites, is really revolving about 
 some other sun, whose position is not yet ascertained. 
 
 79. Double Stars. There is in the vicinity of Vega, 
 the brightest star of the constellation Lyra, a small star 
 called Epsilon Lyra, which appears elongated to some 
 persons of very keen eyesight, and this appearance sug- 
 gests that it may really be composed of two luminous 
 points. It is only necessary to examine it with an opera- 
 glass to see that it really consists of two stars, separated 
 
9^ ASTRONOMY. 
 
 by an interval equal to about a ninth part of the appar- 
 ent diameter of the moon. 
 
 Here, then, we have an example of an easily divided 
 double star, which a keen eye or an opera-glass of small 
 magnifying power is sufficient to separate into its com- 
 ponents. If now we examine each of these components 
 with an instrument of considerable optical power, we find 
 that each consists of two stars so near together that the 
 intervals separating them are not more than the seventieth 
 part of the total distance of the couples themselves : so 
 that we have here a double-double star, or a quadruple star. 
 A star which appears single to the naked eye becomes 
 quadruple when examined with a powerful telescope. 
 
 A century ago only about twenty double stars were 
 known ; now, however, we have catalogues of more than 
 six thousand. 
 
 80. This Union of two Stars is not in all cases Accidental. 
 The first impression is that this proximity of two or 
 more stars is purely accidental, being due to an effect 
 of perspective ; the stars themselves, though differing 
 widely in their distance from us, lying in the same line 
 of sight. 
 
 When, however, these double stars are carefully scru- 
 tinized, it is found that in some cases their components 
 have the same proper motion, while in other cases they 
 do not. Again, those whose components have the same 
 proper motion are often found to revolve about each 
 other in periods of greater or less length, while nothing 
 of the kind is observed in the other class. Hence 
 double stars have come to be classified as optical and 
 physical pairs. Those whose components do not have 
 the same proper motion, and do not revolve about one 
 another, are regarded as optical pairs, or optically double 
 stars. Their apparent proximity is regarded as purely 
 accidental, owing to the fact that, though they are at 
 
ASTRONOMY. 93 
 
 very different distances from us, they happen to be in 
 very nearly the same direction. 
 
 Those whose components have the same proper mo- 
 tion, or have been observed to revolve about one another, 
 are supposed to be about the same distance from the 
 earth and to be physically connected, so as to form sys- 
 tems like that of the sun and the planets. These are 
 called physical pairs, or physically double stars. 
 
 8 1. Theta Orionis. There is a remarkable system of 
 stars in the constellation of Orion, near the centre of the 
 great nebula already mentioned. The unaided sight dis- 
 tinguishes this system only as a luminous point. With 
 the help of a good telescope, however, this point is di- 
 vided into four stars, which are seen in the form of a tra- 
 pezium. When viewed with a telescope of five or six inch 
 aperture, two of the stars of the trapezium are seen to 
 be accompanied by two other very small stars, forming 
 altogether a group of six stars, as shown in Figure 45. 
 
 This sextuple star, known 
 as Theta Orionis, or more _____ 
 commonly as the trape- 
 zium of Orion, probably 
 constitutes a real system, 
 since the five smaller stars 
 have the same proper mo- 
 tion as the principal one. 
 Mr. Lassell has discovered 
 a seventh star in this re- 
 markable system, so that Theta Orionis is a septuple star. 
 
 82. Xi Ursa Majoris. In the constellation of the 
 Great Bear, or Ursa Major, there is a star, designated in 
 the catalogues by the Greek letter , or Xi, which has 
 been known as a double star since 1782. One of the 
 components of this system is of the fourth, the other of 
 the fifth, magnitude. The movement of revolution of the 
 
94 ASTRONOMY. 
 
 second around the first having been detected, a French 
 astronomer, Savary, determined by .calculation the ele- 
 ments of the orbit. The period of revolution is sixty-one 
 years. Since the discovery of the system, then, one rev- 
 olution has been completed, and more than a third of 
 another. 
 
 The elliptical or oval form of the orbit of this binary 
 system is very decided. It is much more elongated than 
 that of any of the planets of the solar system. But 
 among the double stars there are some whose orbits are 
 even more elongated. Such is that of Alpha Centauri, 
 whose period of revolution exceeds seventy-eight years. 
 The orbits of all the binary stars, so far as known, are 
 ellipses, like those of the planets. 
 
 83. Other Binary Stars and their Periods. The fol- 
 lowing are a few of the double stars whose periods have 
 been determined : 
 
 Zeta Herculis 36 years 
 
 Zeta Cancri 59 " 
 
 Mu Coronae Borealis 66 " 
 
 70 Ophiuchi 93 " 
 
 Gamma Virginis 150 " 
 
 6 1 Cygni 450 " 
 
 There is, as seen by this table, great variety in the pe- 
 riods of double stars. But there are others whose periods 
 probably differ even more widely. In Berenice's Hair, 
 and in the Lion, there are two pairs, the first of which 
 seems to have a period of twelve years, while the second 
 seems to have a period of twelve centuries. 
 
 84. The Dimensions of the Orbits of Binary Stars. 
 When we know the distance of the binary stars, we can 
 calculate, not only the form of their orbits and their pe- 
 riods of revolution, but also the dimensions of their orbits. 
 It has been calculated that the mean distance between 
 
ASTRONOMY. 95 
 
 
 
 the components of Alpha Centauri is not less than 
 i 319,000,000 miles. The mean distance of the compan- 
 ion of 6 1 Cygni is about forty-five times the length of 
 the radius of the earth's orbit. 
 
 Of the six thousand double stars six hundred and fifty 
 have been demonstrated to be physically connected systems. 
 
 85. The Sun as a Fixed Star. If now we imagine 
 the sun to be plunged into space to the distance of the 
 nearest fixed star, and calculate, according to the laws 
 of optics, what will be the diminution of its light, we find 
 that it would become of the brightness of a star of the 
 second magnitude, that is, it would shine with the bril- 
 liancy of the Pole Star, or of the principal stars in the 
 constellation of the Great Bear. 
 
 86. The Heavenly Bodies are all in Motion. The 
 stars, then, are manifestly suns, and the double, triple, 
 sextuple, and other multiple stars are systems of revolv- 
 ing suns. Each of these suns is probably attended by 
 systems of planets like our own, which of course could 
 not be seen at their immense distance with the most 
 powerful telescope. It would seem that all the heavenly 
 bodies are in motion, satellites about planets, planets 
 about swns, and suns about suns, and systems of suns 
 about systems of suns ; and that the reason why we do 
 not detect this motion in all cases is that the stars are 
 situated at such enormous distances that their motion 
 cannot be detected in the brief space of two or three 
 thousand years which has elapsed since recorded obser- 
 vations first began. 
 
 We have already seen that the proper motion of the 
 stars amounts at most to about seven seconds a year, 
 and these are probably the very nearest fixed stars. Yet 
 from their known distance and proper motion it has been 
 computed that the following stars must move at the 
 rates given below : 
 
96 ASTRONOMY. 
 
 Arcturus 54 miles a second. 
 
 6 1 Cygni 40 " 
 
 Capella 30 ' 
 
 Sinus. 14 " " 
 
 Alpha Centauri 13 " " 
 
 Vega 13 " " 
 
 It will be remembered that the earth's velocity in its 
 orbit is eighteen miles a second. Notwithstanding this 
 enormous velocity, it has required years of patient ob- 
 servation to establish the fact of the proper motion of 
 the stars. We need not be surprised, then, that the 
 more remote stars appear fixed, though they may be 
 moving at the enormous rate of fifty miles a second. 
 
 SUMMARY. 
 
 Many of the planets are accompanied by systems of 
 satellites. 
 
 Our solar system is a complex system of planets and 
 satellites. (77.) 
 
 Our sun is travelling through space. 
 
 Many of the so-called fixed stars have proper motions. 
 
 (78.) 
 
 Stars which appear close together and have the same 
 proper motion constitute a physical system. (80.) 
 
 Theta Orients is a remarkable system of this kind. (81.) 
 The components of these systems are in many cases 
 known to revolve about a common centre in elliptical 
 orbits. (82-84.) 
 
II. 
 
 PHYSICAL FEATURES OF THE 
 HEAVENLY BODIES. 
 
PHYSICAL FEATURES OF THE 
 HEAVENLY BODIES. 
 
 THE SUN. 
 
 WE have seen that the universe is made up mainly of 
 satellites, planets, and suns, and we have learned some- 
 thing of the motions and distances of these, and have 
 thus got a general notion of the structure of the universe 
 as a whole. We now turn our attention to these bodies 
 to inquire what is known of each individually. We nat- 
 urally begin at the centre of the solar system. 
 
 87. The Size of the Sun. We have already learned 
 that the sun is distant from the earth about 95,000,000 
 miles. Its disc is well known to be circular, and careful 
 measurement shows that it is an exact circle. 
 
 Knowing the distance of the sun, it is an easy problem 
 to find its size. Suppose a pasteboard disc, say about 
 four inches in diameter, be held before the sun, it will be 
 found that it must be held about twelve yards from the 
 eye in order exactly to cover the sun's disc. Now since 
 the distance between the lines in Figure 46. et any two 
 
 Fig. 46- 
 
 points is evidently proportioned to their distance from 
 the vertex of the angle which the lines make, it follows 
 
IOO 
 
 ASTRONOMY. 
 
 that twelve yards is to 95,000,000 miles as four inches is 
 to the diameter of the sun. 
 
 We thus learn that the diameter of the sun is about 112 
 times the diameter of the earth, or 887,076 miles. The cir- 
 cumference of the sun, therefore, exceeds 2,785,400 miles. 
 
 We have already seen that the moon's mean distance 
 from the earth is about thirty times the earth's diameter. 
 If, then, we imagine the centre of the sun to be at the 
 centre of the earth, his circumference would extend be- 
 yond the orbit of the moon by a distance equal to twenty- 
 six diameters of the earth. 
 
 In Figure 47, the inner circle represents the size of the 
 earth, the middle one the moon's orbit, and the outer one 
 the size of the sun, all drawn to the same scale. The 
 
 Fig. 47- 
 
ASTRONOMY. 
 
 volume of the sun is about a million and a half times that 
 Df the earth. 
 
 88. The Sun-Spots. When the sun is examined with 
 \ telescope of moderate magnifying power, the eye being 
 properly protected, his disc usually appears sprinkled with 
 irregularly grouped dark points. These dark spots are 
 the sun-spots. 
 
 Figure 48 gives an idea of the manner in which the 
 spots are distributed, and their grouping at any one 
 time. 
 
 Fig. 48- 
 
 The number of the spots, their relative positions, and 
 their forms are found to vary continually. Sometimes, 
 though rarely, the solar disc is free from them j and some- 
 times as 'many as eighty spots have been visible at once. 
 From a series of observations continuing through a pe- 
 riod of some forty years, it appears that the spots occur 
 with greater frequency at regular intervals. They dimin- 
 ish in number during five or six years, and then increase 
 again through about the same length of time. Their 
 greatest number thus occurs at intervals of ten or twelve 
 years. The last maximum was in 1860. 
 
ASTRONOMY. 
 
 89. The Motion of the Spots. When observed with care 
 during several consecutive days, the spots are seen to 
 vary in fjoth form and position.' But amidst all their 
 variations, a common movement of the whole in the 
 same direction can be distinguished. 
 
 Let us suppose a spot to appear on the eastern edge 
 or limb of the sun. From day to day it will be seen to 
 progress with increasing rapidity until it occupies a cen- 
 tral position on the disc. It still continues to advance, 
 but now with decreasing rapidity, until it finally disap- 
 pears on the western border. The same is true of all 
 the spots, which at first appear scattered over the sun's 
 disc. They all describe, in the same direction, with nearly 
 equal velocities, either straight lines, or curved ones whose 
 convexity always lies in the same direction for all the 
 spots observed at the same time. 
 
 Let us suppose that the particular spot that we have 
 observed is of an oval form, its greatest length being at 
 right angles to the direction of its motion across the 
 sun's disc at the moment when it appeared on the east- 
 ern limb. As it approaches the centre the spot widens, 
 until at the centre it becomes nearly circular ; then, hav- 
 ing passed the centre, its form becomes more and more 
 oval again until its disappearance, its apparent size in one 
 direction meanwhile not having sensibly changed. Fig- 
 ure 49 shows these changes of form during the first and 
 last half of the period of the visibility of the spot. 
 
 Fig. 49. 
 
 About fourteen days is the time during which the spots 
 
ASTRONOMY. 
 
 remain visible, and this time is nearly the same for all, 
 though they do not all traverse arcs of the same length 
 on the sun's surface. 
 
 It is also fourteen days after the disappearance of a 
 spot on the western border before it appears again on the 
 eastern, often changed in form, yet generally recognizable. 
 
 Precise measurements have proved both the general 
 uniformity and the parallelism of these movements. 
 
 90. The Spots are not Planets. It was at first thought 
 that these spots might be caused by small planets revolv- 
 ing about the sun and presenting to us their unillumined 
 faces. But since the time of their disappearance is equal 
 to that of their visibility, they cannot be such planets. 
 For it is evident from Figure 50 that, were they such 
 planets, they would remain invisible 
 
 longer than they are visible. For such 
 a planet would be visible only while de- 
 scribing the arc A B across the sun's 
 disc, while it would be invisible while 
 describing the much longer arc A C B. 
 It was also thought possible to explain 
 the movements of the spots from the t 
 eastern to the western border, by an act- 
 ual translation of them across the sur- 
 face of the sun, the surface itself being 
 immovable. This supposition is, how- 
 ever, inconsistent with their uniformity 
 of movement. 
 
 91. The Sun's Rotation on his Axis. 
 The movements of the spots, then, show 
 
 beyond a doubt that the sun is rotating on an axis from 
 west to east. The change of form of the spots illus- 
 trated in Figure 49, and their unequal rate of motion 
 on different parts of the sun's disc, also prove beyond 
 a doubt that the sun's surface is spherical. These 
 
ASTRONOMY. 
 
 Fig. Si- 
 
 changes of form and of speed are the effect of perspec- 
 tive. The sun, then, like the earth, is not only moving 
 through space, but whirls on its axis as it moves. 
 
 We have already stated that the interval between two 
 successive appearances of the same spot on the same 
 edge of the sun is tvyenty-eight days. The period of ro- 
 tation of the sun is less than this. This will be evident 
 by a reference to Figure 51. 
 
 Let S be the centre of the 
 sun ; a the position of a spot ; 
 and E the position of the 
 earth. The spot will then 
 appear on the centre of the 
 sun. The sun will evidently 
 have made a complete rota- 
 tion when the spot comes 
 upon the line S E again, but 
 it will not appear in the 
 centre of the sun till it comes 
 on the line S F, since the 
 earth has in the mean time 
 passed from E to F. 
 
 Between the two successive 
 appearances of the same spot 
 upon the centre of the sun, 
 the sun will have more than 
 
 completed a rotation. Since we know the angular veloci- 
 ty of the earth in its orbit, we can find how much more 
 than a rotation the sun has completed. For he will evi- 
 dently have completed a rotation plus the angular space 
 that the earth has passed over in twenty-eight days. It 
 is thus found that the sun rotates on its axis once in 
 about twenty-five days. 
 
 92. The Axis of the Sun is not perpendicular to the Plane 
 of the Ecliptic. If the axis of the sun were perpendicular 
 
ASTRONOMY. 
 
 105 
 
 to the plane of the ecliptic, the spots would evidently ap- 
 pear always to describe straight lines across the sun's disc. 
 Observation shows that twice in the year they describe 
 straight lines across the sun, and that for half of the re- 
 maining time they describe curves which are convex to- 
 wards the upper limb of the sun, and the other half curves 
 which are convex towards the lower limb of the sun, as 
 shown in Figure 52. It has thus been found that the 
 sun's axis is inclined 82 45' to the plane of the ecliptic. 
 
 Fig. 52- 
 
 The sun-spots are confined in the main to two zones, 
 situated on each side of the equator. They are seldom 
 observed elsewhere on the sun's disc. 
 
 93. The Appearances of the Spots. We have already 
 learned from the spots on the sun the direction and du- 
 ration of his rotation, and the inclination of his axis to 
 the plane of the ecliptic. We will now study the appear- 
 ance of these curious phenomena more minutely. Fig- 
 ure 53 represents a series of sun-spots. It will be seen 
 that the spots consist almost invariably of one or more 
 dark portions called umbra, which seem black when com- 
 
io6 
 
 ASTRONOMY. 
 
 pared with the luminous parts of the disc. Around these 
 a gray tint forms what is named, improperly, the penum- 
 bra. The majority of spots are composed of one or sev- 
 eral umbrae, enclosed in one penumbra. But sometimes 
 spots appear without the grayish envelope, as also occa- 
 sionally a penumbra without an umbra. 
 
 Fig. 53- 
 
 The forms of the spots, as shown by the drawings, are 
 very varied. The penumbra most frequently reproduces 
 the principal contour of the umbra, and often presents a 
 great variety of shades when examined with a consider- 
 able magnifying power. On the exterior edges of the 
 penumbra, the gray tint seems generally the deepest ; 
 either by the effect of contrast with the brilliant portions 
 that surround it, or because in reality there is at these 
 points a more decided tint. Figure 54 affords a striking 
 example of this aspect of the penumbra. 
 
 This spot presents the peculiarity, not at all unfre- 
 quent, of the division of the dark umbra into several 
 fragments by luminous bridges spanning it, as it were, 
 from one side of the penumbra to the other. 
 
 The umbra itself is far from offering a uniform black 
 tint. In reality it always presents a variety of shades, 
 
ASTRONOMY. 
 
 107 
 
 as if the penumbra and umbra were mingled and their 
 tints mixed up in various proportions. 
 
 Fie. s 
 
 Under the best conditions of air and of instrument, the 
 umbra seems to be pierced, and to afford a view of a 
 much darker portion underneath. This darker portion 
 has been called the nucleus. It appears to be of the 
 most intense blackness, but it must be remembered that 
 the word black as applied to the sun is only comparative. 
 Sir J. Herschel has shown that a ball of ignited quick- 
 lime, in the oxyhydrogen flame, though it seems to give 
 out a light approaching that of the sun, appears, when pro- 
 jected on the sun, as a black spot. 
 
 94. Dimensions of the Spots. The spots sometimes 
 cover enormous areas. It is not uncommon to see one 
 with a surface larger than that of the earth. Schroter 
 measured one whose extent was four times the whole 
 surface of the globe. Its diameters were more than 
 29,000 miles. Sir W. Herschel measured a spot con- 
 sisting of two parts, the diameter of which was not less 
 than 50,000 miles. The most extensive spot measured 
 
io8 
 
 ASTRONOMY. 
 
 was not less than 186,000 miles in its greatest length, 
 and its surface embraced about 25,000,000,000 square 
 miles. 
 
 If the spots are deep rents in the sun's envelope, the 
 larger ones must form gulfs, at the bottom of which the 
 earth might lie like a boulder in the crater of a volcano. 
 
 95. The Form and Size of the Spots are continually 
 changing. Not only are the sun-spots not permanent, 
 rarely lasting for many successive rotations, but their 
 forms and dimensions differ from one rotation to another ; 
 sometimes even within a single day. 
 
 Fig- 55, (An enlarged view of the group A, in Fig. 55, a.) 
 
 The modifications which spots undergo in the course 
 of a rotation are illustrated by Figure 55. These differ- 
 
ASTRONOMY. 109 
 
 ent groups, though easily recognized again, are consider- 
 ably changed in general outline, and still more in detail. 
 
 These changes indicate two phenomena going on simul- 
 taneously, which may be best studied separately. First, 
 there is indicated a proper motion of the spots, more or 
 less rapid, and distinct from the apparent movement pro- 
 duced by rotation. 
 
 The proper motion of the spots was investigated in the 
 most thorough manner by Mr. Carrington, who observed 
 the sun every fine day for more than eight years, from 
 1853 to 1861. After his discoveries there need be no 
 wonder that different observers have varied so greatly in 
 the time they have assigned to the sun's rotation. He 
 shows that all sun-spots have a movement of their own, 
 and that the rapidity of this movement varies regularly 
 with their distance from the solar equator. The spot 
 near the equator travels faster than those farther from 
 it, so that if we take an equatorial spot, we shall say that 
 the sun rotates in about twenty-five days ; while, if we 
 take one situated half way between the equator and the 
 poles, in either hemisphere, we shall say that it rotates 
 in about twenty-eight days. These facts show that we 
 are ignorant of the exact period of the sun's rotation. 
 
 In the second place, the changes in the form of the 
 spots are no less remarkable. Sometimes a spot divides 
 into several separate nuclei ; sometimes many distinct 
 nuclei reunite into one. Arago quotes a, curious instance 
 of a spot which seemed to break upon the surface of the 
 sun, in the same manner as a block of ice thrown upon 
 the frozen surface of a sheet of water divides into several 
 pieces which slide in all directions. 
 
 Diligent observation, moreover, of the umbra and pe- 
 numbra with a powerful instrument, shows that change is 
 going on incessantly in the region of the spots. Some- 
 times after the lapse of an hour, many changes in detail 
 10 
 
110 ASTRONOMY. 
 
 are noticed : here, a portion of the penumbra setting 
 sail across the umbra; there, a portion of the umbra 
 melting from sight ; in another place, an evident change 
 of position and direction in masses which retain their 
 form. 
 
 96. Faculce. These spots are not the only exception 
 to the uniform brightness of the sun's surface. Near the 
 edge of the solar disc, and especially about spots approach- 
 ing the edge, it is quite easy, even with a small telescope, 
 to discern certain very bright streaks of diversified form, 
 quite distinct in outline, and either entirely separate or 
 coalescing in various ways into ridges and net-work. 
 These appearances, which have been called facula, are 
 the most brilliant part of the sun. Where near the limb 
 the spots become invisible, undulated shining ridges still 
 indicate their place. Faculae vary much in magnitude. 
 Professor Phillips has observed them from barely discern- 
 ible, faintly-gleaming, narrow tracts, 1,000 miles long, to 
 continuous, complicated, and heavy ridges, 40,000 miles 
 and more in length, and 1,000 to 4,000 miles broad. 
 
 Ridges of this kind often surround a spot, and here 
 appear more conspicuous ; but sometimes there appears 
 a very broad platform round the spot, and from this the 
 white crumpled ridges extend in various directions. 
 
 There would appear to be a close connection between 
 spots and faculae. An eminent French observer holds 
 that spots are distributed for the most part in groups, 
 with their greatest length parallel to the sun's equator, 
 and that the first spot of the group is the blackest, the 
 most regular, and lasts the longest. As the spots in the 
 wake of the first disappear, they give place to faculae, 
 which cover the region where the spots showed them- 
 selves ; then the original spot appears followed by a train 
 of faculae. 
 
 97. "Pores," "Willow-Leaves? or "Granules:' The 
 
ASTRONOMY. Ill 
 
 whole surface of the sun, except those portions occupied 
 by the spots, is coarsely mottled. When examined with a 
 large instrument it is seen that the surface is made up 
 principally of luminous masses imperfectly separated from 
 each other by rows of minute dark dots called pores. 
 Mr. Nasmyth has recently announced his discovery that 
 these pores are the "polygonal interstices between cer- 
 tain luminous objects of an exceedingly definite shape 
 and general uniformity of size, which is that of the ob- 
 long leaf of the willow-tree." According to other observ- 
 ers, however, these luminous masses present almost every 
 variety of irregular form ; they are " rice grains," gran- 
 ules or granulations, " untidy circular masses," " things 
 twice as long as broad," and so on. 
 
 Mr. Dawes asserts, indeed, that he has seen some 
 nearly in contact differ so greatly in size that one was 
 four or five times as large as another ; and while, in a 
 remarkably bright mass, one somewhat resembled a blunt 
 and ill-shaped arrow-head, another, very much smaller, 
 and within 5" of it, was an irregular trapezium with 
 rounded corners. 
 
 The occasional " willow F ' s ' s6 ' 
 
 leaf" appearance of the 
 penumbra is shown in 
 Figure 56. 
 
 98. Appearances about 
 the Sun during a Total 
 Eclipse. Some minutes 
 before and after, but es- 
 pecially during the total- 
 ity of an eclipse of the sun, 
 a luminous appearance in 
 
 the form of a halo surrounds his disc, and throws in every 
 direction rays of light separated by dark spaces. In 
 many total eclipses, independently of the regular corona 
 
112 ASTRONOMY. 
 
 (as this halo is called), other light portions have been 
 noticed irregularly situated on the sun's contour. The 
 color of the corona which immediately surrounds the dark 
 disc is sometimes of a pearly or silvery white, sometimes 
 yellowish, and even red. 
 
 The explanation generally given of this corona is, that 
 it indicates the presence of a solar atmosphere, envel- 
 oping the radiant body to an enormous distance. 
 
 During the total eclipse of 1842 prominences of vari- 
 ous f6rms and of a reddish color were visible throughout 
 the contour of the moon's limb, during the period of to- 
 tality. Some took the form of mountain peaks ; others 
 rose vertically from the sun's disc, and then turned at 
 right angles; others, again, appeared completely de- 
 tached, like floating clouds. Their tint was sometimes 
 of a bright red, sometimes rosy, here and there variedly 
 greenish-blue. These rose-colored flames or prominences 
 had been noticed as early as 1733, but special attention 
 was not given to them till 1842. Since then they have 
 been observed with great care. 
 
 It has now been proved beyond all question that these 
 protuberances belong to the sun. In the observations of 
 the total eclipse of July, 1860, it was seen that as soon 
 as the last delicate line of light disappeared behind the 
 eastern edge of the moon, the rose-colored prominences 
 were seen on those borders where the solar crescent had 
 just disappeared. On the opposite side they were not 
 yet entirely visible ; their tops extended beyond the ob- 
 scure disc only at its upper and lower parts. The moon's 
 advance hid by degrees the prominences first observed, 
 and exposed to view, at the opposite side, those previ- 
 ously covered. 
 
 In July, 1860, the heliograph of the Kew Observatory 
 was carried to Spain, and photographs of the sun were 
 taken at intervals during the eclipse. These photographs 
 
ASTRONOMY. 113 
 
 showed that the form of these protuberances does not 
 change during the moon's passage across the sun's disc. 
 Similar photographs were taken at Rome by Father Sec- 
 chi, and a comparison of these with those taken in Spain 
 shows that the prominences did not sensibly change their 
 outline during the interval between the occurrence of the 
 eclipse at the two places. 
 
 These facts show that the prominences do not belong 
 to the lunar disc, and are not optical effects produced by 
 its presence, but that they are absolutely parts of the 
 sun itself. 
 
 They were first supposed to be enormous mountains 
 on the surface of the sun. But the forms of many of 
 them, and their occasional complete separation from the 
 solar disc, contradict this hypothesis. All the observed 
 facts lead to the conclusion that these immense appen- 
 dages, rising 25,000 and even 50,000 miles in height and 
 length, are clouds floating in the solar atmosphere, whose 
 presence is indicated by the corona. 
 
 THE NATURE OF SUN-SPOTS. 
 
 99. Wilson's Observations. In 1769 Professor Wilson 
 of Glasgow watched a large spot as it passed across the 
 sun's disc. He first saw it as it was passing towards the 
 western limb. At first the penumbra was seen entirely 
 to surround the umbra. As the spot approached the 
 limb, the penumbra on the side nearest the sun's centre 
 became narrower and narrower, until it finally disap- 
 peared, and the umbra also began to disappear on this 
 side. On the reappearance of the spot on the eastern 
 limb, the penumbra reappeared on the eastern side of 
 the umbra, but had vanished on the western. As the 
 spot approached the sun's centre, the penumbra again 
 became visible on the western side, as a narrow line 
 10* 
 
114 ASTRONOMY. 
 
 which grew broader and broader till the spot reached 
 the centre of the disc, when the breadth of the penum- 
 bra was equal on all sides of the umbra. These appear- 
 ances led Professor Wilson to suppose that the body of 
 the sun is surrounded by a luminous envelope of the 
 consistency of a very dense fog, from which emanate 
 all the solar light and heat, and that the spots are vast 
 cavities or rents in this luminous envelope, through the 
 bottom of which the dark body of the sun becomes visi- 
 ble, the shelving sides of the cavity giving rise to the 
 penumbra. When a spot is near the centre of the sun 
 the shelving sides of the cavity should appear on all 
 sides of the darker bottom ; that is, the umbra should be 
 surrounded on all sides equally by the penumbra. When 
 the spot is near either, limb, the shelving side of the 
 cavity should disappear on the side towards the observer, 
 that is, on the side next the sun's centre, and there should 
 be a penumbra only on the side of the umbra next the 
 sun's limb. (Compare Figure 49.) 
 
 100. HerscheCs Theory, Herschel supposed that the 
 sun is surrounded by an outer or luminous envelope, 
 and an inner non-luminous envelope, somewhat like the 
 stratum of clouds that surrounds our earth. The body 
 of the sun itself he supposed to be dark in comparison 
 with the luminous envelope, and the non-luminous en- 
 velope to be capable of reflecting the light of the lu- 
 minous envelope about it. A spot he supposed to be 
 caused by a rent in one or both of these envelopes. If 
 only the outer envelope was rent, then the spot would 
 be wholly penumbra without any nucleus, since the non- 
 luminous envelope would reflect the light which fell upon 
 it from the outer envelope. If both envelopes were rent, 
 then the spot would have a nucleus, since the dark body 
 of the sun would be revealed. If the opening in the 
 non-luminous envelope were smaller than that in the lu- 
 
ASTRONOMY. 115 
 
 minous envelope, as is usually the case, the spot would 
 appear with a black nucleus surrounded by a penumbra. 
 On this theory, as on Wilson's, the spots are cavities in 
 the sun's luminous atmosphere. 
 
 101. Recent Investigations on the Nature of Sun-spots. 
 A very important and elaborate series of researches on 
 the nature of the sun-spots has been recently begun by 
 Warren De La Rue, President of the Royal Astronomi- 
 cal Society, and Balfour Stewart and Benjamin Loewy of 
 the Kew Observatory. 
 
 These investigators have in their hands all the original 
 drawings of sun-spots executed by Carrington between 
 the years 1853 and 1861, the collection of drawings of 
 the sun made by Schwabe during a course of about forty 
 years, and the photographs of the sun taken by the Kew 
 heliograph. A few pictures were taken by this instru- 
 ment as early as 1858, and since February, 1862, it has 
 been used in continuous observations. 
 
 These investigators have already arrived at several im- 
 portant conclusions. 
 
 An elaborate examination of the drawings and photo- 
 graphs of the sun's spots has sustained Wilson's con- 
 clusion that the umbra of a sun-spot is at a lower level 
 than the penumbra. 
 
 The faculae are regarded as portions of the sun's pho- 
 tosphere raised above the general surface. The fact that 
 the faculas are more conspicuous near the. edge of the 
 sun's disc than at the centre supports this conclusion. 
 For there is good reason to suppose that the sun is sur- 
 rounded by an atmosphere, and the absorption of light 
 by this atmosphere would be much greater near the edge 
 than at the centre; since the light reaching us has to 
 travel through a much greater extent of atmosphere. If, 
 then, the photosphere near the borders should be thrown 
 up to a great elevation, the light coming from it will es- 
 
Il6 ASTRONOMY. 
 
 cape much of this atmosphere. On the other hand, very 
 little will be gained in this way, when the elevation is 
 near the centre of the disc, where the atmospheric ab- 
 sorption is small. The stereoscopic pictures of the sun 
 that have been obtained also show some of the faculae 
 as ridges. 
 
 It is found, also, that the faculae often retain the same 
 appearance for many days together, as if the matter of 
 which they are composed were capable of remaining sus- 
 pended for some time. This permanence of form would 
 seem to show that the faculae cannot be elevations of the 
 nature of waves in a liquid ocean resting on the surface 
 of the sun, but that they are rather of the nature of a 
 cloud ; that is, of solid or liquid matter formed from the 
 condensation of vapor, either slowly sinking or suspended 
 in equilibrium in a gaseous medium. Kirchoff has shown 
 by means of the spectroscope that there exist in the at- 
 mosphere of the sun vapors of such substances as iron, 
 which are condensed into liquids or solids at a com- 
 paratively high temperature. It would be natural, then, 
 that such vapors should be condensed and should float 
 in the sun's atmosphere, as aqueous vapor is condensed 
 and floats in the form of clouds in our atmosphere. The 
 portion of the sun, then, which appears luminous to us, 
 is probably a condensed stratum of those vapors which 
 exist in the sun's atmosphere, and which are capable of 
 condensation at a high temperature. 
 
 A comparison of a large number of spots shows that 
 faculae are, on an average, to the left of their accompany- 
 ing spots. From the way in which the spots often break 
 up, and from the fact that detached portions of lumi- 
 nous matter often appear to float across the spot without 
 producing any permanent alteration, these observers are 
 disposed to think that the umbra and penumbra of a 
 spot both lie beneath the sun's photosphere. 
 
ASTRONOMY. 1 I 7 
 
 They conclude that the spots are produced by the 
 cooling of the sun's photosphere, and they believe that 
 this cooling is occasioned by downward currents in the 
 solar atmosphere which bring the cooler atmosphere of 
 the higher regions down into that of the photosphere. 
 The supposition that the spots are produced by the cool- 
 ing effects of downward currents is supported by the 
 proper motion of the spots. It will be remembered that 
 the spots have all a proper motion in the direction of 
 the sun's rotation, and of greater rapidity in proportion 
 as they are nearer the equator. Now if they are pro- 
 duced by downward currents, the air in the upper re- 
 gions must have a greater velocity than that in the lower 
 regions, and it must consequently tend to increase the 
 velocity of this lower air, which would tend to give the 
 spots a proper motion in the direction of the sun's rota- 
 tion. This velocity in the upper regions would be great- 
 est at the equator, hence the proper motion of the spots 
 should be greatest there. 
 
 But these downward currents should be accompanied 
 with upward currents. There should then be faculae in 
 the neighborhood of the spots. And as the air in the 
 lower regions has less velocity than that in the upper re- 
 gions, the faculae should fall behind the spots. This is 
 exactly confirmed by observation. 
 
 This theory of the nature and cause of the sun-spots 
 is certainly simpler and more satisfactory than that framed 
 by Herschel. 
 
 The same observers have measured the area of the sun- 
 spots on Carrington's drawings and on the photographs 
 of the sun. They have thus discovered that the maxi- 
 mum area of visible spots is always on the part of the 
 sun's disc which is opposite the planet Venus. When 
 Venus is at superior conjunction, the spots attain the 
 greatest area where they cross a line drawn through the 
 
Il8 ' ASTRONOMY. 
 
 centre of the sun's disc perpendicular to the plane of the 
 ecliptic. As Venus passes on from superior conjunction, 
 the spots attain their greatest area to the right of this 
 central line. 
 
 They have found, too, that when Venus is at or near 
 the plane of the sun's equator, the belts of spots ap- 
 proach the sun's equator ; and that when Venus is most 
 distant from that plane, they recede from the equator. 
 The planet Venus, then, has a remarkable influence on 
 the size and position of the sun's spots. They have also 
 found that the area of the spots on crossing the central 
 line on the sun's disc is much greater when Venus and 
 Jupiter are both on the opposite side of the sun from the 
 earth, than when Venus is on the opposite side and Ju- 
 piter on the same side as the earth. This shows that 
 the planet Jupiter has also considerable influence on the 
 sun's spots. 
 
 SUMMARY. 
 
 Place the centre of the sun at the centre of the earth, 
 and his circumference would extend far beyond the moon's 
 orbit. (87.) 
 
 The sun's disc is seldom free from dark patches. These 
 patches are called sun-spots. 
 
 Sun-spots appear in greatest numbers at intervals of 
 about twelve years. (88.) 
 
 These spots belong to the disc of the sun. (90.) 
 
 The rotation of the sun on his axis, and the inclination 
 of his axis to the plane of the ecliptic, have been ascer- 
 tained by means of the sun-spots. (91, 92.) 
 
 The spots have usually an umbra and a penumbra. 
 The umbra is not uniformly dark. (93.) 
 
 The spots sometimes cover enormous areas. (94.) 
 
 The spots have a proper motion in the direction cf 
 
ASTRONOMY. 119 
 
 the sun's rotation. Those near the equator move much 
 faster than those away from it. They are also constantly 
 changing their form. (95.) 
 
 Facula are bright streaks on the sun's disg. They 
 seem to be connected with the spots. They usually ap- 
 pear in the rear of these. (96.) 
 
 The general disc of the sun is coarsely mottled. "Wil- 
 low leaves" are sometimes seen about the spots. (97.) 
 
 During a total eclipse the sun is surrounded by a 
 corona, and by rose-colored clouds. (98.) 
 
 Professor Wilson supposed that the spots are vast 
 rents in the sun's luminous atmosphere, through which 
 the dark body of the sun is visible. (99.) 
 
 According to Herschel's theory the sun is surrounded 
 by two envelopes, the outer one luminous, and the inner 
 one non-luminous. When both envelopes are rent, and 
 the opening in the outer envelope is larger than that in 
 the inner, the spot has both an umbra and a penumbra. 
 (100.) 
 
 An important investigation of the nature of the sun- 
 spots has been recently begun by De La Rue, Stewart, 
 and Loewy. 
 
 They regard the sun's photosphere as of the nature of 
 a cloud, and the faculae as portions of this cloud raised 
 above the general surface. They find that the faculae 
 are more often to the left of the spots than elsewhere. 
 They have decided that both the umbra and penumbra 
 are beneath the sun's photosphere. 
 
 They think the spots are produced by the cooling of 
 the sun's photosphere by downward currents. They 
 have shown that Venus and Jupiter have a marked influ- 
 ence on the sun-spots. (101.) 
 
120 ASTRONOMY. 
 
 MERCURY. 
 
 102. Ifs Distance from the Sun, Period of Revolution, etc. 
 Mercury, as we have seen, is the planet nearest the 
 sun. Its greatest elongation from the sun is about 29 ; 
 hence it is never seen at a great distance from the hori- 
 zon, or long after sunset or before sunrise. And as the 
 atmosphere near the horizon is usually charged with va- 
 pors, Mercury is seldom a very conspicuous object. 
 
 The mean distance of this planet from the sun is 
 37,000,000 miles, and its period of revolution is about 
 three months. Its orbit is a very flat ellipse, so that its 
 distance from the sun varies greatly. At perihelion it is 
 less than 30,000,000 miles from the sun, while at aphe- 
 lion it is more than 44,000,000 miles from him. Its dis- 
 tance from the sun, then, varies by about 15,000,000 
 miles. Its orbit is inclined to the ecliptic about 7, 
 which is more than that of any other of the larger plan- 
 ets. 
 
 If its inferior conjunction occurs when it is near one 
 of its nodes (67), it will be seen to cross the sun. It 
 then appears as a black circular disc projected upon the 
 sun. Accurate measurements taken at a large number 
 of observations of these transits of -Mercury show that 
 the disc is always an exact circle. Hence we conclude 
 that Mercury is an exact sphere. 
 
 103. Its Distance from the Ecfrth, its Diameter, etc. 
 Since the orbit of Mercury lies inside of the orbit of the 
 earth, its distance from our planet must vary greatly. 
 At inferior conjunction it is nearer the earth by the whole 
 diameter of its orbit than it is at superior conjunction. 
 Hence it appears much larger at the former time than 
 at the latter. Its angular diameter varies from 5" to 12". 
 Knowing this angular diameter, and the distance of the 
 
ASTRONOMY. I 2 I 
 
 planet from the earth, we can readily compute its diam- 
 eter in miles by the method already used in the case of 
 the sun (87). Its diameter is thus found to be about 
 3,000 miles. 
 
 When examined with a telescope this planet presents 
 phases exactly like those of the moon. Figure 57 shows 
 
 Fig. 57- 
 
 these phases, and also the comparative size of the planet 
 as seen in different parts of its orbit. It appears at first 
 as a luminous disc, nearly circular, which by degrees is 
 reduced on the side towards the east, until not more 
 than half a circle is visible at the time of its greatest 
 elongation from the sun ; it then becomes a crescent, 
 which grows narrower and narrower, until just before in- 
 ferior conjunction it is visible only as a fine luminous 
 thread. It repeats these phases in the opposite order 
 when it reappears on the other side of the sun. 
 
 1 04. The Explanation of these Phases. These phases 
 prove that Mercury is not self-luminous, but shines by 
 reflected sunlight. One half of the planet is of course 
 always illuminated by the sun, and it is evident that at 
 superior conjunction this illuminated half is turned to- 
 wards the earth, so that its whole disc then appears lu- 
 minous. At inferior conjunction it is equally evident 
 that the illumined half is turned away from the earth ; 
 since it will always be turned toward the sun. At its 
 ii 
 
122 ASTRONOMY. 
 
 greatest elongation half of the illumined hemisphere will 
 be turned towards the earth, and the illumined disc will 
 then appear as a semicircle. Between the greatest elon- 
 gation and superior conjunction more than half of the 
 illumined hemisphere is turned toward the earth ; while 
 between the elongation and inferior conjunction less than 
 half of the illumined hemisphere is turned towards us. 
 
 105. Mercury's Period of Rotation. The great prox- 
 imity of Mercury to the sun renders the observation of 
 this planet somewhat difficult, so that very little is known 
 of its surface. The German astronomer Schroter, who 
 observed Mercury very carefully in the latter part of the 
 last century, considered that he had decided evidence of 
 the existence of high mountains on the planet ; and by 
 watching these he came to the conclusion that Mercury 
 rotates on its axis in a little over twenty-four hours. 
 
 Schroter observed that during the crescent phase of 
 the planet the line which separated the illumined from 
 the dark portion of the disc appeared somewhat jagged, 
 as shown in Figure 58. These markings evidently indi- 
 
 cate the existence of high mountains, which intercept the 
 sunlight, and of valleys plunged in the shade, which lie 
 near the parts of the surface of the planet then illumined. 
 These markings are not always visible, but appear and 
 
ASTRONOMY. 123 
 
 disappear at intervals ; and it was from these intervals 
 that Schroter determined the rotation of the planet. But 
 as he is the only astronomer who has been able to make 
 out these irregularities on the disc of Mercury, the pe- 
 riod of rotation must be considered as still very un- 
 certain. 
 
 1 06. The Inclination of its Orbit, and its Seasons. - 
 Schroter observed some dark bands on the disc of Mer- 
 cury, which he considered as an equatorial zone. It was 
 from the direction of these bands that he deduced the 
 inclination of the axis of rotation to the plane of the 
 planet's orbit. This he estimated at about 20, which 
 would make the equator of Mercury inclined to the plane 
 of the orbit at an angle of about 70. It will be seen 
 that this inclination is about three times as great as that 
 of the earth's equator to the plane of the earth's orbit, or 
 the ecliptic. This inclination, together with the great 
 variation of Mercury's distance from the sun, would give 
 a remarkable variety of seasons, with great extremes of 
 heat and cold. 
 
 Figure 59 shows, according to Schroter, the angle at 
 which Mercury presents himself to the sun at the com- 
 mencement of each season. It will be seen that very 
 extensive zones about the poles enjoy at one season, 
 during the summer, continuous day ; while at another, 
 during their winter, they are plunged in profound dark- 
 ness. It is only during a short period, and near the 
 planet's equinoxes, that these zones see light and dark- 
 ness succeed one another in the same day. 
 
 These polar zones are of course much broader than 
 the corresponding zones on the earth. 
 
 Since the light and heat which a planet receives from 
 the sun diminish as the square of the distance increases, 
 it follows that the intensity of the sunlight at Mercury is 
 about seven times as great as at the earth. 
 
124 
 
 ASTRONOMY. 
 
 Fig. 59- 
 
 It will be noticed in Figure 58 that the illumined part 
 of the disc shades off gradually into the dark part. This 
 gradual shading off indicates the presence of an atmos- 
 phere about Mercury, the darkish part being the zone of 
 twilight which separates the full light of day from the 
 darkness of night This zone of twilight, as at the earth, 
 must be caused by an atmosphere. 
 
 VENUS. 
 
 107. Its Distance from the Sun, Time of Revolution, Di- 
 ameter, etc. The second planet from the sun is Venus. 
 Her mean distance (48) is 69,000,000 miles, and her 
 period of revolution about yj months. 
 
 While the orbit of Mercury differs more from a circle 
 than that of any other planet, the orbit of Venus is found 
 to be nearer a circle than that of any other planet. 
 Hence she is but little nearer the sun at perihelion than 
 at aphelion. Her orbit is inclined to the ecliptic at an 
 
ASTRONOMY. 125 
 
 angle of 3 23'. When examined with a telescope she 
 presents phases like those of Mercury ; proving that she 
 is not self-luminous, but shines with light borrowed from 
 the sun. 
 
 The distance of Venus from the earth varies more than 
 that of Mercury, since the diameter of her orbit is greater 
 than his. At inferior conjunction Venus is of course 
 about 138,000,000 miles nearer the earth than at superior 
 conjunction. Hence the apparent diameter of the planet 
 varies greatly, ranging from 70" to less than 10". The 
 actual diameter of Venus is about 7,800 miles, or a little 
 less than that of the earth. 
 
 Figure 60 shows the apparent size of Venus at its 
 greatest, its mean, and its least distance from the earth. 
 
 Venus appears as an evening star for a period of about 
 9|- months, and is then a morning star for the same length 
 of time. 
 
 1 08. Time of Rotation, Inclination of Axis, etc. Venus 
 is the most conspicuous of all the planets. Her light is 
 often brilliant enough to cast a shadow, and she is some- 
 times visible at midday. Her greatest brilliancy is not 
 near her inferior conjunction, since the illumined portion 
 of her disc is then reduced to a mere thread of light. 
 It occurs at an elongation of about 40, and her phase is 
 ii * 
 
126 ASTRONOMY. 
 
 then about the same as that of the moon three days from 
 new moon. 
 
 The brilliancy of Venus is so great as to render accu- 
 rate observation of her disc almost impossible. We do 
 not know whether she is flattened at the poles, like the 
 earth, or not. 
 
 The terminator of Venus (the line dividing the illu- 
 mined from the dark part of the disc), as seen at times 
 by Schroter, presented considerable Irregularity of out- 
 line. This irregularity, as in the case of Mercury (105), 
 indicates the presence of mountains and valleys. By ob- 
 serving the interval between the disappearance and re- 
 appearance of certain of these irregularities', this astron- 
 omer came to the conclusion that Venus rotates on her 
 axis in a little less than twenty-four hours. 
 
 Schroter made the inclination of the planet's axis to 
 the plane of its orbit about 20, and several other ob- 
 servers have arrived at very nearly the same result. The 
 change of seasons and of the length of day and night 
 would therefore be about the same on Venus as we have 
 supposed them to be on Mercury. 
 
 The gradual shading off of the illumined portion of 
 the disc of Venus indicates the existence of twilight on 
 this planet, and consequently of an atmosphere (106). 
 
 109. Has Venus a Satellite? According to Cassini 
 and several observers of the last century, Venus is at- 
 tended by a satellite. But recent astronomers have not 
 been able to detect it, though they are provided with 
 much better instruments for observation. It is, therefore, 
 now generally believed that this planet has no satellite. 
 
 no. Transits of Venus. Venus, as we have already 
 seen, crosses the sun's disc whenever her inferior con- 
 junction happens near one of her nodes (67). 
 
ASTRONOMY. 127 
 
 THE ZODIACAL LIGHT. 
 
 in. Its Appearance. In the evenings about the time 
 of the vernal equinox, when in our latitude the twilight 
 is of short duration, if we examine the horizon towards 
 the west soon after sunset, we may see a faint light that 
 rises in a triangular form among the constellations. 
 
 This appearance is known as the Zodiacal Light. Those 
 not familiar with it might confound this glimmering with 
 the milky way, or with the ordinary twilight, or even with 
 an aurora. But with a little attention it is impossible to 
 mistake it. Its triangular shape, its elevation, and its 
 inclination to the horizon, all serve to distinguish it. 
 
 As the days lengthen, and with them the duration of 
 twilight, the zodiacal light becomes invisible, at least in 
 our latitude. But it may be again seen before sunrise 
 in the east, about the time of the autumnal equinox, in 
 September and October, when the morning twilight is 
 short. At places favorably situated, even in the temper- 
 ate zone, the zodiacal light can be seen at almost every 
 season of the year. 
 
 In our climate, the light of the zodiacal light is rather 
 more intense than that of the Milky Way, and much 
 more uniform. 
 
 If now we pass from the temperate zone of either hemi- 
 sphere towards the tropical zone, the zodiacal light in- 
 creases in intensity and height ; and it can be observed 
 throughout the year. 
 
 112. Its Cause. The most probable of the many ex- 
 planations that have been given of the zodiacal light is 
 that it is a flattened nebulous body surrounding the sun 
 at some distance. The direction of the axis of the cone 
 of light, if prolonged below the horizon, always passes 
 through the sun, as shown in Figure 61. 
 
128 
 
 ASTRONOMY. 
 Ficr. 6 1. 
 
 It was believed at first that this direction coincided 
 with the solar equator, but it has been found to coincide 
 more nearly with the plane of the earth's orbit, or the 
 ecliptic. 
 
 The distance from the summit of the cone to the mid- 
 dle of its base at the horizon varies with the time of 
 observation. This ring sometimes extends as far as the 
 earth's orbit, and even beyond it ; at other times it is en- 
 closed within this orbit. This may be explained by sup- 
 posing either that the form of the ring is oval, or that it 
 is circular and that the sun does not lie in its centre. 
 
 Some suppose that the zodiacal light is formed of 
 myriads of solid particles analogous to aerolites, having 
 a common general movement, but travelling separately 
 about the / sun as a centre. The light of the ring would 
 thus be produced by the accumulation of this multitude 
 of brilliant points, reflecting towards us the light borrowed 
 by each of them from the sun. Others regard it as a 
 
ASTRONOMY. 1 29 
 
 ring of thin nebulous matter much like the train of com- 
 ets; others as a vaporous ring which surrounds the earth 
 at some distance. 
 
 THE EARTH. 
 
 113. The third planet in the order of distance from 
 the sun is the earth. We have already found its mean 
 distance from the sun to be 95,000,000 miles; that it 
 revolves about the sun in an ellipse, in a period of one 
 year ; that it rotates on its axis in a little less than twenty- 
 four hours; that this axis is inclined to the plane of its 
 orbit by an angle of 66J ; that this inclination gives rise 
 to the change of seasons and the varying length of day 
 and night ; that the, mean diameter of our planet is about 
 8,000 miles; and that it is not a perfect sphere, but is 
 flattened somewhat at the poles. 
 
 The earth has also an atmosphere of known composi- 
 tion, which gives rise to the phenomena of twilight. The 
 land surface of the earth is also jagged with mountains, 
 as we have seen there is reason to believe is also the 
 case with the surface of Mercury and Venus. 
 
 The earth is the first planet in order from the sun that 
 is known to be accompanied by a satellite. The earth, 
 like Mercury and Venus, shines by reflected light, as 
 will be proved hereafter. 
 
 THE MOON. 
 
 114. Her Distance, Diameter, Periodic Time, etc. T]he 
 mean distance of the moon, as we have seen, is about 
 thirty times the diameter of the earth, and her mean an- 
 gular diameter is about 31'. From this her real diameter 
 is found to be somewhat more than 2,000 miles. The 
 moon revolves around the earth in an ellipse whose plane 
 
 9 
 
130 ASTRONOMY. 
 
 is inclined to the plane of the earth's orbit by an angle 
 of about 5. She performs a revolution in about 27 J 
 days. Owing, however, to the 'motion of the earth in 
 its orbit, the synodical revolution of the moon, or the 
 interval between two successive new moons, is about 29 J 
 days. 
 
 115. The Phases of the Moon. The phases of the 
 moon depend on the position of the moon with respect 
 to the sun, or, what amounts to the same thing, her dis- 
 tance from conjunction, which is termed in astronomical 
 language the age of the moon. Being an opaque spher- 
 ical body reflecting the sun's light, she can appear fully 
 illuminated only when opposite the sun, and in all other 
 positions her illuminated disc appears less than a circle. 
 Soon after conjunction with the sun she may be seen as 
 a very narrow crescent, a little above the western hori- 
 zon at sunset; for, being then between the earth and 
 sun, her illuminated surface is in a great measure turned 
 from us. As she advances in her orbit, the dark part 
 gradually diminishes until the moon is 90 from conjunc- 
 tion, which is called the first quarter, and then the illu- 
 mined and unillumined parts are equal. After this point, 
 the illumined surface increases till the moon is in oppo- 
 sition, when she is said to be full, and presents to us 
 her whole enlightened disc. The bright part then begins 
 to diminish, and again forms one half of her surface when 
 the moon is 90 from conjunction, or at the last quarter. 
 It then becomes narrower as she approaches conjunction, 
 till a thin crescent above the eastern horizon shortly be- 
 fore sunrise is all that remains. These phases repeat 
 themselves after the interval of a synodical revolution, 
 and depend upon the position of the visible, with refer- 
 ence to the enlightened, hemisphere of the moon. 
 
 1 1 6. Libration. The most casual observer of the moon 
 can hardly have failed to remark that she always presents 
 
ASTRONOMY. 131 
 
 very nearly the same face towards us, and a little reflec- 
 tion will convince him that the cause of this must lie in 
 the very near equality of her periods of axial rotation 
 and synodical revolution round the earth. If these periods 
 were exactly equal, and the moon's motions exactly uni- 
 form, we should have the same hemisphere turned to- 
 wards us without the slightest variation. But the motion 
 in her orbit is subject to small irregularities, while that 
 on her axis is perfectly uniform, and for this reason a 
 phenomenon termed libration takes place, whereby we 
 occasionally see a little more of one edge of the moon 
 than usual, either on the eastern or western side of her 
 equatorial region. Suppose, for instance, that conjunc- 
 tion occurs when the moon is at perigee, or nearest the 
 earth, and that the moon rotates on its axis at a uni- 
 form rate and once during a sidereal revolution. But 
 the moon moves in her orbit faster at perigee than else- 
 where. She would accordingly perform the first quarter 
 of her revolution before she had performed a quarter of 
 a rotation. We should therefore see a little more of her 
 western edge than we should if she had performed a 
 quarter of her rotation. Again, suppose that conjunc- 
 tion occurs when the moon is at apogee, or farthest from 
 the earth. Then while she is performing a quarter of a 
 revolution, she will perform more than a quarter of a 
 rotation, and we should see more of her eastern edge 
 than we should if she had performed just, a quarter ro- 
 tation. 
 
 This libration, which is due to the moon's unequal 
 rate of motion in her orbit, is usually called libration in 
 longitude. 
 
 The moon, then, rotates on her axis in the mean 
 period of a sidereal revolution, and it has been found by 
 observation that the axis of this rotation is not quite 
 perpendicular to the plane of her orbit. Now since the 
 
132 ASTRONOMY. 
 
 axis always maintains the same direction, it follows that 
 we are enabled at times to see a little more of the polar 
 regions than at others. This phenomenon is called //- 
 bration in latitude. 
 
 Since we are situated four thousand miles above the 
 centre of the earth, we see at the rising of the moon a 
 little more of the western edge than we should if we 
 were viewing the moon from the centre of the earth. 
 For the same reason, we see at the setting of the moon 
 a little more of the eastern edge of the moon than we 
 should if we were situated at the centre of the earth. 
 This phenomenon is called parallactic libration. 
 
 117. The Earth's Phases as seen from the Moon. It 
 is a well-known fact that at the time of new moon the 
 dark part of the moon's surface is partially illumined, so 
 that it becomes visible to the naked eye. This must be 
 due to the light reflected to the moon from the earth. 
 Since at new moon the moon is between the earth and 
 sun, it follows that when it is new moon at the earth, it 
 must be full earth at the moon. Hence while the bright 
 crescent is enjoying full sunlight, the dark part of its 
 surface is enjoying the light of the full earth. 
 
 1 1 8. The Apparent Size of the Moon. The apparent 
 magnitude of the lunar disc not only varies with the dis- 
 tance of -the moon from the earth, but even on the sur- 
 face of our globe, and at the same instant, the disc does 
 not appear of equal magnitude to all observers. It ap- 
 pears larger to an observer who sees the moon rising 
 or setting, than to him who sees it at the zenith. 
 
 In Figure 62 the distance A M of the moon from an 
 observer at A is seen to be nearly equal to its real dis- 
 tance from the centre of the earth, while at the same 
 time its distance A M from an observer at A is 4,000 
 miles less than its distance from the centre of the earth. 
 Hence the moon is nearer an observer at A' by about 
 ^V of its distance than to an observer at A. 
 
ASTRONOMY. 133 
 
 Fig. 62. 
 
 Notwithstanding it is much nearer when at the zenith 
 than at the horizon, it seems to us much larger at the 
 horizon. 
 
 This is a pure illusion, as we become convinced when 
 we measure the disc with accurate instruments, so as to 
 make the result independent of our ordinary way of judg- 
 ing. When the moon is near the horizon, it seems placed 
 beyond all the objects on the surface of the earth in that 
 direction, and therefore farther off than at the zenith, 
 where no intervening objects enable us to judge of its 
 distance. In any case, an object which keeps the same 
 apparent magnitude seems to us, through the instinctive 
 habits of the eye, the larger in proportion as we judge 
 it to be more distant. 
 
 A recent discovery of very great interest shows us that 
 in the case of the moon the word apparent means much 
 more than it does in the case of other celestial bodies. 
 Indeed, its brightness causes our eyes to 'play us false. 
 As is well known, the crescent of the new moon seems 
 part of a much larger sphere than that which it has 
 been said, time out of mind, to " hold in its arms." We 
 now learn that the bright portion of the moon, as seen 
 with our measuring instruments, as well as when seen with 
 the naked eye, covers a larger space in the field of the 
 telescope than it would if it were not so bright. This 
 
134 ASTRONOMY. 
 
 has been recently proved by measuring the dark moon 
 by means of the occultation of a star. In this way the 
 Astronomer Royal of England has shown that the di- 
 ameter of the moon hitherto received is too large by 2". 
 
 119. The Path of the Moon through Space. Since the 
 earth is moving in its orbit at the same time that the 
 moon is revolving about it, it follows that the path de- 
 scribed by the moon through space is much the same as 
 that described by a point on the circumference of a 
 wheel which is rolled over another wheel. If we place a 
 circular disc against the wall, and carefully roll along its 
 edge another circular disc to which a piece of lead pencil 
 has been fastened so as to mark upon the wall, the curve 
 described will somewhat resemble that described by the 
 moon. This curve is called an epicycloid, and it will be 
 seen that at every point it is concave towards the centre 
 of .the larger disc. In the same way the moon's orbit is 
 at every point concave towards the sun. 
 
 120. Harvest Moon. The full moon which occurs 
 nearest to the autumnal equinox has long been called 
 the Harvest Moon, from the fact that the difference be- 
 tween the times of the moon's rising on two successive 
 nights is then at a minimum, and the long duration of 
 moonlight, thus afforded soon after sunset, is very ad- 
 vantageous to the farmer at this busy season. This near 
 coincidence in the times of several successive risings oc- 
 curs every lunar month, when the moon is in the signs 
 Pisces and Aries, but it attracts attention only when the 
 moon is at the full in these signs, and this can happen 
 only in August or September. The least possible differ- 
 ence between two successive risings in the latitude of 
 Boston is about twenty-three minutes. When the moon 
 is in Libra, and at the same time near the descending 
 node of her orbit, the difference between the times of 
 rising on two evenings is the greatest possible, amount- 
 ing to about one hour and seventeen minutes. 
 
ASTRONOMY. 135 
 
 121. The Surface of the Moon. The moon is much 
 the nearest to us of all the heavenly bodies, and we are 
 consequently best acquainted with its surface. The na- 
 ked eye readily discerns that the disc of the full moon 
 is not uniformly bright : light and dark regions diversify 
 it, giving the idea of continents and seas like those on 
 our own globe. In fact, the earlier selenographers con- 
 sidered the dull, grayish spots to be water, and termed 
 them the lunar seas, bays, and lakes. They are so called 
 on lunar maps to the present day, though we have strong 
 evidence to show that if water exists at all on the moon, 
 it must be in very small quantity. 
 
 On examining the moon with suitable magnifying pow> 
 ers, we perceive on every part of the surface, even in 
 the midst of the so-called oceans and seas, ring-like spots, 
 evidently of volcanic character, with extensive chains of 
 mountains and steep isolated rocks, presenting altogether 
 a very rugged and desolate appearance. If we choose 
 for observation the first or last quarter of the moon, the 
 portions near the edge of the illuminated part appear 
 eaten into cavities surrounded by circular walls, which 
 cast shadows away from the sun, at one side towards the 
 interior, and on the other towards the exterior of the 
 cavity. Along the whole line which separates the light 
 and dark parts of the moon, called the terminator, the 
 interior of the ring-like cavities seems quite black, while 
 here and there luminous points show themselves detached 
 from the illuminated portion of the moon. 
 
 These spots indicate mountain tops or ranges, which, 
 according as we observe them at the first or last quarter, 
 are receiving the rays of the moon's rising or setting sun 
 while the lowlands are in the shade. 
 
 Small spots of annular form, which are regarded as 
 craters, are exceedingly numerous, and are seen to cover 
 the whole visible surface of the moon. In some places 
 
136 ASTRONOMY. 
 
 they are thickly crowded together, small volcanoes hav- 
 ing formed on the sides of the large one : in other re- 
 gions they are comparatively isolated. Their dimensions 
 are far greater than those of the largest volcanoes on 
 the earth, the breadth of the chasm occasionally exceed- 
 ing one hundred miles, while the sides of the mountains 
 attain a very considerable elevation. The best time for 
 viewing a crater is when it is 'just clear of the dark part 
 of the moon, or when the sun is just above its horizon. 
 We can then trace the shadows thrown by the side of 
 the mountain upon its interior and exterior surface, and, 
 by measuring these shadows, we may approximate to 
 the true altitude of the mountain. Some of the steep 
 isolated rocks throw their shadows for many miles across 
 the plains surrounding them. 
 
 Of course the angle subtended by the shadow can be 
 directly measured, and since we know the angle sub- 
 tended by the diameter of the moon, and the length of 
 this diameter in miles, we can readily determine the 
 length of the shadow in miles. It will evidently be the 
 same fraction of the diameter in miles, as the angle which 
 it subtends is of the angle subtended by the diameter of 
 the moon. Knowing, then, the length of the shadow in 
 miles, and the height of the sun above the horizon, we 
 can easily ascertain the height of the mountain which 
 casts the shadow. 
 
 We have only to ascertain the length of the shadow 
 cast by a mountain of known height on the earth when 
 the sun is the same distance above the horizon. The 
 height of the lunar mountain will be just as many times 
 greater as its shadow is longer. 
 
 122. Tycho. One of the most remarkable of the lu- 
 nar spots is that called Tycho , which is readily distin- 
 guished in the southern part of the full moon by the 
 number of luminous rays, or streaks of light, which di- 
 
ASTRONOMY. 
 
 -37 
 
 verge from it in a northeasterly direction. Tycho is an 
 annular mountain or crater, no less than fifty-four miles 
 in diameter. The height of the western wall above the 
 interior level is, according to Madler, 17,100 feet, and 
 of the eastern borders somewhat more than 16,000 feet. 
 A mountain nearly a mile high marks the centre of the 
 crater. Tycho is surrounded by a great number of cra- 
 ters, peaks, and ridges of mountains, lying so close to- 
 gether that in some directions it is impossible to find 
 the smallest level place. 
 
 Figure 63 gives a view of the region to the southeast 
 of Tycho, 
 
 Fig. 63. 
 
 This mountain, as we have already said, is the centre 
 of a number of luminous streaks or rays, which extend 
 therefrom over fully one fourth of the moon's disc. The 
 brightest one branches off in a northeasterly direction, 
 and there are others very conspicuous on the western 
 side of the crater. These rays become visible as soon 
 
138 ASTRONOMY. 
 
 as the sun has risen From 20 to 25 above their horizon. 
 Their color is perhaps a little whiter or more silvery than 
 the general lunar surface. Many opinions have been 
 advanced by Cassini, Schroter, Herschel, and others, re- 
 specting the nature of these appearances, and they have 
 been variously styled mountains, streams of lava, and 
 even roads. There is nothing on the surface of the 
 earth bearing the slightest analogy to them. Perhaps 
 the most plausible theory is that first started by Mr. Nas- 
 inyth, that they have been caused by a general volcanic 
 upheaval of the moon's crust in former ages, which has 
 produced an appearance on the lunar surface similar to 
 that of a pane of glass broken by a sharp-pointed in- 
 strument. The mere fact of their divergence from the 
 great crater Tycho proves that it was the focus of this 
 volcanic outbreak, whenever it may have occurred. 
 
 123. Copernicus. Another very beautiful annular moun- 
 tain is that known as Copernicus, shown in Figure 64. 
 
 The diameter of the crater is somewhat larger than 
 that of Tycho, being rather more than fifty-five miles. 
 The highest point is about 11,250 feet above the sur- 
 rounding plains. It is readily discernible on the full 
 moon, but is most favorably viewed when the sun's rays 
 have just reached its eastern side, about the time of 
 quadrature, or first quarter. The shadows of the west- 
 ern side of the crater are then thrown on the interior 
 level, that of the central peak on the same level towards 
 the eastern side, while the shadow of this side of the 
 mountain darkens for some distance the exterior plain 
 on the rugged edge of the moon. Generally speaking, 
 these shadows are extremely well defined. The diver- 
 gent streaks of light from this mountain are best seen 
 near the time of full moon. They vary in breadth from 
 three to ten miles, the principal one branching off to- 
 wards the northeast. 
 
ASTRONOMY. 
 
 Fig. 64. 
 
 139 
 
 124. Kepler. This is also a conspicuous ring-moun- 
 tain, the focus of similar rays of light. The crater is 
 about twenty-two miles in diameter, and the altitude of 
 the eastern edge above the level of the interior is about 
 10,000 feet. 
 
 Tycho, Copernicus, and Kepler are the principal cra- 
 ters which form the radiating points of the luminous 
 streaks which are so remarkable upon the surface of the 
 full moon. 
 
 125. Eratosthenes. This is a very beautiful annular 
 mountain situated at the extremity of the long range 
 called the Apennines, which cover a surface of more 
 than 16,000 square miles. The crater is not less than 
 
14 ASTRONOMY. 
 
 thirty ^seven miles in diameter, and in its centre a steep 
 rock rises 15,800 feet above the level surface of the in- 
 terior. The outside of the circular mountain is about 
 3,300 feet high on the western border, while on the 
 eastern side its height is more than twice as great. 
 
 The volcanic character of the lunar mountains is un- 
 mistakable. All the crust of our satellite is pierced with 
 craters which indicate an innumerable series of volcanic 
 eruptions, some limited to a small space, others embrac- 
 ing an immense area. 
 
 The darkish portions of the moon are supposed to be 
 large plains. 
 
 126. Are there Active Volcanoes on the MOOJI ? In 1787 
 Sir William Herschel announced that he had observed 
 three volcanoes in a state of eruption in different parts 
 of the moon ; and modern astronomers have repeatedly 
 noticed luminous spots in the dark portion of the lunar 
 disc, some of which were so distinct and striking that 
 they might readily be taken for active volcanoes. The 
 prevailing opinion among astronomers, however, is, that 
 these appearances are due to the reflection of the " earth- 
 light" (117) from certain mountain tops, which from their 
 nature or their position have a greater reflective power 
 than other parts of the moon. 
 
 Recent observations, however, show that changes of 
 some kind are still going on in lunar craters. In Oc- 
 tober and November, 1866, Schmidt, the Director of the 
 Observatory of Athens, noticed that the deep crater Linrie, 
 whose diameter is 5.6 miles, had completely disappeared, 
 and in its place there was only " a little whitish luminous 
 cloud." He at once called the attention of other Euro- 
 pean astronomers to the facts, and in December the lo- 
 cality of the lost crater was carefully examined by many 
 of them. All agreed with Schmidt, that Linne could not 
 be seen at the time when it was most favorably situated 
 
ASTRONOMY. 141 
 
 for observation, and when smaller craters in its immedi- 
 ate neighborhood were very distinct with the shadows 
 within them. 
 
 The obscuration, whatever may have been its cause, ap- 
 pears to have ceased in the latter part of December, when 
 the crater was distinctly seen by Dr. Tietjen at Berlin. 
 
 It is said that one of Schroter's maps gives a dark 
 spot in the place of Linne', and that the crater is not to 
 be found on Russell's globe or maps of the year 1797; 
 from which it may be inferred that the crater has previ- 
 ously been obscured.* 
 
 127. The Moon has little or no Atmosphere. If there 
 is a lunar atmosphere, it must be one of great rarity and 
 of no great extent ; otherwise it would give rise to phe- 
 nomena which could not fail to attract the attention of 
 astronomers. 
 
 The two main reasons for thinking that there is no 
 atmosphere of any considerable density at the moon are, 
 (i.) the sharpness of the line which separates the bright 
 and dark portions of her disc, and (2.) the absence of 
 refraction, as shown in the occultation of stars. 
 
 (i.) It is well known that there is no gradual shading 
 off from the illuminated parts of the moon's disc, as there 
 appears to be in the case of Mercury and Venus, and 
 as there is known to be in the case of the earth. There 
 is, therefore, no perceptible twilight on the moon, and 
 consequently no atmosphere, unless of great rarity. 
 
 (2.) According to the well-known laws of refraction, 
 if there were an atmosphere about the moon, the rays of 
 light would be so bent that a star, on passing behind 
 the moon, would be seen even after it was really be- 
 hind the disc, just as the sun is visible after it is really 
 below the horizon ; and so that it would become visible 
 before it had really emerged from behind the disc, just 
 * See Appendix, V. 
 
142 ASTRONOMY. 
 
 as the sun is visible before it is really above the horizon. 
 It would then follow that a star would appear to be be- 
 hind the moon a shorter time than that computed from 
 the known rate of motion and angular diameter of the 
 moon. Now it is found tliat the observed time of the 
 occultation of any star by the moon is very slightly, if 
 at all, shorter than the computed time. Airy has shown 
 that, if the discrepancy of 2 "which he has found (118) 
 between the angular diameter of the moon, as determined 
 by observation, and as computed from the rate of the 
 moon's motion and the time of the occultation of a star, 
 is wholly due to refraction caused by a lunar atmosphere, 
 the refractive power of that atmosphere is only ^oW 
 part of that of the earth's atmosphere ; hence it must 
 be of extreme tenuity. 
 
 If there is no atmosphere at the moon, there can be 
 no water on her surface; for the heat of the sun would 
 cause that water to evaporate, and thus an atmosphere 
 of aqueous vapor would be formed. 
 
 , Furthermore, there has never been discovered any posi- 
 tive evidence of the existence of clouds at the moon, 
 which would be the necessary result of the existence of 
 water there. 
 
 Some astronomers have supposed that the side of the 
 moon turned towards us may be a huge mountain, and 
 that there may really be both air and water on the far- 
 ther side, though not enough to rise above this moun- 
 tain. Both Adams and Le Verrier have, however, shown 
 that such a hypothesis is, to say the least, extremely 
 improbable. 
 
 ECLIPSES. 
 
 128. The Shadows of the Earth and Moon. The earth 
 and moon are two spherical and opaque bodies, and the 
 halves of both are constantly illuminated by the rays of 
 
ASTRONOMY. 143 
 
 the sun, while the other halves are in the shade. The 
 illuminating body is itself a sphere of much greater size. 
 Not only, therefore, have the earth and the moon always 
 one of their hemispheres dark, but each of these bodies 
 throws behind it, in a direction opposite from the sun, 
 a shadow of conical form, the length and diameter of 
 which depend upon the distance and diameter of the il- 
 luminating body, and the diameter of the illuminated 
 body. 
 
 This cone of shade encloses all those parts of space 
 where, by reason of the interposition of the opaque body, 
 no rays of light from the sun can be received. Beyond 
 the apex of this cone of pure shade, which is called the 
 umbra, and in the direction of its axis, are situated those 
 portions of space from which a part of the sun is seen 
 in the form of a luminous ring bordering the obscure 
 disc of the opaque body. Lastly, these two regions are 
 themselves surrounded by what is called the penumbra; 
 or those portions of space which receive light only from 
 a part of the sun, one side of whose luminous disc, is 
 obscured by the disc of the opaque body. The dark- 
 ness of the penumbra at any point is more intense, in 
 proportion as the point is nearer the umbra. 
 
 The moon and the earth in their movements carry 
 with them their cones of umbra and penumbra, and it 
 is by projecting these total or partial shadows upon each 
 other that they produce the phenomena of eclipses. ' 
 
 These various cones are represented in Figure 65. 
 
 129. When Eclipses may Occur. On examining this 
 figure, it will be seen at once why an eclipse of the sun 
 can happen only at the time of new moop, and why, on 
 the other hand, an eclipse of the moon is possible only 
 at full moon. 
 
 In all other positions of the moon, her cone of shade 
 is projected into space away from the earth, and the 
 
144 
 
 ASTRONOMY. 
 
 errestrial cone of shade does not meet the moon. It 
 does not follow, however, that there is an eclipse of the 
 sun at every new moon, or of the moon at every full 
 moon. This would be true if the orbits of the earth 
 round the sun and of the moon round the earth were 
 described in the same plane. Then at each opposition 
 or conjunction the centres of the three bodies would 
 necessarily lie in a straight line. 
 
 But the orbit of the moon is inclined to the ecliptic 
 
ASTRONOMY. 145 
 
 at an angle of about 5, so that it often happens at the 
 time of new moon that our satellite throws its cone of 
 shadow above or below the earth. In like manner, at 
 the time of opposition, the moon, in consequence of her. 
 being out of the plane of the ecliptic, passes sometimes 
 above and sometimes below the cone of the earth's shadow. 
 In such cases there can be no eclipse. 
 
 In order, then, that there should be an eclipse of the 
 sun, new moon must occur when the moon is at or near 
 one of the nodes (67) of her orbit; and in order that 
 there should be an eclipse of the moon, full moon must 
 occur when the moon is at or near one of her nodes. 
 
 130. Eclipses of the Sun. Solar eclipses are of three 
 kinds. When the dark disc of the moon entirely covers 
 the sun, the eclipse is total; when only a portion, large 
 or small, of one side of the sun is covered by the moon, 
 the eclipse is partial ' ; and when the disc of the moon 
 is not large enough to cover the whole disc of the sun, 
 and thus leaves a luminous ring visible around its own 
 body, the eclipse is annular. 
 
 As the moon is much smaller than the sun, it will be 
 understood that it is her small relative distance that 
 causes her disc to appear equal to or greater than that 
 of the sun. This distance varies by reason of the ellip- 
 tical form of the moon's orbit, and hence the lunar disc 
 is sometimes larger, sometimes smaller than, and some- 
 times equal to, that of the sun. 
 
 This is the same as saying that the cone of the moon's 
 real shadow, or umbra, sometimes reaches the earth and 
 sometimes does not. If it reaches the earth there is a 
 total eclipse of the sun to all parts of the earth within 
 it, and a partial eclipse to all parts within the penumbra. 
 This will be readily seen from Figure 66. 
 
 If the cone of the lunar shadow does not reach the 
 earth, there will be an annular eclipse in those places 
 7 J 
 
which are in the direction of the axis of the cone, and 
 a partial eclipse to those which are only within the pe- 
 numbra. This case is represented in Figure 67. 
 
 Fig. 67. 
 
 It will be seen, then, that the conditions under which 
 a total eclipse of the sun is possible are the following: 
 (i.) the moon must be in conjunction, or new ; (2.) she 
 must at the same time be at or near a node ; (3.) her 
 distance from the earth must be less than the length 
 of her shadow. 
 
 The same conditions, except the last, are necessary for 
 an annular eclipse. 
 
 The breadth of the cone of the moon's umbra at the 
 distance of the earth seldom equals 160 miles. Hence 
 a total eclipse is seen only over a very narrow tract ; 
 but, owing to the rotation of the earth, this tract has con- 
 siderable length. 
 
ASTRONOMY. 147 
 
 A total eclipse of the sun is a rare occurrence at best, 
 and a total eclipse at any given place is rarer still. It 
 will be seen from Figure 67 that even the penumbra of 
 the moon's shadow traverses but a small part of the 
 earth ; so that a partial eclipse of the sun is by no means 
 visible to the whole earth. 
 
 Hind thus describes the appearances during the total 
 eclipse of the sun, July 28th, 1851, in Sweden: 
 
 "The aspect of nature during a total eclipse was grand 
 beyond description. A diminution of light over the earth 
 was perceptible a quarter of an hour after the beginning 
 of the eclipse, and about ten minutes before the extinc- 
 tion of the sun the gloom increased very perceptibly. 
 The distant hills looked dull and misty, and the sea as- 
 sumed a dusky appearance, like that it presents during 
 rain. The daylight that remained had a yellowish tinge, 
 and the azure blue of the sky deepened to a purplish- 
 violet hue, particularly towards the north. But, notwith- 
 standing these gradual changes, the observer could hardly 
 be prepared for the wonderful spectacle that presented 
 itself when he withdrew his eye from the telescope, after 
 the totality had come on, to gaze around him for a few 
 seconds. The southern heavens were then of a uniform 
 purple-gray color, the only indication of the sun's posi- 
 tion being the luminous corona, the light of which con- 
 trasted strikingly with that of the surrounding sky. In 
 the zenith, and north of it, the heavens were of a pur- 
 plish-violet, and appeared very near, while in the north- 
 west and northeast, broad bands of yellowish-crimson light, 
 intensely bright, produced an effect which no person who 
 witnessed it can ever forget. The crimson appeared to 
 run over large portions of the sky in these directions ir- 
 respective of the clouds. At higher altitudes the pre- 
 dominant color was purple. All nature seemed to be 
 overshadowed by an unnatural gloom, the distant hills 
 
148 ASTRONOMY. 
 
 were hardly visible ; the sea turned lurid red, and per- 
 sons standing near the observer had a pale, livid look, 
 calculated to produce the most painful sensations. The 
 darkness, if it can be so termed, had no resemblance to 
 that of night. At various places within the shadow, the 
 planets Venus, Mercury, and Mars, and the brighter stars 
 of the first magnitude, were plainly seen during the to- 
 tal eclipse. Venus was distinctly visible at Copenhagen, 
 though the eclipse was only partial in that city; and at 
 Dantzic she continued in view ten minutes after the sun 
 had reappeared. Animals were frequently much affected. 
 At Engelholm, a calf which commenced lowing violently 
 as the gloom deepened, and lay down before the totality 
 had commenced, went on feeding quietly enough very 
 soon after the return of daylight. Cocks crowed at Hel- 
 singborg, though the sun was there hidden only thirty 
 seconds, and the birds sought their resting-places as if 
 night had come on." 
 
 131. Eclipses of the Moon. Like the eclipses of the 
 sun, those of the moon may be either total or partial, but 
 they are never annular, since the breadth of the cone 
 of the earth's shadow at the distance of the moon is al- 
 ways much greater than the diameter of the moon's disc. 
 
 The fundamental difference between the two phenom- 
 ena is, that an eclipse of the sun is visible to only a part 
 of the hemisphere which has him above the horizon, 
 while an eclipse of the moon is visible from every part 
 of the earth from which the moon herself is visible ; and 
 an eclipse of the sun is seen at different stations succes- 
 sively, as the umbra and penumbra of the moon's shadow 
 traverse the earth, while an eclipse of the moon every- 
 where begins and ends at the same instant. The reason 
 of this difference is that the sun's disc is not really dark- 
 ened, but only hidden by the obscure disc of the moon, 
 so that the interposition is an effect of perspective, vary- 
 
ASTRONOMY. 149 
 
 ing according to the respective position of the observer, 
 of the moon, and of the sun. The lunar eclipse is, on the 
 contrary, produced by the real fading out of the moon's 
 light, and the darkness consequent upon it is observed at 
 the same instant wherever the moon is in view. 
 
 When the moon passes through the centre of the earth's 
 shadow the eclipse is total and central. The earth's shad- 
 ow at the moon's distance is, however, so broad that an 
 eclipse may be total without being also central. 
 
 The magnitude of an eclipse, if partial, and the contin- 
 uance of the obscuration, if total, depend upon the direc- 
 tion of the moon's passage through the earth's shadow, 
 which is sufficiently broad to allow of her being hidden 
 by it one hour and fifty minutes, when she passes through 
 its centre. 
 
 It is not possible to ascertain, with any degree of accu- 
 racy, the time when the moon first enters the penumbra, 
 for the darkening effect upon her disc is so slight that 
 some minutes must elapse before sufficient shade is pro- 
 duced to attract attention. Neither does the time of 
 contact with the umbra admit of exact observation, since 
 the penumbra shades off into the umbra by imperceptible 
 degrees. 
 
 When the moon is totally immersed in the dark shad- 
 ow, she does not, except on rare occasions, become in- 
 visible, but assumes a dull reddish hue, somewhat like 
 that of tarnished copper. This arises from the refraction 
 of the sun's rays in passing through the earth's atmos- 
 phere. 
 
 In a total lunar eclipse in 1848, the spots on the moon's 
 surface were distinctly seen by many observers, and the 
 general color of the moon was a full glowing red. Her 
 appearance was so singular that many persons doubted 
 of her being eclipsed at all. 
 
 Once in about eighteen years the earth, sun, and moon 
 
150 ASTRONOMY. 
 
 occupy the same relative positions. This is a fact which 
 the ancients established by observation long before the 
 theory of the celestial movement's had demonstrated its 
 near approach to the truth. If, then, we start from the 
 epoch of an eclipse of the sun or moon, that is to say, 
 from a lunar conjunction or opposition coinciding with 
 one of the moon's nodes, after 18 years the three bodies 
 will be found in situations nearly identical. Hence the 
 eclipses which succeeded one another in the first pe- 
 riod follow again in the same order during the second 
 period. This is the starting point in the calculation of 
 eclipses, but the approximation is too rough for the ex- 
 actness of modern astronomy. Now-a-days the time of 
 eclipses is foretold to a second several years in advance 
 of their occurrence. 
 
 132. O captations. The moon in traversing her orbit 
 round the earth produces another kind of eclipse, to 
 which the name of occultation has been given. A star 
 or planet is said to be occulted when it passes behind 
 the lunar disc. These phenomena have already been 
 mentioned with reference to the question of the existence 
 of an atmosphere on the surface of the moon (127). 
 
 The occultations of the stars are calculated with the 
 same precision as the eclipses, and as they are of fre- 
 quejit occurrence they are of great use to navigators in 
 determining their longitude. As the moon is very near 
 the earth, compared with the distance of the stars and 
 even of the planets, it follows that two observers at dif- 
 ferent points on the earth do not see it projected at the 
 same instant on the same part of the heavens. The oc- 
 cultation of a star does not, therefore, take place to both 
 of them at the same instant of time. 
 
 By correcting these observations for refraction and par- 
 allax, the exact time is found at which an occultation 
 would take place to an observer at tne centre of the 
 
ASTRONOMY. 151 
 
 earth. Now the times at which the occupation of stars 
 would occur to an observer situated at the centre of 
 the earth are computed in Greenwich time and published 
 in the Nautical Almanac. An observer at sea, then, finds 
 by observation the time of occultation as seen from the 
 earth's centre in his own local time, and he can then 
 compare his own local time with Greenwich time, and 
 find the difference between the two. He can then readi- 
 ly determine the longitude of his place. 
 
 As we have already seen, the meridian of a place sweeps 
 over the whole heavens, from the sun around to it again, 
 in twenty-four hours. Hence it will sweep over 15 in 
 one hour, and i in four minutes; and when the sun is 
 on the meridian of a given place, it will be 15 east of 
 the meridian of a place 15 to the west of it. The sun 
 will then come upon the meridian an hour later at the 
 second place, and it will be one o'clock at the more east- 
 erly place when it is twelve o'clock at the more westerly. 
 Hence local time becomes an hour earlier as we travel 
 westward 15. 
 
 If, then, we know that Greenwich time is three hours 
 later than our time, we know that we are 45 west from 
 Greenwich ; and if Greenwich time is two hours earlier 
 than our time, we know that we are 30 east of that place, 
 or that we are in longitude 30 east. 
 
 Not only is the time at which the occultation of the 
 star would occur to an observer at the centre of the 
 earth computed in Greenwich time and published in the 
 Nautical Almanac, but also the time when the moon 
 passes all the principal stars near her path is computed 
 and published in the same manner, as well as the distance 
 of the moon from these principal stars for every day dur- 
 ing the year. 
 
 Thus the heavens become a universal dial over which 
 the moon sweeps as a minute-hand, marking, as she passes 
 
152 ASTRONOMY. 
 
 the fixed stars, Greenwich time to every part of the 
 earth. 
 
 But this hand moves with considerable unsteadiness, 
 now faster and now slower, according as the moon is at 
 perigee or apogee, and subject to various other fluctu- 
 ations ; while by reason of parallax and refraction her 
 real position in front of the dial is seldom what it ap- 
 pears to be, so that it has required the patient observa- 
 tion and study of years to learn to read this time aright. 
 
 The learning to read time accurately by this clock of 
 nature has been one of the greatest triumphs of astron- 
 omy, and is a good illustration of the practical bearing 
 of such scientific studies. 
 
 SUMMARY OF THE MOON AND ECLIPSES. 
 
 The mean distance of the moon is about thirty diameters 
 of the earth; her mean angular diameter about 31'; the 
 inclination of her orbit to the ecliptic about 5; her si- 
 dereal period about 27 J days; and her sy nodical period 
 about 29^ days. (114.) 
 
 The phases of the moon depend upon the position of 
 her visible with reference to her enlightened hemisphere. 
 They repeat themselves after the interval of a synodical 
 revolution. (115.) 
 
 The moon completes a rotation on her axis in the 
 same time that she completes a revolution about the 
 earth. Her rotation on her axis is performed at a uni- 
 form rate, while the rate of her revolution about the 
 earth varies. This gives rise to libration in longitude. The 
 axis of the moon is not quite perpendicular to the plane 
 of her orbit. This gives rise to libration in latitude. We 
 see the moon from a point about 4,000 miles above the 
 centre of the earth. This gives rise to parallactic libra- 
 tion. (116.) 
 
ASTRONOMY. 153 
 
 The earth presents to the moon phases similar to those 
 which the moon presents to us. When it is new moon to 
 us, it is full earth to the moon. (117.) 
 
 The moon is nearest to us when she is in the zenith, 
 but she appears largest when she is near the horizon. 
 Owing to her brightness, the moon appears larger than 
 she really is. (118.) 
 
 The moon describes an epicycloidal path, every part of 
 which is concave toward the sun. (119.) 
 
 The least difference between two successive risings of 
 the moon in our latitude is about twenty-three minutes. 
 When this least difference occurs at the time of full 
 moon, we have what is called the Harvest Moon. (120.) 
 
 The surface of the moon is covered with steep iso- 
 lated rocks, volcanic craters, and extensive mountain 
 chains. The existence of these rocks and mountains is 
 indicated by the shadows which they cast. By means 
 of these shadows we can estimate the height of the ob- 
 jects which cast them. (121.) 
 
 The four most remarkable lunar mountains are Tycho, 
 Copernicus, Kepler, and Eratosthenes. (122-125.) 
 
 There is no evidence of active volcanoes on the moon, 
 though changes of some kind are still going on within the 
 lunar craters. (126.) 
 
 That the moon has little or no atmosphere is shown 
 by the sharpness of the line which separates the bright 
 and dark portions of her disc, and by the absence of re- 
 fraction. (127.) 
 
 The earth and the moon cast conical shadows behind 
 them. (128.) 
 
 When the earth passes through the shadow of the 
 moon, there is an eclipse of the sun, which may be partial, 
 annular, or total. This can happen only at the time of 
 new moon, and when the moon is near her node. As 
 the moon's shadow barely reaches the earth, total 
 7* 
 
154 ASTRONOMY. 
 
 eclipses of the sun are of rare occurrence and of short 
 duration. (129, 130.) 
 
 When the moon passes through the shadow of the 
 earth, there is an eclipse of the moon, which may be either 
 partial or total. This can happen only at full moon, and 
 when the moon is near one of her nodes. In an eclipse 
 of the moon her light is extinguished, while in an eclipse 
 of the sun his light is only hidden by the moon. (129, 
 
 131.) 
 
 The planets and stars are occulted by the moon, and 
 by their occultation longitude at sea is determined. The 
 heavens are a universal dial, upon which the moon points 
 Greenwich time to every part of the earth. (132.) 
 
 METEORIC RINGS. 
 
 133. Shooting stars are those evanescent meteors which 
 dart across the sky at night in all directions, and gener- 
 ally leave behind them luminous trains visible some sec- 
 onds after the extinction of the brighter part. The num- 
 ber of the shooting stars varies greatly with the time of the 
 year ; hence the distinction between sporadic meteors and 
 the showers of shooting stars which appear in the sky in 
 large numbers and generally periodically. During ordi- 
 nary nights, the mean number of shooting stars observed 
 in the interval of an hour is from four to five, according 
 to some observers, and as high as eight, according to 
 others. 
 
 But at two periods of the year, about the loth of Au- 
 gust and the i2th of November, these phenomena are 
 much more numerous, and the number of shooting stars 
 observed in the interval of an hour is often more than 
 tenfold that seen on ordinary nights. The August show- 
 ers used to be popularly known as " St. Lawrence's tears " ; 
 the luminous trains being nothing else to the untutored 
 
ASTRONOMY. 1 55 
 
 people of Ireland than the burning tears of that martyr, 
 whose feast fell on the zoth of August. The November 
 shower is usually more brilliant than the August, and 
 at intervals of about thirty-three years it is of extraordi- 
 nary splendor. 
 
 On the 1 2th of November, 1799, Humboldt, who was 
 then at Cumana, relates that, between the hours of two 
 and five in the morning, the sky was covered with innu- 
 merable luminous trains, which incessantly traversed the 
 celestial vault from north to south, presenting the ap- 
 pearance of fire-works let off at an enormous height ; 
 large meteors, having sometimes an apparent diameter of 
 one and a half times that of the moon, blending their 
 trains with the long, luminous, and phosphorescent paths 
 of the shooting stars. In Brazil, Labrador, Greenland, 
 Germany, and French Guiana, the same phenomena were 
 observed. 
 
 The shower of November i2th, 1833, was no less ex- 
 traordinary. The meteors were observed along the east- 
 ern coast of America, from the Gulf of Mexico as far as 
 Halifax, from nine o'clock in the evening till sunrise, and 
 in some places, even in full daylight, at eight o'clock 
 in the morning. They were so numerous, and visible in 
 so many parts of the sky at once, that in trying to count 
 them one could only hope to arrive at a very rough ap- 
 proximation. At Boston, Prof. Olmsted compared the 
 shower, at the moment of maximum, to half the num- 
 ber of flakes which one sees in the air during an ordinary 
 snow-storm. When the brilliancy of the display was 
 considerably reduced he counted six hundred and fifty in 
 fifteen minutes,' though he confined his observations to a 
 zone which was not a tithe of the visible horizon. He 
 estimated that the number he counted was not more 
 than two thirds of the number which fell ; making the 
 whole number 866 in the zone observed, and some 8,660 
 in all the visible heavens. 
 
156 ASTRONOMY. 
 
 Now the phenomena lasted more than seven hours, 
 and as the above estimate would give an average of 
 34,640 an hour, the number seen at Boston exceeded 
 240,000 ; and yet it must be remembered that the basis 
 of this calculation was obtained at a moment when the 
 display was notably on the decline. 
 
 Again, on the morning of the i4th of November, 1866, 
 an extraordinary display of meteors was seen in England. 
 The display was very brilliant, but those who saw both, 
 pronounced it much less splendid than the show of 1833. 
 
 134. The Probable Cause of these Phenomena. The 
 great majority of the meteors of the November shower 
 radiate in all directions from a point in Leo, called 
 from this fact the radiant point ; while the radiant point 
 of the August shower is in Perseus. These points are 
 precisely those toward which the earth is moving at the 
 time. 
 
 Astronomers have therefore concluded that the appear- 
 ance of shooting stars is caused by the passage of the 
 earth through rings composed of myriads of these bodies, 
 which circulate, like the larger planets, round the sun, and 
 whose parallel movements, seen from the earth, seem to 
 radiate from that part of the heavens which the earth is 
 approaching. The appearance required by this theory is 
 exactly that presented to us. 
 
 Professor Newton, of New Haven, an astronomer who 
 has given much attention to this subject, finds that the 
 average number of meteors which traverse the atmosphere 
 daily, and which are large enough to be visible to the 
 naked eye on a dark, clear night, is no less than 7,500,000 ; 
 and applying the same reasoning to telescopic meteors, the 
 number will have to be increased to 400,000,000. 
 
 It is now generally held, that these little bodies are not 
 scattered uniformly throughout space, or collected into 
 either one or two rings, but that they are collected into 
 
ASTRONOMY. 157 
 
 several rings round the sun ; and that, when the earth in 
 its orbit breaks through one of these rings, or passes near 
 it, her attraction overpowers that of the sun, and causes 
 them to impinge on our atmosphere, where, their motion 
 being arrested and converted into heat and light, they 
 become visible to us as meteors, fire-balls, or shooting 
 stars, according to their size. 
 
 It has been suggested, not without some probability, 
 that the earth's attraction may sometimes retain these 
 meteors as permanent satellites. A French astronomer 
 believes he has detected one of these bodies that revolves 
 around our globe in a period of three hours and twenty 
 minutes. The distance of this singular companion of 
 the moon is 5,000 miles from the surface of the earth. 
 Occasionally these meteors are drawn to the earth by its 
 superior attraction, and fall to the ground as meteoric 
 stones. 
 
 MARS. 
 
 135. His Distance, Period of 'Revolution , etc. The next 
 planet in the order of distance from the sun is Mars. 
 He is consequently the first of those planets whose orbit 
 encloses that of the earth, and which have therefore been 
 called exterior or superior planets. ' Mars appears to the 
 naked eye as the reddest star in the heavens. 
 
 His mean distance from the sun is 145,000,000 miles, 
 but, in consequence of the eccentricity or ^flattened form 
 of his orbit, he is about 27,000,000 miles nearer the sun 
 at perihelion than at aphelion. His sidereal period is 
 somewhat less than two years, and his synodical period 
 somewhat more than two years. 
 
 The plane of Mars's orbit is inclined to the ecliptic 
 at an angle of less than 2. The apparent diameter of 
 the planet varies considerably, since his distance from 
 the earth varies considerably. He must be the diameter 
 
158 ASTRONOMY. 
 
 of the earth's orbit nearer to us at opposition than at 
 conjunction. When nearest the earth his diameter sub- 
 tends an angle of more than 30", while at his greatest 
 distance the diameter subtends an angle of only 4". The 
 real diameter of this planet is about 4,500 miles. When 
 examined with a telescope of sufficient power, the disc 
 of Mars appears perfectly round at opposition and con- 
 junction, while in every other part of his orbit the disc 
 is more or less gibbous, according to the distance of the 
 planet from quadrature, when the illuminated disc differs 
 most from a circle. These phases prove that Mars, like 
 Mercury and Venus, shines with light borrowed from the 
 sun. At opposition and conjunction he turns the same 
 face toward us and toward the sun, and hence we see 
 the whole of his illuminated hemisphere ; while in other 
 parts of his orbit he does not turn quite the same face to 
 us and to the sun, hence he appears more or less gibbous. 
 This planet is most favorably situated for observation 
 at perihelion and opposition. Opposition occurs, as al- 
 ready stated, once in a little over two years ; and opposi- 
 tion and perihelion occur together once in about eight 
 years. 
 
 136. The Physical Characteristics of Mars. When 
 viewed under proper Optical powers, the surface of this 
 planet presents outlines of seas and continents similar to 
 those on our globe, and usually white spots are discerni- 
 ble near the poles, which, from their alternate diminution 
 and increase, according as one pole is turned to or from 
 the sun, are conjectured to be masses of snow. The 
 color of the continents is a dull red ; that of the seas 
 greenish, as by contrast with the land it should be. It is 
 this prevailing color of the land which gives the planet 
 that ruddy light by which it is at all times readily dis- 
 tinguished from the other planets and from the fixed stars. 
 By observing the spots on the surface the time of the 
 
ASTRONOMY. 
 
 159 
 
 axial rotation of Mars has been determined to be about 
 24^ hours. His axis is inclined to the plane of his orbit 
 at an angle of about 61. 
 
 Consequently Mars experiences about the same changes 
 of seasons as the earth, though each season is about twice 
 as long. 
 
 Mars, like the earth, is not perfectly spherical ; it is 
 somewhat flattened at the poles, though the amount of 
 the flattening is not yet accurately ascertained. 
 
 It is quite certain that Mars has an atmosphere of con- 
 siderable density, since small stars are obscured as they 
 
l6o ASTRONOMY. 
 
 approach its disc. The existence of snow near the poles 
 proves that there must be aqueous vapor in the atmos- 
 phere of Mars ; and the existence of the aqueous vapor 
 goes to prove that there are seas on the surface of the 
 planet, as is also indicated by the greenish spots. 
 
 Figure 68 shows the white spots, supposed to be masses 
 of snow, and also the markings on the disc. It will be 
 seen that the spots are not exactly at the poles. 
 
 137. The Inner Group of Planets. We now see that 
 the four planets, Mercury, Venus, the Earth, and Mars, 
 form a group of planets with certain resemblances. They 
 all, so far as known, have an axial rotation of about 
 twenty-four hours ; all have atmospheres ; they differ com- 
 paratively little in size, and are all small in comparison 
 with another group with which we shall soon become ac- 
 quainted ; and only one of them, the earth, has a satellite. 
 
 SUMMARY* OF THE INNER GROUP OF 
 PLANETS. 
 
 The first planet of this group is Mercury. He revolves 
 about the sun in about three months, and rotates on his 
 axis in about twenty-four hours. (102.) 
 
 The orbit of Mercury lies wholly within that of the 
 earth. His diameter is somewhat less than one half that 
 of the earth. He presents phases like the moon. (103.) 
 
 These phases are owing to the fact that Mercury shines 
 by reflected light. (104.) 
 
 Schroter thought he detected spots on the disc of Mer- 
 cury which indicate the presence of mountains. By ob- 
 serving these he decided that this planet rotates on its 
 axis in about twenty-four hours. (105.) 
 
 The existence of twilight shows that Mercury has an 
 atmosphere. (106.) 
 
 The second planet of this group is Venus. Her diam- 
 
ASTRONOMY. l6l 
 
 eter is a little less than that of the earth. She completes 
 a revolution round the sun in about yj months, and pre- 
 sents phases like Mercury. (107.) 
 
 Schroter detected slight irregularities in the terminator 
 of Venus, which indicate the existence of mountains. By 
 observing certain spots he concluded that Venus rotates 
 on her axis in about twenty-four hours. Venus also has 
 an atmosphere. (108.) 
 
 She is believed to have no satellite. (109.) 
 
 The next and largest planet of this group is the earth. 
 This planet is attended by one satellite. (113.) 
 
 The last planet of the inner group is Mars. His orbit 
 lies wholly without that of the earth. He revolves about 
 the sun in a period of somewhat less than two years. The 
 diameter of Mars is a little more than half that of the 
 earth. Mars often appears somewhat gibbous. (135.) 
 
 His disc presents outlines of seas and continents similar 
 to those which exist on the earth, and white spots near 
 the poles, which are thought to be patches of snow. Mars 
 resembles the earth in his change of seasons. He also 
 has an atmosphere of considerable density. (136.) 
 
 The four planets, Mercury, Venus, the Earth, and Mars, 
 have well-marked resemblances. They constitute what 
 may be called the Inner Group of Planets. (137.) 
 
 The Zodiacal Light (in, 112) and Meteoric Rings (133, 
 134) lie within the limits of this group. 
 
 THE MINOR PLANETS. 
 
 138. Bodfs Law. Between the orbit of Mars and 
 that of Jupiter, the next of the planets known to the 
 ancients, there is an interval of 350,000,000 miles, in 
 which no planet was known to exist before the beginning 
 of the present century. 
 
 Three hundred years ago, Kepler had pointed out 
 
162 ASTRONOMY. 
 
 something like a regular progression in the distances of 
 the planets as far as Mars, which was broken in the 
 case of Jupiter, and he is said' to have suspected the 
 existence of another planet in the great space separating 
 these two bodies. The question attracted little further 
 attention until Uranus was discovered by Sir William 
 Herschel in 1781, when several German astronomers re- 
 vived the opinion held by Kepler, and, guided by a law 
 of planetary distances published by Professor Bode of 
 Berlin, even approximated to the period of the supposed 
 latent body. According to this law, the distance of a 
 planet is about double that of the next interior one, and 
 half that of the next exterior one, and, roughly speak- 
 ing, this rate of progression of the planetary distances 
 is found to hold good with this exception. Mars is sit- 
 uated at a distance about twice that of the earth, but 
 very much less than half that of Jupiter ; and again, Ju- 
 piter revolves at half the distance of the next exterior 
 planet, Saturn, but considerably more than twice that of 
 Mars. If, therefore, another planet existed between 
 Mars and Jupiter, the progression of Bode's law, instead 
 of being interrupted at this point, might perhaps be 
 found to hold good as far as Uranus. For this reason, 
 an association of astronomers was formed, and a regular 
 plan of search was devised with a view to the discovery 
 of the suspected planet. 
 
 139. The Discovery of Ceres. Professor Piazzi, Direc- 
 tor of the Observatory at Palermo, repeatedly sought for 
 a star numbered in Wollaston's Catalogue, but finding 
 none in the position there assigned, he observed all the 
 stars of similar brightness in the vicinity. On the ist 
 of January, 1801, or about the time the search for the 
 supposed body was begun, he determined the place of 
 an object shining as a star of the eighth magnitude not 
 far from the position of the missing one. On ,the fol- 
 
ASTRONOMY. 163 
 
 lowing night the place of this star was sensibly altered. 
 Piazzi regarded this object as a comet, and announced 
 its discovery as such on the 24th of January. On the 
 publication of the whole series of positions observed at 
 Palermo, Professor Gauss of Gottingen undertook the 
 determination of the orbit of Piazzi's star, and announced 
 that it revolved round the sun at a mean distance of 
 2.7 times the distance of the earth. This distance agree- 
 ing so closely with that indicated by Bode's law for the 
 planet supposed to exist between Mars and Jupiter, as- 
 tronomers were very soon led to regard Piazzi's comet 
 as in reality a new planet, fulfilling, in a remarkable man- 
 ner, the condition, in respect to distance from the sun, 
 which had been found to hold good for the other mem- 
 bers of the planetary 'system. This new planet was 
 named Ceres. Its minuteness has prevented any exact 
 determination of its diameter. Sir William Herschel's 
 measurement makes it one hundred and sixty-three miles 
 in diameter. Observers have remarked a haziness sur- 
 rounding the planet, which is attributed to the density 
 and extent of its atmosphere. Ceres is generally just 
 beyond the range of unaided vision, though it has been 
 seen without the telescope. 
 
 140. The Discovery of Pallas. In order to find Ceres 
 more readily, Dr. Olbers examined minutely the configu- 
 ration of the small stars lying near her path. On the 
 28th of March, 1802, after observing the planet, he swept 
 with his telescope over the north wing of Virgo, and was 
 astonished to .find a star of the seventh magnitude, where 
 he was certain no star was visible in January and February 
 preceding. In the course of three hours he found that the 
 right ascension and declination of the star had changed. 
 On the follovring evening he found the star had moved 
 considerably, and he became convinced t'iat it was a 
 planet. He named this new body Pallas. Its orbit was 
 
164 ASTRONOMY* 
 
 soon determined by Professor Gauss, who found that its 
 most remarkable peculiarity consisted in the great in- 
 clination of its plane to the ecliptic. This inclination is 
 34, while that of Mercury, which is the greatest among 
 the larger planets, is only 7. Its mean distance from the 
 sun was found to be nearly the same as that of Ceres. 
 
 Dr. Olbers showed that the orbits of the newly discov- 
 ered planets approached very near each other at the as- 
 cending node of Pallas, a circumstance which led him 
 to make his remarkable conjecture as to the common 
 origin of these bodies. He thought that a much larger 
 planet had, in remote ages, existed near the mean dis- 
 tance of Ceres and Pallas ; that, by some tremendous 
 catastrophe, this body had been shattered ; and that the 
 two small planets were among the fragments. This hy- 
 pothesis seemed to be materially strengthened by subse- 
 quent discoveries, though it is now generally admitted to 
 be without foundation. The diameter of Pallas seems 
 to be about 600 miles. 
 
 141. The Discovery of Juno. In 1804 Professor Har- 
 ding, of Lilienthal, while preparing a chart of the small 
 stars lying near the paths of Ceres and Pallas, with a 
 view to assist the identification of these minute bodies, 
 discovered a small object which he recognized as a planet 
 by its movement. This planet he named Juno. 
 
 142. The Discovery of Vesta. Dr. Olbers, following up 
 his idea respecting the origin of this zone of planets, con- 
 sidered, from the fact that the orbits of the three already 
 found intersect one another in Virgo and Cetus, that the 
 explosion must have taken place in one or the other of 
 those regions, and consequently that all the fragments 
 should pass through them. Provided with an ordinary 
 night glass, he examined every month the small stars of 
 Virgo and of Cetus, according as the one or the other 
 of these constellations was the more favorably situated 
 
ASTRONOMY. 165 
 
 for observation. In 1807 he discovered a small star in 
 Virgo, where there had been none on a previous exami- 
 nation, and he soon satisfied himself that the star was 
 really in motion, and thus recognized it as a planet. This 
 planet was named Vesta. Its diameter is about 300 miles. 
 Dr. Gibers continued his systematic examination of the 
 small stars of Virgo and Cetus between the years 1808 
 and 1816, and was so closely on the watch for a moving 
 body, that he considered it highly improbable that a planet 
 could have passed through either of these regions in the 
 interval without detection. No further discovery being 
 made, the plan was relinquished in 1816. 
 
 143. More Recent Discoveries of Minor Planets. After 
 Dr. Olbers discontinued his search for planets, the subject 
 appears to have attracted little attention until Hencke, 
 an amateur astronomer, took up the search with a zeal 
 and diligence which could hardly fail in producing some 
 important result, and he was rewarded in 1845 by the dis- 
 covery of a fifth planet, which was named Astrcea, and in 
 1847 by the discovery of Hebe. Since 1845 tne discovery 
 of these bodies has been very frequent, and their number 
 has now reached 95. 
 
 144. The Group of Minor Planets. There is, then, be- 
 tween Mars and Jupiter, a group of minute planets, spread 
 through a zone some 50,000,000 miles in diameter. Their 
 orbits are generally more flattened than those of the larger 
 planets, and their planes are more inclined to the ecliptic ; 
 though they differ greatly in this respect, since the orbits 
 of some of them nearly coincide with the ecliptic. There 
 is good reason to suppose that many more will be dis- 
 covered. 
 
 These planets are often called asteroids (star-like bodies). 
 
1 66 ASTRONOMY. 
 
 SUMMARY OF THE MINOR PLANETS. 
 
 Kepler suspected the existence of an unknown planet 
 between Mars and Jupiter. The discovery of Uranus in 
 1781 led the German astronomers to undertake a syste- 
 matic search for this suspected body. They were guided 
 by Bode's law of planetary distances. (138.) 
 
 In 1801 Pipzzi discovered Ceres, but supposed it to be a 
 comet. Professor Gauss showed it to be a planet, and that 
 it is at about the distance from the sun required by Bode's 
 law. (139.) 
 
 In 1802 Dr. Olbers discovered Pallas, The marked 
 peculiarity of this planet is the great inclination of its orbit 
 to the plane of the ecliptic. Since near the ascending 
 node of Pallas the orbit of this planet and of Ceres very 
 nearly coincide, Dr. Olbers was led to believe that Ceres 
 and Pallas were the fragments of a broken planet. (140.) 
 
 In 1804 Juno was discovered by Harding. (141.) 
 
 Dr. Olbers now began a systematic search for other 
 fragments of his broken planet. In 1807 he discovered 
 Vesta. He continued his search till 1816 without further 
 fruit. (142.) 
 
 No more of these minute planets were discovered till 
 1845, when Hencke discovered Astraa. In 1847 ne dis- 
 covered Hebe. Since that time these bodies have been 
 discovered with considerable frequency. Their number 
 now reaches 95. Astronomers do not now believe that 
 these bodies are fragments of a broken planet. (143-) 
 
 The Minor Planets form a well-marked group. (144.) 
 
ASTRONOMY. 167 
 
 JUPITER. 
 
 145. Its Distance, Period, Size, etc. From the regions 
 of space where we have just seen the smallest members 
 of our system moving in their orbits, we pass abruptly to 
 a group of planets of a very different order. The first 
 planet of this group is Jupiter. 
 
 To the naked eye, Jupiter appears as a Star of the first 
 magnitude, the brightness of which is sometimes sufficient 
 to cast a shadow. It is the most brilliant of the planets 
 except Venus. 
 
 The mean distance of this planet from the sun is 
 496,000,000 miles. He moves in an orbit which differs 
 considerably from a circle, so that his distance from the 
 sun at aphelion is about 48,000,000 miles greater than 
 at perihelion. Of course the difference of his distance 
 from the earth at conjunction and opposition is still 
 greater. He completes a revolution in about twelve 
 years. 
 
 The plane of Jupiter's orbit very nearly coincides with 
 that of the ecliptic, being inclined to it by an angle of a 
 little over i. 
 
 The diameter of Jupiter is about 89,000 miles, or about 
 eleven times the diameter of the earth. The bulk, there- 
 fore, of this immense planet is about 1400 times that 
 of our globe. If seen at the distance of. our satellite, 
 his disc would cover a space in the sky 1200 times that 
 occupied by the disc of the full moon. Yet this mass is 
 travelling through space with a velocity about eighty times 
 that of a cannon ball. 
 
 Jupiter, like the earth, is not a perfect sphere, but an 
 ellipsoid flattened at the poles. This flattening is much 
 greater than in the case of the earth. 
 
 As has already been stated (77), Jupiter is accom- 
 
1 68 ASTRONOMY. 
 
 panied by four satellites. These appear in the telescope 
 as so many points of light oscillating in short periods 
 across the planet 
 
 146. Its Physical Characteristics. On examining the 
 surface of Jupiter with a telescope, we see no appearance 
 of regular continents or seas, as on the surface of Mars ; 
 but daik streaks, or belts, are found to cross his disc, pre- 
 senting some of the modifications of clouds in our own 
 atmosphere. Occasionally these belts retain nearly the 
 same form and position for months together, while at 
 other times they undergo great and sudden changes, and, 
 in one or two instances, have been observed to break up 
 and spread themselves over the whole disc of the planet. 
 Generally there are two belts much more strongly marked 
 than the rest, and more nearly permanent in their charac- 
 ter, one situated a little north and the other a little south 
 of the planet's equator. The prevailing opinion among 
 astronomers is that these phenomena are produced by dis- 
 turbances in the planet's atmosphere, which occasionally 
 render its dark body visible ; and as the belts are found 
 to traverse the disc in lines uniformly parallel to Jupiter's 
 equator, (see Figure 69,) we are naturally led to the 
 conclusion that these disturbances are connected with the 
 rotation of the planet on its axis, in the same way that the 
 trade winds on the earth are connected with its rotation 
 on its axis. 
 
 In July, 1665, Cassini, of Paris, remarked a black spot 
 of considerable apparent magnitude on the upper edge 
 of the southern belt of Jupiter, which remained visible 
 two years. This spot, or one supposed to be identical 
 with it, has repeatedly appeared since that time, but at 
 very irregular intervals. 
 
 In 1834, a remarkable spot was discovered on the north- 
 ern belt. It was black and well defined ; about two thirds 
 of its breadth was above the belt, and one third upon it. 
 
 
ASTRONOMY. 169 
 
 Fig. 69. 
 
 Shortly after this spot was first noticed a second distinct 
 spot was discovered on the same belt. These spots re- 
 mained wholly unchanged for nearly a year. Cassini no- 
 ticed that the spot of 1665 appeared to traverse the disc of 
 the planet from east to west. It was very conspicuous near 
 the centre of the disc, but gradually faded away as it ap- 
 proached the western limb. The motion seemed quickest 
 when the spot was near the centre", and became slower 
 towards the edge of the planet. Hence he inferred that 
 the spot adhered to the surface of the planet, and was car- 
 ried across the disc by the rotation of Jupiter upon his 
 axis. This hypothesis would account fully for the ap- 
 pearances observed. By closely watching the movements 
 of the spot, Cassini ascertained that the time of rotation 
 of the planet was 9 hours 56 minutes. 
 
 By careful observations of the spots of 1834 the time 
 
 of rotation was found to be about half a minute less. 
 
 This enormous globe, whose diameter is eleven times 
 
 greater than that of the earth, is therefore whirled upon 
 
 8 
 
1 70 ASTRONOMY. 
 
 its axis in less than ten hours. The axis of rotation is 
 very nearly perpendicular to the plane of the orbit. 
 
 147. The Satellites of Jupiter. These bodies were dis- 
 covered by Galileo in 1610. They shine with the bril- 
 liancy of stars between the sixth and seventh magnitude ; 
 but owing to their proximity to the planet they are invisi- 
 ble to the naked eye. 
 
 Their configuration is continually changing. Sometimes 
 they are all situated on one side of the planet, though 
 more often one at least is found on each side. In very 
 rare instances all four have been invisible, as on the 2ist 
 of August, 1867, when the planet appeared thus unattend- 
 ed for one hour and three quarters. It is not a rare oc- 
 currence to find only one satellite visible. 
 
 Sir William Herschel, from a long series of observa- 
 tions on the satellites, concluded that they rotate on 
 their axis in the time of one synodical revolution around 
 Jupiter, thus presenting an analogy to our own satellite. 
 He was led to this conclusion on remarking the great 
 changes in the relative brightness of the satellites in 
 different positions, which were found to follow such a 
 law as could be reconciled only with this hypothesis. 
 
 148. The Eclipses of these Satellites. If Jupiter were 
 a self-luminous body, the satellites would disappear only 
 when they pass behind him. But they disappear at other 
 times and in such a way as to show that the planet must 
 be an opaque, non-luminous body. This will be seen by 
 reference to Figure 70. 
 
 If Jupiter be non-luminous, he will cast a shadow di- 
 rectly away from the sun, as shown in the figure. The 
 satellites will then disappear, not only when they pass 
 behind the planet (as in the case of the satellites m and 
 m " when the earth is at E\ but also when they pass 
 through the shadow of the planet (as in the case of m 
 when the earth is at E') ; and this they are found to do. 
 
ASTRONOMY. 
 Fig. 70. 
 
 171 
 
 When they disappear behind the planet they are occulted ; 
 when they pass through the shadow they are eclipsed. 
 The entrance of the satellite into the shadow is called 
 its immersion, and its exit from the shadow its emersion. 
 The shadow is sometimes so projected that both the im- 
 mersion and emersion of the satellite can be seen, and 
 at other times so that only one of them can be seen. 
 Three of the satellites are totally eclipsed at every revolu- 
 tion, while the fourth is often only partially eclipsed, or 
 
172 ASTRONOMY. 
 
 not eclipsed at all, since its orbit is inclined to the orbit 
 of Jupiter by a greater angle than that of the others. 
 
 When a satellite passes between -us and Jupiter it makes 
 a transit across his disc. As seen by the rigure the shad- 
 ow of the satellite, as m ', is often projected on the disc at 
 a different place from the satellite itself. The shadow 
 always appears as a round black spot upon the disc, while 
 the satellite usually appears as a bright spot, often brighter 
 than the general disc of Jupiter. They have, however, 
 been observed as dark spots, a phenomenon which can be 
 accounted for only by supposing that such spots really 
 exist on the satellites themselves, for their illuminated face 
 must be turned towards us at the time. 
 
 SATURN. 
 
 149. Distance, Period, Size, etc. The next planet in 
 the order of distance from the sun is Saturn, who per- 
 forms his revolution in about 29^ years, at a mean dis- 
 tance of 909,000,000 miles from the sun, in an orbit con- 
 siderably flattened, and inclined to the ecliptic at an angle 
 of about 2-J degrees. 
 
 The diameter of Saturn is found to be about 73,000 
 miles, or about nine times that of the earth. The bulk of 
 Saturn is consequently about eight hundred times that of 
 the earth. 
 
 Though belts are frequently observed with good tele- 
 scopes on the surface of Saturn, they are much less dis- 
 tinct than those of Jupiter. Spots are of rare occurrence. 
 One was seen by Sir William Herschel in 1780 for several 
 days, and another quite distinct was seen in 1847. 
 
 In 1793, Sir W. Herschel saw a quintuple belt. By 
 very frequent and careful examination of the appearance 
 of this belt he ascertained that the time of rotation of 
 Saturn is a little over ten hours. 
 
ASTRONOMY. 173 
 
 The axis of rotation is inclined to the plane of the 
 planet's orbit at an angle of about 63. His seasons are 
 therefore more diversified than those of Jupiter. 
 
 150. The Satellites and the Rings of Saturn. Though 
 Saturn is smaller than Jupiter, his system is far more com- 
 plicated. He is attended by eight satellites. While the 
 satellites of Jupiter are known respectively as the first, 
 second, third, and fourth, those of Saturn have mythologi- 
 cal names. Their names in the order of distance are 
 Mimas, Enceladus, Tethys, Dione, Rhea, Titan, Hype- 
 rion, and Japetus. Of these Titan is the largest. But 
 the most interesting feature of the Saturnian system is his 
 rings. 
 
 When Galileo turned his newly constructed telescope 
 upon Saturn, he saw that the figure of the planet was not 
 round as in the case of Jupiter. At first he thought it to 
 be oblong, but on further examination he concluded that 
 the planet consisted of a large globe, with a smaller one 
 on each side of it. Continuing his observation he re- 
 marked that this appearance was not constantly the 
 same, the appendages on each side of the central globe 
 gradually diminishing until they vanished entirely, and left 
 the planet nearly round, without anything extraordinary 
 about it. He therefore concluded that he had been 
 mocked by an optical illusion. 
 
 Huyghens, who possessed telescopes of greater power 
 than those of the Italian astronomer, was the first who 
 gave a correct explanation of these varied appearances, 
 and detected a luminous ring surrounding the globe of 
 Saturn. In 1675, Cassini discovered a division separat- 
 ing the ring into two concentric rings. This division had 
 been detected ten years previously by two English ama- 
 teurs. 
 
 The ring of Saturn may be described as broad and 
 flat, situated exactly in the plane of the planet's equator, 
 
174 
 
 ASTRONOMY. 
 
 an .1 consequently inclined to the ecliptic at an angle of 
 about 28. It keeps this same inclination throughout the 
 revolution of Saturn. The plane of the ring therefore 
 intersects the ecliptic. It is owing to this inclination 
 that the ring is sometimes observed as a broad ellipse, 
 
 at other times as a straight line barely discernible with 
 the most powerful telescopes, and that at other times the 
 ring entirely disappears. These phases of the ring will 
 be understood by reference to Figure 71. 
 
 In two positions of the planet the plane of the ring is 
 seen to pass through the centre of the sun, and of course 
 
ASTRONOMY. 1 75 
 
 only its edge is illumined. Now the ring is estimated to 
 be about one hundred miles thick. This thickness, at the 
 distance of Saturn, .would subtend an angle just about 
 equal to that of a good-sized pin at the distance of two 
 miles. Hence in these two positions the ring will appear 
 as a line of light discernible only with the most powerful 
 telescopes. Suppose that some time before the ring came 
 into the position marked 1848 the earth was at A : then 
 the plane of the ring would pass between the earth and 
 the sun, and the unillumined side of the ring would be 
 turned towards us, and the ring would of course disap- 
 pear. So, too, if some time after the ring came into this 
 position the earth were at B, the plane of the ring would 
 again pass between the earth and the sun, and the ring 
 would again disappear. At the positions marked 1855 
 and 1869, the ring would appear as a broad ellipse. 
 
 More recent observations go to show that the two di- 
 visions of Saturn's ring are further subdivided, so as to 
 constitute a multiple ring. 
 
 The most recent, and at the same time one of the most 
 remarkable discoveries with reference to the rings of 
 Saturn, is that of a dusky or obscure ring, nearer to the 
 planet than the intensely bright one. This dusky ring 
 seems to have been first noticed by Dr. Galle of Berlin, 
 but this notice attracted but little attention till 1850, when 
 the phenomenon was remarked by Prof. Bond, of Cam- 
 bridge, Mass., and by Mr. Dawes, of England. The latter 
 detected a division of the obscure ring. 
 
 This newly discovered ring is quite transparent, allowing 
 the disc of the planet to be seen through it. 
 
 Fig. 72 represents Saturn with his system of rings. 
 
 When the ring last appeared, as a mere line, in 1861 
 and 1862, singular appendages, like clouds of less intense 
 light, were noticed lying on each side of the ring. 
 
 The ring of Saturn has been supposed to be solid, and 
 
to be liquid; and able mathematicians have in turn de- 
 monstrated that it can be neither. It is now held by some 
 that it is composed of innumerable little satellites revolv- 
 ing about the planet, in the plane of his equator. 
 
 The system of rings seems to be increasing in breadth 
 at the rate of about twenty-nine miles a year. 
 
 URANUS. 
 
 151. Its Discovery. Previous to the year 1781, the only 
 planets known, beside the one we inhabit, were Mercury, 
 Venus, Mars, Jupiter, and Saturn. All of these are more 
 or less conspicuous to the naked eye, and were recognized 
 
ASTRONOMY. 177 
 
 from the earliest antiquity as wandering bodies. Saturn 
 was supposed to be the most distant member of the solar 
 system, and very little suspicion of the existence of an 
 exterior planet was entertained. The close examination 
 of the heavens, begun by Sir William Herschel in 1781, 
 led to a discovery which more than doubled the area of 
 our system. 
 
 On the i3th of March, 1781, while exploring with his 
 telescope the constellation of the Twins, he observed a 
 star, the disc of which attracted his attention. Perceiving, 
 after a few nights of observation, that the new body moved, 
 he at first mistook it for a comet ; but it soon became evi- 
 dent that it was a new planet, outside the orbit of Saturn. 
 
 152. Its Period, Distance, Size, etc. This planet may 
 just be discerned by a person of very good eyesight, 
 without a telescope. Uranus revolves about the sun in a 
 period of about eighty-four years, at a mean distance of 
 1,828,000,000 miles, in an elliptical orbit, whose plane is 
 inclined to the ecliptic at an angle of less than i. Its 
 diameter is about 36,000 miles. 
 
 No telescopes hitherto constructed have succeeded in 
 showing any spots or belts upon this planet, owing to its 
 enormous distance and the consequent minuteness of its 
 disc. The time of its rotation, and the position of its 
 axis with respect to the plane of its orbit, are, therefore, 
 unknown, and are likely to remain so. 
 
 153. Its Satellites. Sir William Herschel. thought he 
 had detected six satellites of this planet, but it is now 
 pretty well established that there are but four. It is a 
 curious fact that the satellites of Uranus, unlike those of 
 the earth, Jupiter, and Saturn, revolve in a retrograde direc- 
 tion, that is, from east to west, and that their orbits 
 are inclined at a very large angle to that of the planet. 
 
 8* L 
 
178 ASTRONOMY. 
 
 NEPTUNE. 
 
 154. Its Period, Distance, Size, etc. The next planet in 
 the order of distance from the sun, and, so far as we know, 
 the last of the solar system, is Neptune. He revolves 
 around the sun in a period of 164 years, at a mean dis- 
 tance of 2,862,000,000 miles, in an orbit inclined to the 
 ecliptic at an angle of a little less than 2. His diameter 
 is about 35,000 miles. No spots can be detected on his 
 disc, and consequently nothing is known about his time of 
 rotation or the inclination of his axis. He is certainly at- 
 tended by one satellite, which, like those of Uranus, moves 
 in a retrograde direction. 
 
 155. Its Discovery. Though we know so little of this 
 most distant member of our system, yet the circumstances 
 of its discovery give it an enduring interest. 
 
 It will be shown, further on, that the planets, by their 
 mutual action, disturb one another's orbits to a slight ex- 
 tent, so that none of them describe exact ellipses. It had 
 been noticed for many years that the motion of Uranus 
 was not exactly what it was calculated it should be, after 
 making allowance for all known causes of disturbance. 
 Two young mathematicians, M. Le Verrier, of France, and 
 Mr. Adams, of England, were led, unknown to each other, 
 to inquire into the cause of this apparent anomaly, and 
 both soon came to the conclusion that a planet of consid- 
 erable magnitude must exist outside the orbit of Uranus. 
 Their next object was to ascertain the position of the 
 planet amongst the stars, with a view to its actual discov- 
 ery in the telescope ; but the problem to be solved was 
 one of excessive difficulty, so much so, in fact, that sev- 
 eral of the most eminent astronomers had declared their 
 conviction that the place of the latent planet could never 
 be discovered by calculation. M. Le Verrier and Mr. 
 
ASTRONOMY. 179 
 
 Adams were of a different opinion, and finally succeeded in 
 their researches, which assigned nearly the same position 
 to the body whose influence had been so visibly exercised 
 on the movements of Uranus. Mr. Adams, however, did 
 not make his conclusions public through the press, and 
 much of the first glory of this great discovery was conse- 
 quently given to the French astronomer, who had an- 
 nounced the position of the new planet to the Academy 
 of Sciences at Paris in the summer of 1846. On the 23d 
 of September, of the same year, Dr. Galle, of the Royal 
 Observatory, Berlin, acting upon the urgent representa- 
 tions of M. Le Verrier, contained in a letter which reached 
 Berlin at this date, turned the large telescope of the 
 observatory to that part of the heavens in which M. Le 
 Verrier had informed him he would find the disturbing 
 planet. Hardly was this done when a pretty bright tele- 
 scopic star appeared in the field of view, at a point where 
 no such object was marked in a carefully prepared map 
 of that part of the heavens. This proved to be the pre- 
 dicted planet, and the name Neptune was given to it by the 
 common consent of M. Le Verrier, Mr. Adams, and the 
 chief astronomers of Europe. 
 
 In calculating the position of this planet, they had as- 
 sumed, according to Bode's law, that it would be about 
 twice as distant as Uranus. But the mean distance of 
 Neptune is found to be considerably less than double that 
 of Uranus ; hence this law, which led to the discovery of 
 minor planets, and helped in the discovery of Neptune, has 
 singularly enough been overthrown by these discoveries. 
 
 156. The Outer Group of Planets. The third outer 
 group of planets comprises the large bodies outside the 
 ring of telescopic planets. Jupiter, Saturn, Uranus, and 
 Neptune belong to this group. So far as known, they 
 rotate in periods of about ten hours, and three of them 
 at least are attended by a number of satellites. They 
 have also a very slight density. 
 
l8o ASTRONOMY. 
 
 SUMMARY OF THE OUTER GROUP OF 
 PLANETS. 
 
 The first and largest planet of this group is Jupiter. 
 His diameter is about eleven times that of the earth. 
 He completes a revolution in about twelve years, and is 
 attended by four satellites. (144.) 
 
 The disc of Jupiter is crossed by a number of parallel 
 belts, which sometimes resemble clouds. The most strong- 
 ly marked of these are situated near the equator of the 
 planet. They are probably due to a disturbance in Ju- 
 piter's atmosphere analogous to our trade winds. By ob- 
 servation of certain well-marked spots Jupiter has been 
 found to rotate on his axis in a little less than ten hours. 
 
 (145.) 
 
 The satellites of Jupiter were first discovered in 1610. 
 They are occulted when they pass behind the planet ; 
 eclipsed when they pass into its shadow ; and make tran- 
 sits across the planet's disc when they pass between it 
 and the sun. At rare intervals Jupiter is seen without 
 satellites. (146, 147.) 
 
 The next planet of this group is Saturn. He is not so 
 large as Jupiter, his diameter being but nine times that of 
 the earth. He completes a revolution in about 29 \ years. 
 He has belts, but they are less marked and less perma- 
 nent than those of Jupiter. He is found to rotate on his 
 axis in about ten hours. (148.) 
 
 Saturn is attended by eight satellites, and by a most re- 
 markable system of rings. These rings are parallel to the 
 plane of the planet's equator, and inclined to that of its 
 orbit at an angle of about 28. It is owing to this in- 
 clination that the rings sometimes appear as broad ellipses, 
 and at other times as mere straight lines. The rings 
 occasionally disappear entirely. Little is known of the 
 
ASTRONOMY. l8l 
 
 physical constitution of these rings. They are certainly 
 several in number, and appear to be slowly increasing 
 in breadth. (149.) 
 
 Mercury, Venus, Mars, Jupiter, and Saturn are the only 
 planets visible to the naked eye, and up to the year 1781, 
 they were the only ones known to exist In that year 
 Herschel announced the discovery of a new planet, since 
 named Uranus. (150.) 
 
 Uranus is about twice as distant as Jupiter, and his 
 diameter is about five times that of the earth. He com- 
 pletes a revolution in about 84 years, but nothing is known 
 about his rotation on his axis. (151.) 
 
 He is attended by at least four satellites, all of which 
 have a retrograde motion. (152.) 
 
 The last member of this group, and, so far as we know, 
 of our planetary system, is Neptune. His disc is about 
 the same as that of Uranus. He completes a revolution 
 in about 164 years, while nothing is known about his 
 rotation. Neptune is attended by one satellite, which has 
 a retrograde motion. (153.) 
 
 A peculiar interest attaches itself to this remote body, 
 owing to the circumstances of its discovery. (154.) 
 
 The planets, so far as known, all rotate on their axes 
 from west to east. They also revolve about the sun from 
 west to east, while the satellites, with the exception of 
 those of Uranus and Neptune, revolve about their pri- 
 maries from west to east. The sun and moon also rotate 
 from west to east. 
 
 COMETS. 
 
 157. There is another group of well-known bodies 
 called Comets, which differ in so many respects from 
 the planets that they seem hardly to belong to the same 
 system. 
 
1 82 ASTRONOMY. 
 
 These bodies are observed only in those parts of their 
 orbits which are nearest to the sun. They are not con- 
 fined, like the larger planets, to the zodiac, but appear in 
 every quarter of the heavens, and move in every possible 
 direction. They usually continue visible a few weeks or 
 months, and very rarely so long as a year. Their ap- 
 pearance, with some few exceptions, is nebulous or cloud- 
 like, whence it is inferred that they consist of masses of 
 vapor, though in a highly attenuated state, since very- 
 small stars are often seen through them. 
 
 The more conspicuous comets are accompanied by a 
 tail, or train of light, which sometimes stretches over an 
 arc of the heavens of 50 or upwards, but more fre- 
 quently is of much less extent. 
 
 The same comet may assume very different appearances 
 during its visibility, according to its position with respect 
 to the earth and sun. When first perceptible, a comet 
 resembles a little spot of faint light upon the dark ground 
 of the sky as it approaches the sun its brightness in- 
 creases, and the tail begins to show itself. Generally the 
 comet is brightest when it arrives near its perihelion, and 
 gradually fades away as it recedes from the sun, until it 
 cannot be seen with the best telescopes we possess. 
 
 Some few have become so intensely brilliant as to be 
 seen in full daylight. A remarkable instance of this kind 
 occurred in 1843, when a comet was discovered within 
 a few degrees of the sun himself; and there are one or 
 two similar cases on record. 
 
 The brighter or more condensed part of a comet, from 
 which the tail proceeds, is called the nucleus ; and the 
 nebulous matter surrounding the nucleus is termed the 
 coma ; frequently the nucleus and coma are included un- 
 der the general term head. Some comets have no nuclei, 
 their light being nearly uniform. 
 
 The tail of a comet is merely a prolongation of the neb- 
 
ASTRONOMY. 183 
 
 ulous envelope surrounding the nucleus, and it almost 
 always extends in a direction opposite to that of the sun 
 at the time. In some cases it is long and straight ; in 
 others, curved near the extremity, or divided into two 
 or more branches. A few comets have exhibited two 
 distinct tails. The real length of this train has some- 
 times exceeded 100 or 150 millions of miles ; that of the 
 great comet of 1843 is sa id to have been 200 millions of 
 miles long. 
 
 Comparatively few of the many comets that visit our 
 system are visible to the naked eye. Most of them are 
 faint filmy masses, without tails, which can be seen only 
 with the telescope. 
 
 It is supposed that the general form of the orbits of 
 these bodies is a highly elongated ellipse. 
 
 158. ff alley's and other famous Comets. Astronomers 
 have ascertained with great precision the periods which 
 certain comets require to perform their revolutions round 
 the sun, and are able to predict the times of their reap- 
 pearance, and their paths among the stars. This was first 
 done by Dr. Halley, in the case of the comet observed in 
 1682, which he discovered to be the same that had ap- 
 peared in 1456, 1531, and 1607, and hence concluded 
 that its revolution is accomplished in about seventy- 
 five years. He foretold its reappearance in 1759, which 
 actually took place after a retardation of between one 
 and two years. The same body appeared again in 1835, 
 and will again visit our solar system about the year 
 1911. It may be traced in history as far back as the 
 year n B. C. 
 
 A comet called Encke's has a period of 3^ years; 
 another, Bielcts^ of 6f years ; and several others perform 
 their revolutions in from five to eight years. 
 
 There are a few comets, besides the ones above men- 
 tioned, which complete their journey round the sun in 
 
184 ASTRONOMY. 
 
 from sixty to eighty years ; but it is certain that by far 
 the greater number require hundreds or even thousands 
 of years to perform their revolutions. When this is the 
 case, it becomes almost impossible to assign their exact 
 periods. 
 
 Remarkable comets appeared in 1680 and 1843, both 
 of which approached so near to the sun as almost to 
 graze his surface. The comet of 1811 has acquired great 
 celebrity. It remained visible to the naked eye several 
 months, shining with the lustre of the brighter stars, and 
 attended by a beautiful fan-shaped tail. This body is 
 supposed to require upwards of 3000 years to complete 
 its excursion through space. 
 
 The splendid comet of 1858, generally known as Dona- 
 tfs y will long be remembered for the remarkable physical 
 appearances it presented in the telescope, as well as on 
 account of its imposing aspect to the naked eye. It is 
 presumed to have a period of revolution of about 2100 
 years. 
 
 Hardly less famous in future times will be the grand 
 comet which appeared in 1861. This comet had a tail 
 100 degrees in length. Its period of revolution would 
 appear to be much shorter than that of Donati's comet, 
 probably not exceeding 450 years. 
 
 It is probable that there are many thousands of comets 
 belonging to the solar system, of which a large proportion 
 never come sufficiently near the sun to be seen from the 
 Earth. 
 
 SUMMARY. 
 
 The comets are a group of bodies quite unlike the 
 planets. They are visible only when near the sun. They 
 appear in every quarter of the heavens, and move in every 
 possible direction. 
 
ASTRONOMY. 185 
 
 The largest comets consist of a nucleus, a coma, and a 
 tail. Their trains are often of great length. A comet 
 usually changes its appearance considerably during its 
 visibility. 
 
 Comparatively few comets are visible to the naked 
 eye. (157.) 
 
 Several of the comets are known to return to the sun 
 at intervals of greater or less length. 
 
 Some of the 'most famous comets are Halley's, which 
 has a period of about seventy-five years ; EnckJs, whose 
 period is about three and a half years; those of 1680 and 
 1843, which approached very near the sun ; that of 1811, 
 which remained visible several months, and was attended 
 by a beautiful fan-shaped tail ; Donati's, which is thought 
 to have a period of about 2100 years; and that of 1861, 
 noted for the splendor of its train. (158.) 
 
 THE FIXED STARS. 
 
 159. We have already seen (78) that the stars are not 
 absolutely fixed : many of them are known to be moving 
 at the rate of several miles a second. It is only owing to 
 their immense distance from us and from one another that 
 their configurations do no{ appear to change. The most 
 noticeable feature of the fix^ed stars is their scintillation or 
 twinkling, which contrasts so strongly with the steady light 
 of the principal planets. This twinkling, is an optical 
 phenomenon, supposed to be due to what is termed the 
 interference of light. Humboldt states that in the pure air 
 of Cumana, in South America, the stars do not twinkle 
 after they attain an elevation, on the average, of 15 above 
 the horizon. Hence we must conclude that the twinkling 
 of the stars is due to atmospheric conditions. 
 
 1 60. Their Number. The actual number of stars vis- 
 ible to the naked eye, at the same time, on a clear, dark 
 
1 86 ASTRONOMY. 
 
 night, is between two and three thousand, though a person 
 forming an estimate of their number from casual observa- 
 tion is almost certain to make it very much larger. It is a 
 well-ascertained fact that, in the whole heavens, the stars 
 which can be distinctly seen without the telescope, by any 
 one gifted with good sight, do not exceed six thousand. 
 
 The telescopic -stars are innumerable. It has been con- 
 jectured that more than twenty millions might be seen with 
 one of Herschel's twenty-feet reflectors ; and if we could 
 greatly increase the power of our telescopes, there is no 
 doubt that the number actually discernible would be vastly 
 augmented. 
 
 161. Magnitudes. The stars are divided, according to 
 their degrees of brightness, into separate classes, called 
 magnitudes. The most conspicuous are termed stars of 
 the first magnitude : there are about twenty of these. 
 The next in order of intensity of light are stars of the 
 second magnitude, which are about fifty or sixty in number. 
 Of the third magnitude there are two hundred or upwards, 
 and many more of the fourth, fifth, and sixth. These six 
 classes comprise all the stars that can be well seen with 
 the naked eye on a clear night. Telescopes in common 
 use will show fainter stars to the tenth magnitude inclusive, 
 while the powerful instruments in observatories reveal an 
 almost infinite multitude of , others, even down to the 
 eighteenth or twentieth magnitudes. 
 
 This classification of the stars is, to a great degree, 
 arbitrary, so that it is not unusual to find astronomers dif- 
 fering greatly in their estimates of brightness. 
 
 162. Constellations* For the sake of more readily dis- 
 tinguishing the stars, and referring to any particular quar- 
 ter of the heavens, they have been arranged into groups 
 called constellations, each named from some object to 
 which the configuration of its stars may be supposed to 
 
 * See Appendix, VI. 
 
ASTRONOMY. 187 
 
 bear a resemblance. Many are figures 01 heroes, birds, 
 and animals, connected with the fables of classical my- 
 thology. This mode of grouping the stars is of very 
 ancient date. 
 
 There are twelve constellations in the zodiac (a belt of 
 the heavens extending 8 on each side of the ecliptic, and 
 including the paths of all the larger planets), and hence 
 called the zodiacal constellations, viz. Aries, Taurus, Gemini, 
 Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricor- 
 nus, Aquarius, Pisces. These are also the names of the 
 twelve signs, or divisions of 30 each, into which the zodiac 
 was formerly divided; but the effect of precession (20), 
 which throws back the place of the equinox among the 
 stars from year to year, prevents a constant agreement 
 between these constellations and the corresponding signs. 
 
 163. Names of the Stars. Many of the brighter stars 
 had proper names assigned to them at a very early date, 
 as Sirius, Arcturus, Rigel, Aldebaran, etc., and by these 
 names they are still commonly distinguished. 
 
 The stars are now usually designated by the letters of 
 the Greek alphabet, to which the genitive of the Latin 
 name of the constellation is added, The brightest star is 
 called a (alpha), the next /3 (beta), and so on. Thus, Al- 
 debaran is termed a Tauri ; Rigel, Orionis ; Sirius, a 
 Canis Majoris. 
 
 164. The Color of the Stars. Many of the stars shine 
 with colored light, as red, blue, green, or yellow. 
 
 These colors are exhibited in striking contrast in many 
 of the double stars. Combinations of blue and yellow, or 
 green and yellow, are not uncommon, while in fewer cases 
 we find one star white and the other purple, or one white 
 and the other red. . In several instances each star has a 
 rosy light. 
 
 The following are a few of the most interesting colored 
 double stars : 
 
i88 
 
 ASTRONOMY. 
 
 Name of star. Color of larger one. 
 
 y (gamma) Andromedae, Orange, 
 
 Color of smaller one. 
 
 Sea-green. 
 
 a Piscium, 
 
 Cygni, 
 
 77 (eta) Cassiopeise, 
 
 a- (sigma) Cassiopeiae, 
 
 (zeta) Coronse, 
 
 A star in Argo, 
 
 A star in Centaurus, 
 
 Pale green, Blue. 
 
 Yellow, Sapphire-blue. 
 
 Yellow, Purple. 
 
 Greenish, Fine blue. 
 
 White, Light purple. 
 
 Pale rose, Greenish blue. 
 
 Scarlet, Scarlet. 
 
 Single stars of a fiery red or deep orange color are 
 common enough. Of the first color may be mentioned 
 Aldebaran, Antares, and Betelgeuse. Arcturus is a good 
 example of an orange star. Isolated stars of a deep blue 
 or green color are very rarely found. 
 
 It is now a well-established fact that the stars change 
 their color. Sirius was described as a fiery red star by 
 the ancients. Some years ago it was pure white, while it 
 is now becoming of a decided green color. Capella was 
 also called a red star by the ancients ; it was afterwards 
 described as a yellow star ; and is now bluish. Many other 
 instances of change of color, though less decided, have 
 been detected. 
 
 165. Variable Stars. Besides those stars which are 
 known to undergo changes of color, there are many stars, 
 not only among those visible to the naked eye, but also 
 belonging tb telescopic classes, which exhibit periodical 
 changes of brilliancy. These are called variable stars. 
 
 Algol, or j3 (beta), in the constellation Perseus, is one 
 of the most interesting of the variable stars. For about 
 2 d i3 h it shines as an ordinary star of the second magni- 
 tude, and is therefore conspicuously visible to the naked 
 eye. In somewhat less than four hours it diminishes to 
 the fourth magnitude, and thus remains about twenty 
 minutes ; it then as rapidly increases to the second, and 
 continues so for another period of 2 d i3 h , after which 
 
ASTRONOMY. 189 
 
 similar changes recur. The exact period in which all 
 these variations are performed is 2 d 2o h 48 m 55 s . 
 
 Another remarkable star of this kind is o (omicron) in 
 Cetus, often termed Mira, or the wonderful star. It goes 
 through all its changes in 334 days, but exhibits some 
 curious irregularities. When brightest it usually shines 
 as a star of the second magnitude, yet on certain occa- 
 sions has not appeared brighter than the fourth. Between 
 five and six months afterwards it disappears altogether. 
 Sometimes it will shine without perceptible change of 
 brightness for a whole month ; at others there is a very 
 sensible alteration in a few days. Its variability was dis- 
 covered in the seventeenth century. 
 
 The list of variable stars visible to the naked eye is 
 pretty numerous. Among these are the following : 
 
 8 (delta) Cephei, goes through its changes in 5 d. 9 h. 
 
 77 Aquilae, " " 7*4 
 
 a Herculis, " " 66 days. 
 
 A star in Aquila, " " 72 " 
 
 A star in Corona Borealis, " 323 " 
 
 A star near x (chi) Cygni, " 406 " 
 
 30 Hydrae, " 442 
 
 In some cases the periods extend to many years. 34 
 Cygni, a star whose fluctuations were noticed as long since 
 as 1600, is supposed to complete its cycle of changes in 
 about eighteen years. 
 
 The bright star Capella, in the constellation Auriga, is 
 believed to have increased in lustre during the present 
 century, while within the same period one of the seven 
 bright stars (delta) in Ursa Major, forming the Dipper, 
 has diminished. Many instances of a similar kind might 
 be mentioned. 
 
 Telescopic variable stars are very numerous, and have 
 lately excited much attention. 
 
I QO ASTRONOMY. 
 
 166. Irregular or Temporary Stars. In the present 
 state of our knowledge, it appears necessary to distin- 
 guish between the variable star's, properly so called, 
 which go through their changes with some degree of 
 regularity, and are either always visible or seen at short 
 intervals, and those wonderful objects that have occasion- 
 ally burst forth in the heavens with a brilliancy in some 
 instances far surpassing the light of stars of the first 
 magnitude, or even the lustre of Jupiter and Venus, re- 
 maining thus for a short time, and then gradually fading 
 away. This latter class are called irregular or temporary 
 stars. 
 
 The most celebrated star of this kind recorded in his- 
 tory is one which made its appearance in 1572, and 
 attracted the attention of Tycho de Brahe, the Danish 
 astronomer, who has left us a particular description of 
 the various changes it underwent while it continued within 
 view. It was situated in Cassiopeia, one of the circum- 
 polar constellations, was first seen early in the autumn 
 of 1572, and afterwards dwindled down, until it became 
 so faint, in March, 1574, that Tycho could no longer per- 
 ceive it. During the early part -of its apparition it far 
 surpassed Sirius, and even Jupiter, in brilliancy, and 
 could only be compared to the planet Venus when she 
 is in her most favorable position with respect to the 
 earth. Persons with keen sight could see the star at 
 noon-day ; and at night it was discernible through clouds 
 that obscured every other object. It twinkled more than 
 the ordinary fixed stars ; was first white, then yellow, and 
 finally very red. 
 
 Another temporary star became suddenly visible in Ophi- 
 uchus, in 1604, and was observed by Kepler. Though 
 somewhat inferior to Venus, it exceeded Jupiter and 
 Saturn in splendor. Like Tycho's star, it twinkled far 
 more than its neighbors, but was not characterized by 
 
ASTRONOMY. 19 1 
 
 successive changes of color ; when clear from the vapors 
 prevalent about the horizon, it was always white. This 
 object remained visible till March, 1606, and then disap- 
 peared. 
 
 Other stars, evidently of the same class, are mentioned 
 by historians in remote times. One of a less conspicuous 
 character was discovered by Anthelme, in 1670, not far 
 from ft Cygni ; and another in April, 1848, in the constel- 
 lation Ophiuchus, which rose to the fourth magnitude, 
 and has now faded away to the twelfth, so that it cannot 
 be seen without a good telescope. 
 
 In May, 1866, a remarkable temporary star appeared 
 in the constellation of Corona Borealis. At its greatest 
 brilliancy it was somewhat above the second magnitude. 
 It rapidly faded away and early in June was not above 
 the ninth magnitude. It may be that these temporary 
 stars are merely variable stars of long period. 
 
 167. The Via Lactea, or Milky Way. The Via Lactea, 
 Galaxy, or Milky Way, as it is variously termed, is that 
 whitish luminous band of irregular form which is seen on 
 a dark night stretching across the heavens from one side 
 of the horizon to the other. 
 
 To the naked eye it presents merely a diffused milky 
 light, stronger in some parts than in others ; but when 
 examined with a powerful telescope it is found to consist 
 of myriads of stars, of millions upon millions of suns, 
 so crowded together that only their united, light reaches 
 the unassisted eye. 
 
 The general course of the Milky Way is in a great cir- 
 cle, inclined about 63 to the celestial equator, and inter- 
 secting it in the constellations Cetus and Virgo. 
 
 The distribution of the telescopic stars within its limits 
 is far from uniform. In some regions several thousands 
 (or as many as are seen by the naked eye on a clear 
 night over the whole firmament) are crowded together 
 
192 ASTRONOMY. 
 
 within the space of a square degree : in others a few glit- 
 tering points only are scattered on the black ground of 
 the heavens. It presents in some- parts a bright glow of 
 light to the naked eye, from the closeness of the constitu- 
 ent stars ; in others there are dark spaces with scarcely 
 a single star upon them. A remarkable instance of the 
 kind occurs in the broad stream of the Via Lactea, near 
 the Southern Cross, where its luminosity is very con- 
 siderable ; but there exists in the midst of it a dark 
 oval or pear-shaped vacancy, distinguished by the early 
 navigators under the name of the Coal-Sack. Similar 
 vacancies occur in the constellations Scorpio and Ophi- 
 uchus. 
 
 From the results of a numerical estimate of the stars 
 at various distances from the circle of the Via Lactea, it 
 has been proved that the stars are fewest in number near 
 the poles of that circle, and increase slowly at first, 
 afterwards more rapidly until we arrive at the Milky 
 Way itself, where their number is greatest. 
 
 Hence it is inferred that the stars which cover our 
 heavens are not uniformly distributed throughout space, 
 but, as described by Sir John Herschel, " form a stratum, 
 of which the thickness is small in comparison with its 
 length and breadth." The solar system would appear to 
 be placed somewhat to the northern side of the middle 
 of its thickness, since the density of the stars is rather 
 greater to the south than to the north of the plane of the 
 Via Lactea. From these and other considerations, Sir 
 William Herschel was led to regard our starry firmament 
 as possessing in reality a form of which Figure 73 will 
 convey some idea, one portion being subdivided into two 
 branches slightly inclined to each other. 
 
 The earth being placed at S (not far from the point of 
 divergence of the two streams), the stars in the direction 
 of b and b would appear comparatively few in number, 
 
ASTRONOMY. 
 
 but would increase rapidly as the line of vision ap- 
 proached e, e, or f, in which directions we should see 
 them most densely crowded, the rate of transition from 
 the poorer regions to those richest in stars being such 
 as we have alluded to above. 
 
 Near the intersection of the streams e and <?, few stars 
 would present themselves, and there would consequently 
 be a dark space, or rather a space thinly covered with 
 stars, included within the two branches of the Milky 
 Way. This exactly represents the actual appearance 
 of the heavens : the luminosity of the Milky Way does 
 separate into two distinct streams of light, which remain 
 thus over an arc of about 150, and then unite again. 
 
 1 68. Clusters of Stars and Nebula. On casting our 
 eyes over the heavens on a clear dark evening, we at 
 once perceive that in some directions the stars are clus- 
 tered together, and in a few instances so compressed 
 that the unaided eye cannot separate the members of 
 the group, which assumes a hazy, undefined, or cloud- 
 like appearance. 
 
 Among these close assemblages of stars may be men- 
 tioned the Pleiades in Taurus, Praesepe (popularly termed 
 the Beehive) in Cancer, and a remarkable group in the 
 9 M 
 
194 ASTRONOMY. 
 
 sword-handle of Perseus, in which the stars are readily 
 seen with a common night-glass, though the whole has 
 a blurred aspect to the naked eye. 
 
 One of the most magnificent globular clusters in the 
 northern hemisphere occurs in the constellation Hercules, 
 between the stars Eta and Zeta. It is^visible to the naked 
 eye on dark nights as a hazy-looking object ; and the stars 
 composing it are readily seen with a telescope of moder- 
 ate power. When examined with a powerful instrument, 
 its aspect is grand beyond conception : the stars, which 
 are coarsely scattered at the borders, come up to a per- 
 fect blaze in the centre. It is shown in Figure 74. 
 
 Fig. 74- 
 
 There is another cluster in the constellation Centaurus, 
 of which Figure 75 is a representation. To the naked eye 
 it appears like a nebulous or hazy star of the fourth mag- 
 nitude ; while in the telescope it is found to cover a space 
 two thirds of the apparent diameter of the Moon, over 
 which the stars are congregated in countless numbers. 
 
ASTRONOMY. 
 Fig- 75- 
 
 169. Nebulous Stars. The nebulce have been already 
 described (75). In some instances, a faint nebulosity, 
 usually of a circular figure and several minutes in di- 
 ameter, envelopes a star which is placed in or very near 
 the centre. Such stars are called nebulous stars. There 
 is nothing in their appearance to distinguish them from 
 others entirely destitute of such appendages ; nor can 
 the nebulosity in which they are situated be resolved 
 into stars with any telescopes hitherto constructed. As 
 instances of nebulous stars, may be mentioned one of 
 the fifth magnitude, numbered 55 in Andromeda, and 
 one of the eighth magnitude on the borders of Perseus 
 and Taurus, particularly pointed out by Sir William Her- 
 schel as a remarkakble object of this class. 
 
 170. Variable Nebula. Nebulae, as well as stars, are 
 known sometimes to change in brilliancy. A remarkable 
 case of this kind is that of a nebula situated near Epsilon 
 
196 ASTRONOMY. 
 
 Tauri. At the time of its discovery in 1852 it was easily 
 seen with a good telescope, whereas in 1861 and 1862 it 
 was invisible with instruments of far greater power, thus 
 proving that its light must have undergone very consid- 
 erable diminution in the course of a few years. A small 
 star close to this nebula likewise faded within the same 
 lapse of time. No probable cause has yet been assigned 
 for this variation in the brightness of a nebula. 
 
 171. The Nubeculce, or Magellanic Clouds. In the south- 
 ern hemisphere, not far from the pole of the equator, are 
 two nebulous clouds of unequal extent, the greater cover- 
 ing an area about four times that of the lesser one. They 
 were termed Magellanic clouds, after Magellan the navi- 
 gator, a name still in very common use, but on astronomi- 
 cal maps they are usually called the nubecula, major and 
 minor. 
 
 Both these cloud-like masses are distinctly visible to the 
 naked eye when the moon is absent ; the smaller one, 
 however, disappears in strong moonlight. Their light is 
 white and diffused, resembling that of the Milky Way. 
 Sir John Herschel examined these remarkable objects 
 with his powerful instrument at the Cape of Good Hope, 
 and describes them as consisting of swarms of stars, 
 globular clusters, and nebulae of various kinds, some por- 
 tions being quite irresolvable, and presenting the same 
 milky appearance in the telescope that the nubeculae them- 
 selves do to the naked eye. 
 
 It is believed that the nubeculae are independent of the 
 Via Lactea, since they offer combinations of nebulous 
 forms which rarely occur in that zone. 
 
ASTRONOMY. 197 
 
 SUMMARY. 
 
 The stars are not absolutely fixed. Their twinkling is 
 due to atmospheric conditions, and is caused by interference. 
 
 (159.) 
 
 The number of stars in the whole heavens, visible to 
 the naked eye, is about 6,000. The telescopic stars are in- 
 numerable. ( 1 60. ) 
 
 There are about 20 stars of the first magnitude; about 
 50 or 60 of the second ; and some 200 of the third. The 
 faintest stars that can be seen without the aid of the tele- 
 scope are of the sixth magnitude. (161.) 
 
 The stars are arranged in groups called constellations. 
 Twelve of these are called zodiacal constellations. (162.) 
 
 Many of the brightest stars have proper names, but stars 
 are usually designated by the letters of the Greek alpha- 
 bet. ,(163.) 
 
 Many stars shine with colored light, and in double stars 
 the colors of the components are often contrasted. A few 
 stars are known to change their color. (164.) 
 
 Stars often undergo changes of brightness. Sometimes 
 the variations are periodic, like those of Algol, Mira, and 
 some others. (165.) In other instances the changes are 
 temporary, as is the case with Tycho's and Kepler's stars. 
 But the changes of the temporary stars may be periodic, 
 recurring at very long intervals. This seems to be the 
 case with the temporary star of 1866. (166.) 
 
 The stars are most numerous in the vicinity of the 
 circle of the Milky Way, and fewest in number near the 
 poles of that circle. (167.) 
 
 The stars are also often collected into clusters, some of 
 which are visible to the unaided eye, as in the case of the 
 Pleiades, Praesepe, and the faint cluster in the sword 
 handle of Perseus ; others, like the cluster in Hercules, 
 
198 ASTRONOMY. 
 
 and that in Centaurus, can be made out only with a tele- 
 scope. (168.) 
 
 Stars which are enveloped in a' faint nebulosity are 
 called nebulous stars. (169.) 
 
 The nebulae are sometimes variable. (170.) 
 Near the south celestial pole are two nebulous masses 
 called the Magellanic clouds, or Nubecula. (171.) 
 
III. 
 
 GRAY IT Y, 
 
 
 
 OR THE FORCE BY WHICH THE HEAVENLY 
 BODIES ACT UPON ONE ANOTHER. 
 
GRAVITY. 
 
 THE LAWS OF MOTION. 
 
 172. First Law of Motion. When a body is put in mo- 
 tion, it will keep on moving in a straight line with unvary- 
 ing velocity, unless some forces act upon it. This fact is 
 called \hzfirst law of motion. It is impossible to establish 
 this fact by direct experiment, since we cannot put a body 
 in motion where no forces shaH act upon it ; and since we 
 cannot observe its motion through an infinite distance and 
 time. If a wheel be made to rotate or a pendulum made 
 to vibrate in the air, they soon come to rest. But the fric- 
 tion of the turning point, and the resistance of the air, are 
 constantly offering hindrance to their motion. It is found 
 that if the friction be diminished by more delicate adjust- 
 ment of their points of support, they will keep in motion a 
 proportionally longer time. Again, the resistance of the air 
 can be got rid of by putting the wheel or pendulum under 
 the exhausted receiver of an air-pump. When the resist- 
 ance of the air is thus removed, and the friction reduced 
 to the least possible amount, the bodies are found to keep 
 up their motion a very long time. Hence we must con- 
 clude that, if we could get rid of all external hindrances, 
 the wheel, when once started, would keep on rotating with 
 an unvarying velocity, and also that the pendulum would 
 keep on vibrating at the same rate. 
 9* 
 
202 ASTRONOMY. 
 
 Neither of these is an example of motion in a straight 
 line, but from these circular motions we conclude that a 
 body when once put in motion, and' not acted upon by any 
 force, would move in a straight line with a uniform velocity. 
 For mathematical investigation has shown that if the parts 
 of a body when unconstrained would move in a straight 
 line with uniform velocity, then, when they are so con- 
 strained by their connection with one another that they are 
 obliged to move in circles, the body will rotate with a uni- 
 form velocity; and that if the parts of a body, when uncon- 
 strained, would not move in straight lines with an unvary- 
 ing velocity, then they would not rotate with a uniform 
 velocity. Mathematical investigation has also shown that 
 the only way to account for the uniform vibration of a free 
 pendulum is to suppose that the pendulum-ball would 
 move in a straight line with a uniform rate, if left to itself 
 after it has been once started. 
 
 173. The Planets and Satellites are acted on by some 
 Force. We have seen that all the planets and satellites 
 move in curved lines ; hence they must be acted on by 
 some force, and this force must be constant in its action, 
 since they move in straight lines in no part of their orbits. 
 
 174. Second Law of Motion. It is well known that 
 when a body is held in the hand it presses upon it, and 
 when it is left unsupported it falls to the ground. This 
 shows that there is a force acting between the earth and 
 the body, which draws the two together. It is this force 
 which gives bodies weight ; that is, which causes them to 
 exert pressure. It is therefore called gravity. 
 
 The second law of motion is, that when a moving body 
 is acted upon by gravity alone, it will, at a given time, be 
 just as far from the point which it would have reached had 
 it been left to itself, as it would have been had it been at 
 rest at that point in the first place, and been acted upon by 
 gravity alone during the same time. 
 
ASTRONOMY. 
 
 20 3 
 
 Suppose that a body, for instance, is moving in the di- 
 rection of A B (Figure 77) with a velocity which would 
 carry it from A to B in one sec- 
 ond of time, and suppose that 
 the force of gravity would draw 
 it in the same time from a posi- 
 tion of rest at A to C; then at 
 the end of the second the body 
 will be found at D, having been 
 pulled away from the place B, 
 which it would have reached 
 with the original direction and 
 
 velocity, just as much as if pulled away from the state 
 of rest. That is, BD just equals AC. 
 
 This law may be illustrated by experiments in the follow- 
 ing manner: AB (Figure 78) is a board; CD an arm 
 
 Fig. 78. 
 
 moving upon it, turning on a hinge at C, and driven by a 
 spring E ; at the end D of the arm is a hollow, with its 
 opening in the side of the arm large enough to contain a 
 small ball, so that when the arm is driven by the spring 
 , the ball will be thrown horizontally from the hollow 
 at D ; at F is another chamber opening downwards, its 
 lower opening being stopped by a board G, which will be 
 
204 ASTRONOMY. 
 
 knocked away by a blow of the arm CD ; then it is plain 
 that if one ball be put in D and another in JE, the very same 
 movement which throws one ball forward causes the other 
 ball to drop at the same instant ; and, if the second law of 
 motion be true, one of them will fall down vertically to the 
 floor at H at the sanje instant at which the other, which is 
 projected forward, reaches the floor at K. And the two 
 balls do reach the floor at the same instant ; proving that 
 if a ball is thrown horizontally, it falls from that horizontal 
 line down to the ground in the same time as a ball which 
 dropped from a state of rest. 
 
 This experiment is equally applicable to an inclined 
 throw, if the floor upon which the balls fall be inclined 
 exactly in the same degree. 
 
 175. AtwoocTs Machine. The same is found to be true 
 whatever be the direction in which the ball is projected ; 
 though the apparatus used in the above illustration is not 
 suited to show this when the ball is thrown either verti- 
 cally upward or downward. The case in which the body 
 is projected vertically downward can be best illustrated by 
 an instrument called Atwood's machine, shown in Figure 
 79. It consists of an upright column, with a pulley at 
 the top arranged to run with the least possible friction. 
 Over this pulley passes a cord, to which are attached the 
 equal weights B and E. C and F are movable shelves, 
 the former of which has a circular hole in the centre 
 large enough to let the weight B pass through it. A is 
 a clock beating seconds, and carried by the pendulum D. 
 When we wish to make the weight B fall, we place upon 
 it a small horizontal bar of iron, which is too long to 
 pass through the hole in the shelf C. When, therefore, 
 the weight drops through this hole, the bar will be caught 
 off and will remain upon the shelf. 
 
 If the weight B with the bar upon it be allowed to fall, 
 it will be found that the force of gravity will pull it down 
 
ASTRONOMY. 
 
 20 5 
 
 one inch during one second. Fi & 79- 
 
 Now adjust the shelf C so that 
 the bar shall be removed at the 
 end of the first second ; it will 
 then be found that the weight 
 will fall two inches the next sec- 
 ond. At the end of the first 
 second, then, the weight is pro- 
 jected vertically downward with 
 a velocity of two inches a sec- 
 ond. If now the bar is left on 
 during both seconds, the weight 
 will be found to have fallen 
 three inches during the second 
 second. Hence the force of 
 gravity pulls the weight down 
 the second second an inch far- 
 ther than its velocity at the be- 
 ginning of this second would 
 have carried it ; that is, just as 
 far as gravity would have pulled 
 it from a state of rest. 
 
 By means of this same ma- 
 chine the case of a body pro- 
 jected vertically upward can be 
 illustrated. While one of the 
 weights is falling the other 
 weight is rising. Suppose that 
 one bar be placed upon the as- 
 cending weight, and two on the 
 descending weight ; the second 
 a little heavier than the first, so 
 that it shall bear the same ratio 
 to the whole weight now as the one bar used at first. We 
 have already seen that this bar, acting during one second, 
 
206 ASTRONOMY. 
 
 will give one of the weights a velocity downward of two 
 inches a second, and the other weight the same velocity 
 upward. Suppose now that at the" end of the first second 
 both bars be caught off the descending weight, the other 
 weight will rise not two inches but only one during the next 
 second. Had it not been for the action of gravity upon 
 the bar resting on it, it would have risen two inches. But 
 we have already seen that gravity acting upon this bar 
 will cause the weight to fall one inch from a state of rest ; 
 hence it is pulled just as far from the place it would have 
 reached as it would have been pulled from a state of 
 rest. 
 
 This action of gravity upon a moving body causes it to 
 move in a curve in every case except when the body is 
 moving vertically upward or downward. In the first of 
 these cases it merely retards the motion of the body at a 
 uniform rate, and in the second case it accelerates it in 
 the same manner. 
 
 176. Curvilinear Motion. The form of the curve de- 
 scribed by a moving ball depends upon the velocity with 
 
 which it is moving and 
 
 r ig. 80. 
 
 the strength of the 
 force of gravity. The 
 velocity of the body 
 being the same, the 
 greater the force of 
 gravity, the more rap- 
 idly does the path described by the body curve. This is 
 shown in Figure 80. If the ball is moving with a velocity 
 which would carry it from A to B in a second, and the 
 force of gravity would carry it from a state of rest at A to 
 C in the same time, then A D will be the curvature of its 
 path, BD being equal to A C. If gravity could carry 
 it from A to O in a second, then A D' would represent 
 the curvature of its path, B D' being equal to A C. 
 
ASTRONOMY. 207 
 
 A D' obviously curves more rapidly than A D. Again, 
 the force of gravity being the same, the less the ve- 
 locity with which the ball 
 
 ' Fig. 81. 
 
 is moving, the more rap- 
 idly does its path curve. 
 Thus, in Figure 81, if the 
 force of gravity would car- 
 ry the body from a state 
 of rest at A to C in a second, and the velocity of the 
 body be such that it would move from A to B in the 
 same time, then A D will represent its path. But if its 
 velocity would carry it from A to B' in a second, then A D' 
 would represent its path. But A D obviously curves more 
 rapidly than A D'. Everybody knows that when a stone 
 is thrown from the hand, its path is much curved, and it 
 reaches the ground before it has gone far. But if you 
 watch the motion of a cannon ball, which you may do if 
 you stand behind a cannon when it is fired, as you can then 
 see the ball from the time it leaves the cannon's mouth to 
 a distance of half a mile or more, you will perceive that 
 its path is curved, but very much less curved than the path 
 of the stone : in fact it is nearly straight. The ball drops 
 downward through the same space as the stone in one sec- 
 ond of time, but it moves much farther in a horizontal di- 
 rection in the same time. 
 
 177. The Force which curves the Paths of the Planets is 
 always directed towards the Sim. Since the planets are 
 carried along with the sun in his journey among the stars, 
 it would seem that there must be some force which holds 
 them together. Is this the same force as that which 
 curves their orbit, and as that which draws a stone to 
 the earth ? Since the path of a planet curves round in 
 the same direction throughout its whole extent, the force 
 which curves this path must be constantly pulling the 
 planet towards some point inside its orbit. 
 
208 
 
 ASTRONOMY. 
 
 Fig. 82. 
 
 Long before the theory of gravitation was established 
 by Newton, Kepler had discovered that if a line be drawn 
 from the sun to a planet, this line sweeps over equal areas 
 in equal times in every part of the planet's orbit. 
 
 In Figure 82, suppose S to be the position of the sun, 
 and the curved line to be the orbit of the planet. Sup- 
 pose the planet to be at a, moving in the direction a b 
 
 with a velocity which would 
 carry it to b in a unit of 
 time, and that a force pull- 
 ing it toward the sun acts 
 upon it for only an instant, 
 giving it a velocity which 
 would carry it to g in the 
 same time. Draw the line 
 b c parallel to a g and take 
 b c equal to ag; the point 
 c will be the position of the 
 body at the end of the unit 
 of time, and the straight 
 
 line a c will be the path passed over by the body. If the 
 body were left to itself the next unit of time, it would 
 pass on in a straight line to //, a distance equal to a c. 
 Suppose now it be acted upon by another instantaneous 
 impulse drawing it towards the sun, and sufficient to carry 
 it from a state of rest at c to / in the same time ; its 
 position at the end of the time will be at ^, found by 
 drawing d e equal and parallel to c f, and its path will 
 be the straight line c e. Since d e is parallel to c f y the 
 two triangles See and S c d have the same base and equal 
 altitudes, and are consequently equal. 
 
 But a c and cd are also equal, and the two triangles a S c 
 and c S d have equal bases and the same altitude, since 
 their vertices are at the same point ; hence these triangles 
 are equal, and therefore S a c is equal to S c e. So long 
 
ASTRONOMY. 209 
 
 then as the planet is subjected to a succession of instanta- 
 neous impulses at equal intervals which draw it towards 
 the sun, the areas passed over by an imaginary line joining 
 the planet and the sun during each of these intervals will 
 be equal. This will be true whatever be the duration of 
 the intervals and the strength of the instantaneous im- 
 pulses, whether these impulses are equal or not. It will 
 therefore be true when the interval between the succes- 
 sive impulses, equal or not, is infinitely small ; that is, 
 when the force drawing the planet toward the sun acts 
 continuously. In this case the path becomes a curve, 
 that is, a line bent at every point Not only are these tri- 
 angles equal when the impulses are directed toward the sun, 
 but they will not be equal when the impulses are directed 
 toward any other point. The force, then, that curves the 
 paths of the planets must be directed toward the sun. The 
 same is true of the moon's path and the earth. 
 
 178. The Force that deflects the Moon's Path is the 
 same as that which draws a Stone to the Earth. Having 
 thus determined from Kepler's second law that the force 
 which deflects the moon's path is directed towards the 
 earth, Newton inquired whether this force was the same 
 as that which drew a stone to the earth, on the supposi- 
 tion that this force, like light, diminishes in intensity as 
 the square of the distance increases ; that is, becomes 
 four and nine times less when the distance becomes 
 twice or thrice as great. 
 
 In order to understand how Newton pursued this in- 
 quiry, we must see how gravity causes bodies to fall at 
 the surface of the earth. 
 
 179. Gravity would cause all Bodies to fall at* the same 
 Rate, were it not for the Resistance offered by the Air. 
 As we observe bodies light and heavy falling through 
 the air, we come to think that the force of gravity causes 
 heavy bodies to fall more rapidly than light ones ; but if 
 
 N 
 
210 
 
 ASTRONOMY. 
 
 Fig. 83. 
 
 we place a coin and a feather in a long glass tube and ex- 
 haust the air completely, on inverting the tube (Figure 
 83) the two bodies will fall through it in the same time. 
 It is therefore the resistance of the air 
 which causes a light body to fall more 
 slowly through the atmosphere than a 
 heavy one does. 
 
 When therefore the force of gravity 
 is unimpeded in its action, it will cause 
 every body, whatever may be its size, 
 shape, or density, to fall with exactly 
 the same speed. We next inquire how 
 far gravity will cause a body to fall in a 
 second of time. This is determined 
 by means of the pendulum. 
 
 THE PENDULUM. 
 
 1 80. A pendulum is a heavy body 
 suspended from a fixed point by means 
 of a cord or rod. When the centre of 
 gravity of the body is directly under 
 the point of support, the body remains 
 at rest ; but if the body be drawn out 
 of this position, it will, on being re- 
 leased, fall towards a vertical line pass- 
 ing through the point of support, and 
 when it has reached this line it will, 
 owing to its inertia, pass beyond it. On coming to rest, it 
 again falls toward this vertical line and again passes be- 
 yond, and thus continues to oscillate from side to side. 
 
 In studying the movements of the pendulum, mathema- 
 ticians have considered two kinds of pendulum, which they 
 have called the simple pendulum and the compound pen- 
 dulum. 
 
ASTRONOMY. 
 
 211 
 
 Fig. 84. 
 
 
 1 
 
 1 8 1. The Simple Pendulum. A simple pendulum con- 
 sists of a material point, suspended to a fixed point by 
 means of a thread without weight, perfectly flexible, and 
 incapable of stretching. Such a pendulum has of course 
 no real existence ; but we can approach 
 sufficiently near to it, for purposes of il- 
 lustration, by suspending a small lead 
 bullet to a fixed point by means of a 
 fine silk thread. 
 
 182. First Law of the Oscillation of the 
 Pendulum. Suppose d, in Figure 84, 
 to be a leaden ball hanging by a fine 
 silk thread. Pull it to one side so that it 
 shall vibrate through an arc of some 3, 
 and count the number of its oscillations 
 in a minute. Now bring it to rest again, 
 and draw it to one side so that it shall 
 oscillate through an arc of 2, and again 
 count its oscillations in a minute. Again 
 bring the ball to rest, then cause it to 
 oscillate through an arc of i, and count 
 the oscillations in a minute. In all three cases the num- 
 ber of oscillations in a minute will be equal. 
 
 By an oscillation is meant the whole of the pendulum's 
 movement in one direction. The arc through which the 
 pendulum oscillates is called the amplitude of its oscilla- 
 tion. 
 
 The above experiment shows that when the length of the 
 pendulum remains the same, and the amplitude of the oscilla- 
 tion does not exceed 3, the pendulum always oscillates in the 
 same time, whatever be the amplitude of the oscillation. 
 
 This singular property of the pendulum is called its 
 isochronism, from two Greek words signifying equal times, 
 and the oscillations of the pendulum are said to be isoch- 
 ronous. 
 
212 ASTRONOMY. 
 
 183. Second Law of the Oscillation of the Pendulum. 
 Let d and r, in figure 84, be two pendulums exactly alike, 
 except that the ball of one is lead and of the other ivory. 
 Let each oscillate through a small arc, and count its 
 oscillations in a minute. It will be found that, making 
 allowance for the resistance of the air, each performs the 
 same number of oscillations in the same time. This gives 
 the second law of the oscillation of the pendulum, namely : 
 
 for pendulums of the same length the duration of the oscilla- 
 tion is the same, whatever be the substance of which the pen- 
 dulum is formed. 
 
 184. Third Law of the Oscillation of the Pendulum. 
 Let b, in Figure 84, be a pendulum one fourth the length 
 of <r, and a another, one ninth the length of c. Set each 
 oscillating through a small arc, and count the oscillations 
 of each in a minute. It will be found that b oscillates 
 twice as fast as c t and a thr.ee times as fast as c. This 
 shows that, for pendulums of unequal length, the duration of 
 the oscillation is proportional to the square root of the length ; 
 that is, the lengths of the pendulum being made 4, 9, and 
 1 6 times greater, the duration of the oscillation of the 
 pendulum will be only 2, 3, and 4 times longer. This is 
 the third law of the oscillation of the pendulum. 
 
 185. Fourth Law of the Oscillation of the Pendulum. 
 It is found that when a pendulum of a given length is 
 placed on different parts of the earth's surface, the dura- 
 tion of the oscillations is not always the same. Towards 
 the poles it is found to oscillate more rapidly than at the 
 equator. Mathematicians have shown that this is because 
 the force of gravity is stronger at the poles. They have 
 shown that, in different parts of the earth the duration of the 
 oscillations for pendulums of the same length is in the inverse 
 ratio of the square root of the intensity of gravity ; that is, 
 if the intensity of gravity were four times as great in one 
 place as in another, the duration of the oscillations of a 
 
ASTRONOMY. 213 
 
 pendulum of the same length would be half as great, and 
 so on. 
 
 1 86. The Formula of the Pendulum. Let / represent 
 the duration of an oscillation ; /, the length of the pendu- 
 lum ; g, the intensity of gravity, that is, the velocity ac- 
 quired at the end of a second by a body which falls in a 
 vacuum ; and *- = 3.i4i6 : and mathematicians have found 
 that the above laws can be summed up in the following 
 expression : 
 
 g 
 
 This expression is called the formula of the pendulum. 
 
 187. The Compound Pe?idulum. The simple pendulum, 
 as has been stated, can have no real existence. Every 
 pendulum actually used is a compound pendulum, consist- 
 ing of a heavy weight suspended from a fixed point by 
 means of a rod of wood or metal. The particles of such 
 a pendulum must of course be at different distances from 
 the point of suspension, and must therefore tend to oscil- 
 late in different times. Hence the time of oscillation of 
 the whole pendulum will npt be the same a that of a sim- 
 ple pendulum of the same length. 
 
 The compound pendulum may be regarded as consisting 
 of as many simple pendulums as it contains particles. If 
 these were free to move, they would oscillate in times de- 
 pending upon their distances from the point of suspension ; 
 but since they are united in one body, they are all com- 
 pelled to oscillate in 'the same time. Consequently, the 
 oscillations of the particles near the point of suspension 
 are retarded by the slower oscillations of the particles be- 
 low them ; and, on the other hand, the oscillations of the 
 particles near the lower end of the pendulum are acceler- 
 ated by the more rapid oscillations of those above them. 
 At some point between these there must be a particle 
 whose oscillation is neither retarded nor accelerated, all 
 
214 ASTRONOMY. 
 
 the particles above having just the same tendency to oscil- 
 late faster that those below have to oscillate slower. This 
 point is called the centre of oscillation, and it is obvious 
 that the time of oscillation of a compound pendulum is 
 the same as that of a simple pendulum whose length is 
 equal to the distance of the centre of oscillation from the 
 point of suspension. This distance is the virtual length 
 of the pendulum, and the formula given above (186) will 
 apply to compound pendulums by making /= their virtual 
 length. By the length of a pendulum, whatever may be its 
 form, we are always to understand the virtual length, unless 
 the reverse is expressly stated. 
 
 When the form of the pendulum is given, the position 
 of the centre of oscillation can be calculated by methods 
 belonging to the higher mathematics. It can also be 
 found experimentally by making use of a remarkable prop- 
 erty of the compound pendulum, by virtue of which, if 
 such a pendulum be inverted and suspended by its centre 
 of oscillation, its former point of suspension will become 
 its new centre of oscillation, and the time of vibration will 
 be the same as before ; or, as it is usually expressed, the 
 centres of oscillation and suspension are interchangeable. 
 
 To find the centre of oscillation, then, we have only to 
 reverse a pendulum, and by trial find the point at which it 
 must be suspended in order to oscillate in the same time 
 as it did before it was reversed. A pendulum constructed 
 for this purpose is called a reversible pendulum. 
 
 1 8 8. The Use of the Pendulum for measuring the Force of 
 Gravity. By transposing, we get from the equation above 
 
 (185) g = I 2 ; from which, when we know the length 
 
 of a pendulum which oscillates in a given time, T, we can 
 easily calculate the value of g for the place of experiment. 
 If, in the last equation, we make T= i, then /denotes the 
 length of a pendulum beating seconds, and we find that 
 
ASTRONOMY. 215 
 
 g = 1 7T 2 . In order, then, to measure the intensity of 
 gravity at any place, we have only to oscillate a pendulum 
 whose virtual length is known, and observe the length of 
 a single oscillation. This is readily done by counting a 
 large number of oscillations, and observing the time occu- 
 pied by the whole number. This time, divided by the 
 number of oscillations, gives the time of a single oscilla- 
 tion very accurately, because any error which may have 
 been made in observing the time is thus greatly divided. 
 
 Now it has been found that a pendulum beating seconds 
 at London must be 39.13929 inches in length. Substitut- 
 ing this value, and also that of ir 2 in the equation, g = I ^r 2 , 
 we get g = 386 inches. 
 
 Since the velocity of a ball is zero at starting, and at the 
 end of a second it attains the velocity of 386 inches, its 
 mean velocity would be 193 inches, and this is evidently 
 the distance the body would be drawn towards the earth by 
 gravity in a second of time. 
 
 We have thus found the answer to the question asked in 
 section 179, and have proved that gravity causes a body to 
 fall sixteen feet in a second of time. 
 
 SUMMARY OF THE PENDULUM. 
 
 A pendulum is a heavy body suspended from a fixed 
 point by means of a cord or rod. (180.) 
 
 The laws of the oscillation of the pendulum are best 
 investigated by means of a simple pendulum. (181.) 
 
 These laws are four in number. 
 
 i st. When the length of the pendulum remains the same, 
 and the amplitude of the oscillations does not exceed 3, the 
 pendulum always oscillates in the same time. (182.) 
 
 2d. For pendulums of the same length, the duration of the 
 oscillations is the same, whatever be the substance of which 
 the pendulum is formed. (183.) 
 
2l6 ASTRO XO MY. 
 
 3d. For pendulums of different lengths, at the same place y 
 the duration of the oscillation is proportional to the square 
 root of the lengths. (184.) 
 
 4th. /// different parts of the earth the duration of the os- 
 cillation for pendulums of the same length is in the inverse 
 ratio of the square root of the intensity of gravity. (185.) 
 
 These laws can be summed up in the following expres- 
 sion, called the formula of the pendulum : 
 
 The pendulum in actual use is a compound pendu- 
 lum. (187.) 
 
 The pendulum is used for measuring the force of grav- 
 ity. (188.) 
 
 GRAVITY ACTS BETWEEN THE EARTH AND 
 THE MOON. 
 
 189. The Intensity of Gravity varies directly as the Mass 
 of the Body acted upon by this Force. It has been shown, 
 by the falling of bodies in a vacuum (179), and the pen- 
 dulum (188), that gravity acting upon a body at rest will 
 cause it to fall one hundred and ninety-three inches in a 
 second, whatever may be the amount of matter that the 
 body contains. But if one body contains twice the 
 amount of matter that another does, it will clearly take 
 twice the force to pull it through the same distance. 
 Hence the intensity of gravity acting upon bodies near 
 the earth must vary directly as the amount of matter which 
 they contain, or as the mass of the bodies. 
 
 190. The Moon's Path is curved by the Force of Grav- 
 ity. We now return to the consideration of the Moon's 
 path, and the force which deflects it. (178). 
 
 We have found that gravity acts between the earth and 
 
ASTRONOMY. 2 I 7 
 
 a body near its surface with a force whose intensity varies 
 directly as the mass of the body, and is sufficient to draw 
 it from a state of rest 193 inches in a. second. 
 
 If, then, the earth's attraction at the distance of 3,959 
 miles from its centre draws a body 193 inches in a second, 
 how far in a second ought it to draw a body distant 
 238,800 miles from this centre, supposing that the force 
 diminishes in proportion as the square of the distance 
 increases ? This distance will, of course, diminish with 
 the intensity of gravity, and can easily be ascertained by 
 squaring these two numbers, rinding how many times the 
 less of these squares is contained in the greater, and di- 
 viding 193 inches by the quotient. This distance is thus 
 found to be .05305 of an inch. We must Fig 8s> 
 
 now find how much the moon's path is -m, M 
 
 really deflected in one second of time. 
 Let J5, in Figure 85, represent the position 
 of the earth ; M, the position of the moon ; 
 and Mm, the direction in which the moon 
 is moving at the instant. Let Mm be the 
 distance the moon would pass over in one second of time 
 if nothing interfered with her motion. Then m JVwill be 
 the distance the moon is drawn towards the earth in this 
 time. Now, considering the moon as moving in a cir- 
 cle whose semidiameter is her mean distance, E M is 
 238,800 ; .the whole circumference is 1,500,450 miles ; and 
 her periodic time is 27 days, 7 hours, 43 minutes. Dividing 
 the length of the whole orbit by the number of seconds in 
 her periodic time, we find her velocity in any part of her 
 orbit, as at M, is .6356 of a mile. This is the distance, 
 Mm, that she would have travelled, had no force inter- 
 fered with her motion. But E M m is a right-angled trian- 
 gle, and we know the length of the sides E Mand Mm. 
 By squaring these and extracting the square root of their 
 sum, we find the length of the hypothenuse E m to be 
 
2l8 ASTRONOMY. 
 
 238,800.0000008459 miles. But m TV is equal to m E mi- 
 nus E N. Therefore m N is equal to .0000008459 of a 
 mile, or .0536 of an' inch. This is found to be almost ex- 
 actly the same distance that the moon ought to be drawn 
 to the earth in a second of time, provided she is drawn 
 downward by the same force which draws a stone to the 
 earth, the intensity of the force having diminished as the 
 square of the distance has increased. This slight differ- 
 ence is exactly accounted for by disturbing causes which 
 are known to exist. It is therefore certain that the attrac- 
 tion of the earth which causes the stone to fall, and the 
 attraction of the earth which bends the moon's path from 
 a straight line to a circle, are really the same attraction, 
 only diminished for the moon in the inverse proportion 
 of the square of her distance. 
 
 If we had taken the interval of an hour instead of a 
 second, we should have found that the moon was drawn to 
 the earth 10.963 miles ; and we should have found that 
 a stone at the distance of the moon would have fallen 
 through a corresponding space in the same time. 
 
 GRAVITY ACTS BETWEEN THE SUN AND 
 
 PLANETS, AND BETWEEN PLANETS 
 
 AND THEIR MOONS. 
 
 191. The Paths of the Earth and of Jupiter are curved 
 by the Force of Gravity. We will proceed to see whether 
 the paths of the planets are curved by gravity. 
 
 Let us first compare the spaces through which the sun 
 draws the planets in one hour ; and, as an instance, we 
 will take the earth and Jupiter. In Fig. 86 let E F be 
 the path described by the earth in one hour, and E e the 
 path in a straight line which the earth would have de- 
 scribed in one hour if nothing had disturbed it ; and let 
 J K be the path described by Jupiter in one hour ; and 
 
ASTRONOMY. 
 
 219 
 
 Jj the path Jupiter would have described in one hour if 
 nothing had disturbed it. Then e F is the space through 
 which the sun's attraction has drawn the 
 earth in one hour, and / K the space 
 through which the sun's attraction has 
 drawn Jupiter in one hour. We wish to 
 find the ratio of e F toy K. Taking C 
 E as 95,000,000 miles, the circumfer- 
 ence of the earth's orbit is 596,900,000 
 miles, which the earth describes in 365.26 
 days; and therefore the line Ee, which 
 is the earth's motion in one hour, is 
 68,091 miles. Adding the square of 
 C to the square of E e, and extracting 
 the square root of the sum, we find that 
 C e is 95,000,024.402 miles ; and there- 
 fore e F, the space through which the 
 sun draws the earth in an hour, is 24.402 
 miles. For Jupiter, C J is 494,000,000 
 miles ; the circumference of its orbit 
 is therefore 3,104,000,000 miles; which is described in 
 4,332.62 days ; therefore Jj\ the motion in one hour, is 
 29,850 miles ; and the length of Cj t found in the same 
 manner, is 494,000,000.9019 miles; and j K, the space 
 through which the sun draws Jupiter in one hour, is 0.9019 
 miles. 
 
 The distances through which these planets are drawn 
 towards the sun are therefore in the ratio of 24.402 to 
 0.9019. But if we compute, from the rule of the inverse 
 square of the distances, what would be the proportion of 
 the force of the sun on the earth to the force of the sun 
 on Jupiter, we find that it is the proportion of 24.402 to 
 0.9024. These proportions may be regarded as exactly 
 the same, the trifling difference between them arising 
 mainly from the circumstance that we have used only round 
 
220 ASTRONOMY. 
 
 numbers for the distances of the two planets from the sun. 
 It is true, then, for these two planets that the strength of 
 the sun's attraction is inversely proportional to the square 
 of the distance of the attracted body from the sun. 
 
 192. The Paths of all the Planets and their Satellites are 
 curved by Gravity. If we should compare any two plan- 
 ets in the same way, we should arrive at the same conclu- 
 sion. 
 
 In fact it has been demonstrated that whenever the rule 
 known as Kepler's third law (42) holds, namely, that 
 " the squares of the periodic times of several bodies mov- 
 ing round a central body are proportional to the cubes of 
 the distances of the several bodies from that central body," 
 then it will be found, by a process exactly similar to 
 that which we have gone through, that the effects of the 
 central body's attraction at the different distances are in- 
 versely as the squares of the distances. Now, this law was 
 discovered by Kepler, long before the theory of gravita- 
 tion was invented, to hold in regard to the times and dis- 
 tances of the planets in their revolutions round the sun. 
 Moreover, in regard to the four satellites of Jupiter, the 
 same law holds. For we are able without difficulty to 
 observe their periodic times ; we are able also to ascertain 
 their angular distance from Jupiter ; and from this, know- 
 ing the distance of Jupiter from the earth in miles, we can 
 compute the distance of each satellite from Jupiter in 
 miles. We thus find that the squares of their times are 
 proportional to the cubes of their distances. Consequently 
 the attraction of Jupiter upon his several satellites is in- 
 versely proportional to the squares of their distances from 
 him. In like manner it is found that the attraction of 
 Saturn upon his eight satellites is inversely proportional 
 to the squares of their distances from him ; and, so far as 
 we can examine, the same law holds with regard to the 
 attraction of Uranus and Neptune on their satellites. 
 
ASTRONOMY. 
 
 221 
 
 Thus, for every body which we know around which other 
 bodies revolve, the force of attraction of the central body 
 on the different bodies that revolve round it is inversely 
 proportional to the squares of their distances. 
 
 193. Gravity causes the Planets and their Moons to move 
 in Ellipses. Kepler also discovered that the planets do 
 not move in circles but ellipses. Hence their distance 
 from the sun varies. We have now found it true that the 
 attraction of the central body upon the bodies revolving 
 about it follows the law of the inverse squares of the dis- 
 tances ; does this law hold in the case of each planet as its 
 distance from the sun varies ? 
 
 We have already seen that when a planet moves in an 
 ellipse, the deflecting force must be directed to the focus 
 of the ellipse, in order that a line drawn from that focus to 
 the planet may describe equal areas in equal times. Since 
 the planets are thus constantly pulled towards the sun, and 
 since they at times really approach him, it would seem 
 that they would be unable to recede from him again. 
 
 194. The Resolution of Forces. Before we show how it 
 is that a planet can thus recede from the sun, we must 
 explain what is called the resolution of forces. This may 
 be illustrated by the apparatus represented in Figure 87. 
 
 Fig. 87. 
 
 Suppose A and B to be two pulleys, fixed upon an up- 
 right frame, and suppose two cords to pass over them, 
 
222 ASTRONOMY. 
 
 carrying the two weights, C and Z>, at their ends ; and 
 where they meet at E let a third cord be attached, carry- 
 ing the weight -F; then the tension or pull produced by 
 this one weight F, acting at the point , supports two 
 tensions in different directions acting at the same point, 
 namely, the tension .produced by the weight C acting in 
 the direction E A, and the tension produced by the weight 
 D acting in the direction E B. Thus we may say, that 
 one pull in the direction E F exerts two pulls in different 
 directions, A E and B E, for it keeps the two cords 
 strained so as to support the two other weights. We may 
 say, on the other hand, that these two outside weights, C 
 and Z>, support the middle one. The three pulls of the 
 cords keep the point E in equilibrium ; but they will sup- 
 port it only in one position, according to the amount of 
 weight which is hung to each cord. If we put another 
 weight upon C, the position of the point E and the direc- 
 tion of the cords will immediately change. Regarding 
 the action of the two tensions in the directions E A, 
 E B, as supporting the one tension in the direction E F, 
 this may be considered as an instance of the combination 
 of forces ; and regarding the one tension in the direc- 
 tion E F, as supporting two in the directions A J5, E B, 
 this may be considered as an instance of the resolution 
 of forces, the one force in the direction E F being re- 
 solved into two forces in the directions A E, BE, and 
 producing in all respects the same effects as two forces in 
 the directions A E, B E. 
 
 Having, then, a force in any one direction, we may re- 
 solve it into two forces acting in any two directions suited 
 to the nature of the case, and we may use those two forces 
 instead of the one original force. 
 
 195. We can now see how it is that when a planet has 
 once begun to approach to the sun, it can recede again 
 from it. Suppose, in Figure 88, a planet is moving from /, 
 
ASTRONOMY. 
 
 223 
 
 through M, towards L. The attraction of the sun pulls it 
 the direction of the line MS. Upon the principle of 
 
 in 
 
 the resolution of forces, we may consider the force in the 
 direction of MS to be resolved into two, one of which is in 
 
 the direction of JVM, perpendicular to the orbit, and the 
 other is in the direction of O M, parallel to that part of the 
 orbit. Now that part of the force which is in the direction 
 JVM, perpendicular to the orbit, makes the orbit curved. 
 But that part which acts in the direction of O M, parallel 
 to the orbit, produces a different ef- Fig. 8 9 . 
 
 feet ; it accelerates the planet's mo- 
 tion in its orbit. Thus, in going 
 from / towards Z, the planet is made 
 to go quicker and quicker. If the 
 diagram (Figure 88) be turned in 
 such a manner that MS is vertical, 
 S being downwards, the planet is 
 under the same circumstances as a ball rolling down a hill. 
 If a ball is going down a hill, as at M, Figure 89, the force 
 of gravity, which is in the direction MS, may be resolved 
 
224 ASTRONOMY. 
 
 into two parts, one of which acts in the direction IV M, 
 perpendicular to the hillside, and merely presses the ball 
 towards the hill ; the other acts in the direction O Af, 
 making it go the faster down the hill. In this manner, as 
 long as the planet goes from k through M towards Z, it is 
 going quicker and quicker. It has been explained above 
 (176), that the curvature of a planet's orbit, or the curvature 
 of the path of a cannon-ball, depends upon two circum- 
 stances ; one is the velocity with which it is going, and 
 the other is the force which acts to bend its path. The 
 greater its speed, the less its path is curved. Conse- 
 quently, as the planet is going so fast in the neighbor- 
 hood of K, its orbit may be very little curved there, even 
 though the sun is there pulling it with a very great force. 
 The effect of this is, that the planet passes the sun and 
 begins to recede from it. But it does not recede perpet- 
 ually. Suppose, for instance, that it has reached the point 
 M' ; the force of the sun in the direction M'S may be re- 
 solved into two, in the directions N'M', O M' , of which 
 the former only curves the orbit, while the latter retards 
 the planet in its movement in the orbit. Therefore, as 
 the planet recedes from the sun, it goes more and more 
 slowly, till at last its velocity may be diminished so much, 
 that the power of the sun, reduced as it is there, is enabled 
 to bring it back again. Thus the planet goes on in its orbit, 
 alternately approaching to, and receding from, the sun. 
 
 196. In Figure 8, let KA and ka be the path in a 
 straight line which the planet would describe in an hour in 
 those parts of its orbit : then will A B and a b be the dis- 
 tance which the planet is drawn towards the sun in an hour 
 in each of those positions. Now, by a somewhat difficult 
 mathematical investigation, it can be shown that the lines 
 A B and a b stand in the inverse ratio of the squares of the 
 distances S K and S k, and this is found to be true of the 
 planet at any two positions in its orbit. We therefore con- 
 
ASTRONOMY. 225 
 
 elude, that when any body moves in an elliptical orbit round 
 a certain body situated in the focus of this ellipse, the de- 
 flecting force, exerted by the central body, varies in the 
 inverse proportion of the squares of the distances between 
 the two bodies. 
 
 GRAVITY ACTS BETWEEN THE SUN AND 
 COMETS. 
 
 197. The Parabolic Motion of Comets. There is, how- 
 ever, another remarkable class of bodies of which we have 
 already spoken ; namely, the comets. Can the curved form 
 of their paths be accounted for on the supposition that 
 they are drawn toward the sun by the same force as the 
 planets ? A few of the comets, as has been stated (157), are 
 now known to move in very long ellipses, and to return 
 periodically to our sight. Of course their motion can be 
 accounted for in the same way as that of the planets ; but, 
 in Newton's time, the idea of a periodical comet was wholly 
 unknown ; and it is now certain that many of the comets, 
 after visiting the sun, never return to him again. 
 
 But since curvature of the path of a planet depends both 
 upon the force which draws it towards the sun and upon its 
 velocity, we can readily see that the velocity of a planet 
 might be so great that its path would never be bent around 
 enough to bring it back to the sun. Newton showed, by 
 an investigation similar to that made in the case of an 
 elliptical orbit, that a body subject to the attraction of a 
 central body (as the sun) might, if the Fig ^ 
 
 force varied inversely as the square of 
 the distance, describe the curve called 
 the parabola; but no other law of force 
 would account for the description of 
 such a curve. The form of the para- 
 bola is represented in Figure 90, C be- 
 
 10* o 
 
226 ASTRONOMY. 
 
 ing the sun ; and this curve, it is evident, possesses two 
 of the peculiarities which distinguish the motions of 
 comets ; it comes very near to the sun at one part, and 
 it goes off to an indefinitely great distance at other parts. 
 Now, when Newton had found out that the same laws of 
 gravitation which were established from the consideration 
 of elliptical motion would account for motion in a parab- 
 ola, he began to try whether the parabola would not repre- 
 sent the motion of a comet. It was found, that by taking 
 a parabola of certain dimensions, and in a certain position, 
 the motions of the comet which had been observed most 
 accurately could be represented with the utmost precision. 
 Since that time, the same investigation has been repeated 
 for hundreds of comets ; and it has been found, in every 
 instance, that the comet's movements could be exactly 
 represented by supposing it to move in a parabola of proper 
 dimensions and in the proper position, the sun being always 
 situated at a certain point called the focus of the parabola. 
 This investigation tends most powerfully to confirm the law 
 of gravitation ; showing that the same moving body, which 
 at one time is very near to the sun, and at another time is 
 inconceivably distant from it, is subject to an attraction of 
 the sun varying inversely as. the square of the distance. 
 
 GRAVITY ACTS AMONG ALL THE HEAVENLY 
 BODIES. 
 
 198. The Moorfs Perturbations. We \have seen that 
 the sun attracts the earth. Does it also attract the moon ? 
 If so, as these bodies are always either at different dis- 
 tances from the sun, or lie in different directions from the 
 sun, they will be differently attracted by him ; and hence 
 their relative motions will be disturbed. We find that these 
 motions are thus disturbed, giving rise to what are called 
 perturbations. These perturbations were discovered from 
 
ASTRONOMY. 
 
 227 
 
 observation long before the theory of gravitation was in- 
 vented. One of the first triumphs of the theory was their 
 complete explanation. We shall attempt here to explain 
 only the one which is called the Moon's Variation. 
 
 In Figure 91, suppose E to be the earth, M' M" M'" 
 M"" the moon's orbit, and C the sun. The sun, by the 
 
 Fig. 
 
 law of gravitation, attracts bodies which 
 are near with greater force than those 
 which are far distant from it. There- 
 fore, when the moon is at M' the sun 
 attracts the moon more than the earth, 
 and tends to pull the moon away from 
 the earth. When the moon is at M"' 
 the sun attracts the earth more than 
 the moon, and therefore tends to pull 
 the earth from the moon, producing the 
 same effect as at M' or tending to sep- 
 arate them. When the moon is at M" 
 the force of the sun on the moon is nearly the same as the 
 force of the sun upon the earth, but it is in a different di- 
 rection. If the sun pulls the earth through the space E e, 
 and if it also pulls the moon through the same space M"m, 
 these attractions tend to bring the earth and the moon 
 nearer together, because the two bodies are moved as it 
 were along the sides of a wedge which grows narrower 
 and narrower. Thus, at M' and M'" the action of the 
 sun tends to separate the earth and the moon, and at M" 
 and M"" the action tends to bring the earth and the 
 moon together. 
 
 One might perhaps infer from this that the moon's orbit 
 is elongated in the direction M' M'" -, but the effect is 
 exactly the opposite. The fact really is, that the moon's 
 orbit is elongated in the direction M" M"". And it can 
 easily be shown that it must be so. The moon, we will 
 suppose, is travelling from M"" to M'. All this time the 
 
228 ASTRONOMY. 
 
 sun is attracting her more than the earth, and therefore 
 increasing her velocity till she reaches M' '. When she is 
 passing from M' to M" the sun is pulling her back, and 
 her velocity is diminished till she reaches M". From this 
 point her velocity increases again till she reaches M'", and 
 then diminishes again till she reaches M"" . Therefore, 
 when the moon is nearest to the sun, and farthest from the 
 sun, she is moving with the greatest velocity ; when she is 
 at those parts of her orbit at which her distance from the 
 sun is equal to the earth's distance from the sun, she is 
 moving with the least velocity. We have learned that the 
 curvature of the orbit depends on two considerations. One 
 is the velocity \ and the greater the velocity is, the less the 
 orbit will be curved. The other is the force ; and the less 
 the force is, the less the orbit will be curved. Since, then, 
 the velocity is greatest at M' and M"', and the force di- 
 rected to the earth is least (because the sun's disturbing 
 force there diminishes the earth's attraction), the orbit 
 must be the least curved there. At M" and M"" the ve- 
 locity has been considerably diminished ; the force which 
 draws the moon towards the earth is greatest there (be- 
 cause the sun's disturbing force there increases the earth's 
 attraction), and therefore the orbit must be most curved 
 there. The only way of reconciling these conclusions is 
 by saying that the orbit is lengthened in the direction 
 M" M"" ; a conclusion opposite to what we should have 
 supposed if we had not investigated closely this remark- 
 able phenomenon. It will easily be understood that the 
 amount of this effect is modified in some degree by the 
 change which the earth's attraction undergoes in conse- 
 quence of the change of the moon's distance, (the earth's 
 attractive force varying inversely as the square of the 
 moon's distance,) but still the reasoning applies with per- 
 fect accuracy to the kind of alteration which is produced 
 in the moon's orbit. 
 
ASTRONOMY. 229 
 
 This particular inequality was discovered by Tycho 
 de Brahe before gravitation was known ; and it was ex- 
 plained by Newton as a result of gravitation. There are 
 other perturbations, even more important than this, which 
 were discovered before gravitation was known, and which 
 were most fully and accurately explained by gravitation. 
 
 199. The Mutual Perturbations of the Planets. Again, 
 it is found that there are disturbances in the motions of 
 the planets generally ; and these disturbances can be ex- 
 plained only by supposing that every planet attracts every 
 other planet, and that therefore the motions of the planets 
 are not exactly the same as if only the sun attracted them. 
 These disturbances are exceedingly complicated. There 
 is one kind, however, of which possibly some notion may 
 be given. They are the most remarkable in Jupiter and 
 Saturn. There are many books, 
 written as late as the beginning 
 of the present century, in which 
 the motions of Jupiter and Saturn 
 are spoken of as irreconcilable with 
 the theory of gravitation. It was 
 one of the grand discoveries of La 
 Place that the great disturbances 
 of those two planets are caused by 
 what is called the "inequality of 
 long period," requiring some hundreds of years to go 
 through all its changes. 
 
 Let Figure 92 represent the orbits of Jupiter and Sat- 
 .urn. They are both ellipses, and the positions of their 
 axes do not correspond. Now, the thing which La Place 
 pointed out as affecting the perturbations of these planets 
 is one which applies more or less to several other planets ; 
 namely, that the periodic times of Jupiter and Saturn are 
 very nearly in the proportion of two small numbers, 2 to 5. 
 
 Inasmuch as these periodic times are in the proportion 
 
230 ASTRONOMY. 
 
 of 2 to 5, it follows that, while Saturn is describing two 
 thirds of a revolution in its orbit, Jupiter is describing 
 almost exactly five thirds of a revolution in its orbit. If, 
 therefore, the two planets have been in conjunction, then 
 about twenty years afterwards Saturn has described two 
 thirds of a revolution, and Jupiter a whole revolution and 
 two thirds, and the planets will be in conjunction again, 
 but not in the same parts of their orbits as before, but in 
 parts farther on by two thirds of a revolution. Thus, in 
 Figure 92, suppose i i to be the place of the first conjunc- 
 tion of which we are speaking. Saturn describes two thirds 
 of his orbit as far as the figure 2. Jupiter goes on describ- 
 ing a whole revolution and two thirds of a revolution, and 
 arrives at the same time at the figure 2 in his orbit, and 
 the planets are in conjunction at 2 2. Saturn goes on de- 
 scribing two thirds of the orbit again, and comes to figure 
 3. Jupiter goes on describing a whole revolution and two 
 thirds of another, and he comes to figure 3, and they are 
 in conjunction there. The next time they are in conjunc- 
 tion at figure 4, the next at figure 5, and the next at figure 
 6, and so on. These conjunctions occur in this manner 
 from the circumstance that the periodic times are nearly 
 in the proportion pf 2 to 5 ; there are three points of the 
 orbit at nearly equal distances, at which the conjunctions 
 occur. 
 
 But we will suppose that they occurred exactly at three 
 equidistant points, and that time after time they happened 
 exactly at the same points. It is plain that in that case 
 there would be a remarkable effect of the disturbances, 
 particularly at those parts of the orbit i i, 2 2, 3 3, etc., 
 where Jupiter and Saturn are nearer to each other than at 
 other times. They are very large planets ; each of them 
 larger than all the rest of the solar system, except the sun. 
 They exercise very great attractive force each upon the 
 other ; and therefore they would disturb each other in a 
 
ASTRONOMY. 231 
 
 very great degree, if their conjunctions occurred exactly 
 "at the same place. 
 
 Now, these conjunctions do not occur exactly at the 
 same place. The periodic times are nearly in the propor- 
 tion of 2 to 5, but not exactly in that proportion. Conse- 
 quently their places of conjunction travel on, until after a 
 certain time the points of conjunction of the series i, 4, 7, 
 etc., would have travelled on until they met the series 3, 6, 
 9, etc. A period of not less than nine hundred years is 
 required for this change. 
 
 Now, so long as three conjunctions take place at any 
 definite set of points, the effect on the orbits is of one 
 kind. As they travel on, the effect is of another descrip- 
 tion (because, from the eccentricity of their orbits, the dis- 
 tance between the planets at conjunction is not the same), 
 and so they go on changing slowly until the points of the 
 series i, 4, 7, etc., are extended so far as to join the series 
 3, 6, 9, etc. ; and then the conjunctions of the two planets 
 occur at the same points of their orbits as at first, and the 
 effect of each planet in disturbing the other is the same as 
 at first ; and thus we have the same thing recurring over 
 and over again for ages. During one half of each period 
 of nine hundred years, the effect that one planet has upon 
 the other is, that its orbit has been slowly changing ; and 
 then, during the other half, it comes back to what it was 
 before. Suppose that, during half the nine hundred years, 
 one planet has been causing the other to move a little 
 quicker, and that, during the other half of that nine hun- 
 dred years, it has been causing it to move a little slower ; 
 although that change maybe extremely small as regards the 
 velocity of the planets, yet, as that velocity has four hun- 
 dred and fifty years to produce its effect in one way, and 
 an equal time to produce its effect in the opposite way, it 
 does produce a considerable irregularity. If the place of 
 Saturn be calculated on the ' supposition that its periodic 
 
232 ASTRONOMY. 
 
 time is always the same, then at one time its real place will 
 be behind its computed place by about one degree, and 
 four hundred and fifty years later its real place will be be- 
 fore its computed place by about one degree, so that in 
 four hundred and fifty years it will seem to have gained 
 two degrees. The corresponding disturbances of Jupiter 
 are not quite so large. 
 
 These are the most remarkable of all the planetary dis- 
 turbances, their magnitude being greater than any other, 
 fon account of the magnitude of the planets, and the eccen- 
 tricity of their orbits. There are, however, others of the 
 same kind. One of these depends upon the circumstance, 
 that eight times the periodic time of the earth is very near- 
 ly equal to thirteen times the periodic time of Venus. 
 
 We have attempted to explain only one limited class of 
 perturbations. There are some which may be described 
 as a slow increase and decrease of the eccentricities of the 
 orbits, and a slow change in the direction of the longer 
 axes of the orbits ; but there are others of which no intelli- 
 gible account can be given in an elementary book. 
 
 200. The Calculation of the Amount of these Perturba- 
 tions. In order, however, to bring these theories into 
 actual calculation, it is necessary to know not only the 
 general tendency of the disturbances, but also their actual 
 magnitude. In the perturbations produced by the earth, 
 by Jupiter, and by Saturn, there is no difficulty in doing 
 this. We have shown (191) that we can calculate the 
 number of miles through which the earth's attraction draws 
 the moon in one hour. We know also (179) that the 
 earth's attraction draws every body at the earth's surface 
 through the same space in the same time ; so that a ball of 
 lead and a feather will fall to the ground with equal speed, 
 if the resistance of the air is removed. We say, therefore, 
 that the earth's attraction would draw a planet through the 
 same space as the moon, provided the planet were at the 
 
ASTRONOMY. 233 
 
 moon's distance ; and, for the greater distance of the planet. 
 we must, by the law of gravitation, diminish that space in 
 the inverse proportion of the square of the distance. We 
 have already learned (192) how to compute the space 
 through which the sun draws a planet in one hour ; and 
 therefore the problem now is, to compute the motion of a 
 planet, knowing exactly how far, and in what direction, 
 the sun will draw it in one hour, and also knowing exactly 
 how far, and in what direction, the earth will draw it in 
 one hour. 
 
 In like manner we can, from observations of Jupiter's 
 satellites, compute how far Jupiter draws one of his satel- 
 lites in one hour, and therefore how far Jupiter would 
 draw a planet at the same distance in one hour : and then 
 by the law of gravitation we can compute (by the propor- 
 tion of inverse squares of the distances) how far Jupiter 
 will draw a planet at any distance in one hour ; and this is 
 to be combined, in computation, with the space through 
 which the sun will draw the planet in one hour. In like 
 manner, by similar observations of Saturn's satellites, and 
 similar reasoning, we can find how far Saturn will draw any 
 planet in one hour, and we can combine this with the space 
 through which the sun would draw it in one hour. Thus 
 we are enabled to compute completely the perturbations 
 which these three planets produce in any other planets. 
 
 20 1. Do the Planets' Motions, as computed with these Dis- 
 turbances, agree with what we see in actual Observation ? 
 They do agree most perfectly. Perhaps the best proof 
 which can be given of the care with which astronomers 
 have looked to this matter, is the following. The meas- 
 ures of the distances of Jupiter's moons in use till within 
 the last sixteen years, had not been made with due ac- 
 curacy; and, in consequence, the perturbations produced 
 by Jupiter had all been computed too small by about one 
 fiftieth part. So great a discordance manifested itself 
 
234 ASTRONOMY. 
 
 * 
 
 between the computed and the observed motions of some 
 of the planets, that many of the German astronomers 
 expressed themselves doubtful of the truth of the law of 
 gravitation. Airy, the Astronomer Royal of England, was 
 led to make a new set of observations of Jupiter's satel- 
 lites, and discovered that these bodies were farther from 
 Jupiter than was supposed, that the space through which 
 Jupiter drew them in an hour was greater than was sup- 
 posed, and that the perturbations ought to be increased 
 by about one fiftieth part. On using the corrected per- 
 turbations, the computed and the observed places of the 
 planets agreed perfectly. 
 
 The motions of our moon are sensibly disturbed by the 
 planet Venus. An irregularity, which had been discovered 
 by observation, and had puzzled all astronomers for fifty 
 years, was explained a short time ago by Professor Han- 
 sen, of Gotha, on the theory of gravitation, as a very curi- 
 ous effect of the attraction of Venus. 
 
 202. The Theory of Gravitation holds good throughout the 
 known Universe. We thus see that the theory of gravita- 
 tion holds good as far as the solar system extends. We 
 have learned, moreover, that the binary stars which have 
 been observed to revolve about one another all move in 
 elliptical orbits. Hence, they must act upon one another 
 with a force which varies inversely as the square of the 
 distance. Hence, the law of gravitation seems to hold, as 
 far as we are able to extend our observations into space. 
 
 SUMMARY. 
 
 From the rotating of a wheel, and the vibrating of a 
 free pendulum in a vacuum, we infer that a moving body 
 will continue to move in a straight line and with a uniform 
 velocity until it is acted upon by some force. (172.) 
 
 By means of a projecting machine and Atwood's ma- 
 
ASTRONOMY. 235 
 
 chine, we find that a moving body, when acted upon by 
 gravity alone, will, at any given time, be just as far from the 
 point which it would have readied had it been left to itself, 
 as it would have been had it been at rest at that point in the 
 first place and been acted upon by gravity alone during the 
 same time. (174, 175-) 
 
 By the falling of bodies in a vacuum, and by the pendu- 
 lum, we find that gravity acts upon a body near the earth 
 with a force whose intensity varies directly as the mass of 
 the body, and is sufficient to draw it from a state of rest 
 one hundred and ninety-three inches in a second. (179, 
 1 88, 189.) 
 
 The planets and their moons all describe curved paths. 
 Hence they must be acted upon by some force. (173.) 
 
 They all describe equal areas in equal time. Hence the 
 force which curves their paths must, in the case of the 
 planets, be directed toward the sun, and, in the case of 
 the moons, toward the planet about which they revolve. 
 
 (177-) 
 
 At the distance of the moon, gravity, if its intensity di- 
 minishes as the square of the distance increases, will cause 
 a body to fall towards the earth .05305 of an inch. It is 
 found by computation that, when allowance is made for 
 disturbing causes which are known to exist, the moon is 
 drawn toward the earth exactly this distance each second. 
 Hence we conclude that gravity acts between the earth and 
 the moon with a force whose intensity varies ^directly as the 
 mass of the body acted upon, and inversely as the square 
 of its distance. (190.) 
 
 It is found by computation that, during a given time, all 
 the planets are drawn toward the sun, a distance which 
 varies inversely as the square of their distance from him. 
 Hence they must be acted upon by a force which varies 
 directly as their mass and inversely as the square of their 
 distance from the sun. It is also found that the planets 
 
236 ASTRONOMY. 
 
 must be acted upon by such a force, in order that they 
 may move in ellipses. From this we conclude that gravity 
 acts between the sun and the planets. For a like reason 
 we conclude that gravity acts between the planets and their 
 moons. (191-196.) 
 
 The comets describe elliptical and parabolic orbits. 
 Hence they must be acted upon by gravity. (197.) 
 
 The perturbations of the moon show that gravity must 
 act between the sun and the moon, as well as between the 
 sun and the earth, and the earth and the moon. (198.) 
 
 The perturbations of the planets can all be exactly ac- 
 counted for by supposing that each acts upon every other 
 with a force -varying directly as the mass and inversely as 
 the square of the distance of these bodies. Hence we con- 
 clude that gravity acts among all the bodies of the solar 
 system. (199-201.) 
 
 The binary and multiple stars revolve about one another 
 in elliptical orbits. Hence we conclude that gravity acts 
 between stars and stars as well as among the members of 
 our solar system. (202.) 
 
 The planets not only describe ellipses which differ from 
 one another in their eccentricity and their inclination to 
 the ecliptic, but the path described by each planet is con- 
 stantly undergoing changes in each of these particulars. 
 These changes go on increasing in one direction for a 
 certain length of time, when they again begin to diminish. 
 It has been shown by mathematical investigations that 
 these changes can in no case reach such a point as to 
 break up the present order of our system, provided that 
 system be acted upon by no external force, but that they 
 all repeat themselves in cycles which are in some cases 
 of enormous length. 
 
 These changes of very long period are often called 
 secular changes. 
 
ASTRONOMY. 237 
 
 GRAVITY ACTS UPON THE PARTICLES OF 
 MATTER. 
 
 203. We have now learned that gravity acts upon all 
 the heavenly bodies with a force varying directly as their 
 masses, and inversely as the squares of their distances 
 from one another. Does gravity act upon these bodies as 
 wholes, or upon the particles of which they are composed ? 
 
 204. The Tides. If the force acting between the sun 
 and the earth, and between the moon and the earth, acts 
 upon the particles of which the earth is made up, those 
 particles which are nearest the sun or moon ought to be 
 pulled more strongly than those which are farther away, 
 and, if they were free to move, they ought to be drawn 
 away from those behind them. But the particles of water' 
 have great freedom of motion among themselves. Are the 
 waters of the ocean heaped up under the sun and moon, 
 as they should be if gravity acts, not upon the earth as 
 a whole, but upon the particles of which it is composed ? 
 
 Now it is well known that tides exist in the ocean, and 
 that the tidal wave follows the moon in her daily round. 
 The particles of water nearest the moon are then drawn 
 
 Fig- 93- 
 
238 
 
 ASTRONOMY. 
 
 away from those behind them, thus giving rise to the tides. 
 It is only the mutual attraction among the particles of 
 which the earth is composed, that keeps these particles 
 from being drawn entirely away from the earth. 
 
 On the side of the earth opposite the moon, the particles 
 of the water are dra.wn less strongly than those of the solid 
 
 ea*rth which are nearer the moon. For this reason the 
 solid part of the earth is here drawn away from the water. 
 This gives rise to a tidal wave also on the part of the 
 ocean opposite the moon. 
 
 The tides follow the moon generally, but not entirely. 
 
ASTRONOMY. 
 
 239 
 
 They do not follow the time of the moon's meridian pas- 
 sage by. the same interval at all times ; and they are much 
 larger shortly after new moon and full moon than at other 
 times. From a careful examination of all the phenomena 
 of tides, it appears that they may be most accurately rep- 
 resented by the combination of two independent tides, the 
 larger produced by the moon (as shown in Figure 93), and 
 
 Fig. 95- 
 
 the smaller produced by the sun. When these two tides 
 are added together, they make a very large, tide (as shown 
 in Figure 94), which is called a spring-tide; but when the 
 high water produced by the sun is combined with the low 
 water produced by the moon, and the low water produced 
 by the sun is combined with the high water produced by 
 the moon (see Figure 95), a small tide is produced, which 
 is called a neap-tide. We conclude then that the force of 
 gravity which acts between the sun and the earth, and be- 
 tween the moon and the earth, does not act upon the earth 
 
240 ASTRONOMY. 
 
 as a whole, but upon each particle of which the earth is 
 composed. 
 
 205. The Spheroidal Form of the. Earth. Another im- 
 portant fact bearing upon the theory of gravitation is the 
 spheroidal form of the earth. 
 
 We have seen in Part First of this work (138) that the 
 materials of the earth are evidently the result of burning. 
 The heat developed by this combustion must have been 
 sufficient to reduce the whole mass to the liquid state. It 
 then slowly solidified at the surface, forming the rocks and 
 soil. There is the best of evidence that the interior of 
 the earth is still a molten mass. Portions of this molten 
 matter are often poured forth from the craters of volca- 
 noes, which act as so many safety-valves to relieve the 
 pent-up forces within. Again, in deep mines the tempera- 
 ture, as we descend, is found to increase at a rate which 
 shows that a few miles below the surface the heat must be 
 sufficient to fuse all known rocks. 
 
 The earth was, then, without doubt, once a liquid mass ; 
 and, obeying the tendency of all liquids, would have shaped 
 itself into a perfect sphere, had nothing interfered with this 
 tendency. But we have already seen that the earth is not 
 a perfect sphere, but is flattened at the poles, and protrudes 
 at the equator. How can this form be explained ? 
 
 Fig. 96. 
 
 When the hoop, in Figure 96, is made to rotate rapidly 
 on its axis, it flattens in the direction of the axis, and 
 bulges out in the direction at right angles to this axis. To 
 
ASTRONOMY. 241 
 
 understand why the hoop bulges out in this way we must 
 remember the first law of motion, namely, that when a 
 body is once put in motion it will move on a straight 
 line if it can. No matter in what way the part of the hoop 
 a is put in motion, it Las no tendency to move in a circle, 
 but will move in a horizontal straight line, if this is possi- 
 ble. By motion in a straight line, this part a would go far- 
 ther and farther from the central bar. In order to keep it 
 at the same distance from the central bar, a restraining 
 force is necessary. The term centrifugal force has been 
 used to express the tendency of the various parts of the 
 hoop to get farther off from the central bar. This term is 
 not a good one, since there is in reality no force. Cen- 
 trifugal tendency would be less objectionable. 
 
 The form that the hoop assumes depends upon this 
 centrifugal tendency, and upon the restraining force of 
 the hoop which keeps 'the parts from moving in a straight 
 line.' The less this restraining force, and the greater the 
 centrifugal tendency, the more flattened the hoop becomes. 
 
 In the same way, the flattened form of the earth must be 
 accounted for by the centrifugal tendency of its parts 
 when in the liquid state, developed by its rotation on its 
 axis, together with the restraining force which binds the 
 particles of the earth together. 
 
 Now, it has been found by careful investigation, that the 
 present form of the earth can be accounted for by the 
 action of the centrifugal tendency, on the supposition that 
 every particle of the earth attracts every other particle with 
 a force varying in the inverse ratio of the square of the dis- 
 tance. We have, then, an evidence here, that every parti- 
 cle of matter in a body attracts every other particle in the 
 inverse ratio of the square of the distance ; and, in the 
 case of tides, an evidence that the sun and moon attract 
 every particle of the earth in the inverse ratio of the 
 square of the distance. 
 
 ii p 
 
242 ASTRONOMY. 
 
 206. The Precession of the Equinoxes is caused by Gravity. 
 The precession of the equinoxes has already been de- 
 scribed (70). According to the theory of gravitation, the 
 sun's attraction is stronger at A (Figure 97) than at C, 
 since A is nearer than C. Hence the sun is always acting 
 on A, the part nearest to it, as if it were pulling it away 
 from the earth's centre. If it pulled the centre and the 
 surface of the earth equally, it would not tend to separate 
 them ; but since it pulls the former at A more than the 
 latter, it tends to draw it away from the centre towards S. 
 
 In like manner, as the sun pulls the centre more power- 
 fully than it pulls B, it tends to separate them, not by pull- 
 ing the opposite side B from the centre, but by pulling the 
 centre from the opposite side B. The general effect of 
 the sun's attraction, therefore, as tending to affect the dif- 
 ferent parts of the earth, is this : that it tends to pull the 
 nearest parts towards the sun, and to push the most dis- 
 tant parts from the sun. 
 
 If the earth were a perfect sphere, this would be a mat- 
 ter of no consequence : it would produce tides of the sea, 
 but it would not affect the motion of the solid parts. But 
 the earth, as we have seen, is not a sphere ; it is flattened 
 like a turnip, or has the form of a spheroid. Moreover, 
 the axis of the earth is not perpendicular to the ecliptic; 
 the earth's equator, at all times except the equinoxes, is 
 inclined to the line joining the earth's centre with the sun. 
 
 Let us now consider the position of the earth at the 
 winter solstice, shown in Figure 97. The North Pole is 
 away from the sun ; the South Pole is turned towards 
 the sun. This spheroidal earth, at this time, has its pro- 
 tuberance, not turned exactly towards the sun, but raised 
 above it. As we have seen, the attraction of the sun is 
 pulling the part D of the earth more strongly than it pulls 
 the centre. The immediate tendency of that action is to 
 bring the part D . towards #, supposing a to be in the plane 
 
ASTRONOMY. 243 
 
 Fig. 97. 
 
 passing through the centre of the sun and the centre of the 
 earth. This is because the force pulling D towards the sun 
 is equivalent to two other forces : one in the direction of 
 CD, tending to pull D from C; and the other acting at 
 right angles to this direction, tending to carry D towards a. 
 In like manner, as the sun attracts the centre of the earth 
 more than it attracts the protuberance E, which amounts 
 to the same thing as pushing the protuberance E away 
 from the sun, there is a tendency to bring E towards b. 
 The immediate tendency of the sun's pulling, therefore, is 
 so to change the position of the earth that its axis will be- 
 come more nearly perpendicular to the plane of the eclip- 
 tic ; but this tendency to change the inclination of the axis 
 is entirely modified by the rotation of the earth. Undoubt- 
 edly, if the earth were not revolving, and if the earth were 
 of a spheroidal shape, the attraction of the sun would tend 
 to pull it into such a position that the axis of the earth 
 would become perpendicular to the line S C ; or (if in the 
 position of the winter solstice) it would beconte perpendic- 
 ular to the plane of the ecliptic ; but, in consequence of 
 the rotation of the earth, the attraction produces a wholly 
 different effect. Let us consider the motion of a mountain 
 in the earth's protuberance, which, passing through the 
 point c on the distant side of the earth, would, in the semi- 
 revolution of half a day, describe the arc c D e, if the sun 
 did not act on it (c and e being the points at which this 
 circle c D e intersects the plane of the ecliptic, or the plane 
 
244 ASTRONOMY. 
 
 of the circle a b that passes through the sun). While the 
 protuberant mountain is describing the path c D e it is con- 
 stantly nearer to the sun than the earth's centre is ; the dif- 
 ference of the sun's action therefore tends to pull that 
 mountain towards S, and therefore (as it cannot be sepa- 
 rated from the earth) to pull it downwards, 'giving to the 
 earth a tilting movement ; it will, therefore, through the 
 mountain's whole course, from <r, make it describe a lower 
 curve than it would otherwise have described, and will 
 make it describe the curve cfg instead of the curve c D e. 
 The result of this is, that, as it mounts from ctof, the sun's 
 downward pull draws it towards the ecliptic, and conse- 
 quently renders its path less steep than it would otherwise 
 be. At / it will be a very little lower than it would other- 
 wise have been at D ; but as the sun's downward pull still 
 acts upon it till it comes to g, the steepness of its path be- 
 tween yand^is increased more than belongs naturally to 
 its elevation at f, and becomes in fact the same as it was 
 at f, or very nearly so ; so that the inclination of the path 
 to the plane of the circle a b is the same as at first. But, 
 instead of crossing the circle a b at <?, it will cross at^.- in 
 other words, it will, in consequence of the sun's action, 
 come to the crossing place earlier than it would have come 
 had the sun not acted. In the remaining half of its rota- 
 tion, from g towards c again, it is farther from the sun than 
 the earth's centre is ; therefore the sun's action does, in 
 fact, tend to push it away (as already explained) ; and as it 
 cannot be separated from the earth, this force tends to push 
 the mountain upwards towards the circle , tilting the earth 
 in the same direction as before ; the mountain, therefore, 
 in this part^will move in a path higher than it would have 
 moved in without the sun's action, and therefore it will 
 come to its intersection with the circle a b sooner than it 
 would if not subject to that action. The inclination of its 
 path (just as in the former half of its rotation) will not be 
 
 
ASTRONOMY. 245 
 
 altered. Thus the effect produced by this action of the 
 sun, in both halves of the rotation of this mountain is, that 
 it comes to the place of intersection with the plane of the 
 circle a b, or with the plane of the ecliptic, sooner than it 
 otherwise would. And whatever number of points or 
 mountains in the protuberant part of the earth we consider, 
 we shall find the same effect for every one ; and therefore, 
 the effect of the sun's action upon the entire protuberance 
 will be the same; that is, its inclination to the circle a b, 
 or the plane of the ecliptic, will not be altered ; but the 
 places in which it crosses that plane will be perpetually 
 altering in such a direction as to meet the direction of 
 rotation of the earth. 
 
 We have spoken as if the protuberance were the only 
 part to be considered. In reality, this protuberance is 
 attached to the remaining spherical part of the earth ; but 
 the action of the sun on the different masses of that spheri- 
 cal part balances exactly ; so that we need not consider the 
 sun's action upon it at all. The only effect, therefore, of 
 that spherical part will be to impede the motion which the 
 protuberant part would otherwise have : not to destroy it, 
 but to diminish it. 
 
 On the whole, therefore, the effect of the sun's action on 
 the spheroidal earth will be, that the points at which the 
 earth's equator intersects the plane of the ecliptic move 
 very slowly in the direction opposite to that in which the 
 earth revolves ; but the inclination is not altered. 
 
 All that I have said here applies to the position of the 
 earth at the winter solstice. But if we consider the earth 
 at the summer solstice, on the opposite side of the sun, we 
 shall find that the effect of the sun's action is exactly the 
 same. At the equinoxes, the plane of the earth's equator 
 passes through the sun, and then the sun's action does not 
 tend to tilt the earth at all, and consequently does not tend 
 to alter the position of its equator ; but at all other times 
 
246 ASTRONOMY. 
 
 the sun's action produces a motion, greater or less, of the 
 intersection of the earth's equator with the plane of the 
 ecliptic, in a direction opposite to that of the earth's rota- 
 tion. And this is the motion called the precession of the 
 equinoxes. 
 
 It is to be observed that the principal part of this pre- 
 cession is produced, not by the sun, but by the moon. 
 The moon's mass is not a twenty millionth part of the 
 sun's, but she is four hundred times as near as the sun. 
 Still she does not pull the earth as a mass with more than 
 a hundred and twentieth part of the sun's force. But since 
 the difference of the distances of the different parts of the 
 earth from the moon bears a greater proportion to the 
 whole distance than in the case of the sun, the effect of 
 the moon in pulling the nearer parts of the earth from the 
 earth's centre, and in pushing the more distant parts of 
 the earth from the earth's centre, is about treble the effect 
 of the sun. 
 
 We now see that the precession of the equinoxes is per- 
 fectly explained by the supposition that the sun attracts 
 every particle of the earth, and that it cannot be explained 
 without making this supposition. 
 
 SUMMARY. 
 
 Every particle of matter in our solar system acts upon 
 every other particle with a force varying inversely as the 
 square of their distance from one another. 
 
 This supposition is necessary to explain the tides (204), 
 the spheroidal form of the earth (205), and fa& precession of 
 the equinoxes. (206.) 
 
 The tides result from the struggle between the attraction 
 of gravity among the particles of the earth, and that be- 
 tween the particles of the earth and those of the sun and 
 moon. (204.) 
 
ASTRONOMY. 247 
 
 The spheroidal form of the earth resulted from the strug- 
 gle between the attraction of gravity among the particles 
 of the earth, and the centrifugal tendency of the particles 
 of the earth in the neighborhood of the equator, when the 
 earth was in the liquid state. (205). 
 
 The precession of the equinoxes is the result of the struggle 
 between the attraction of the sun and moon upon the 
 earth's equatorial protuberance, and the tendency of this 
 ring always to rotate in the same plane. (206). 
 
 HOW TO FIND THE WEIGHT OF THE 
 HEAVENLY BODIES. 
 
 207. The Weight of the Sun and Planets. Having thus 
 established the law of gravitation, we next inquire after the 
 strength of this force. Of course we know nothing about 
 the absolute strength of this or any force. We only know 
 their relative strength, and we must compare the force 
 exerted between two bodies with the force exerted between 
 the earth and a pound of water. We want, first, to find 
 the weight of the earth ; that is, to find how the force act- 
 ing between any given body and a pound of water com- 
 pares with the force acting between this same body and 
 the earth. 
 
 208. The Schehallien Experiment. The first experiment 
 for ascertaining this was made at the Schehallien moun- 
 tain, in Scotland. It was argued that if the theory of 
 gravitation were true, that is to say, if attraction were 
 produced, not by a tendency to the centre of the earth, or 
 to any special point, but to every particle of the earth's 
 structure, then, by the fundamental law of gravitation, the 
 attraction of a mountain would be a sensible thing ; for a 
 mountain is a part of the earth, with this difference only, 
 that though the mountain is small in comparison with the 
 earth, yet you get so close to the mountain, that its effect 
 
248 ASTRONOMY. 
 
 may be very sensible as compared with the effect produced 
 by the rest of the earth. Some parts of the earth are eight 
 thousand miles from us, and their attraction will be com- 
 paratively small. It was therefore thought worth while to 
 ascertain whether the attraction of a mountain, would be 
 sensibly felt. 
 
 The Schehallien mountain ranges east and west. It was 
 possible to make astronomical observations on the north 
 and south sides ; and it was also possible to connect the 
 two places of observation by triangulation (54). Suppose 
 
 Fig- 95- 
 
 Figure 95 to represent a section of the mountain, north 
 and south ; and JV the northern, S the southern observ- 
 ing station. Observations were made at JV and 6* upon 
 stars with the Zenith Sector (53). By the use of this in- 
 strument the difference of the directions of gravity at these 
 two stations was found, exactly in the same manner as the 
 difference of the directions of gravity in the two stations 
 in Figure 25. 
 
 The direction of gravity at each station is the result of 
 the gravity of the whole earth (as considered for a moment 
 independently of the mountain), combined with the attrac- 
 tion of the mountain. Supposing that at JV, if there were 
 no mountain, the direction of gravity would be N e; then 
 introducing the supposition of the mountain, the attraction 
 of the mountain would pull the plumb-line sideways to- 
 
ASTRONOMY. 249 
 
 wards the centre of the mountain, and the direction of the 
 gravity would be N E. And in like manner, supposing 
 that if there were no mountain, the direction of the gravity 
 at S would be S F; then, introducing the mountain, the 
 effect of its attraction is to pull the plumb-line towards the 
 centre of the mountain, and the direction of gravity would 
 be Sf. We see, then, the effect of the mountain. At JV 
 the direction of gravity is N E instead of N e^ and at S 
 the direction of gravity is Sf instead of S F, that is to 
 say, the two directions which are taken by the plumb-line 
 of the Zenith Sector, make a greater angle than they would 
 if the mountain were not there. 
 
 Now we know the general dimensions of the earth ; we 
 know what the inclination of the plumb-line at N and S 
 would be if there were no mountain in the case. If, then, 
 we can find the distance from our observing station at N 
 to that at S, then we can tell from that distance how much 
 the directions of the plumb-line at Nand S would be in- 
 clined if there were no mountain ; and we can compare 
 that inclination with the inclination observed by means of 
 the Zenith Sector. 
 
 Accordingly, the observations were made in exactly the 
 same manner as those made for determining the figure of 
 the earth (53-56). The Zenith Sector was carried to IV, 
 and certain stars were observed ; the Zenith Sector was 
 then carried to S, and the same stars were observed at 
 that place. By means of these observations of the stars, 
 the actual inclinations of the plumb-line at the two places 
 were found. The next thing done was to carry a survey 
 by triangulation across the mountain. This was done in 
 the most careful way in which the best surveyors of the 
 time could accomplish the task. The result was, that the 
 distance between the stations was found to be such, that, 
 supposing there were no mountain in the case, the in- 
 clination of the two plumb-lines ought to be 41 seconds, 
 n* 
 
250 ASTRONOMY. 
 
 It was found, from the observations by the Zenith Sec- 
 tor, that the inclination of the plumb-lines actually was 
 53 seconds. 
 
 The difference between the two was the effect of the 
 mountain. The mountain had pulled the plumb-line at 
 one station in one direction, and at the other station in the 
 opposite direction, to such a degree, that the two plumb- 
 lines, instead of making an angle of 41 seconds, made an 
 angle of 53 seconds ; or, in other words, the sum of the 
 effects of the two attractions of the mountain, on opposite 
 sides, was twelve seconds. 
 
 The next thing was, to draw from this observation a de- 
 termination of the mean density of the earth. The moun- 
 tain was surveyed, mapped, levelled, and measured, in 
 every way, so completely that a model of it might have 
 been made ; it was then (for the sake of calculation) con- 
 ceived to be divided into prisms of various forms : the at- 
 traction of every one of these was computed, on the sup- 
 position that the mountain had the same density as the 
 mean density of the earth ; and by means of this, the at- 
 traction of the whole mountain was found on the same 
 supposition. 
 
 Thus it was found, that, if the density of the mountain 
 had been the same as the mean density of the earth, the 
 sum of the effects of the attractions of the mountain at JV 
 and *S would have been about ^'37 part of gravity. But 
 the observed sum of effects was 12 seconds, which cor- 
 responds to -pnhri- P art of gravity. Hence the density of 
 the mountain is only about f of the earth's mean density ; 
 or the earth's mean density is nearly double the moun- 
 tain's density. The nature of the rocks composing the 
 mountain was carefully examined, and their density as 
 compared with that of water was ascertained; and thus 
 the mean density of the earth was found to be something 
 less than five times the density of water. 
 
ASTRONOMY. 25 1 
 
 209. The Cavendish Experiment. After this another 
 set of experiments was made ; first by Mr. Henry Caven- 
 dish, a rich man, much attached to science (from whom 
 the experiment of which we are speaking received the 
 name of the Cavendish Experiment) ; afterwards by a Dr. 
 Reich; and finally, in a very much more complete way, 
 by Mr. Francis Baily, as the active member of a commit- 
 tee of the Astronomical Society of London, to whom funds 
 were supplied by the British Government. 
 
 The shape in which the apparatus is represented, in 
 Figure 96, is that in which it was used by Mr. Baily. 
 There are two small balls, A, B> (generally about two' 
 
 inches in diameter,) carried on a rod A C J3, suspended by 
 a single wire D , or by two wires at a small distance from 
 each other. By means of a telescope, the positions of 
 these balls were observed from a distance. It was of the 
 utmost consequence that the observer should not go near, 
 not only to prevent his shaking the apparatus, but also 
 because 'the warmth of the body would create currents of 
 air that would disturb everything very much, even though 
 the balls were enclosed in double boxes, lined with gilt 
 paper, to prevent as much as possible the influence of such 
 
252 ASTRONOMY. 
 
 currents. When the position of the small balls had been 
 observed, large balls of lead, F, G, about twelve inches in 
 diameter, which moved upon a turning frame, were brought 
 near to them ; but still they were separated from each 
 other by half a dozen thicknesses of wooden boxes, so that 
 no effect could be produced except by the attraction of 
 the large balls. Observations were then made to see how 
 much these smaller balls were attracted out of their places 
 by the large ones. By another movement of the turning 
 frame, the larger balls could be brought to the position 
 H K. In every case, the motion of the small balls pro- 
 duced by the attraction of the larger ones was undeniably 
 apparent. The small balls were always put into a state of 
 vibration by this attraction ; then by observing the extreme 
 distances to which they swing both ways, and taking the 
 middle place between those extreme distances, we find the 
 place at which the attraction of the large balls would hold 
 them steady. 
 
 Suppose, now, the attraction of the large balls was found 
 to pull the small balls an inch away from their former place 
 of rest, what amount of dead pull does that show? In 
 order to ascertain this we must compare the vibrations of 
 the balls with those of an ordinary pendulum. 
 
 We have seen that when a pendulum-ball is pulled aside 
 and let go, it begins to vibrate. The force of gravity act- 
 ing upon the pendulum-ball is resolved into two parts, one 
 of which acts on the ball in the direction of the pendulum- 
 rod, and the other sideways. The former of course does 
 not affect the movement of the pendulum at all ; it is the 
 latter which causes the pendulum to vibrate. This latter 
 force increases with the distance the pendulum is pulled 
 aside, and always bears the same ratio to the weight of 
 the pendulum-ball as the distance the ball is drawn aside 
 bears to the length of the pendulum. As a pendulum 
 beating seconds is 39.139 inches long, the force which 
 
ASTRONOMY. 253 
 
 will pull it one inch sideways will then be re/Tire f i ts 
 weight. 
 
 In the case of the lead balls suspended by a wire, when 
 they are pulled aside by the large balls, they begin to vi- 
 brate. This vibration is caused by the torsion, or twist, 
 of the wire. This torsion increases with the distance the 
 balls are pulled aside, precisely as the force which causes 
 the pendulum to vibrate increases, with the distance it is 
 pulled aside. Hence the balls will vibrate exactly like a 
 pendulum. If, then, the balls vibrate in one second, and 
 are pulled aside one inch, the force which pulls them 
 aside must bear the same proportion to their weight that 
 the force which pulls a seconds pendulum one inch aside 
 .bears to the weight of the pendulum-ball ; that is, it must 
 be ^.T^ of their weight. 
 
 Then it is known, as a general theorem regarding vibra- 
 tions, that, to make the vibrations twice as slow, we must 
 have forces (for the same distances of displacement) four 
 times as small ; and so in proportion to the inverse square 
 of the times of vibration. Thus if balls or anything else 
 vibrate once in ten seconds, the dead pull sideways cor- 
 responding to an inch of displacement is -5737? f their 
 weight. So that, in fact, all that we now want for our cal- 
 culation, is the time of vibration of the suspended balls. 
 This is very .easily observed ; and then, on the principles 
 already explained, there is no difficulty in computing the 
 dead pull sideways corresponding to a sideways displace- 
 ment of one inch ; and then (by altering this in the pro- 
 portion of the observed displacement, whatever it may be) 
 the sideways dead pull or attraction corresponding to any 
 observed displacement is readily found. The delicacy of 
 this method of observing and computing the attraction of 
 the large balls may be judged from the fact that the whole 
 attraction amounted to only about 2-ff,<jj<j,Tnnr P art f the 
 weight of the small balls, and that the uncertainty in the 
 
254 ASTRONOMY. 
 
 measure of this very small quantity did not amount proba- 
 bly to 5 V or s\y of the whole. 
 
 Then the next step was this : knowing the size of the 
 large balls and their distances from the small balls in the 
 experiment, and knowing also the size of the earth, and 
 the distance of the small' balls from the centre of the earth, 
 we can calculate what would be the proportion of the at- 
 traction of the large balls on the small balls to the attrac- 
 tion of the earth on the small balls (that is, the weight of 
 the small balls), if the leaden balls had the same density 
 as the mean density of the earth. It was found that this 
 would produce a smaller attraction than that computed 
 from the observations. Consequently, the mean density 
 of the earth is less than the density of lead in the same 
 proportion ; and thus the mean density of the earth is 
 found to be 5.67 times the density of water. 
 
 210. Another Method of finding the Weight of the Earth. 
 It has been found that if the law of universal gravita- 
 tion be true, the attraction of the whole earth, considered 
 as a sphere, on a body at its surface, is the same as if the 
 whole matter of the earth were collected at its centre. 
 It has -also been found that the attraction of the earth on a 
 body within its surface is the same as if the spherical shell 
 situated between the body and the earth's surface were re- 
 moved ; or is the same as if all the matter situated nearer 
 to the earth's centre than the body were collected at the 
 centre, and all the matter situated at a greater distance 
 were removed. 
 
 If the earth were of uniform density throughout, it would 
 follow from these propositions that the force of gravity at 
 the bottom of a mine would be less than the force at the 
 top. To show this, suppose that the mine reached half- 
 way to the centre of the earth. Then (since the volumes 
 of spheres vary as the cubes of their diameters) the quan- 
 tity of matter nearer to the earth's centre than the bottom 
 
 
ASTRONOMY. 255 
 
 of the mine would be only one eighth of the whole quan- 
 tity of matter in the earth. But the attraction of a quantity 
 of matter at the earth's centre would be more powerful on 
 a body at the bottom of a mine than on one at the top, in 
 the inverse ratio of the squares of the distances of the 
 bodies from the earth's centre ; that is, in the present case, 
 in the ratio of four to one. Hence the attraction on a 
 body at the bottom of a mine would be, on the whole, less 
 than the attraction on a body at the top, in the ratio of 
 one to two. 
 
 If, however, the earth be not of uniform density, but its 
 density increase towards the centre, then, though the at- 
 tracting mass which acts on a body at the bottom of the 
 mine be smaller, yet the diminution in the force of gravity 
 so occasioned may be more than compensated by the com- 
 parative nearness of the attracted body to the denser parts 
 of the earth. From the two laws of the attraction of 
 spheres, which have been stated above, it is possible to 
 calculate the ratio which the force of gravity at the bottom 
 of the mine would bear to that at the top, on any supposi- 
 tion we choose to make as to the ratio between the mean 
 density of the earth and the density at the surface ; so that, 
 if we know one ratio we can immediately infer the other. 
 Now, pendulum observations afford us the means of deter- 
 mining the force of gravity at any place ; and therefore, if 
 the times of vibration of a pendulum at the top and bottom 
 of a mine be found, the ratio of the force of gravity at the 
 top to that at the bottom may be calculated, and thence 
 the ratio of the mean density of the earth to that of its 
 surface. 
 
 The pendulum is made of metal ; it turns with a hard 
 steel prism, having a very fine edge, upon plates of agate, 
 or some very hard stone. It swings like the pendulum of 
 a clock. But it must be observed that a clock pendu- 
 lum will not do for this purpose, because there are other 
 
256 ASTRONOMY. 
 
 forces besides gravity acting upon it ; that is to say, the 
 clock weights acting through the train of the clock wheels. 
 It is necessary to have a detached pendulum. Now we 
 wish to know how many vibrations that pendulum would 
 make in a day. 
 
 In modern experiments of this kind, the vibrations of 
 the detached pendulum have been compared with the vibra- 
 tions of a clock pendulum. The mode usually adopted is 
 this : a detached pendulum is placed in front of a clock ; 
 a person is watching with a telescope ; he watches when 
 the two pendulums are going the same way ; he remarks 
 whether the vibrations of the detached pendulum recur 
 faster or slower than those of the clock pendulum ; he sees 
 that the vibrations separate more and more, till the two 
 pendulums actually move in opposite ways ; after this, they 
 begin to move more nearly in the same way, and at length 
 move exactly in the same way. Perhaps the number of 
 vibrations between these two agreements of motion may 
 be 500. If we can determine the time when the two pen- 
 dulums swing the same way, we find how long it is before 
 one pendulum gains two vibrations upon the other. Then 
 suppose that the detached pendulum is going slower than 
 the clock pendulum ; and suppose that 7 J minutes elapse 
 between two agreements of motion of the pendulum : this 
 shows that while the clock has gone y| minutes, or while 
 its pendulum has made 450 vibrations, the detached pen- 
 dulum has made only 448 vibrations. Now, the clock is 
 going day and night, and by means of observation with the 
 transit instrument, we can find how many hours, minutes, 
 and seconds the clock hands pass over in one day, or how 
 many vibrations the clock pendulum makes in one day. 
 Then, as the detached pendulum makes 448 vibrations for 
 every 450 made by the clock pendulum, we find at once 
 how many vibrations the detached pendulum makes in 
 t\venty-four hours. 
 
ASTRONOMY. 257 
 
 Some corrections for the effect of temperature in altering 
 the length of the pendulum, and for other circumstances, 
 are necessary. The method just described is exceedingly 
 delicate. There is no difficulty in ascertaining by it the 
 number of vibrations which the detached pendulum will 
 make in a day, with no greater error than one tenth of a 
 vibration, or with an error not exceeding one eight hundred 
 thousandth part of the whole. 
 
 This mode of determining the weight of the earth was 
 put in practice by Airy, the Astronomer Royal of England, 
 at the Harton Coal Pit, in the year 1854. The mean den- 
 sity deduced from his observations is 6.565 times that of 
 water : a value considerably exceeding that found from the 
 Schehallien and Cavendish experiments. 
 
 Each cubit foot of the earth is thus found to weigh, on 
 an average, about six times as much as a cubic foot of 
 water. In the earth there are 259,800,000,000 cubic miles, 
 and in each cubic mile 147,200,000,000 cubic feet. From 
 these data the whole weight of the earth may be readily 
 found. 
 
 211. The Weight of the Sun. We have already seen 
 that the motion of a body in a second, when drawn by 
 gravity, is directly proportional to the force acting upon it 
 Remembering this, we can easily find the weight of the 
 sun as compared with that of the earth. 
 
 We have found, in Figure 85, that the earth draws the 
 moon through 10.963 miles in one hour, the moon being 
 at the distance of 238,800 miles from the earth ; and 
 in Figure 86, that the sun draws the earth through 24.402 
 miles in one hour, the earth being at the distance of 
 95,000,000 miles from the sun. In order to compare 
 these attractions, we must reduce them both to the same 
 distance. If the earth draws the moon through 10.963 
 miles in an hour when at the distance of 238,800 miles, 
 how far would it draw the moon in an hour if it were at 
 
 Q 
 
258 ASTRONOMY. 
 
 the distance of 95,000,000 miles? Diminishing 10.963 in 
 the proportion of the inverse squares of the distances, 
 we find that the earth would draw the moon through 
 0.00006927 mile or 4.389 inches in an hour, if it were at 
 the distance of 95,000,000 miles. Comparing this with 
 24.402 miles, through which the sun draws the earth or 
 moon when at the same distance, we find that the sun's 
 attraction is 352,280 times as great as the earth's, and 
 therefore, that the sun's mass is 352,280 times as great as 
 the earth's. 
 
 We have learned (87) that the sun's bulk is some 
 1,400,000 times as great as the earth's bulk. Therefore 
 the sun's mean density is only about J of the earth's mean 
 density, or about 1.4 times the density of water. 
 
 212. The Weight of the Planets. The method which 
 has been used above for comparing the mass of the earth 
 with that of the sun, is also used for comparing the mass 
 of Jupiter, Saturn, Uranus, or Neptune, with that of the 
 sun ; and in all cases where the moons can be easily ob- 
 served, it can be applied with very great accuracy. For 
 those planets which have no moons there is considerable 
 uncertainty. The only way in which their weight can be 
 determined is by their disturbance of other planets. For 
 instance, in certain positions, the earth is disturbed by 
 Mars a few seconds, say six or eight. We compute what 
 would be the amount of perturbation if the planet Mars 
 were as big, or half as big, as the earth, and we alter the 
 supposition till we find a mass which will produce pertur- 
 bations equal to those which we observe. This is the pro- 
 cess of trial and error, which has already been described. 
 In this manner the masses of Mars and Venus are deter- 
 mined. That of Mars is not very certain ; that of Venus 
 is more certain, both because it produces larger pertur- 
 bations of the earth, and because its attraction tends to 
 produce a continual change in the plane of the ecliptic, 
 
ASTRONOMY. 259 
 
 which in many years amounts to a very sensible quantity. 
 The mass of Mercury is still very uncertain. Lately at- 
 tempts have been made to deduce it from the perturba- 
 tions which Mercury produces in the motions of one of 
 the comets. 
 
 213. The Weight of the Moon obtained from the Tides. 
 There is, however, one mass which is more important than 
 the others, and that is the mass of the moon. There are 
 several methods by which this mass is determined. 
 
 One method is by comparing the tides at different times* 
 By comparing the spring-tides with the neap-tides, we can 
 find the proportion of the effect produced by the moon to 
 that produced by the sun. Now, the tides are produced, 
 not by the whole attraction of the moon and the sun upon 
 the water, but by the difference between their attraction 
 upon the water and their attraction upon the mass of the 
 earth, by which difference the moon (and also the sun) 
 draws the water nearest to it away from the earth, and 
 draws the earth away from the water which is farthest from 
 the moon. 
 
 With proper investigation it is possible to find, from the 
 tidal effects of the sun and moon, the proportion of their 
 differences of attraction. And knowing this proportion, 
 and knowing the distances of the sun and moon, we can 
 find the proportion of their masses. 
 
 214. Another Method of finding the Moon's Weight. 
 
 In Figure 100, suppose C to be the sun,. E the earth, 
 M the moon. We have spoken continually of the sun's 
 attraction upon the earth, and of the earth's revolution 
 round the sun, as if the sun were the only body whose 
 attraction influenced in a material degree the earth's move- 
 ment. But in reality the moon also acts in a very sen- 
 sible degree upon the earth. And the immediate effect 
 upon the motion of the earth can be found. Draw a 
 line from E to M, and in this line take the point G, so 
 
260 
 
 ASTRONOMY. 
 
 that the proportion of E G to G M is the 
 same as the proportion of the weight of 
 M to the weight of E ; or so that if E 
 and M were like two balls fastened upon 
 the ends of a rod, they would balance at G. 
 This point would be their common centre 
 of gravity. Then investigation shows that 
 the motion of the earth may be almost 
 exactly represented by saying that the point 
 G travels round the sun in an ellipse, de- 
 scribing areas proportional to the times 
 (according to Kepler's laws), and that the 
 earth E revolves round the point G in a 
 month, being always on the side opposite 
 to the moon. 
 
 Consequently, the direction in which the earth would 
 be seen from the sun (and therefore the direction in which 
 the sun is seen from the earth) depends in a certain degree 
 on the distance E G. And, therefore, if we observe the 
 sun regularly, and if we compute where we ought to see 
 the sun, according to Kepler's laws, the difference between 
 these two directions will be the angle E C G ; and know- 
 ing the distance C G, we can then compute the length of 
 E G, and the proportion which it bears to G M; and this 
 proportion is the same as the proportion of the mass of 
 the moon to the mass of the earth. 
 
 These different methods agree very well in giving the 
 result that the mass of the moon is about V of the earth's 
 mass. 
 
ASTRONOMY. 261 
 
 SUMMARY. 
 
 The earth weighs about six times as much as a globe of 
 water of the same size would weigh. 
 
 The weight of the earth can be found in three ways : 
 
 (i.) By comparing the attraction exerted by the whole 
 earth with that exerted by a mountain, and then ascertain- 
 ing the density of the mountain ; as in the Schehallien ex- 
 periment. (208.) 
 
 (2.) By comparing the force exerted by the earth upon 
 two small balls of lead with that exerted upon the same by 
 two large balls of lead ; as in the Cavendish experiment. 
 (209.) 
 
 (3.) By observing the vibration of a pendulum at the 
 earth's surface, and at the bottom of a deep mine ; as in 
 the Harton Coal Pit experiment. (210.) 
 
 Knowing the weight of the earth, the weight of the sun 
 can be found by comparing the distance the moon is drawn 
 by the earth in an hour with the distance the sun draws 
 the earth in the same time. (211.) 
 
 Having found the weight of the sun, we can find the 
 weight of any planet which has moons by comparing the dis- 
 tance they draw their moons in an hour with the distance 
 they themselves are drawn by the sun in the same time. 
 
 The weight of those planets which have no moons can be 
 found by the perturbations they cause in .the motions of 
 other planets. (212.) * 
 
 The weight of the moon can be found by comparing her 
 effect with that of the sun in producing the tides (213), and 
 by means of the apparent displacement of the sun, occa- 
 sioned by the action of the moon upon the earth. (214.) 
 
 The earth not only draws the moon towards itself, but is 
 also itself drawn towards the moon ; and the moon does 
 not really revolve about the earth, but both these bodies 
 
262 ASTRONOMY. 
 
 revolve about their common centre of gravity. This centre 
 of gravity is very much nearer the earth than the moon, 
 because the mass of the earth is much greater than that of 
 the moon. (214.) 
 
 The same thing is true of the sun and the planets. He 
 not only draws the planets towards himself, but is himself 
 drawn towards them ; and they do not really revolve about 
 him as a centre, but both they and he revolve about their 
 common centre of gravity. Since the mass of the sun 
 very much exceeds that of all the planets, the common 
 centre of gravity of the whole solar system lies within the 
 surface of the sun. 
 
 So, too, in the binary and multiple stars, there is no one 
 star about which the others revolve, but each revolves 
 about the common centre of gravity of the system. If 
 both components of a binary system have equal masses, 
 their common centre of gravity would be midway between 
 them. 
 
 GENERAL SUMMARY. 
 
 When a free pendulum is vibrating in any part of the 
 earth except at the equator, its direction of vibration ap- 
 pears constantly to change ; and from this we know that 
 the earth must rotate on its axis from west to east once 
 in twenty-four hours. 
 
 The planets follow such irregular paths among the 
 stars that their motion can be explained only by suppos- 
 ing that they all describe ellipses which have the sun at 
 one focus ; and the motion of the moons can be explained 
 only on the supposition that they describe ellipses about 
 their planets. 
 
 The time it takes the earth to complete a revolution 
 about the sun is found by direct observation ; and then, 
 by observing their synodical revolutions, the sidereal 
 periods of the planets can be computed. 
 
ASTRONOMY. 263 
 
 The relative distances of the earth and the planets from 
 the sun are found by observing the greatest elongation of 
 the inferior planets, and the daily retrogression of the 
 superior planets at the time of their opposition. 
 
 The real distance from the earth to the sun is found by 
 observation of the transits of Venus, and by measuring 
 an arc of the earth's meridian. 
 
 Telescopes which are pointed at the moon from Green- 
 wich and the Cape of Good Hope, differ in direction ; 
 and by measuring this difference of direction, the dis- 
 tance of the moon from the earth is ascertained. 
 
 When a telescope is pointed to a fixed star, from oppo- 
 site points of the earth's orbit, there is often an appreciable 
 difference in its direction. This difference can be measured, 
 and, by means of it, we can find the distance of the stars. 
 
 All the stars in the neighborhood of the constellation 
 Hercules appear to be spreading away from a point in that 
 constellation; and from this we know that our sun is 
 travelling through space towards that point. 
 
 The stars are slowly changing their configurations, and 
 must therefore be in motion. 
 
 The sun is about a million and a half times as large as 
 the earth ; he rotates on his axis in about twenty-five days ; 
 he is surrounded by an atmosphere several thousand miles 
 in depth ; and his photosphere is probably a stratum of 
 clouds suspended in this atmosphere. The spots on his 
 disc are probably caused by the cooling, of portions of 
 these clouds by downward currents ; while the faculae are 
 caused by the raising of other portions into ridges by up- 
 ward currents. 
 
 The moon presents a very rough and rugged surface ; 
 and there are indications of similar inequalities in the case 
 of Mercury, Venus, and Mars. 
 
 The four inner planets are all of moderate size. They 
 all have atmospheres, and all appear to rotate on their axes 
 
264 ASTRONOMY. 
 
 in about twenty-four hours ; and of these, the earth alone 
 has a moon. The four outer planets form another group, 
 and differ strikingly from these in their enormous size, 
 their rapid rotation on their axes, and in their complex 
 systems of satellites. Between this inner and outer group 
 of planets there is a large number of telescopic bodies, 
 forming the well-marked group of the Minor Planets. 
 
 Many of the stars change their color and their bright- 
 ness. Some undergo these changes in short and regular 
 periods, and others at long and perhaps irregular intervals. 
 
 The vibration of a free pendulum in a vacuum can be 
 explained only on the supposition that a moving body 
 always tends to move in a straight line and with an un- 
 varying velocity. 
 
 Gravity has the same effect upon a moving body as 
 upon a body at rest. 
 
 Gravity acting upon a body near the earth causes it to 
 fall from a state of rest 193 inches in a second. 
 
 Since the planets and moons describe equal areas in 
 equal times, the force which deflects their paths must be 
 directed in the case of the planets towards the sun, and in 
 the case of the moons towards their planets. 
 
 On the supposition that a stone at the distance of the 
 moon would be still acted upon by gravity, but with a force 
 which diminishes as the square of the distance from the 
 earth's centre increases, it would fall just as far in a unit 
 of time as the moon is drawn towards the earth in the 
 same time. We therefore conclude that gravity extends to 
 the moon. 
 
 The distances the planets are drawn towards the sun 
 in a given time are exactly in the inverse ratio of the 
 squares of their distances from him ; and the force which 
 causes a planet to describe an ellipse must vary inversely 
 as the square of its distance from the sun. Hence we 
 conclude that gravity acts between the sun and the 
 planets. 
 
ASTRONOMY. 265 
 
 The perturbations of the planets can be explained only 
 by the supposition that each attracts the others with a 
 force which varies directly as the mass of the bodies acted 
 upon, and inversely as the square of their distances from 
 one another. We therefore conclude that all the members 
 of the solar system are acted upon by gravity. 
 
 Many of the stars move in elliptical orbits. Hence we 
 conclude that gravity acts among all the heavenly bodies. 
 
 The tides, the spheroidal form of the earth, and the 
 precession of the equinoxes can be explained only on the 
 supposition that gravity acts among the particles of the 
 earth, and between these and the sun and moon. Gravity 
 therefore acts upon the heavenly bodies, not as wholes, 
 but upon the particles of which they are composed. 
 
 By comparing the pull exerted by one piece of lead 
 upon another with the pull exerted by the earth upon the 
 sun, we are able to express the pull of the earth in pounds. 
 The distance a body is pulled from a state of rest in a sec- 
 ond is directly proportional to the effective pull of gravity 
 acting upon it. The earth's gravity can then be compared 
 with that of the sun by comparing the distance the moon 
 is drawn through by the earth in a second with the dis- 
 tance the earth is drawn through in a second by the sun. 
 The gravity of a planet which has a moon can be compared 
 with the gravity of the sun by comparing the distance the 
 planet draws its moon in a given time with the distance 
 the sun draws the planet in the same tinxe. The weight 
 of a planet without a moon can be found by comparing its 
 disturbance of another planet's motion with the disturb- 
 ance of the same planet's motion by a planet whose weight 
 is known. 
 
266 ASTRONOMY. 
 
 CONCLUSION. 
 
 WE have now become somewhat acquainted with the 
 heavenly bodies, and with the force by which they act 
 upon one another. 
 
 Our attention was first called to the motions of these 
 bodies, and we find that they are all describing accurate 
 circles about the earth from east to west once in twenty- 
 four hours. An examination of the vibration of a free pen- 
 dulum taught us, however, that the earth is rotating from 
 west to east, and that the motion we had first observed is 
 only apparent. We soon, however, discovered that certain 
 of these bodies are moving eastward among the stars with 
 considerable rapidity, and usually in very irregular paths. 
 We noticed the rude and complex systems by which the 
 ancients attempted to account for these motions, and were 
 taught by Kepler that these bodies, together with the 
 earth, form a group by themselves, and that they all, ex- 
 cept the moon, revolve in ellipses about the sun. These 
 bodies are the planets. 
 
 We next inquired how long it takes each of these bodies 
 to complete a revolution about the sun, and the simple 
 observation of the interval between two successive con- 
 junctions of the sun with the same fixed star, and with 
 each of the planets, enabled us to answer this inquiry. 
 
 ' We next sought the relative distances of the planets from 
 the sun, and were enabled to find these distances by simply 
 observing the greatest elongation of the inferior planets 
 and the retrogression of the superior planets during one 
 day when they are in opposition. We then found the ac- 
 tual distance of the earth from the sun simply by observ- 
 ing a transit of Venus, and by measuring a short distance 
 upon the earth. 
 
 We next directed our attention to the moon, and saw 
 
ASTRONOMY. 267 
 
 that her motion could be explained only on the supposi- 
 tion that she revolves about the earth in an ellipse ; and 
 that her distance from the earth's centre could be found by 
 simply pointing a telescope at her from the observatories 
 at Greenwich and the Cape of Good Hope, and measuring 
 the inclination of these telescopes to each other. 
 
 Having learned so much about the motions and dis- 
 tances of the moon and the planets, we next inquired the 
 distance between our earth and the stars. We found that 
 in some cases the telescope does not have quite the same 
 direction when pointed at a fixed star from opposite points 
 in the earth's orbit, and that we can measure this differ- 
 ence of direction, and thus ascertain the distance of the 
 stars from the earth. This inquiry led us to the unex- 
 pected conclusion that our sidereal system is so vast, that, 
 were all the stars which compose it suddenly destroyed, it 
 would be some four years before light, travelling with the 
 velocity of 190,000 miles a second, could inform us of the 
 destruction of the nearest, and several thousand years be- 
 fore it could inform us of the destruction of the most 
 remote. And at the same time we caught sight of outly- 
 ing sidereal systems, which probably are not inferior -in 
 magnitude to our own, but which even with the aid of a 
 telescope appear only as minute patches of hazy light. 
 
 Since our sun at the distance of the fixed stars would 
 shine only as a star of the second magnitude, we saw that 
 all the stars are suns ; and a more careful examination of 
 these bodies taught us that they appear fixed only because 
 they are separated from us by such immense distances. 
 We found that our sun is moving toward a point in the 
 constellation Hercules ; that many of the stars have prop- 
 er motions ; and that Arcturus and other stars are really 
 moving through space with a velocity about six hundred 
 times that of a cannon-ball. 
 
 We thus learned that our sun, moons, and planets prob- 
 
263 ASTRONOMY. 
 
 ably form but one of millions of such groups, and that 
 while in each of these groups the moons are revolving 
 about the planets and the planets about the suns, the 
 suns themselves are revolving about one another in sys- 
 tems more or less complicated. 
 
 After having thus learned the motions and distances of 
 the members of our solar system, and the motions and dis- 
 tances of a few of the stars, we next inquired what is known 
 of the physical features of each of these bodies. On this 
 point we found our knowledge to be extremely limited. 
 The telescope has revealed to us that there are rocks, 
 mountains, and volcanic craters upon the surface of the 
 moon, and we think that Mercury, Venus, and Mars re- 
 semble the earth and moon in this respect. We know 
 that the earth and, Mars rotate on their axes in about 
 twenty-four hours, and we think that Mercury and Venus 
 rotate in the same time. We know that each one of these 
 planets has an atmosphere. We know nothing of the 
 physical constitution of the minor planets. And of the 
 outer planets, we know only that Jupiter and Saturn rotate 
 on their axes in about ten hours, and that Jupiter is at- 
 tended by four moons, and Saturn by eight moons and a 
 complex system of rings. Of Uranus and Neptune we 
 know only that they are attended by a few moons, whose 
 motions are retrograde. We know that the sun rotates on 
 his axis in about twenty-five days, that he has an atmos- 
 phere several thousand miles deep, and that there are dark 
 spots on his disc. 
 
 We think that in the atmosphere of the sun the vapors 
 of such substances as iron, which pass from the gaseous 
 to the liquid state at a temperature above a white heat, 
 condense into a cloudy stratum, giving rise to the solar 
 photosphere, and that these clouds are sometimes cooled 
 by downward and sometimes lifted into ridges by up- 
 ward currents, and that this is the cause of the spots and 
 faculx. 
 
ASTRONOMY. 269 
 
 We next learned that a moving body when left to itself 
 will always move in a straight line and with uniform ve- 
 locity. 
 
 A further study of the paths of bodies falling to the 
 earth, and of those of the heavenly bodies, taught us that 
 these bodies are all acted upon by a force which tends to 
 draw them together, and whose intensity varies directly as 
 the mass of the bodies acted upon and inversely as their 
 distance from one another ; and that this force is the 
 same as that which draws a stone to the earth. 
 
 We have found that the action of this force is so well 
 understood that we can explain by it not only the general 
 form of the paths described by the heavenly bodies, but the 
 many and complicated disturbances which the planets 
 cause in one another's motions ; that we are able to pre- 
 dict disturbances whose existence had not been revealed 
 by observation, and by the study of perturbations already 
 observed to point out the position of planets before un- 
 known. 
 
 We have fo'undy too, that the knowledge of the force 
 which acts among the heavenly bodies and through planet- 
 ary distances is of no less practical value than the knowl- 
 edge of the forces of affinity and electricity which act 
 among the atoms and molecules of matter and through 
 atomic and molecular spaces. For it is only by a correct 
 knowledge of the action of this force that astronomers be- 
 come acquainted with all the irregularities of the moon's 
 motion, and are enabled to construct tables by which 
 navigators at sea can read longitude from the heavens 
 with accuracy. 
 
 We have thus seen that the groupings and movements 
 of the heavenly bodies result from a single force acting 
 among them ; and that, by a study of these groupings and 
 movements, we have arrived at a complete knowledge of 
 the law by which this force acts. 
 
270 ASTRONOMY. 
 
 In another part of this Course we have seen that bodies 
 are made up of atoms which are grouped into molecules 
 and into masses. Are these atoms also in motion, and are 
 their groupings and movements regulated by a single force 
 acting among them ; and are electricity, light, and heat 
 only disturbances of these atomic and molecular move- 
 ments ? The achievements of astronomy lead us to hope 
 that we may at a future day be able to measure the minute 
 distances between the atoms, and to discover in what paths 
 they move and the laws by which the force acting among 
 them is governed. 
 
IV. 
 
 ORIGIN, TRANSMUTATION, AND 
 CONSERVATION OF ENERGY. 
 
ORIGIN, TRANSMUTATION, AND CON- 
 SERVATION OF ENERGY. 
 
 215. Actual and Potential Energy. A weight at rest on 
 the ground cannot move, or do work of any kind. It is 
 therefore said to have no energy, or ability to do work. If 
 the same weight is raised from the ground and suspended, 
 it still manifests no energy ; that is, so long as it remains 
 suspended it can do no work. The moment it is released, 
 however, it begins to fall, and in falling can drive a clock, 
 or do other work. While, then, a weight rests on the earth, 
 it has no energy, and it is not possible for it to manifest 
 any. When the weight is raised from the earth, it may not 
 manifest any energy, but it is always possible for it to do 
 so. In this case it is said to have a possible or potential 
 energy. When the weight is falling it has an actual or dy- 
 namical energy. Every moving body, then, has a dynami- 
 cal energy ; and every body which is so situated that it can 
 be moved by gravity has a potential energy. 
 
 216. Mechanical, Molecular, and Muscular Energy. 
 When, as in the case of the falling weight, th'e motion of a 
 body is visible, its energy is called mechanical. But we 
 have seen that heat can separate and rearrange the mole- 
 cules of a body, and, in so doing, it does work. Again, 
 light can effect chemical changes ; and electricity in motion 
 can turn a magnetic needle, or make a magnet. The mo- 
 tions which manifest themselves as heat, light, and elec- 
 tricity are invisible. They are not movements of a body 
 
 12* R 
 
274 CONSERVATION OF ENERGY. 
 
 as a whole, but of its molecules among themselves. The 
 energy of these movements is called molecular. 
 
 The movements of bodies which manifest themselves as 
 sound are either visible, or can be easily made so. The 
 energy of these movements, then, is to be regarded as 
 mechanical rather than as molecular. 
 
 The energy manifested in the bodies of animals is called 
 .muscular energy. 
 
 There are, then, three kinds of dynamical energy, 
 rthat manifested in ordinary motion and in a sounding 
 .body, called mechanical energy ; that manifested in the 
 molecular movements of light, heat, and electricity, called 
 molecidar energy ; and that manifested in the bodies of 
 animals, called muscular energy. 
 
 It must be understood, however, that these kinds of 
 energy do not differ in themselves, but only in the way in 
 .which they are manifested. 
 
 217. Affinity, Cohesion, and Gravity are the Forces which 
 tend to convert Potential into Dynamical Energy. We have 
 seen that a weight raised from the earth has a potential 
 energy, which gravity tends to convert into dynamical 
 energy. When the molecules of a body are separated by 
 melting and boiling, cohesion tends to draw them together 
 again, and thus to convert their potential into dynamical 
 energy, which appears as heat Again, when the elements 
 of a compound are separated, they have a potential energy, 
 since it is possible for them to unite again. The force 
 which tends to draw them together, and thus to convert 
 their potential into dynamical energy, is affinity. 
 
 When, therefore, the atoms of different elements are 
 separated, they have a potential energy, which affinity 
 tends to convert into dynamical energy. When the mole- 
 cules of a body are separated, they have a potential energy, 
 which cohesion tends to convert into dynamical energy. 
 When bodies are separated, they have a potential en- 
 
CONSERVATION OF ENERGY. 275 
 
 ergy, which gravity tends to convert into dynamical 
 energy. The first two forces act through insensible dis- 
 tances, and give rise to molecular energy ; the last acts 
 through all distances, and gives rise to mechanical energy.* 
 
 218. Mechanical Energy may be converted into Heat. 
 We have a familiar illustration of this in the lighting of a 
 friction match. A portion of the energy employed in rub- 
 bing the match is converted by the friction into heat, which 
 ignites the phosphorus. Here there is a double transfer 
 of energy. The muscular energy of the arm is converted 
 into mechanical energy in the moving match, and a part 
 of this into heat by the friction. 
 
 Before matches were invented, the flint and steel were 
 used for the same purpose. The steel was struck against 
 the flint, and the spark obtained was caught in tinder. A 
 part of the mechanical energy of the steel appeared as 
 heat in the spark. 
 
 Indians are said to obtain fire by vigorously rubbing to- 
 gether two pieces of dry wood. In this case, too, the heat 
 is nothing but mechanical energy appearing in a new 
 form. 
 
 Iron can be heated red-hot by hammering it. And, 
 generally, heat is developed by friction and percussion. 
 
 219. Count Rumford's Experiment. Until recently, heat 
 has been regarded as a substance, or a form of matter. It 
 was supposed that this substance was taken up by bodies 
 much as water is taken up by a sponge, and in this state it 
 \vas said to be latent ; but when bodies were rubbed or 
 struck together, a portion of the heat was squeezed out of 
 them, and thus became sensible. The more heat a body 
 could take up and render latent, the greater was said to be 
 its capacity for heat. 
 
 This theory was first attacked by Count Rumford, in 
 
 * Magnetism, like gravity, tends to draw bodies together ; but it 
 does not, like gravity, act upon all bodies. 
 
276 CONSERVATION OF ENERGY. 
 
 1798. While superintending the boring of cannon in the 
 workshops of the Military Arsenal at Munich, he was 
 struck by the high temperature which the cannon acquired 
 in the process, and the still more intense heat of the metal- 
 lic chips separated from it by the borer. He was thus led 
 to inquire into the source of this heat. Was it squeezed 
 out of the chips ? If so, their capacity for heat must be 
 reduced sufficiently to account for all the heat rendered 
 sensible. He found, however, that the chips had exactly 
 the same capacity for heat as slices of the same metal cut 
 off by a fine saw where heating was avoided. It was evi- 
 dent, then, that the heat could not have been furnished at 
 the expense of the metallic chips. 
 
 Count Rumford then constructed a machine for the 
 express purpose of generating heat by friction. It con- 
 sisted of a metallic cylinder, which was turned on its axis 
 by horse-power while a blunt borer was forced against its 
 solid bottom. To measure the heat, a small hole was 
 bored into the cylinder, in which was placed a thermome- 
 ter. At the beginning of the experiment the temperature 
 of the cylinder was 60. At the end of 30 minutes, or 
 after the cylinder had made 960 revolutions, the tempera- 
 ture had risen to 130. He now removed the dust which 
 the borer had detached from the bottom of the cylinder, 
 and found it to weigh only 837 grains, or less than two 
 ounces. " Is it possible," he exclaimed, " that the very 
 considerable quantity of heat produced in this experiment 
 a quantity which actually raised the temperature of 113 
 pounds of gun-metal at least. 70 Fahrenheit could have 
 been furnished by so inconsiderable a quantity of metallic 
 dust, and this merely in consequence of a change in its 
 capacity for heat ? " But he found by careful experiment 
 that the capacity of the metal for heat was changed very 
 slightly, if at all, by the boring. He concluded, therefore, 
 that heat could not be a material substance, but was merely 
 
CONSERVATION OF ENERGY. 277 
 
 a mode of motion. The mechanical motion of the borer 
 had been converted into molecular motion, and appeared 
 as heat. 
 
 220. Sir Humphrey Davy 's Experiment. Sir Humphrey 
 Davy proved that heat is not material, by an experiment 
 even more conclusive than Count Rumford's. 
 
 We have already seen that a large amount of heat is 
 rendered latent in converting ice into water. A pound of 
 water, therefore, contains considerably more heat than a 
 pound of ice ; and, of course, it would be impossible to 
 melt ice by the heat squeezed out of it. But Sir Hum- 
 phrey Davy found that he could melt ice by rubbing two 
 pieces of it together. If, then, heat is material, the fric- 
 tion must have induced some change in the pieces of ice 
 which enabled them to attract heat from the bodies with 
 which they were in contact. He next, by means of clock- 
 work, caused two pieces of ice to rub together in an ex- 
 hausted receiver, and they melted as before, showing that 
 the heat could not have been taken from the air. It 
 might, however, have been conducted to the ice through 
 the pump-plate and the clock-work. He next placed a 
 piece of ice upon the pump-plate, and set the clock-work 
 upon that ; and the ice was again melted by the friction. 
 If the heat had been drawn up through the ice, the ice 
 would have been colder at the top than at the bottom. 
 But he had cut a groove in the upper face of the ice, and 
 had filled it with water. As the temperature of the ice 
 was 32, this water would have frozen had the temperature 
 of this surface fallen ; but the water did not freeze. It 
 was evident, then, that the heat could not have come up 
 through the pump-plate. It might still be objected that 
 the heat could have come by radiation from the receiver ; 
 but the receiver was kept colder than the ice, and hence 
 must have radiated less heat to the ice than the ice radi- 
 ated back again. 
 
278 CONSERVATION OF ENERGY. 
 
 If, then, heat is matter, we are driven to the conclusion 
 that this matter must have been created by the friction. 
 Now, we know that in the friction mechanical energy dis- 
 appeared, while heat was produced. The only rational 
 inference, then, seems to be, that the mechanical energy 
 was transformed into heat ; in other words, that the me- 
 chanical motion of the ice was converted into the molecu- 
 lar motion of heat. 
 
 221. All Mechanical Energy is ultimately converted into 
 Heat. When a falling body strikes the earth, it becomes 
 heated. In this case the whole energy of the body is con- 
 verted into heat. When bodies are rubbed together, their 
 energy, as we have seen, is converted into heat. 
 
 The energy of a running stream is gradually converted 
 into heat by the friction against its banks and bed and 
 among its particles. If it is made to turn the wheels of a 
 factory on its way, the rubbing of the parts of the ma- 
 chinery against each other and against the air, together 
 with the various kinds of work done by the machinery, 
 converts the mechanical energy of the water-wheel into 
 heat. 
 
 A railway train is really stopped by the conversion of its 
 motion into heat. When this has to be done quickly, the 
 change is hastened by increasing the friction by means of 
 the brakes. On the other hand, in order to prevent the 
 loss of energy while the train is in motion, the axles of 
 the wheels are kept carefully oiled, that they may turn 
 with as little friction as possible. 
 
 When unlike substances are rubbed together, a part of 
 the energy is first converted into electricity, but ultimately 
 into heat. 
 
 222. When Mechanical Energy is converted into Heat, the 
 same Amount of Energy always gives rise to the same 
 Amount of Heat. This was first shown by Joule, who 
 began his experiments in 1843 and continued them till 
 
CONSERVATION OF ENERGY. 
 
 279 
 
 1849. He converted mechanical energy into heat by 
 means of friction. He first examined cases of the friction 
 of solids against liquids. The apparatus used for this pur- 
 pose is shown in Figure 101. B is a cylindrical box hold- 
 
 Fig. 101. 
 
 ing the liquid. In the centre of the box is an upright axis, 
 to which are attached eight paddles like the one shown in 
 the figure. These revolve between four stationary vanes, 
 which prevent the liquid from being carried round. The 
 paddles are turned by means of the cord r and the weight 
 W. The size of the weight is such that it descends with- 
 out acquiring any velocity, and hence all its energy is 
 expended in the friction of the paddles.' The degree to 
 which the liquid became heated by the friction was shown 
 by a thermometer at /. Knowing the weight of the liquid, 
 its specific heat, and the rise of temperature during the 
 experiment, the amount of heat generated could be readily 
 calculated. 
 
 With this machine Joule found that, whatever the liquid 
 he used, a weight of one pound falling through 772 feet, 
 
280 CONSERVATION OI-' ENERGY. 
 
 or 772 pounds falling one foot, generated heat enough to 
 raise one pound of water one degree Fahrenheit in tem- 
 perature, or one unit #f heat, as it is called. 
 
 He also found that, when solids were rubbed together by 
 the action of a falling weight, one pound falling through 
 772 feet generated a unit of heat. In this experiment iron 
 discs were made to rotate together, one against the other, 
 in a vessel of mercury. 
 
 If a metallic disc be put into rapid rotation and then 
 brought between the poles of a powerful electro-magnet, it 
 soon comes to rest.. It will now be found very difficult to 
 turn it, and that it becomes heated as it rotates. Joule 
 found in this case, as in the others, that, if the disc were 
 turned by a falling weight, one pound descending 772 feet 
 generated a unit of heat. 
 
 The force necessary to raise one pound one foot is 
 called a foot-pound ; and this is the same force which a 
 pound acquires in falling one foot from a state of rest. 
 
 We see, then, that when mechanical energy is converted 
 into heat, the same amount of energy always gives rise to 
 the same amount of heat, and that 772 foot-pounds of 
 mechanical force are equivalent to one unit of heat. For 
 this reason, we call 772 foot-pounds the mechanical equiva- 
 lent of heat. 
 
 223. Heat may be converted into Mechanical Energy. 
 The steam-engine is a contrivance for converting heat into 
 mechanical energy. The heat converts the water into 
 steam, and gives to this steam an expansive force ; and 
 this expansive force is made to move a piston by means of 
 the arrangement shown in Figure 102. The steam coming 
 from the boiler by the tube x passes into the box d. From 
 this box run two pipes, tf.and b, for carrying the steam, 
 one above and the other below the piston. A sliding- 
 valve y is so arranged that it always closes one of these 
 pipes. In the right-hand figure, the lower pipe b is open, 
 
CONSERVATION OF ENERGY. 
 
 28l 
 
 and the steam can pass in under the piston and force it up. 
 At the same time, the steam which has done its work on 
 the other side of the piston passes out through the pipes a 
 
 Fig. 102. 
 
 and O. The sliding-valve is connected by means of the 
 rod i with the crank of the engine, so that it moves up and 
 down as the piston moves down and up. As soon, then, 
 as the piston has reached the top of 'the cylinder, the 
 sliding-valve is brought into the position shown in the left- 
 hand figure. The steam now passes into the cylinder 
 above the piston by the pipe a and forces the piston down, 
 while the steam on the other side which has done its work 
 goes out through b and O. The sliding-valve is now in 
 the position shown in the right-hand figure, and the piston 
 is driven up again as before ; and thus it keeps on moving 
 
282 CONSERVATION OF ENERGY. 
 
 up and down, or in and out. By means of a crank it can 
 be made to drive machinery. 
 
 224. The same Amount of Heat always gives rise to the 
 
 same Amount of Mechanical Energy. In Figure 103, C is 
 
 a box a foot square. Suppose a a to be a 
 
 Fig. 103. 
 
 partition one foot from the bottom, so as to 
 shut in a cubic foot of air. Suppose this 
 partition to be immovable, and the air be- 
 neath to be heated. Its elastic force will 
 be increased, but it cannot expand. We 
 will next suppose that a a is movable, but 
 without weight, and that the air beneath is 
 heated as before. On raising its tempera- 
 ture 490 its volume will be doubled, and 
 a a will of course be raised one foot to b b. In raising 
 a a one foot it has had to raise the air above it. Now, 
 this air presses 15 pounds upon every square inch, and 
 15 X 144 = 2,160 pounds upon the whole surface. From 
 the specific heat of air, we know that to raise a cubic 
 foot of air 490, when it is free to expand, 9.5 units of 
 heat are required. 
 
 But we have seen that a part of the heat which enters a 
 body is used in expanding it, and a part in raising its tem- 
 perature. In the above experiment, how much heat is 
 used in raising the temperature ? This is equivalent to 
 asking how much heat is required to raise the cubic foot 
 of air 490 when it is not allowed to expand. We have 
 learned that the computed velocity of sound in air is less 
 than its observed velocity, and that this is owing to the 
 heat developed in the compressed portion of the sound- 
 wave. From the ratio which exists between the observed 
 and the computed velocity, it is found that the specific heat 
 of air when free to expand must be 1.42 of its heat when 
 not allowed to expand. Hence the heat required to raise 
 the temperature of the cubic foot of air 490, when it is 
 
CONSERVATION OF ENERGY. 
 
 2 8 3 
 
 not allowed to expand, is found by the following proportion 
 to be 6.7 units : 
 
 1.42 : i = 9.5 : 6.7. 
 
 The amount of heat, then, used in expanding the air 
 that is, in raising 2,160 pounds one foot high is 2.8 
 units. Dividing 2,160 by 2.8, we get 772, nearly. 
 
 Since there is no cohesion among the particles of air, 
 the whole expansive force is used in raising the weight. 
 
 There is a prevalent impression that the expanding of 
 air is in itself a cooling process (that is, consumes heat) ; 
 but this is not the case, unless the air in expanding per- 
 forms work. This was proved by Joule in the following 
 manner. In Figure 104 we 
 have two strong vessels, of Fi s- 10 4- 
 
 which A contains air com- 
 pressed under a pressure of 
 some 20 atmospheres, while 
 in B is a vacuum. The two 
 are connected by a tube with 
 a stop-cock. The whole ap- 
 paratus is placed in a vessel 
 of water. After the tempera- 
 ture of the water has been 
 very carefully ascertained, 
 
 open the stop-cock and allow the air to expand. The 
 temperature of the water remains unchanged. As there is 
 no resistance to the expansion of the air, no heat is con- 
 sumed in the expansion. 
 
 We see, then, that 772 foot-pounds of mechanical force 
 are equivalent to a unit of heat, and that a unit of heat is 
 equivalent to 772 foot-pounds of mechanical force. 
 
 225. The Molecular Energy produced by Cohesion is con- 
 verted into Heat. We have seen that the heat which 
 enters a body is employed in three ways, in raising the 
 
284 CONSERVATION OF ENERGY. 
 
 temperature of the body, in expanding it, and in changing 
 its state. A body is expanded by the separation of its 
 molecules ; and its state is changed either by the separa- 
 tion or the rearrangement of its molecules. A part of the 
 heat, then, which enters a body performs work ; and, as 
 this work is done within the body, it is called interior work. 
 We have already noticed that, when it does this interior 
 work, it gives to the molecules potential energy ; and that, 
 when these molecules are brought together again by cohe- 
 sion, the potential energy appears as heat. The enormous 
 strength of the cohesive force is shown by the amount of 
 heat which it requires to melt ice, or to convert water into 
 steam. We have seen that merely to melt a pound of ice 
 at a temperature of 32 Fahrenheit requires 143 units of 
 heat, which is equivalent to the force required to lift 
 10,396 pounds, or about 55 tons, a foot high. And to 
 convert a pound of boiling water into steam requires 967 
 units of heat, equivalent to the force required to lift 
 746,524 pounds, or about 373 tons, a foot high. The 
 force of gravity is almost as nothing compared with this 
 molecular force. 
 
 226. The Molecular Energy of Affinity is sometimes con- 
 verted into Electricity. We have seen that, in all the 
 forms of voltaic battery, electricity is generated by chemi- 
 cal action. Here the energy of affinity is converted into 
 electricity. The same amount of chemical action always 
 gives rise to the same amount of electricity. 
 
 227. The Energy of Affinity always gives rise to Heat. 
 Every form of chemical combination develops heat, which 
 is nothing but the energy of affinity reappearing in a new 
 form. The strength of affinity is shown by the amount of 
 heat developed when oxygen combines with hydrogen. 
 The heat thus generated can be found by the apparatus 
 shown in Figure 105. Two measures of hydrogen and 
 one of oxygen are put into the strong copper vessel #, and 
 
CONSERVATION OF ENERGY. 285 
 
 this vessel is put into a larger one filled with water. This 
 in turn is suspended in a cylinder with a movable cover at 
 each end, and the whole is enclosed in a fourth cylindrical 
 vessel, which may be rotated on a horizontal axis. The 
 
 Fig. 105. 
 
 apparatus is first rotated for some time, in order to bring 
 all its parts to the same temperature, which is measured by 
 a very delicate thermometer. The electric current is sent 
 through the vessel a, where it heats a fine platinum wire 
 red-hot, and explodes the mixed gases. The apparatus is 
 again rotated about half a minute to make* the temperature 
 uniform throughout, and the temperature is again measured 
 by the thermometer. The rise of temperature shows the 
 amount of heat generated by the combination of the gases. 
 It is found in this way that, when the oxygen combines 
 with one pound of hydrogen, 61,000 units of heat are gen- 
 erated. Hence the force which has combined the two 
 gases is equal to 61,000 X 772 = 47,092,000 foot-poundSj 
 
286 
 
 CONSERVATION OF ENERGY. 
 
 or the force necessary to raise 23,546 tons a foot high, or 
 to throw one ton to a height of more than four miles. 
 
 We see, then, that the force even of cohesion is insignifi- 
 cant compared with that of affinity. 
 
 By a modification of the apparatus described above, it 
 is found that a pound of carbon, in combining with oxy- 
 gen, gives out about 14,500 units of heat, equivalent to 
 11,194,000 foot-pounds. 
 
 228. The Energy of Affinity sometimes reappears as Mus- 
 cular Force. The body is continually wasting away. The 
 waste is supplied by the food we eat. The waste products 
 of the body are burned-up food, that is, the elements of 
 the food combined with oxygen. The energy of this com- 
 bination reappears as heat and muscular force. The ma- 
 terials of the body, as we have seen, are either tertiary 
 (compounds of oxygen, hydrogen, and carbon) or qua- 
 ternary (compounds of oxygen, hydrogen, carbon, and 
 nitrogen). It has been found that the muscular energy is 
 mainly due to the combustion of the former. 
 
 We have now seen that the energy of affinity may be con- 
 verted into electricity, heat, and muscular force. Through 
 any one of these it may be converted into mechanical 
 force. The electricity, for instance, may be made to de- 
 velop magnetism, and thus to drive an electro-magnetic 
 engine ; the heat may be made to work a steam-engine 
 and the muscular energy may be employed in moving the 
 body, or in any form of manual labor. 
 
 It is mainly the affinity of oxygen which develops these 
 different forms of energy. In ordinary combustion and 
 respiration, the substance with which the oxygen unites is 
 mainly carbon. 
 
 229. Energy may be transmuted, but not destroyed. We 
 have now seen that the mechanical energy of motion, as 
 well as that of affinity, may be converted into heat, light, 
 and electricity. Heat and light are only different mani- 
 
CONSERVATION OF ENERGY. 287 
 
 festations of the same agent ; and heat and electricity are 
 mutually convertible. The energy of affinity may also be 
 converted into muscular energy. Heat is the form of 
 energy into which all the other forms of energy seem des- 
 tined ultimately to be converted. In all these transforma- 
 tions no energy is lost. The heat which finally results 
 from them may either be radiated into space (where it may 
 become insensible on account of its extreme diffusion), or 
 else it may be made to separate atoms, molecules, and 
 masses, and thus to confer potential energy upon them. 
 When these are drawn together again by affinity, cohesion, 
 and gravity, they develop the same amount of energy which 
 was consumed in separating them. 
 
 Energy, like matter, may assume a great variety of 
 forms ; but, like matter, it is wholly indestructible. 
 
 230. Source of Energy. If left to itself, affinity would 
 soon bring all dissimilar atoms together, and lock them up 
 in compounds ; cohesion would bring all the molecules of 
 these compounds together, and lock them up in solids ; 
 and gravity would bring all these solids together, and hold 
 them in its iron grasp ; while the heat developed by these 
 forces would be radiated into space, and our earth become 
 one dreary waste, void of all signs of life and activity. 
 What, then, is the source of the energy which is thus 
 manifesting itself in Protean forms ? 
 
 Let us consider, first, the energy developed by gravity. 
 This energy is seen in the winds, the falling rain, and run- 
 ning streams. The atmosphere on each side of the equa- 
 tor is an immense wheel. The side of this wheel next the 
 equator is continually expanded, and thus made lighter by 
 the heat of the sun. Hence gravity pulls down the colder 
 and heavier side in the polar regions, and thus the wheel 
 is made to turn round and round. Were it not for the 
 sun's heat, it would soon come to rest. 
 
 Again, the heat of the sun evaporates the waters of the 
 
288 CONSERVATION OF ENERGY. 
 
 ocean, and in their gaseous state they are swept round with 
 the atmospheric wheel till they come to colder regions, 
 where they are condensed, and fall to the earth as rain, 
 and flow to the ocean in rivers. It is due, then, to the 
 heat which comes to the earth in the sunbeam, that gravity 
 can thus unceasingly manifest its energy. 
 
 The energy of chemical affinity which is manifested in 
 heat, light, and muscular force is, as we have seen, devel- 
 oped by its action between oxygen and carbon. How are 
 these elements separated from carbonic acid, so that they 
 may be reunited by affinity ? 
 
 Place a leafy plant in a glass vessel, and let a current of 
 carbonic acid stream over it in the dark, and no change 
 takes place. Let the same gas stream over the plant in 
 the sunshine, and a part of it will disappear, and be re- 
 placed by oxygen. When acted upon by the sunbeams, 
 leaves of plants remove carbonic acid from the air, sepa- 
 rate its carbon and oxygen, retain the former, and give the 
 latter back to the air. When plants are consumed by com- 
 bustion in our furnaces, and by respiration in our bodies, 
 this oxygen combines with carbon and develops energy, 
 which appears as mechanical force in our engines, and as 
 muscular force in our bodies. 
 
 In the summer, when more sunshine than we need is 
 poured upon the earth, a part of it is absorbed by the 
 leaves of plants, and used to decompose carbonic acid, to 
 build up the varied forms of vegetable life. In this way, 
 the forests and the fields become vast storehouses of force 
 which has been gathered from the sunbeam. When, there- 
 fore, we burn fuel in our stoves and food in our bodies, the 
 light, heat, and muscular force developed are only the re- 
 appearance in another form of the sunbeams stored up in 
 plants. 
 
 But this process of gathering force from the sunlight 
 has been going on for ages ; and when we burn anthracite 
 
CONSERVATION OF ENERGY. 289 
 
 or bituminous coal, we are merely releasing the sunbeams 
 imprisoned in plants which grew upon the earth before it 
 became the dwelling-place of man. 
 
 The energy of affinity, then, like that of gravity, is noth- 
 ing but transmuted sunshine. 
 
 The only form of energy known to us which does not 
 come to the earth in the sunbeam is that developed by 
 the ebb and flow of the tidal wave. This wave is dragged 
 round the earth mainly by the attraction of the moon ; and 
 it acts as a brake upon the earth's rotation, since it is 
 drawn from east to west while the earth is turning from 
 west to east. The energy of this wave, then, is developed 
 at the expense of the earth's motion on its axis ; and it 
 must tend to retard this motion, though to so slight a 
 degree that the observations of thousands of years have 
 not served to make it appreciable. 
 
 231. The Amount of Heat given out by the Sun. In 
 Figure 106 we have an apparatus for measuring the heat 
 
 Fig. 106. 
 
2QO CONSERVATION OF ENERGY. 
 
 radiated to the earth by the sun. At one end of the in- 
 strument there is a shallow iron box, the cover of which is 
 blackened. The box is filled with mercury, into which a 
 delicate thermometer is introduced. At the other end of 
 the instrument is a disc of the same diameter as the box. 
 If the instrument be set in such a way that the shadow of 
 the box just covers the disc, it is evident that the sun's 
 rays will fall perpendicularly upon the cover. In the first 
 place, the instrument, sheltered from the sun, is allowed to 
 radiate its heat into the clear sky for five minutes, and its 
 loss of heat is noted. It is then turned to the sun for the 
 same length of time, and its gain of heat noted. It is 
 then turned again toward the sky, and after five minutes its 
 loss of heat is again noted. The mean between this loss 
 and its loss during the first five minutes will be its loss 
 during the five minutes it was turned towards the sun. 
 This loss added to the gain already observed will be the 
 whole heat which it received from the sun in five minutes. 
 
 Now, as one half of the earth is always turned towards 
 the sun, the amount of heat received by the earth in five 
 minutes will be as many times greater than that received 
 by the box as the surface of a great circle of the earth is 
 greater than that of the cover of the box. Making allow- 
 ance for the heat absorbed by the atmosphere, it has been 
 calculated that the amount received by the earth during a 
 year would be sufficient to melt a layer of ice 100 feet 
 thick and covering the whole earth. But the sun radiates 
 heat into space in every other direction as well as towards 
 the earth ; and if we conceive a hollow sphere to surround 
 the sun at the distance of the earth, our planet would 
 
 cover only of its surface. Hence the sun ra- 
 
 j 2,300,000,000 
 
 diates into space 2,300,000,000 times as much heat as 
 the earth receives. Sir John Herschel has calculated that 
 if a cylinder of ice 45 miles thick were darted into the sun 
 with the velocity of light (190,000 miles a second), it might 
 
CONSERVATION OF ENERGY. 291 
 
 be melted by the heat radiated by the sun, without lower- 
 ing the temperature of the sun itself. 
 
 232. Source of the Surfs Heat. What, then, is the 
 source of this enormous amount of heat ? 
 
 It has been supposed by some that the materials of the 
 sun are undergoing combustion, and that this combustion 
 develops the light and heat which it sends forth. There 
 are, however, no substances known to us whose burning 
 would produce so much heat for so long a time as we 
 know the sun has been shining. Carbon is one of the 
 most combustible substances with which we are acquaint- 
 ed ; but if the sun, large as he is, were a mass of pure 
 carbon, and were burning at a rate sufficient to produce 
 the light and heat that he is giving out, he would be utterly 
 consumed in 5,000 years. It seems hardly possible, then, 
 that the solar light and heat can be generated by ordinary 
 combustion. 
 
 One of the most satisfactory theories of the origin of the 
 solar heat is that recently devised by a German physician, 
 Mayer, and known as the meteoric theory. 
 
 We have seen that a pound- weight which has fallen 
 through 772 feet will, when its motion is arrested, generate 
 a unit of heat. Now, we know that a body falling that 
 distance will acquire a velocity of about 223 feet a second. 
 Hence a pound ball moving with a velocity of 223 feet 
 a second will generate a unit of heat when its motion is 
 arrested. We know, too, that the velocity with which a 
 falling body strikes the ground is in proportion to the 
 square root of the height from which it falls ; that is, in 
 order to double or treble its velocity, a body must fall from 
 four or nine times the height. A pound ball, then, moving 
 with a velocity of twice 223 feet a second will be able to 
 generate 4 units of heat ; one moving with thrice this 
 velocity, 9 units of heat ; and so on. When, therefore, 
 we know the weight of a body and the speed with which it 
 
292 CONSERVATION OF ENERGY. 
 
 is moving, we can easily calculate how much heat will be 
 generated on stopping it. 
 
 Were the earth's motion arrested, its elements would 
 melt with fervent heat, and most of them would be con- 
 verted into vapor. Were the earth to fall into the sun, the 
 heat generated by the shock would be sufficient to keep 
 up the solar light and heat for 95 years. We know that 
 countless swarms of meteoric bodies are revolving in rings 
 about the sun, and the well-known retardation of Encke's 
 comet shows that these bodies must be moving in a resist- 
 ing medium. If so, they must eventually be drawn into 
 the sun, and, from the velocity with which they must strike, 
 it has been shown that they could fall in sufficient numbers 
 to generate all the light and heat of the sun, without in- 
 creasing his magnitude enough to be detected, since ac- 
 curate measures of his diameter were first made. This 
 theory of the sun's heat was first published by Mayer in 
 1848, and was further developed by Thomson in 1854. 
 
 The following account of the meteoric theory, as devel- 
 oped by Thomson, is taken from Tyndall : 
 
 " ' In conclusion, then,' writes Professor Thomson, ' the 
 source of energy from which solar heat is derived is un- 
 doubtedly meteoric The principal source per- 
 haps the sole appreciable efficient source is in bodies 
 circulating round the sun, at present inside the earth's 
 orbit, in the sunlight by us called " zodiacal light." The 
 store of energy for future sunlight is at present partly 
 dynamical, that of the motions of these bodies round 
 the sun ; and partly potential, that of their gravitation 
 towards the sun. This latter is gradually being spent, half 
 against the resisting medium, and half in causing a con- 
 tinuous increase of the former. Each meteor thus goes 
 on moving faster and faster, and getting nearer and nearer 
 the centre, until some time, very suddenly, it gets so much 
 entangled in the solar atmosphere as to begin to lose ve- 
 

 CONSERVATION OF ENERGY. 293 
 
 locity. In a few seconds more it is at rest on the sun's 
 surface, and the energy given up is vibrated across the 
 district where it was gathered during so many ages, ulti- 
 mately to penetrate, as light, the remotest regions of 
 space.' 
 
 " From the tables published by Professor Thomson I ex- 
 tract the following interesting data, firstly with reference to 
 the amount of heat equivalent to the rotation of the sun 
 and planets round their axes, the amount, that is, which 
 would be generated supposing a brake applied at the sur- 
 faces of the sun and planets until the motion of rotation 
 was entirely stopped ; secondly, with reference to the 
 amount of heat due to the sun's gravitation, the heat, 
 that is, which would be developed by each of the planets 
 in falling into the sun. The quantity of heat is expressed 
 in terms of the time during which it would cover the solar 
 emission. 
 
 Heat of Gravitation, equal to Solar Heat of Rotation, equal to Solar 
 Emission for a Period of Emission for a Period of 
 
 Sun 1 16 years 6 days. 
 
 Mercury . . . 6 years 2 14 days 15 " 
 
 Venus .... 83 " 227 " 99 
 
 Earth .... 94 " 303 " 81 " 
 
 Mars .... 12 " 252 " 7 " 
 
 Jupiter . . . 32,240 " . . . . 14 144 
 
 Saturn . . . 9,650 " . . . . 2 " 127 u 
 
 Uranus . . . 1,610 " . . . . 71 " 
 Neptune . . 1,890 " . . . . 
 
 " Thus, if the planet Mercury were to strike the sun, the 
 quantity of heat generated would cover the solar emission 
 for nearly seven years ; while the shock of Jupiter would 
 cover the loss of 32,240 years. The heat of rotation of 
 the sun and planets, taken together, would cover the solar 
 emission for 134 years ; while the total heat of gravitation 
 (that produced by the planets falling into the sun) would 
 cover the emission for 45,589 years. 
 
294 CONSERVATION OF ENERGY. 
 
 " Whatever be the ultimate fate of the theory here 
 sketched, it is a great thing to be able to state the condi- 
 tions which certainly would produce a sun, to be able to 
 discern in the force of gravity, acting upon dark matter, 
 the source from which the starry heavens may have been 
 derived ; for, whether the sun be produced and his emission 
 maintained by the collision of cosmical masses or not, there 
 .cannot be a doubt as to the competence of the cause as- 
 .signed to produce the effects ascribed to it. Solar light and 
 solar heat lie latent in the force which pulls an apple to the 
 ground. The potential energy of gravitation was the origi- 
 nal form of all the energy in the universe. As surely as the 
 weights of a clock run down to their lowest position, from 
 which they can never rise again unless fresh energy is com- 
 municated to them from some source not yet exhausted, so 
 surely must planet after planet creep in, age by age, to- 
 wards the sun. When each comes within a few hundred 
 thousand miles of his surface, if he is still incandescent, 
 it must be melted and driven into vapor by radiant heat. 
 Nor, if he be crusted over and become dark and cool ex- 
 ternally, can the doomed planet escape its fiery end. If it 
 'does not become incandescent, like a shooting-star, by fric- 
 tion in its passage through his atmosphere, its first- graze 
 on his surface must produce a stupendous flash of light 
 and heat. It may be at once, or it may be after two or 
 three bounds like a cannon-shot ricochetting on a surface 
 of earth or water, the whole mass must be crushed, melted, 
 and evaporated by a crash, generating in a moment some 
 thousands of times as much heat as a coal of the same 
 size would produce by burning." 
 
 233. The Nebular Hypothesis. According to Laplace, 
 the material of our solar system was once a nebulous mass 
 of extreme tenuity, and the sun, moon, and planets were 
 formed by its gradual condensation. Let us suppose such 
 a nebulous mass slowly rotating, and gradually cooling by 
 
CONSERVATION OF ENERGY. 295 
 
 radiation into space. As it cools, it must begin to con- 
 tract ; and as it contracts, its rotation must be quickened, 
 since the matter at the surface must be moving faster than 
 nearer the centre. It thus goes on contracting and rotat- 
 ing faster and faster, until the centrifugal tendency becomes 
 so great that cohesion and gravity can no longer hold it 
 together. A ring is then detached from the circumfer- 
 ence, which continues to rotate by itself. The central 
 mass goes on contracting and rotating with ever-increasing 
 velocity, until a second ring is thrown off. In this way, 
 ring after ring is detached, and all these rings continue to 
 rotate round the central mass in the same direction. But 
 the rings themselves would go on condensing, and at last 
 they would be likely to break up, each forming one or sev- 
 eral globular masses. These would, of course, all revolve 
 about the central mass in the same direction, and their 
 condensation would cause them to rotate on their axes ; 
 and it has been proved that, with the exception of one or 
 two of the outer ones, they must all rotate on their axes in 
 the same direction in which they revolve in their orbits. 
 
 But as these masses condensed, their rotation would be 
 accelerated, and they would be very likely to throw off 
 rings, which would either remain as rings, or be condensed 
 into secondary masses revolving about their primaries. 
 
 The central mass, of course, forms the sun ; the rings 
 which it throws off, the planets ; and the rings thrown off 
 by the planets, the moons. In the case of Saturn, a part 
 of the rings still remain uncondensed, while a part appear 
 as moons. 
 
 The rings thrown off by the central mass usually con- 
 densed into one body, but, in the case of th:. minor plan- 
 ets and the meteoric rings, into many. 
 
 234. Helmholttfs Theory of Solar Heat. The nebular 
 hypothesis not only accounts for the motion of the planets, 
 but it explains the internal heat of the earth and the solar 
 
296 CONSERVATION OF ENERGY. 
 
 heat ; for, as the molecules of the nebulous mass 'were 
 drawn nearer and nearer together, their potential energy 
 must have been converted into heat.* Helmholtz has 
 made this the basis of his theory of solar heat, an account 
 of which is given by Tyndall as follows : 
 
 " He starts from the nebular hypothesis of Laplace, and, 
 assuming the nebulous matter in the first instance to have 
 been of extreme tenuity, he determines the amount of heat 
 generated by its condensation to the present solar system. 
 Supposing the -specific heat of the condensing mass to be 
 the same as that of water, then the heat of condensation 
 would be sufficient to raise their temperature 28,000,000 
 Centigrade. By far the greater part of this heat was 
 wasted ages ago in space. The most intense terrestrial 
 combustion that we can command is that of oxygen and 
 hydrogen, and the temperature of the pure oxyhydrogen 
 flame is 8,06 1 C. The temperature of a hydrogen flame, 
 burning in air, is 3,259 C. ; while that of the lime-light, 
 which shines with such sunlike brilliancy, is estimated at 
 2,000 C. What conception, then, can we form of a tem- 
 perature more than thirteen thousand times that of the 
 Drummond light ? If our system were composed of pure 
 coal and burnt up, the heat produced by its combustion 
 would only amount to -^ of that generated by the* con- 
 densation of the nebulous matter to form our solar system. 
 Helmholtz supposes this condensation to continue ; that a 
 virtual falling down of the superficial portions of the sun 
 towards the centre still takes place, a continual develop- 
 ment of heat being the result. However this may be, he 
 shows by calculation that the shrinking of the sun's di- 
 ameter by - of its present length would generate an 
 
 * It would seem at first that this heat would prevent further con- 
 densation, but it is gradually radiated off into space, and as the mole- 
 cules come nearer together the force of gravity increases more rapidly 
 than the repulsive force of the remaining heat. 
 
CONSERVATION OF ENERGY. 297 
 
 amotint of heat competent to cover the solar emission for 
 2,000 years ; while the* shrinking of the sun from its pres- 
 ent mean density to that of the earth would have its equiv- 
 alent in an amount of heat competent to cover the present 
 solar emission for 17,000,000 of years. 
 
 " < But,' continues Helmholtz, ' though the store of our 
 planetary system is so immense that it has not been sensi- 
 bly diminished by the incessant emission which has gone 
 on during the period of man's history, and though the time 
 which must elapse before a sensible change in the condi- 
 tion of our planetary system can occur is totally beyond 
 our comprehension, the inexorable laws of mechanics show 
 that this store, which can only suffer loss and not gain, 
 must finally be exhausted. Shall we terrify ourselves by 
 this thought ? We are in the habit of measuring the 
 greatness of the universe, and the wisdom displayed'in it, 
 by the duration and the profit which it promises to our 
 own race ; but the past history of the earth shows the in- 
 significance of the interval during which man has had his 
 dwelling here. What the museums of Europe show us of 
 the remains of Egypt and Assyria we gaze upon with silent 
 wonder, in despair of being able to carry back our thoughts 
 to a period so remote. Still, the human race must have 
 existed and multiplied for ages before the Pyramids could 
 have been erected. We estimate the duration of human 
 history at 6,000 years ; but, vast as this time may appear 
 to us, what is it in comparison with the period during 
 which the earth bore successive series of rank plants and 
 mighty animals, but no men ? periods during which, in 
 "nir own neighborhood (Konigsberg), the amber -tree 
 bloomed, and dropped its costly gum on the earth and 
 in the sea ; when in Europe and North America groves 
 of tropical palms flourished, in which gigantic lizards, and, 
 after them, elephants, whose mighty remains are still buried 
 in the earth, found a home. Different geologists, proceed- 
 13* 
 
298 CONSERVATION OF ENERGY. 
 
 ing from different premises, have sought to estimate the 
 length of the above period, and they set it down from one 
 to nine millions of years. The time during which the 
 earth has generated organic beings is again small com- 
 pared with the ages during which the world was a mass of 
 molten rocks. The experiments of Bischof upon basalt 
 show that our globe would require 350 millions of years to 
 cool down from 2,000 to 200 Centigrade. And with 
 regard to the period during which the first nebulous 
 masses condensed, to form our planetary system, conjec- 
 ture must entirely cease. The history of man, therefore, 
 is but a minute ripple in the infinite ocean of time. For 
 a much longer period than that during which he has al- 
 ready occupied this world, the existence of a state of inor- 
 ganic nature, favorable to man's continuance here, seems 
 to be secured ; so that for ourselves, and for long genera- 
 tions after us, we have nothing to fear. But the same 
 forces of air and water, and of the volcanic interior, which 
 produced former geologic revolutions, burying one series 
 of living forms after another, still act upon the earth's 
 crust. They, rather than those distant cosmical changes 
 of which we have spoken, will put an end to the human 
 race, and perhaps compel us to make way for new and 
 more complete forms of life, as the lizard and the mam- 
 moth have given way to us and our contemporaries/ " 
 
 It will be noticed that Mayer's theory is not inconsistent 
 with that of Helmholtz, but supplementary to it. The 
 former merely assumes that the meteors and planets, which 
 were thrown off from the nebulous mass as it condensed, 
 are slowly falling into it again. When these shall all have 
 fallen into it and the condensation shall have ceased, our 
 sun will cease to shine, like many other stars which have 
 disappeared from the heavens. 
 
ASTRONOMY. 299 
 
 SUMMARY. 
 
 When bodies or their molecules are in motion, they are 
 said to have an actual energy and when they are so situ- 
 ated that they can be moved by gravity or by the molecu- 
 lar forces, they are said to have a potential energy. (215.) 
 
 Energy may be mechanical, molecular, or muscular. 
 (216.) 
 
 Affinity, cohesion, and gravity are the forces which are 
 constantly tending to convert potential into actual energy. 
 
 (217.) 
 
 Heat is not a substance, but only a mode of motion, as 
 was shown by Count Rumford and by Sir Humphrey 
 Davy. (219, 220.) 
 
 Mechanical energy may be converted into heat, into 
 which, .in fact, all mechanical energy is ultimately con- 
 verted. (218, 221.) 
 
 The same amount of mechanical energy, on conversion 
 into heat, always gives rise to the same amount of heat. 
 
 (222.) 
 
 Heat may be again converted into mechanical energy ; 
 and the same amount of heat always gives rise to the same 
 amount of mechanical energy. (223, 224.) 
 
 The energy of affinity is converted partially into elec- 
 tricity, partially into heat, and partially into muscular en- 
 ergy. (225-228.) 
 
 The strength of affinity is shown by tlie great amount of 
 heat generated in the burning of hydrogen and carbon. 
 
 However energy may be transmuted, it can never be 
 destroyed. (229.) 
 
 All the energy manifested at the surface of the earth, 
 except that of the tides, is drawn from the sunbeams. 
 
300 ASTRONOMY. 
 
 The sun radiates sufficient heat to melt a cylinder of ice 
 45 miles thick, at the rate of 190,000 miles a second. 
 
 According to Mayer, the solar heat is developed by 
 meteoric showers ; according to Helmholtz, by the grad- 
 ual condensation of the sun. (232 - 234.) 
 
APPENDIX. 
 
APPENDIX 
 
 Fig. i. 
 
 I. 
 
 1. A right triangle is one which contains a right angle. 
 Thus A C J3, Figure I, is a right 
 
 triangle. 
 
 2. An oblique triangle is one which 
 does not contain a right angle. 
 
 Every oblique triangle can be re- 
 solved into two right triangles by 
 dropping a perpendicular from one 
 of the angles upon the opposite side. 
 
 Thus in Figure 2, by dropping the 
 perpendicular C P, two right trian- 
 gles, A P C and B P C, are formed. 
 
 In Figure 3, by dropping the per- 
 pendicular B P upon A C produced, i 
 we get two right triangles, A P B 
 and C P B. 
 
 2. The sine of an angle is the quo- 
 tient of the opposite side divided by 
 the hypothenuse. Thus, by desig- 
 nating the angles by the large let- 
 ters and the sides opposite them 
 by the corresponding small ones, we / - 
 have in Figure i, 
 
 Fig. 2. 
 
 Fig. 3- 
 
 sin A = -, sin B 
 
 and sin C 
 
 
 The sine of a right angle equals unity. 
 
34 
 
 APPENDIX. 
 
 In Figures 2 and 3, we have 
 
 s~* T) s* r> T? zy 
 
 sin A = -.--. sin B = , and sin C = . 
 t> a a 
 
 BCA+BCP = 180. 
 
 When the sum of two angles is 180, the angles are said 
 to be supplements of each other. 
 
 /? 7-* 
 
 It will be seen that, in Figure 3, - - is the sine of both 
 B C A and B C P. 
 
 An angle and its supplement have the same sine. 
 
 3. The sides of a plane triangle are proportional to the sines 
 of their opposite angles. 
 
 In Figure i, we have 
 
 c sin A. c 
 
 B . A a 
 sm A = -, a 
 
 c sin 
 
 c sin C. c 
 
 sin A 
 b 
 
 c 
 sin C 
 
 whence 
 
 sin A 
 
 a 
 sin A 
 
 b 
 sin B 
 
 b 
 sin B 
 
 c 
 sin C 
 
 c 
 
 sin C 
 which, converted into proportions, give 
 
 
 a 
 
 sin A = b 
 
 sin B 
 
 
 a 
 
 sin A = c 
 
 sin C 
 
 
 b 
 
 sin B = c 
 
 sin C 
 
 and these, by 
 
 transposi 
 
 ng the mean 
 
 s, give 
 
 
 a 
 
 b = sin A 
 
 sin B 
 
 
 a 
 
 c = sin A 
 
 sin C 
 
 
 b 
 
 c = sin B 
 
 sin C 
 
 In Figure 2, we have 
 
 .*f.cr. 
 
 - CP < CP = 
 
 b sin A 
 
 whence 
 
 b sin ^4 = a sin 
 
APPENDIX. 305 
 
 which, converted into a proportion, gives 
 
 a : b = sin A : sin B. 
 In Figure 3, we have 
 sin A = ~, B P = c sin A 
 
 sin C = , B P = a sin C 
 
 a 
 
 whence a sin C = c sin A 
 
 which, converted into a proportion, gives 
 
 a : c = sin A : sin C. 
 
 By dropping a perpendicular from A upon Z? C produced, 
 it can be found in the same way that 
 
 b : c = sin B : sin C 
 
 In both right and oblique triangles, then, the sides are pro- 
 portional to the sines of their opposite angles, 
 
 4. It is shown in Geometry that two right triangles which 
 have an acute angle of one equal to an acute angle of the 
 other, have their corresponding sides proportional. Hence 
 whatever the length of the sides b and c in the right triangle, 
 
 Figure i, - and - will have the same values as long as the an- 
 gles A and B remain the same. The value of the sine, then, 
 depends wholly on the size of the angle. 
 
 The value of the sines have been computed for every an- 
 gle between o and 90, and these values have been arranged 
 in tables called " Tables of Natural Sines." 
 
 5. By means of (3), the other parts of a plane triangle can 
 be found when one side and two angles are given. 
 
 To find the third angle, subtract the sum of the given an- 
 gles from 1 80. 
 
 To find ,the other sides, form a proportion as follows : As 
 the sine of the angle opposite the given side is to the sine of 
 the angle opposite the required side, so is the given side to 
 the required side. 
 
 Thus in the triangle ABC, Figure 2, given the side a, and 
 the angles B and C. 
 
 To find the angle A. 
 
 180 (B -4- Q = A. 
 
 T 
 
306 APPENDIX. 
 
 To find the side b. 
 
 sin A : sin B = a : b. 
 
 Find the side c. 
 
 Since one of the angles of a right triangle is always a right 
 angle, the parts of such a triangle can be computed when one 
 side and one acute angle are given. 
 
 In the right triangle ABC, Figure I, given the side c and 
 fthe angle A. Find the other parts. 
 
 6. By means of (3), the other parts of a plane triangle can 
 !be computed when two sides and an angle opposite one of them 
 are given. 
 
 To find a second angle, form the following proportion : As 
 the side opposite the given angle is to the side opposite the 
 required angle, so is the sine of the given angle to the sine 
 of the required angle. 
 
 After the second angle is found the case becomes the same 
 as (5). 
 
 In the triangle A B C, Figure 2, given a and c and the an- 
 gle A. Find B, C, and b. 
 
 II. 
 
 The horizon is the plane which at any point on the earth 
 would separate the visible from the invisible part of the heav- 
 ens, if the earth were everywhere level like the surface of the 
 sea. It divides the celestial sphere into two equal parts, and 
 its intersection with it forms the circumference of a great circle. 
 Every part of this circumference is 90 from the zenith. 
 
 At the equator the celestial poles are just 90 from the ze- 
 nith, hence the horizon will pass through these, and its plane 
 will coincide in direction with the earth's axis. As we go 
 north from the equator, the zenith passes northward, and the 
 horizon passes below the north pole and becomes more and 
 more inclined to the earth's axis till we reach the pole, when 
 the inclination becomes 90. As we go southward from the 
 equator, a corresponding change takes place. 
 
APPENDIX. 307 
 
 III. 
 
 THE CALENDAR. 
 
 OLD AND NEW STYLE. 
 
 THE solar year, or the interval between two successive pas- 
 sages of the same equinox by the sun, is 365 days, 5 hours, 
 48 minutes, 48 seconds. If then we reckon only 365 days to a 
 common or civil year, the sun will come to the equinox 5 hours, 
 48 minutes, 48 seconds, or nearly a quarter of a day, later each 
 year ; so that, if the sun entered Aries on the 2oth of March 
 one year, he would enter it on the 2ist four years after, on the 
 22d eight years after, and so on. Thus in a comparatively 
 short time the spring months would come in the winter, and 
 the summer months in the spring. 
 
 Among different ancient nations different methods of com- 
 puting the year were in use. Some reckoned it by the revo- 
 lutions of the moon ; some by that of the sun : but none, so 
 far as we know, made proper allowances for deficiencies and 
 excesses. Twelve moons fell short of the true year ; thirteen 
 exceeded it : 365 days were not enough ; 366 were too many. 
 To prevent the confusion resulting from these errors, Julius 
 Caesar reformed the calendar by making the year consist of 
 365 days, 6 hours (which is hence called a Julian year), and 
 made every fourth year consist of 366 days. This method of 
 reckoning is called Old Style. 
 
 But as this made the year somewhat too long, and the error 
 in 1582 amounted to ten days, Pope Gregory XIII., in order to 
 bring the vernal equinox back to the 2ist of March again, or- 
 dered ten days to be struck out of that year ; calling the next 
 clay after the 4th of October the I5th. And to prevent similar 
 confusion in the future he decreed that three leap-years should 
 be omitted in the course of every 400 years. This way of 
 reckoning time is called New Style. It was immediately 
 adopted by most of the European nations, but was not accepted 
 
308 APPENDIX. 
 
 by the English until the year 1752. The error then amounted 
 to ii days, which were taken from the month of September, by 
 calling the 3d of that month the Hth. 
 
 According to the Gregorian calendar, every year whose num- 
 ber is divisible by 4 is a leap-year; except that in the case of the 
 years whose numbers are exact hundreds, those only are leap- 
 years which are divisible by 4 after cutting off the last two 
 figures. Thus, the years 1600, 2000, 2400, etc., are leap-years ; 
 1700, 1800, 1900, 2100, 2200, etc., are not. Under this mode of 
 reckoning, the error will not amount to a day in 5,000 years. 
 
 THE DOMINICAL LETTER. 
 
 The Dominical Letter for any year is that which we often see 
 placed against Sunday in the almanacs, and is always one of 
 the first seven in the alphabet. Since a common year consists 
 of 365 days, if this number be divided by 7, the number of days 
 in a week, there will be a remainder of one. Hence a year 
 commonly begins one day later in the week than the preced- 
 ing one did. If a year of 365 days begins on Sunday, the next 
 will begin on Monday ; if it begins on Thursday, the next will 
 begin on Friday; and so on. If Sunday falls on the ist of 
 January, the first letter of the alphabet, or A, is the Dominical 
 Letter. If Sunday falls on the 7th of January (as it will the 
 next year, unless the first be leap-year) the seventh letter, G, is 
 the Dominical Letter. If Sunday falls on the 6th of January 
 (as it will the third year, unless the first or second be leap-year) 
 the sixth letter, F, will be the Dominical Letter. Thus, if there 
 were no leap-years, the Dominical Letters would regularly fol- 
 low a retrograde order, G, F, E, D, C, B, A. 
 
 But leap years have 366 days ; which, divided by 7, leaves 2 
 remainder. Hence the years following leap-years will begin 
 two days later in the week than the leap-years did. To prevent 
 the interruption which would hence occur in the order of the 
 Dominical Letters, leap-years have two Dominical Letters ; 
 one indicating Sunday till the 29th of February, and the other 
 for the rest of the year. 
 
 By Table I. below, the Dominical Letter for any year (New 
 Style) for 4,000 years from the beginning of the Christian 
 
APPENDIX. 
 
 309 
 
 Era may be found ; and it will be readily seen how the Table 
 could be extended indefinitely. 
 
 To find the Dominical Letter by this Table, look for the hun- 
 dreds of years at the top, and for the years below a hundred at 
 the left hand. 
 
 TABLE I. 
 
 TABLE II. 
 
 
 Centuries. 
 
 
 A B 
 
 C 
 
 D 
 
 E 
 
 F 
 
 G 
 
 
 100 200 
 
 500 600 
 
 300 400 
 
 700 800 
 
 
 I 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 
 900 1000 
 
 IIOO'l2OO 
 
 Jan. 31. 
 
 8 9 
 
 IO 
 
 ii 
 
 12 
 
 13 
 
 H 
 
 Years less than 
 One Hundred. 
 
 1300 1400 
 1700' 1800 
 
 2100 2200 
 2500 26OO 
 
 I 5 00 
 
 1900 
 2300 
 2700 
 
 1600 
 
 2OOO 
 2400 
 2800 
 
 Oct. 31. 
 
 15 16 
 
 22 23 
 29 30 
 
 17 
 
 24 
 
 18 
 
 25 
 
 19 
 26 
 
 20 
 27 
 
 21 
 
 28 
 
 
 29003000 
 
 3IOO 
 
 3200 
 
 
 
 
 
 T 
 
 2 
 
 
 
 A 
 
 
 33003400 
 3700 3800 
 
 3500 
 3000 
 
 3 boo 
 
 4000 
 
 Feb. 28-29. 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 ii 
 
 
 C 
 
 E 
 
 G 
 
 BA 
 
 March 31. 
 
 12 
 
 
 H 
 
 
 ib 
 
 17 
 
 18 
 
 I 
 
 29 
 
 57 
 
 85 
 86 
 
 B 
 
 D 
 
 r' 
 
 F 
 
 G 
 
 Nov. 30. 
 
 26 
 
 27 
 
 28 
 
 29 
 
 30 
 
 -4 
 
 3* 
 
 .. 
 
 3 
 
 31 
 
 5Q 
 
 87 
 
 G 
 
 B 
 
 D 
 
 E 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 4 
 
 I 
 
 7 
 
 1^ 
 
 33 
 34 
 35 
 
 61 
 62 
 63 
 
 88 
 
 89 
 90 
 91 
 
 FE 
 D 
 C 
 B 
 
 AG 
 
 F 
 E 
 D 
 
 CB 
 A 
 G 
 F 
 
 DC 
 B 
 A 
 G 
 
 April 30. 
 
 July 31 
 
 2 
 
 9 
 16 
 
 23 
 
 3 
 
 IO 
 
 24 
 
 4 
 ii 
 
 18 
 
 5 
 
 12 
 19 
 26 
 
 6 
 
 *3 
 20 
 
 27 
 
 7 
 
 H 
 
 21 
 
 28 
 
 8 
 15 
 
 22 
 29 
 
 
 
 
 
 \C, 
 
 C P, 
 
 ED 
 
 FE 
 
 
 6^ 
 
 <J 
 
 
 * * 
 
 " 
 
 * ' 
 
 
 9 
 
 
 
 37 
 
 65 
 
 92 
 93 
 
 F 
 
 "AT 
 
 TT 
 
 
 
 j. 
 
 7 
 
 .1 
 
 8 
 
 2 
 
 9 
 
 J 
 
 IO 
 
 4 
 
 IT 
 
 5 
 
 T2 
 
 10 
 
 ii 
 
 12 
 
 39 
 40 
 
 66 
 67 
 68 
 
 94 
 95 
 96 
 
 D 
 CB 
 
 G 
 F 
 ED 
 
 B 
 A 
 GF 
 
 C 
 B 
 AG 
 
 Aug. 31. 
 
 20 
 
 ?7 
 
 H 
 
 21 
 
 28 
 
 15 
 22 
 
 29 
 
 16 
 
 2 3 
 30 
 
 17 
 
 24 
 
 31 
 
 18 
 25 
 
 26 
 
 n 
 
 41 
 
 69 
 
 97 
 
 A 
 
 C 
 
 E 
 
 I 
 
 
 
 
 
 
 
 I 
 
 2 
 
 H 
 
 n 
 
 42 
 43 
 44 
 
 70 
 
 71 
 72 
 
 98 
 99 
 
 G 
 F 
 ED 
 
 B 
 A 
 
 GF 
 
 D 
 
 C 
 
 BA 
 
 E 
 D 
 CB 
 
 Sept. 30. 
 
 3 
 
 10 
 
 4 
 ii 
 18 
 
 5 
 
 12 
 IQ 
 
 6 
 13 
 
 20 
 
 7 
 H 
 
 21 
 
 8 
 
 22 
 
 ,1 
 
 23 
 
 17 
 
 45 
 
 73 
 
 
 C 
 
 E 
 
 c; 
 
 A 
 
 Dec. 31. 
 
 24 
 
 2S 
 
 26 
 
 27 
 
 28 
 
 2$ 
 
 30 
 
 18 
 
 46 
 
 74 
 
 
 B 
 
 D 
 
 F 
 
 G 
 
 
 
 
 
 
 
 
 
 19 
 
 47 
 
 75 
 
 
 A 
 
 C 
 
 E 
 
 F 
 
 
 
 j 
 
 2 3 
 
 
 
 6 
 
 20 
 
 48 
 
 76 
 
 
 GF 
 
 BA 
 
 DC 
 
 ED 
 
 
 7 
 
 8 
 
 9 10 
 
 II 
 
 12 
 
 13 
 
 21 
 
 4') 
 
 77 
 
 . . 
 
 E 
 
 G 
 
 B 
 
 C 
 
 May 31. 
 
 H 
 
 15.16! 17 
 
 18 19 
 
 20 
 
 22 
 
 50 
 
 78 
 
 
 D 
 
 F 
 
 A 
 
 B 
 
 
 21 
 
 22 ' 23 I 24 
 
 25 26 
 
 27 
 
 27 
 
 c i 
 
 7Q 
 
 
 C 
 
 |V 
 
 /~V 
 
 A 
 
 
 "S 
 
 2O IO i 31 
 
 
 
 
 24 
 
 52 
 
 80 
 
 
 BA 
 
 DC 
 
 FE 
 
 GF 
 
 
 
 
 
 
 
 
 
 
 
 
 I 2 
 
 T. 
 
 25 
 
 53 
 
 IT 
 
 T7 
 
 G 
 
 IT 
 
 ~D~~E~ 
 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 9 
 
 IO 
 
 26 
 
 54 
 
 82 
 
 
 F 
 
 A 
 
 C D 
 
 June 30. 
 
 ii 
 
 12 '13 
 
 14 
 
 IS 
 
 16 
 
 17 
 
 27 
 
 55 
 
 8s 
 
 
 E 
 
 G 
 
 B C 
 
 
 18 
 
 19 2O 
 
 21 
 
 22 
 
 23 
 
 24 
 
 28 
 
 56 
 
 84 
 
 .. 'DCFE 
 
 AGBA 
 
 
 25 
 
 26 27 
 
 28 
 
 29 
 
 3 
 
 
310 APPENDIX. 
 
 Thus, the letter for 1867 will be opposite the number 67, and 
 in the column having 1800 at the top ; that is, it will be F. In 
 the same way, the letters for 1868, which is a leap-year, will 
 be found to be ED. 
 
 Having the Dominical Letter of any year, Table II. shows 
 what days of every month of the year will be Sundays. 
 
 To find the Sundays of any month in the year by this Table, 
 look in the column under the Dominical Letter, opposite the 
 name of the month given at the left. 
 
 From the Sundays the date of any other day of the week can 
 be readily found. 
 
 Thus if we wish to know on what day of the week Christmas 
 will fall in 1867, we look opposite December under the letter F, 
 (which we have found to be the Dominical Letter for the year,) 
 and find that the 22d of the month is a Sunday. The 25th, or 
 Christmas, will then be Wednesday. 
 
 In the same way we may find the day Of the week corre- 
 sponding to any date (New Style) in history. For instance, the 
 I7th of June, 1775, the day of the fight at Bunker Hill, is found 
 to have been a Saturday. 
 
 These two Tables then serve as a perpetual almanac. 
 
 THE GOLDEN NUMBER. 
 
 It has been found that after a period of 19 years the sun, 
 earth, and moon occupy nearly the same relative positions. 
 Starting then with new moon or full moon, it is evident that 
 after the expiration of this period it will be new moon or full 
 moon again. Hence the phases of the moon which succeed- 
 ed one another in the first period will repeat themselves in 
 the same order in the second. 
 
 This period is called the Cycle of the Moon, and the number 
 19 is known as the Golden Number. 
 
 To find the Golden Number for any year, add I to the num- 
 ber of that year, divide by 19, and the remainder is the Golden 
 Number. If nothing remains, the Golden Number is 19. 
 
 In Table III. the Golden Numbers under the months stand 
 against the days of new moon in the left hand column. It is 
 adapted chiefly to the second year after leap year, and will in- 
 
APPENDIX. 311 
 
 dicate the time of new moon (within one day) till the year 1900. 
 A perfectly correct table of this kind cannot be easily made. 
 
 To show the use of the Table, suppose we wish to know 
 nearly the time of new moon in September, 1867. By the rule 
 given above, we find the Golden Number for the year to be 6. 
 Looking in the Table under September, we find the number 6 
 opposite the 27th day of the month. 
 
 The error can in no case exceed one day. 
 
 TABLE III. 
 
 I 
 
 > 
 
 1 
 
 > 
 
 February. 
 
 j~ 
 
 
 PS 
 
 I 
 
 |h 
 
 rt 
 
 
 
 
 >, 
 
 's 
 > > 
 
 ti 
 
 1 
 
 < 
 
 September. 
 
 October. 
 
 1 
 
 
 December. 
 
 I 
 
 ~9~ 
 
 
 9 
 
 17 
 
 17 
 
 
 
 
 
 II 
 
 
 19 
 
 2 
 
 
 17 
 
 - . . 
 
 
 6 
 
 H 
 
 H 
 
 3 
 
 II 
 
 
 19 
 
 
 3 
 
 17 
 
 6 
 
 17 
 
 '.6 
 
 
 
 3 
 
 ii 
 
 
 19 
 
 8 
 
 *8 
 
 4 
 
 6 
 
 
 6 
 
 H 
 
 H 
 
 3 
 
 
 . . 
 
 ig 
 
 8 
 
 . . 
 
 16 
 
 
 
 H 
 
 
 
 3 
 
 ii 
 
 n 
 
 19 
 
 8 
 
 
 16 
 
 
 6 
 
 H 
 
 3 
 
 14 
 
 3 
 
 
 
 19 
 
 
 
 16 
 
 5 
 
 5 
 
 7 
 
 3 
 
 
 3 
 
 ii 
 
 ii 
 
 19 
 
 
 'i 
 
 16 
 
 
 
 13 
 
 8 
 
 
 ii 
 
 
 
 19 
 
 8 
 
 8 
 
 16 
 
 5 
 
 5 
 
 13 
 
 
 9 
 
 ii 
 
 19 
 
 ii 
 
 19 
 
 
 
 
 
 
 '3 
 
 
 2 
 
 10 
 
 
 
 19 
 
 8 
 
 | 
 
 16 
 
 1 6 
 
 5 
 
 13 
 
 
 2 
 
 IO 
 
 ii 
 
 19 
 
 8 
 
 
 
 
 
 5 
 
 J 3 
 
 2 
 
 2 
 
 IO 
 
 
 12 
 
 8 
 
 16 
 
 's 
 
 16 
 
 16 
 
 5 
 
 
 
 
 10 
 
 
 18 
 
 13 
 
 
 
 
 . . 
 
 5 
 
 13 
 
 13 
 
 2 
 
 10 
 
 
 18 
 
 7 
 
 H 
 
 16 
 
 5 
 
 16 
 
 5 
 
 
 
 2 
 
 IO 
 
 18 
 
 is 
 
 7 
 
 
 15 
 
 5 
 
 
 5 
 
 13 
 
 13 
 
 2 
 
 
 
 
 7 
 
 
 15 
 
 16 
 
 
 !3 
 
 
 
 2 
 
 10 
 
 10 
 
 18 
 
 7 
 
 
 15 
 
 
 17 
 
 13 
 
 2 
 
 13 
 
 2 
 
 
 
 18 
 
 7 
 
 
 15 
 
 4 
 
 4 
 
 18 
 
 2 
 
 
 2 
 
 IO 
 
 10 
 
 18 
 
 
 
 15 
 
 
 
 12 
 
 19 
 
 
 IO 
 
 
 . . 
 
 18 
 
 7 
 
 7 
 
 15 
 
 4 
 
 4 
 
 12 
 
 
 20 
 
 IO 
 
 18 
 
 IO 
 
 18 
 
 
 
 15 
 
 
 
 12 
 
 I 
 
 I 
 
 21 
 
 18 
 
 
 18 
 
 7 
 
 7 
 
 15 
 
 
 4 
 
 12 
 
 
 
 9 
 
 22 
 
 
 7 
 
 
 
 15 
 
 4 
 
 4 
 
 12 
 
 I 
 
 I 
 
 9 
 
 
 23 
 
 7 
 
 15 
 
 7 
 
 15 
 
 
 
 12 
 
 
 
 9 
 
 17 
 
 17 
 
 24 
 
 
 
 15 
 
 4 
 
 4 
 
 12 
 
 
 I 
 
 9 
 
 
 
 6 
 
 25 
 
 15 
 
 4 
 
 
 
 12 
 
 
 I 
 
 9 
 
 i? 
 
 17 
 
 *6 
 
 
 26 
 
 4 
 
 
 4 
 
 12 
 
 
 I 
 
 
 
 
 6 
 
 . . 
 
 H 
 
 27 
 
 
 12 
 
 
 I 
 
 I 
 
 9 
 
 9 
 
 17 
 
 '6 
 
 . . 
 
 H 
 
 
 28 
 
 12 
 
 I 
 
 12 
 
 
 9 
 
 
 17 
 
 6 
 
 H 
 
 H 
 
 3 
 
 3 
 
 29 
 
 I 
 
 
 I 
 
 9 
 
 
 17 
 
 
 
 
 3 
 
 
 ii 
 
 30 
 
 
 
 
 
 17 
 
 6 
 
 'e 
 
 14 
 
 3 
 
 
 ii 
 
 
 31 
 
 9 
 
 
 
 9 
 
 
 
 
 
 
 H 
 
 3 
 
 
 
 ii 
 
 
 19 
 
312 
 
 APPENDIX. 
 
 EPACT. 
 
 A solar year, as we have seen, is about 365 days, 6 hours ; a 
 lunar year, of 12 lunar months, is about 354 days, 9 hours. 
 The difference of nearly u days between the two is the An- 
 nual Epact. Since the epact of one year is n days, that of 2 
 years will be 22 days ; of 3 years 33 days, or rather 3 days, be- 
 ing 3 days over a lunar month. Thus, by yearly adding n, 
 and casting out the 3o's, it will be found that on every igth 
 year 29 remains ; which is reckoned a complete lunar month, 
 and the epact is o. Thus the cycle of epacts expires with the 
 lunar cycle, or that of the Golden Numbers ; and on every igth 
 year the solar and lunar years begin together. 
 
 By the epact of any year the moon's age (115) for the \st 
 of January is shown. 
 
 Table IV. gives the Golden Numbers with the corresponding 
 Epacts till the year 1900. 
 
 TABLE IV. 
 
 Golden 
 No. 
 
 Epact. 
 
 Golden 
 No. 
 
 Epact. 
 
 Golden 
 No. 
 
 Epact. 
 
 Golden 
 No. 
 
 Epact. 
 
 Golden 
 No. 
 
 Epact. 
 
 , 
 
 O 
 
 5 
 
 H 
 
 9 
 
 28 
 
 13 
 
 12 
 
 17 
 
 26 
 
 2 
 
 II 
 
 6 
 
 25 
 
 IO 
 
 9 
 
 14 
 
 2 3 
 
 18 
 
 7 
 
 3 
 
 22 
 
 7 
 
 6 
 
 II 
 
 20 
 
 15 
 
 4 
 
 19 
 
 18 
 
 4 
 
 3 
 
 8 
 
 17 
 
 12 
 
 1 
 
 16 
 
 15 
 
 
 
 IV. 
 
 THE METRIC SYSTEM. 
 
 SINCE the measurement of length is required for almost 
 every purpose of construction, as well as for every intelligible 
 statement of the size of material objects and their distance from 
 one another, it is indispensable that every community should 
 fix upon some common standard, some well known unit, by 
 whose repetition and subdivision length, distance, and size, 
 whether great or small, can be expressed in words and 
 numbers. 
 
APPENDIX. 3 13 
 
 The standards which almost all communities have taken 
 for their unit of length, have been either some portion of 
 the human body, such as the length of the arm, of the fore- 
 arm (the ell or cubit), of the foot, of the breadth of the hand 
 (span or palm), or the length of the ordinary step (pace) ; 
 and for measuring smaller lengths, the length of certain 
 cereal grains, such as those of rice or barley (the barley- 
 corn}. 
 
 Thus an old English statute defined an inch as the length 
 of three barleycorns. 
 
 But no part of the body of a full grown man has invariably 
 the same length ; hence it became necessary for each com- 
 munity to take the length of a particular fore-arm or foot for 
 their unit. In this way the units fixed upon by different com- 
 munities did not agree with one another. Thus we find the 
 length of the Roman foot equivalent to 1 1.6 of our inches ; the 
 English to 12 ; the Grecian to 12.1 ; the French to 12.8 ; and 
 the Egyptian to 13.1. 
 
 The English unit is the yard, which is said to have been in- 
 troduced by King Henry the First, who ordered that the ulna, 
 or ancient ell, which corresponds to the modern yard, should 
 be made the exact length of his own arm, and that the other 
 measures of length should be based upon it. 
 
 In 1790, at the time of the French Revolution, that people 
 undertook to establish a new metrical system, and sought for 
 some natural object of invariable length upon which to base 
 their unit of length. They chose the length of a meridian of 
 the globe, and they called the ten- millionth part of a quadrant 
 of the meridian a metre. They then set about measuring an 
 arc of a meridian so as to compute exactly the length of its 
 quadrant. A mistake was made in this computation, so that 
 the French metre does not correctly represent the ten-millionth 
 part of the quadrant of a meridian. 
 
 As nations come into closer relations with one another, it 
 becomes more and more desirable that they should have a 
 common metrical system. 
 
 Accordingly many governments, and among them our own, 
 have enacted that the French metre shall be regarded as a 
 legal unit of measure. 
 14 
 
314 APPENDIX. 
 
 There are, however, objections to this unit. It is true it is 
 based upon the quadrant of a meridian, which is of invariable 
 length, but it does not represent a ten-millionth of that quad- 
 rant accurately. 
 
 We have already seen that the radius or diameter of the 
 earth is the natural unit with which we begin the measurement 
 of the distance of the heavenly bodies. Hence it would be 
 much more convenient that the unit of linear measurement 
 should be based upon the diameter of the earth than upon the 
 length of a meridian, and it would be a great objection to the 
 French metre that it is not based upon the length of the 
 earth's diameter, even if it represented accurately what it pro- 
 fesses to do. 
 
 Now, Sir John Herschel has called attention to the fact 
 that if the English inch were made .001 longer than it now 
 is, then 50 such inches would represent almost exactly a ten- 
 millionth part of the polar diameter of the earth. He conse- 
 quently proposes 50 such inches as the unit of measure, and 
 would call it a module. This seems on the whole the most 
 satisfactory unit that has been proposed. 
 
 It has been proposed that the length of a pendulum beating 
 seconds be taken as the unit of length. This unit would dif- 
 fer but little from the metre. 
 
 It has this advantage ; that it is much easier to measure the 
 length of such a pendulum accurately than to measure the arc 
 of a meridian. But the length of the pendulum beating sec- 
 onds as a standard of length has the same disadvantage that 
 the human foot has for the same purpose. It has already been 
 seen that pendulums which beat seconds in different parts of 
 the earth are not all of the same length. If then the length of 
 a seconds pendulum is to be taken as a standard, it must be 
 stated at what particular place the pendulum is to beat sec- 
 onds. 
 
 Having decided upon a unit of length it is necessary to 
 decide according to what scale this unit shall be multiplied 
 or divided. The French have multiplied and divided their 
 metre on the decimal scale, as the following table shows. 
 
APPENDIX. 315 
 
 TABLE OF LINEAR MEASURE. 
 
 10 millimetres 
 
 = I centimetre 
 
 10 centimetres* 
 
 = i decimetre 
 
 10 decimetres 
 
 == I metre 
 
 10 metres 
 
 = i decametre 
 
 10 decametres 
 
 = I hectometre 
 
 10 hectometres 
 
 = i kilometre. 
 
 The names of the higher orders of units, or the multiples of 
 the metre, are formed from the word metre by means of pre- 
 fixes taken from the Greek numerals : namely, deca-(io), hecto- 
 (100), //<?-( i, ooo). 
 
 The names of the lower orders of units, or the subdivisions 
 of the metre, are formed in a similar manner by means of pre- 
 fixes taken from the Latin numerals: namely, deci-(iv\ centi- 
 ( i oo), milli-(\ ,000). 
 
 This is certainly a great improvement upon our clumsy mul- 
 tiplication and subdivision of the yard and foot. 
 
 It is very desirable that the units of length, of capacity, and 
 of weight, should be connected in some natural manner. This 
 the French do very neatly. The cubic decimetre is their unit 
 of capacity, and is called a litre. This litre is multiplied and 
 divided decimally in the same way as the metre, as is seen in 
 the following table. 
 
 TABLE OF MEASURES OF CAPACITY. 
 
 10 millilitres = i centilitre 
 
 10 centilitres = decilitre 
 
 10 decilitres = litre 
 
 10 litres = decalitre 
 
 10 decalitres = hectolitre 
 
 10 hectolitres = kilolitre. 
 
 The names of the higher and lower orders of units are formed 
 from the name of the litre, in the way explained under the pre- 
 ceding table. 
 
 They have taken the weight of a cubic centimetre of water, 
 
 * The new five-cent piece (1866) is 2 centimetres in diameter, and weighs 5 
 grammes. 
 
316 APPENDIX. 
 
 at a temperature of 4 Centigrade in a vacuum, as their unit 
 of weight, and have called it a gramme. This also they -mul- 
 tiply and divide decimally, according to the following table. 
 
 TABLE OF WEIGHTS. 
 
 10 milligrammes 
 10 centigrammes 
 10 decigrammes 
 10 grammes 
 10 decagrammes 
 10 hectogrammes 
 
 centigramme 
 
 decigramme 
 
 gramme 
 
 decagramme 
 
 hectogramme 
 
 kilogramme. 
 
 The names are formed from the word gramme by means of 
 prefixes, in the same manner as those in the other tables. 
 
 It would probably be impossible to improve upon the method 
 in which the French have multiplied and subdivided the unit of 
 measure, and in which they have connected the units of length, 
 capacity, and weight. 
 
 Our unit of weight is the grain. This is defined as the 
 weight of such an amount of distilled water that, at a tempera- 
 ture of 62 Fahrenheit, 252.46 such grains shall fill a cubic 
 inch. A pound avoirdupois contains 7,000 of these grains ; 
 and an imperial gallon of distilled water at a temperature of 
 62 F. 70,000 of them. This gallon is our unit of capacity. 
 An ounce contains 437^ such grains. According to this sys- 
 tem a cubic foot of distilled water at a temperature of 62 
 F. contains 997.145 ounces, falling short of 1,000 ounces by 
 nearly three ounces. It is evident that nothing could be 
 more clumsy than the way in which we connect our units of 
 weight, of capacity, and of length. 
 
 But, Sir John Herschel has called attention to the fact that 
 if our inch, and consequently our foot, were increased .001 in 
 length, then a cubic foot of water at the temperature of 62 F. 
 would contain almost exactly 1,000 ounces, and that it would 
 require only the slightest change in the value of the ounce to 
 make it contain exactly 1,000 ounces. Thus by taking the 
 ounce thus slightly modified as our unit of weight, it would be 
 connected decimally with our unit of length. Also our half- 
 pint, which he proposes to call a beaker, would be just .01 of a 
 cubic foot in capacity. And by taking this as our unit of capa- 
 
APPENDIX. 3.17 
 
 city, our units of length, of weight, and of capacity would all be 
 connected decimally. "And thus," as Sir John Herschel says, 
 "the change which would place our system of linear measure 
 on a perfectly faultless basis, would at the same time rescue 
 our weights and our measures of capacity from their present 
 utter confusion, and secure that other advantage, second only 
 in importance to the former, of connecting them decimally with 
 that system on a regular, intelligible, and easily remembered 
 principle, and that, too, by an alteration practically imper- 
 ceptible in both cases, and interfering with no one of our 
 usages and denominations." 
 
 These units once established, they could of course be divided 
 and multiplied decimally in the same way as the French units 
 are. If these decimal divisions and multiples were found more 
 convenient than the old ones, they would soon displace them, 
 as the decimal system in our currency has displaced the old 
 system of pounds, shillings, and pence. 
 
 V. 
 
 THE latest observations upon Limit (according to Silliman's 
 Journal, July, 1867), appear to show in the centre of the bright 
 spot covering the former crater a minute black spot indicating 
 a crater of about six hundred yards diameter. The original 
 crater appears to have been a deep one, and about ten thousand 
 yards in diameter. This small crater was so plainly visible as 
 to have been noticed (independently as it would seem) by Dr. 
 Schmidt at Athens, by Father Secchi at Rome, and by Pro- 
 fessor Lyman at New Haven. It was detected at New Haven 
 three days after the sun had risen over the horizon of Linnt, 
 and when the sun was therefore 30 or 35 liigh upon it. These 
 observations show that any change which has taken place is 
 not in the nature of a development of a cloud, but imply rather 
 that the old crater has been filled up by an eruption from 
 the small one now visible. 
 
APPENDIX. 
 
 TABLES. 
 THE SUN AND PRINCIPAL PLANETS. 
 
 
 
 
 Time of 
 
 Inclination 
 
 Mean j 
 
 
 
 
 Name. 
 
 ,0 
 
 Axial 
 
 of Orbit 
 
 Diameter Volume. 
 
 Mass. 
 
 '2 
 
 
 cl 
 
 Rotation. 
 
 to Ecliptic. 
 
 in Miles. 
 
 
 o 
 
 
 
 h. m. s. 
 
 O 1 M 
 
 1 
 
 
 
 The Sun 
 
 e 
 
 600 
 
 
 887,000 . 1416000 
 
 354936 
 
 0-25 
 
 Mercury 
 
 
 24 5 28 
 
 708 
 
 2,950 ! 0.059 
 
 O.IlS 
 
 2.01 
 
 Venus 
 
 <j> 
 
 23 21 21 
 
 3 23 31 
 
 7,800! 0.912 
 
 0.883 
 
 0.97 
 
 The Earth 
 
 
 
 23 5 6 4 
 
 
 7,912 1 i.ooo 
 
 I.OOO 
 
 I.OO 
 
 Mars 
 
 
 
 24 37 22 
 
 i 5i 5 
 
 4,500! 0.183 
 
 0.132 
 
 0.72 
 
 Jupiter 
 
 H 
 
 9 55 26 : i 18 40 
 
 88,000 1412.000 
 
 338.034 
 
 0.24 
 
 Saturn 
 
 h 
 
 10 29 1712 29 28 
 
 73,000 770.000 
 
 101.064 
 
 0.13 
 
 Uranus 
 
 
 
 o 46 30 
 
 36,000 ! 95 900 
 
 14.789 
 
 0.15 
 
 Neptune 
 
 W 
 
 
 i 46 59 
 
 35,000 s 89.500 
 
 24.648 
 
 0.27 
 
 THE PLANETS (continue^ 
 
 
 
 
 
 Relative 
 
 Name. 
 
 Sidereal Period 
 in Days. 
 
 Relative 
 Distance 
 from Sun. 
 
 Mean Distance from 
 Sun in Miles. 
 
 Li^ht ami 
 Heat re- 
 ceived from 
 
 
 
 
 
 Sun. 
 
 Mercury 
 
 87.969 
 
 0.387 
 
 37,OOO,OOO 
 
 6.67 
 
 Venus 
 
 224.701 
 
 0.723 
 
 69,000,000 
 
 I.9I 
 
 Earth 
 
 365-256 
 
 I.OOO 
 
 95,OOO,OOO 
 
 I.OO 
 
 Mars 
 
 686.980 
 
 1.524 
 
 I45,OOO,OOO 
 
 0-43 
 
 Jupiter 
 
 4,332.585 
 
 5.203 
 
 436,000,000 
 
 0.037 
 
 Saturn 
 
 10.759.220 
 
 9-539 
 
 9O9,OOO,COO 
 
 O.OII 
 
 Uranus 
 
 30,686.821 
 
 19.183 
 
 I,828,OOO,OOO 
 
 0.003 
 
 Neptune 
 
 60,126.722 
 
 30.037 
 
 2,862,OOO,OOO 
 
 O.OOI 
 
 THE MOON. 
 
 Mean Distance from the Earth 238,900 miles. 
 
 Sidereal Period of Revolution 27 d 7 h 43 11.46'. 
 
 Synodical Period of Revolution 29* I2 h 44 2.87'. 
 
 Diameter 2160 miles. 
 
 Inclination of the Orbit 5 8' 48". 
 
 Density (the Earth = i) 05657. 
 
 Mass (the Earth = i) ^. 
 
APPENDIX. 
 
 319 
 
 THE MINOR PLANETS. 
 
 No. 
 
 Name. 
 
 Date of Discovery. 
 
 Discoverer. 
 
 Sidereal 
 Rev. in 
 Days. 
 
 I 
 
 Ceres 
 
 1 80 1, Jan. i 
 
 
 1680 
 
 2 
 
 Pallas 
 
 1802, March 28 
 
 Gibers 
 
 1682 
 
 3 
 
 Juno 
 
 1804. Sent i 
 
 Harding . 
 
 icq6 
 
 I 
 
 Vesta 
 
 1807 March 29 
 
 Olbers 
 
 1 726 
 
 c 
 
 Astrcea 
 
 1845, Dec - 8 
 
 Hencke 
 
 ISI2 
 
 i 
 
 Hebe. 
 
 1847, July I 
 
 Hencke. . 
 
 1 770 
 
 7 
 
 Iris 
 
 1847 Aug 13 
 
 Hind 
 
 M/y 
 I 34.6 
 
 8 
 
 Flora 
 
 1847 ^ ct J 8 
 
 Hind 
 
 I IQ7 
 
 q 
 
 Metis 
 
 1848, April 25 
 
 Graham .... 
 
 iA yj 
 
 1^4.6 
 
 IO 
 
 Hygieia 
 
 1849, April 12 
 
 Gasparis . . 
 
 2O47 
 
 ii 
 
 Pavthenope 
 
 1850 May ii 
 
 Luther. 
 
 I4O7 
 
 T- 
 
 Victoria 
 
 1850 Sept 13 
 
 Hind 
 
 1 3O7 
 
 n 
 
 E^eria 
 
 i8co Nov 2 
 
 Gasparis 
 
 5VJ 
 
 I C. 1 1 
 
 14 
 
 Irene 
 
 1851, May 19 
 
 Hind 
 
 1 J 1 1 
 
 I s IQ 
 
 1C 
 
 Eunomia 
 
 l8sl Tlllv 2Q 
 
 Gasparis . 
 
 I ^7O 
 
 16 
 
 Psvche 
 
 1852 March 1 7 
 
 Gasparis 
 
 1 D/v 
 l828 
 
 17 
 
 Thetis 
 
 1852, April 17 
 
 Luther 
 
 1 42 1 
 
 18 
 
 Melpomene . . . 
 
 1852, June 24 
 
 Hind . . . 
 
 1271 
 
 IQ 
 
 Fortuna 
 
 1832 Aug 22 
 
 Hind . . . 
 
 1 7Q7 
 
 2O 
 
 Massilia 
 
 1852, Sept. 19 
 
 Gasparis 
 
 1 6V6 
 IT.OS 
 
 21 
 
 Lutetia 
 
 1852, Nov. 15 
 
 Goldschmidt 
 
 1388 
 
 22 
 
 Calliope 
 
 1852, Nov. 16 
 
 Hind . 
 
 1817 
 
 2"? 
 
 Thalia 
 
 1852, Dec. 15 
 
 Hind 
 
 jcc6 
 
 24 
 
 Themis 
 
 18^1, April ? 
 
 Gasparis 
 
 I DD" 
 2O7O 
 
 25 
 
 Phocaea 
 
 18^. April 7 
 
 Chacornac . 
 
 I7C8 
 
 26 
 
 Proserpine .... 
 
 1857, May 5 
 
 Luther 
 
 ii; 80 
 
 27 
 
 Euterpe 
 
 1853 Nov 8 
 
 Hind 
 
 
 28 
 
 Uellona 
 
 1854, March I 
 
 Luther 
 
 J j 1 j 
 1692 
 
 29 
 
 Amphitrite. . . . 
 
 1854, March I 
 
 Marth 
 
 1 4.Q2 
 
 JQ 
 
 Urania 
 
 l8?4, Tulv 22 
 
 Hind 
 
 
 71 
 
 Euphrosyne . . . 
 
 1854, Sept. i 
 
 Ferguson 
 
 j^y 
 2048 
 
 72 
 
 Pomona 
 
 1854, Oct. 26 
 
 Goldschmidt 
 
 r C2I 
 
 33 
 
 -24 
 
 Polyhymnia . . . 
 Circe 
 
 1854, Oct. 28 
 1855, April 6 
 
 Chacornac 
 
 1^1 
 1778 
 
 35 
 
 Eeucothea .... 
 
 1855, April 19 
 
 Luther 
 
 iuuy 
 
 IQO7 
 
 36 
 
 Atalanta 
 
 18^, Oct. c 
 
 Goldschmidt 
 
 1664 
 
 VJ 
 
 Fides 
 
 i8cc, Oct c 
 
 Luther 
 
 
 38 
 
 Lecla 
 
 i8c6 Jan 12 
 
 
 i j u y 
 
 70 
 
 Lsetitia 
 
 1856, Feb. 8 
 
 Chacornac 
 
 lv b7 
 1684 
 
 40 
 4-1 
 
 Harmonia . . . 
 Daphne 
 
 1856, March 3 1 
 1856, May 22 
 
 Goldschmidt 
 
 1247 
 
 1681 
 
 42 
 
 Isis 
 
 18^6, May 27 
 
 Pogson 
 
 I 7Q2 
 
 43 
 
 Ariadne 
 
 1857, April 15 
 
 Pogson 
 
 I iqc 
 
 44 
 
 Nysa 
 
 i8c7 Mav 27 
 
 
 
 45 
 
 Eugenia 
 
 18^7 Tune 27 
 
 
 '379 
 1678 
 
 46 
 
 Hestia 
 
 1857, Aug. 16 
 
 Po"son 
 
 I4.7O 
 
 48 
 
 Melete*...... 
 Aglaia 
 
 1857, Sept. 9 
 1857, Sept. 15 
 
 Goldschmidt 
 Luther 
 
 1529 
 
 1788 
 
 * Goldschmidt at first believed it to be Daphne (41), but, finding its period differ- 
 ent, called it Pseudo-Daphne. It was not seen from 1857 to 1861, when Schubert 
 rediscovered it and named it Melete. 
 
320 
 
 APPENDIX. 
 
 No. 
 
 Name. 
 
 Date of Discovery. 
 
 Discoverer. 
 
 Sidereal 
 Rev. in 
 Days. 
 
 49 
 
 Doris 
 
 18^7, Sept. IQ 
 
 Goldschmidt 
 
 2OO7 
 
 CQ 
 
 Pales 
 
 i8c.7. Sent IQ 
 
 Goldschmidt 
 
 TQ7C 
 
 CI 
 
 Virginia 
 
 18^,7, Oct. 4 
 
 Ferguson 
 
 ^y/j 
 i ^76 
 
 C2 
 
 Nemausa 
 
 1858, Jan. 22 
 
 Laurent. . 
 
 1778 
 
 C7 
 
 Europa 
 
 1858, Feb 6 
 
 Goidschmidt 
 
 i jj 
 
 CA 
 
 Calvpso 
 
 1858, April 4 
 
 Luther 
 
 x yyj 
 i^A8 
 
 t;S 
 
 Alexandra 
 
 1858, Sept. 10 
 
 Goldschmidt 
 
 1674 
 
 5* 
 
 Pandora 
 
 1858, Sept. 10 
 
 Searle 
 
 "OT 1 
 
 l6?d. 
 
 C7 
 
 Mnemosyne . . . 
 
 1859, Sept. 22 
 
 Luther 
 
 2O AQ 
 
 58 
 
 Concordia .... 
 
 1860, March 24 
 
 Luther 
 
 161 c. 
 
 cq 
 
 Danae 
 
 i 860 Sept 9 
 
 
 
 60 
 
 Olympia (Elpis) 
 
 1860, Sept. 12 
 
 Chacornac 
 
 l67A 
 
 6r 
 
 Erato 
 
 1860 Sept 14 
 
 Forster 
 
 2O2" 1 
 
 62" 
 
 Echo .... 
 
 1860 Sept 1 1 
 
 
 
 63 
 
 Ausonia 
 
 1 86 1, Feb. 10 
 
 Gasparis 
 
 1 OJ^ 
 I 7 C C 
 
 64 
 
 Angelina 
 
 1 86 1, March 4 
 
 Tempel 
 
 I 6bb 
 1601 
 
 *5 
 
 Cybele 
 
 1 86 1, March 8 
 
 Tern pel . . 
 
 2711 
 
 66 
 
 
 1861 April 9 
 
 Tuttle 
 
 1588 
 
 67 
 
 Asia 
 
 1 86 1 April 17 
 
 
 I 7C 
 
 68 
 
 Hesperia 
 
 1861 April 29 
 
 
 1 J/J 
 1807 
 
 69 
 
 Leto 
 
 1 86 1 April 29 
 
 Luther 
 
 io yj 
 1601 
 
 7o 
 
 Panopea . 
 
 1861 May 5 
 
 Goldschmidt 
 
 I CA2 
 
 71 
 
 Feronia 
 
 1861 May 29 
 
 
 *M* 
 
 72 
 
 Niobe . . . 
 
 1861 Aucr. 1 1 
 
 Luther 
 
 *245 
 1671 
 
 73 
 
 Clytie 
 
 1862, April 7 
 
 Tuttle . 
 
 ICQO 
 
 74 
 
 Galatea 
 
 1862 Aug 29 
 
 Tempel 
 
 1691 
 
 75 
 
 Eurydice 
 
 1862, Sept. 22 
 
 Peters 
 
 ICQ4 
 
 76 
 
 Freia 
 
 1862, Oct. 21 
 
 d'Arrest . 
 
 2080 
 
 77 
 
 Frierera. . 
 
 1862 Nov 12 
 
 Peters 
 
 I ^06 
 
 78 
 
 Diana 
 
 1863, March 15 
 
 Luther. . . . 
 
 ICC4 
 
 70 
 
 Eurynome .... 
 
 1867. Sept. 14 
 
 Watson 
 
 1 7QO 
 
 80 
 
 Sappho . 
 
 1864 May 2 
 
 Pogson 
 
 I27O 
 
 81 
 
 Terpsichore . . . 
 
 1864, Sept. 30 
 
 Tempel 
 
 1607 
 
 8^ 
 
 Alcmene 
 
 1864 Nov 27 
 
 Luther. . 
 
 1 6 CQ 
 
 8-? 
 
 Keatrix . 
 
 186^ April 26 
 
 Gasparis 
 
 1781 
 
 84 
 
 Clio 
 
 1865 Aug. 26 
 
 Luther 
 
 1J01 
 
 I77Q 
 
 85 
 
 Jo 
 
 1865 Sept. 19 
 
 Peters . . 
 
 jc87 
 
 86 
 
 Semele . 
 
 1866 Jan 4 
 
 Tietjen 
 
 IQ87 
 
 87 
 
 Sylvia 
 
 1866 May 1 6 
 
 Pogson 
 
 2784 
 
 88 
 
 Thisbe 
 
 1866 June 15 
 
 Peters . . . 
 
 j67C 
 
 80 
 
 Julia 
 
 1866, Aug. 6 
 
 Stephan 
 
 1472 
 
 9 
 
 Antiope 
 
 1866, Oct. ii 
 
 Luther 
 
 2O7I 
 
 01 
 
 
 1866 Nov 4 
 
 Stephan 
 
 
 Q2 
 
 Undina ... 
 
 186? Tulv 7 
 
 Peters 
 
 2086 
 
 07 
 
 
 1867, Aucr. 24 
 
 Watson 
 
 1669 
 
 Q4 
 
 
 1867 Sept 6 
 
 Watson 
 
 
 (S 
 
 
 1867, Nov. 23 
 
 Luther. . . . 
 
 
 p 
 
 
 
 
 
I 
 APPENDIX. 321 
 
 The numerical order of the minor planets differs some- 
 what in the lists of English and French astronomers. 
 
 Of the first eighty-nine of these planets, the nearest to the 
 sun is Flora, whose mean distance is 201,274,000 miles. 
 
 The farthest from the sun is Sylvia, with a mean distance of 
 about 319,500,000 miles. 
 
 The least eccentric orbit is that of Europa, which is even 
 nearer to an exact circle than the orbit of Venus. The most 
 eccentric orbit is that of Polyhymnia, whose aphelion distance 
 is rather more than double its perihelion distance. 
 
 The orbit of Massilia has the least inclination to the eclip- 
 tic, or o 41' ; that of Pallas the greatest inclination, or 34 42'. 
 
 The brightest planet is Vesta, which appears at times as a 
 star of the sixth magnitude. The faintest is Atalanta, which, 
 under the most favorable circumstances, is scarcely above the 
 thirteenth magnitude. 
 
 The largest planet, according to some authorities, is Pallas. 
 Lament makes its diameter 670 miles, but Galle only 172 miles. 
 According to others, Vesta is the largest, with a diameter of 228 
 miles. The more recently discovered planets are all so small 
 that it is impossible to tell which is smallest. The diameters 
 of those numbered 5 - 39, as given by Chambers, range from 
 12 miles (Eunomid) up to in miles (Hygieid). 
 
 Of these planets (up to the ninety-fourth inclusive), fifteen 
 have been discovered in the United States, Euphrosyne, Vir- 
 ginia, Pandora, Echo, Maia, Feronia, Clytie, Eurydice, Frigga, 
 Eurynome, lo, Thisbe, and Undina, with the 93d and 94th, which 
 are not yet (January, 1868) named. 
 
 In several cases minor planets have been discovered inde- 
 pendently by two or more observers, each knowing nothing of 
 what the other had done. Thus, Irene 'was discovered by 
 Hind, May 19, 1851, and by Gasparis, May 23; Massilia, by 
 Gasparis, September 19, 1852, and by Chacornac, September 
 20; Amphitrite, by Marth, March I, 1854, by Pogson, March 2, 
 and by Chacornac, March 3. 
 
 14* 
 
322 
 
 APPENDIX. 
 
 MOONS OF JUPITER. 
 
 Moon. 
 
 Sidereal Period 
 of Revolution. 
 
 Distance in Radii 
 of Jupiter. 
 
 Mean Distance 
 in Miles. 
 
 I. 
 
 d. h. in. 
 I 18 28 
 
 6.049 
 
 278,542 
 
 II. 
 
 3 13 IS 
 
 9.623 
 
 442,904 
 
 III. 
 IV. 
 
 7 3 43 
 16 16 32 
 
 I5-350 
 26.998 
 
 706,714 
 I,20O,OOO 
 
 MOONS OF SATURN. 
 
 Moon. 
 
 Sidereal Period 
 of Revolution. 
 
 Distance in Radii 
 of Saturn. 
 
 Mean Distance 
 in Miles. 
 
 I. 
 
 d. h. m. 
 22 36 
 
 3-36I 
 
 Il8,COO 
 
 II. 
 III. 
 
 I 8 58 
 I 21 18 
 
 4.313 
 5-340 
 
 152,000 
 188,000 
 
 IV. 
 
 2 17 41 
 
 6.840 
 
 240,000 
 
 V. 
 
 4 12 25 
 
 9-553 
 
 336,000 
 
 VI. 
 
 .15 22 41 
 
 22.145 
 
 778,000 
 
 VII. 
 
 21 12 
 
 28.000 
 
 94O,COO 
 
 VIII. 
 
 .79 7 55 
 
 64-359 
 
 2,268,OCO 
 
 MOONS OF URANUS. 
 
 Moon. 
 
 Sidereal Period 
 of Revolution. 
 
 Distance in Radii 
 of Uranus. 
 
 Mean Distance 
 in Miles. 
 
 I. 
 
 d. h. m. 
 2 12 17 
 
 6.940 
 
 119,994 
 
 II. 
 III. 
 IV. 
 
 4 3 28 
 8 16 56 
 13 ii 7 
 
 9.720 
 15.890 
 2I.27O 
 
 170,863 
 288,600 
 380,000 
 
 MOON OF NEPTUNE. 
 
 Sidereal Period of Revolution 5* 2O h 5o m 45 s . 
 
 Mean Distance from Neptune 236,000 miles. 
 
APPENDIX. 323 
 
 THE CONSTELLATIONS. 
 
 1. ALL the stars in the heavens have been divided into 
 groups called constellations (162). Many of these were recog- 
 nized and named at a very early period ; and some of them, as 
 Orion, are mentioned in the Old Testament. 
 
 The method of naming the stars in each constellation has 
 been explained above (163). The characters and names of the 
 Greek alphabet are as follows : 
 
 a, Alpha. v, Nu. 
 
 0, Beta. , Xi. 
 
 y, Gamma. o, Omicron. 
 
 8, Delta. IT, Pi- 
 
 , Epsilon. p, Rho. 
 
 , Zeta. <r, Sigma. 
 
 rj, Eta. r, Tau. 
 
 0, Theta. u, Upsilon. 
 
 1, Iota. <, Phi. 
 K, Kappa. x, Chi. 
 A, Lambda. ^, Psi. 
 
 p, Mu. o>, Omega. 
 
 If a constellation has more stars than can be named from the 
 Greek alphabet, the Roman alphabet is used in the same way ; 
 and when both alphabets are exhausted, numbers are used. 
 
 2. Circumpolar Constellations. One of the most important 
 constellations, and one easily recognized, is the Great Bear, or 
 Ursa Major. It is represented in Plate I. at the end of this 
 volume. It may be known by the seven stars forming "the 
 Dipper," or " Charles's Wain," as it is* sometimes called. 
 These stars are designated by the first seven letters of the 
 Greek alphabet ; and the name and position of each should be 
 carefully fixed in the mind, as we shall have frequent occasion 
 to refer to them. The Bear's feet are marked by three pairs of 
 stars. These and the star in the nose can be readily found by 
 means of the lines drawn on the chart. It may be remarked 
 here, that in all cases the stars thus connected by lines are the 
 leading stars of the constellation, and should be thoroughly 
 
324 APPENDIX. 
 
 learned. The stars a and are called the Pointers. If a line 
 be drawn from /3 to a, and prolonged about five times the dis- 
 tance between them, it will pass near an isolated star of the sec- 
 ond magnitude known as the Pole Star, or Polaris. This is 
 the brightest star in the Little Bear, or Ursa Minor (Plate II.). 
 It is in the end of the handle of a second and smaller "dip- 
 per." The stars /3 and y of this constellation are quite bright, 
 and are nearly parallel with e and of the other Bear. 
 
 On the opposite side of the Pole Star from the Great Bear, 
 and at about the same distance, is another conspicuous constel- 
 lation, called Cassiopeia. Its five brightest stars form an irreg- 
 ular W, opening towards the Pole Star (Plate II.). 
 
 About half-way between the two Dippers three stars of the 
 third magnitude will be seen, the only stars at all prominent 
 in that neighborhood. These belong to Draco, or the Dragon. 
 The chart will show that the other stars in the body of the 
 monster form an irregular curve around the Little Bear, while 
 the head is marked by four stars arranged in a trapezium. 
 Two of these stars, and y, are quite bright. A little less than 
 half-way from Cassiopeia to the head of the Dragon is the con- 
 stellation Cepheus, five stars of which form an irregular K. 
 
 These five constellations never set in our latitude, and are 
 called circttmpolar constellations (page 5). 
 
 3. Constellations visible in September. We will now study 
 the remaining constellations visible in our latitude, beginning 
 with those which are above the horizon at eight o'clock in the 
 evening, about the middle of September. At this time the 
 Great Bear will be low down in the northwest, and the Drag- 
 on's head nearly in the zenith. If we draw a line from to T; of 
 the Great Bear and prolong it, we shall find that it will pass 
 near a reddish star of the first magnitude. This star is called 
 Arcturns, or a Bootis, since it is the brightest star in the con- 
 stellation Bootes. Of its other conspicuous stars, four form a 
 cross. These and the remaining stars of the constellation can 
 be readily traced with the aid of Plate III. 
 
 Near the Dragon's head (Plate IV.) maybe seen a very bright 
 star of the first magnitude, shining with a pure white light. 
 This star is Vega, or a Lyres. Of this and some of the other 
 stars in the Lyre we shall have occasion to speak hereafter. 
 
APPENDIX. 325 
 
 If we draw a line from Arcturus to Vega (Plate III.)i it will 
 pass through two constellations, the Crown, or Corona Bore- 
 alts, and Hercules. The former is about one third of the way 
 from Arcturus to Vega, and consists of a semicircle of six stars, 
 the brightest of which is called Alphecca, or Gemma Coroncs, 
 the gem of the Crown. 
 
 Hercules is about half-way between the Crown and Vega. 
 This constellation is marked by a trapezoid of stars of the third 
 magnitude. A star in one foot is near the Dragon's head ; there 
 is also a star in each shoulder, and one in the face. 
 
 Just across the Milky Way from Vega (Plate V.) is a star of 
 the first magnitude, called Altair or a Aquilce. This star marks 
 the constellation Aquila, or the Eagle, and may be recognized 
 by a small star on each side of it. These are the only important 
 stars in this constellation. 
 
 In the Milky Way, between Altair and Cassiopeia (Plate IV.), 
 there is a large constellation called Cygnus, or the Swan. Six 
 of its stars form a large cross, by which it will be readily known. 
 a Cygni is often called Deneb. It forms a large isosceles tri- 
 angle with Altair and Vega. 
 
 Low down in the south, on the edge of the Milky Way (Plate 
 VI.), is a constellation called Sagittarius, or the Archer. It may 
 be known by five stars forming an inverted dipper, often called 
 "the Milk-dipper." The head is marked by a small triangle. 
 The other stars, as seen by the map, may be grouped so as to 
 represent a bow and an arrow. 
 
 Low in the southwest is a bright red star called Antares, or 
 a Scorpionis. This constellation is described below (12). 
 
 The space between Sagittarius and Hercules and Scorpio is 
 occupied by the Serpent (Serpens] and the Serpent-bearer, or 
 Ophiuchus (Plates VI. and VII.). The head of the Serpent is 
 near the Crown, and marked by a small triangle. The head of 
 Ophiuchus is close to the head of Hercules, and may be known 
 by a star of the second magnitude. Each shoulder is marked 
 by a pair of stars. His feet are near the Scorpion. The Ser- 
 pent can be best traced with the aid of the map. 
 
 Nearly on a line with Arcturus and y Ursae Majoris (Plate I.), 
 and rather nearer the latter, is an isolated star of the third mag- 
 nitude, called Cor Caroli, or Charles's Heart. This is the only 
 
326 APPENDIX. 
 
 prominent star in the constellation of Canes Venatici, or the 
 Him ting Dogs. 
 
 Cassiopeia is almost due east of the Pole Star. A line 
 drawn from the latter through Cassiopeiae, and prolonged, 
 passes through two stars of the second and third magnitude. 
 These, with two others farther to the south, form a large 
 square, called the Square of Pegasus. Three of these, as seen 
 by the map (Plate V.), belong to the constellation Pegasus, or 
 the Winged Horse, a. Pegasi is called Markab, and /3 is called 
 Algenib. The bright stars in the neck and nose can be found 
 by the map. 
 
 The fourth star in the Square of Pegasus belongs (Plate VIII.) 
 to the constellation Andromeda. Nearly in a line with a Pegasi 
 and this star are two other bright stars belonging to Androm- 
 eda. The stars in her belt may be found by the map. 
 
 Following the direction of the line of stars in Andromeda just 
 mentioned, and bending a little towards the east, we come to 
 Algol, or /3 Persei, a remarkable variable star (165). This star 
 may be readily recognized from the fact that, together with 
 and y Andromedae and the four stars in the Square of Pegasus, 
 it forms a figure similar in outline to the Dipper in Ursa Major, 
 but much larger. If the handle of this great Dipper is made 
 straight instead of being bent, the star in the end of it is a Per- 
 sei, of the second magnitude. This star has one of the third 
 magnitude on each side of it. The other stars in Perseus may 
 be found by the chart. 
 
 Just below 6 in the head of Pegasus (Plate IX.) are three stars 
 of the third and fourth magnitudes, forming a small arc. These 
 mark the urn of Aquarius, the Water-bearer. His body con- 
 sists of a trapezium of four stars of the third and fourth magni- 
 tudes. Small clusters of stars show the course of the water 
 flowing from his urn. 
 
 This stream enters the mouth of the Southern Fish, or Piscis 
 Australis. The only bright star in this constellation is Fomal- 
 haut, which is of the first magnitude, and at this time will be 
 low down in the southeast. 
 
 To the south of Aquarius is Capricornus, or the Goat. He 
 is marked by three pairs of stars arranged in a triangle. One 
 pair is in his head, another in his tail, and the third in his knees. 
 
APPENDIX. 327 
 
 Near Altair (Plate V.), and a little higher up, is a small-dia- 
 mond of stars forming the Dolphin, or Delphinus. 
 
 A little to the west of the Dolphin, in the Milky Way, are four 
 stars of the fourth magnitude, which form the constellation Sa- 
 gitta, or the Arrow. 
 
 4. Constellations visible in October. If we look at the 
 heavens at ight o'clock on the I5th of October, we shall see 
 that all the constellations described above have shifted some- 
 what towards the west. Arcturus and Antares have set. In the 
 east, below Andromeda (Plate X.), we see a pair of bright stars, 
 which are the only conspicuous ones in Aries, or the Ram. 
 
 About half-way between Aries and y Andromedae are three 
 stars which form a small triangle. This constellation is called 
 Triangulum, or the Triangle. 
 
 Between Aries and Pegasus is the constellation Pisces, or the 
 Fishes. The southernmost Fish may be recognized by a penta- 
 gon of small stars lying below the back of Pegasus. There are 
 no conspicuous stars in the other Fish, which is directly below 
 Andromeda. The stars in the band connecting the Fishes may 
 be traced with the help of the map. 
 
 5. Constellations visible in November. At eight o'clock in 
 the evening on the 15th of November, we see at a glance that 
 the constellations with which we have become acquainted have 
 moved yet farther to the westward. Bootes, the Crown, Ophi- 
 uchus, and the Archer have set ; Pegasus, Cassiopeia, and 
 Andromeda are overhead ; while new constellations appear in 
 the east. 
 
 We notice at once (Plate XL) a very bright star in the north- 
 east, directly below Perseus. This is Capella, or a Auriga. 
 There are five other conspicuous stars in Auriga, or the Chari- 
 oteer; and with Capella they form an irregular pentagon. 
 
 Somewhat to the eastward (Plate XII.), and a little lower 
 down, is a very bright red star. This is Aldebaran, or a Tauri. 
 It is familiarly known as the Bull's eye. It will be noticed by 
 the map that it is at one end of a V which forms the face of the 
 Bull. This group is known as the Hyades. Somewhat above 
 the Hyades is a smaller group, called the Pleiades, more com- 
 monly known as the Seven Stars, though few persons can dis- 
 tinguish more than six. The bright star on the northern horn, 
 
328 APPENDIX. 
 
 or /3 Tauri, is also in the foot of Auriga, and counts as y of that 
 constellation. 
 
 All the space between Taurus and the Southern Fish, and 
 below Aries and Pisces (Plate XIII.), is occupied by Cetus, the 
 Whale. The head is marked by a triangle of rather conspicu- 
 ous stars below Aries ; the tail, by a bright star of the second 
 magnitude, which is now just about as far above the horizon as 
 Fomalhaut. On the body are five stars, forming a sort of sickle. 
 About half-way between this sickle and the triangle, in the head, 
 is o Ceti, also called Mira, or the wonderful star (165). 
 
 6. Constellations visible in December. At eight o'clock in 
 the evening in the middle of December, we shall find that Her- 
 cules, Aquila, and Capricornus have sunk below the horizon ; 
 while Vega and the Swan are on the point of setting. The 
 Great Bear is climbing up in the northeast. In the east we be- 
 hold by far the most brilliant group of constellations we have 
 yet seen. Capella and Aldebaran are now high up ; and below 
 the former (Plate XII.) is the splendid constellation of Orion. 
 His belt t made up of three stars in a straight line, will be recog- 
 nized at once. Above this, on one shoulder, is a star of the first 
 magnitude, called Betelgeuse, or a Orionis. About as far from 
 the belt, on the other side, is another star of the first magnitude, 
 called Rigel. There are two other fainter stars which form a 
 large trapezium with Betelgeuse and Rigel. The three small 
 stars below the belt are upon the sword. 
 
 Below Orion (Plate XIV.) is a small trapezium of stars which 
 are in the constellation of Lepus, or the Hare. The head is 
 marked by a small triangle, as seen on the map. 
 
 To the north of Orion, and a little lower down (Plate XII.), 
 are two bright stars near together, one of the first and the other 
 of the second magnitude. The latter is caJled Castor, and the 
 former Pollux. They are in the constellation Gemini, or the 
 Twins. A line of three smaller stars just in the edge of the 
 Milky Way marks the feet, and another line of three the knees. 
 Pollux forms a large triangle with Capella and Betelgeuse. 
 
 7. Constellations visible in January. At eight in the even- 
 ing on the 1 5th of January, Vega, Altair, the Dolphin, Aquarius 
 and Fomalhaut have disappeared in the west ; Deneb and the 
 Square of Pegasus are near the horizon j while Capella and 
 
APPENDIX. 329 
 
 Aldebaran are nearly overhead. Two stars of exceeding bril- 
 liancy have come, up in the west. The one farthest to the 
 south (Plate XIV.) is the brightest star in the whole heavens. 
 It is called Sirius, or the Dog-star ; and is in the constellation 
 of Cam's Major, or the Great Dog, which can be readily traced 
 by the lines on the map. 
 
 The other bright star is between Sirius and Pollux (Plate 
 XII.), and is called Procyon. It is in Cam's Minor, or the Lit- 
 tle Dog. The only other prominent star in this constellation is 
 one of the third magnitude near Procyon. 
 
 Procyon, Sirius, and Betelgeuse form a large equilateral 
 triangle. 
 
 Orion and the group of constellations about it constitute by 
 far the most brilliant portion of the heavens, as seen in our lat- 
 itude. There are, in all, but about twenty stars of the first mag- 
 nitude, and seven of these are in this immediate vicinity. 
 
 8. Constellations visible in February. If we look at the 
 heavens at the same time in the evening about the middle of 
 February, we shall miss Cygnus and Pegasus from the west. 
 Auriga and Orion are nearly overhead. 
 
 Southeast of the Great Bear (Plate XV.) is a red star of the 
 first magnitude, called Regulus, in the constellation of Leo, or 
 the Lion. There are five stars near Regulus, which together 
 with it form a group often called the Sickle. The star in the 
 tail is Denebola, which makes a right-angled triangle with two 
 others near it. 
 
 Between Leo and Gemini is the constellation Cancer, or the 
 Crab. It contains no bright stars, but a remarkable cluster of 
 small stars called Prasepe, or sometimes the Beehive. 
 
 Below Regulus (Plate XIV.) is a bright red star of the second 
 magnitude, called Cor Hydra, or the Hydra's Heart. The head 
 of Hydra is marked by five small stars. The coils of the mon- 
 ster can be traced by the map. A portion of the constellation 
 is on Plate XVI. 
 
 9. Constellations visible in March. At the middle of 
 March, the heavens will have shifted round somewhat towards 
 the west ; but all the conspicuous constellations of the preced- 
 ing month are still visible, while no new ones at all brilliant 
 have come into view. 
 
330 APPENDIX. 
 
 If we draw a line from the end of the Great Bear's tail to 
 Denebola, it will pass through two constellations, Canes Ve- 
 natici, mentioned above ; and Coma Berenices, or Berenice's 
 Hair, a large cluster of faint stars (Plate XV.). 
 
 10. Constellations "visible in April. At the middle of April, 
 Aries and Andromeda have set ; Taurus, Orion, and Canis 
 Major are sinking towards the west ; the Great Bear and the 
 Lion are overhead ; Arcturus has risen in the northeast (Plate 
 XVI.) ; and some way to the south of this is seen a star of the 
 first magnitude, which forms a large triangle with Arcturus and 
 Denebola. It is called Spica Virginis, and is the chief star in 
 the constellation Virgo, or the Virgin. The stars on the breast 
 and wings can be found with the aid of the map. 
 
 South of Virgo is a trapezium of four stars, which are in the 
 constellation of Corvus, or the Crow. 
 
 11. Constellations "visible in May. At the middle of May, 
 Taurus, Orion, and Canis Major have set ; Vega has just come 
 up in the northeast ; and between Vega and Arcturus we again 
 see Hercules and Corona. Below Spica are two stars of the 
 second magnitude, belonging to the constellation Libra, or the 
 Balance. A star of the fourth magnitude forms a triangle 
 with these, and marks one pan of the balance (Plate VII.). 
 
 12. Constellations visible in June.\n. June we shall find 
 that Canis Minor, Perseus, Auriga, and Gemini have either set, 
 or are on the point of setting ; Arcturus is overhead; Cygnus 
 and Aquila are just rising. Ophiuchus is well up ; and low in 
 the southeast we see again the red star Antares, in the constel- 
 lation Scorpio, or the Scorpion (Plate VI.). There is a star of 
 the third magnitude on each side of Antares, and several stars 
 of the third and fourth magnitudes in the head and claws. The 
 configuration of these stars is much like a boy's kite with a long 
 tail. Scorpio is a very brilliant constellation, and is seen to bet- 
 ter advantage in July and August. 
 
 13. Constellations visible in July and August. We have 
 now described all the important constellations visible in our lat- 
 itude. Those which are seen in July and August are mainly 
 those described under the last two or three months, and under 
 September. 
 
 14. Southern Circumpolar Constellations. There are a 
 
APPENDIX. 
 
 331 
 
 number of constellations near the South Pole of the heavens 
 which never rise in our latitude, just as there are some near 
 the North Pole which never set. These are called the soiith- 
 ern circumpolar constellations , and are shown in Plate XVII. 
 
 CONSTELLATIONS VISIBLE EACH MONTH. 
 
 ffi^^ THE following table gives the constellations visible at 8 o'clock in the even- 
 ing, about the middle of each month. The stars opposite the names of the constel- 
 lations indicate those visible in the month designated at the top. 
 
 Name of 
 Constellation. 
 
 ex 
 <u 
 C/2 
 
 o 
 
 o 
 
 g 
 
 6 
 
 S 
 
 1 
 
 A 
 
 & 
 
 N 
 
 "C 
 
 ex 
 
 < 
 
 t^, 
 
 rt 
 
 ^ 
 
 <u 
 
 3 
 > 
 
 >-, 
 
 "3 
 
 *> 
 
 < 
 
 Bootes 
 
 * 
 
 
 
 
 
 
 
 * 
 
 * 
 
 * 
 
 * 
 
 
 Corona Borealis 
 
 * 
 
 * 
 
 
 
 
 
 
 
 * 
 
 * 
 
 * 
 
 
 Ophiuchus 
 
 * 
 
 
 
 
 
 
 
 
 
 * 
 
 
 
 Sagittarius 
 
 * 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 Hercules 
 
 * 
 
 
 
 
 
 
 
 
 * 
 
 * 
 
 
 
 Lyra 
 
 * 
 
 
 * 
 
 
 
 
 
 
 
 * 
 
 
 
 Aquila 
 
 * 
 
 
 
 
 
 
 
 
 
 
 
 
 Delphinus 
 
 * 
 
 
 
 
 
 
 
 
 
 
 
 
 Capricornus 
 
 * 
 
 
 
 
 
 
 
 
 
 
 
 
 Cygnus 
 
 # 
 
 
 
 * 
 
 
 
 
 
 
 * 
 
 * 
 
 
 Sagitta 
 
 * 
 
 
 
 
 
 
 
 
 
 
 * 
 
 
 Aquarius 
 
 * 
 
 
 
 * 
 
 
 
 
 
 
 
 
 
 Piscis Australis 
 
 * 
 
 
 
 * 
 
 
 
 
 
 
 
 
 
 Pegasus 
 
 * 
 
 
 
 
 * 
 
 
 
 
 
 
 
 
 Andromeda 
 
 * 
 
 
 
 
 * 
 
 * 
 
 * 
 
 
 
 
 
 
 Perseus 
 
 # 
 
 
 
 
 * 
 
 * 
 
 
 
 # 
 
 
 
 
 
 Aries 
 
 
 
 
 
 * 
 
 # 
 
 * 
 
 
 
 
 
 
 Pisces 
 
 
 
 
 
 * 
 
 
 
 
 
 
 
 
 Cetus 
 
 
 
 
 
 * 
 
 * 
 
 
 
 
 
 
 
 Triangulum 
 
 
 
 * 
 
 
 * 
 
 # 
 
 * 
 
 
 
 
 
 
 Auriga 
 
 
 
 * 
 
 * 
 
 # 
 
 * 
 
 * 
 
 * 
 
 * 
 
 
 
 
 Taurus 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Lepus 
 
 
 
 
 * 
 
 * 
 
 * 
 
 
 
 
 
 
 
 Orion 
 
 
 
 
 * 
 
 * 
 
 # 
 
 
 * 
 
 
 
 
 
 Gemini 
 
 
 
 
 # 
 
 * 
 
 * 
 
 
 
 
 * 
 
 
 
 
 Canis Major 
 
 
 
 
 
 # 
 
 * 
 
 
 * 
 
 
 
 
 
 " Minor 
 
 
 
 
 
 # 
 
 # 
 
 
 * 
 
 * 
 
 
 
 
 Cancer 
 
 
 
 
 
 
 * 
 
 
 * 
 
 * 
 
 * 
 
 
 
 Hydra 
 
 
 
 
 
 
 * 
 
 
 * 
 
 # 
 
 * 
 
 
 
 Leo 
 
 
 
 
 
 
 * 
 
 
 * 
 
 * 
 
 * 
 
 * 
 
 
 Coma Berenices 
 
 
 
 
 
 
 
 * 
 
 * 
 
 * 
 
 * 
 
 * 
 
 * 
 
 Canes Venatici 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Virgo 
 
 
 
 
 
 
 
 
 * 
 
 * 
 
 *- 
 
 * 
 
 * 
 
 Corvus 
 
 
 
 
 
 
 
 
 * 
 
 * 
 
 * 
 
 * 
 
 
 Libra 
 
 
 
 
 
 
 
 
 
 * 
 
 * 
 
 * 
 
 * 
 
 Scorpio 
 
 
 
 
 
 
 
 
 
 
 * 
 
 * 
 
 * 
 
332 APPENDIX. 
 
 The following are the circiunpolar constellations which are 
 visible all the year round: Ursa Major, Ursa Minor, Draco, 
 Cassiopeia, and Cepheus. 
 
 STARS OF THE FIRST MAGNITUDE. 
 
 THE following is a list of the stars of the first magnitude, in 
 the order of their brightness : 
 
 1. Sirius, or a Canis Majoris. 
 
 2. 17 Argus ((variable}. 
 
 3. Canopus, or a Argus. 
 
 4. a Centauri. 
 
 5. Arcturus, or a Bootis. 
 
 6. Rigel, or /? Orionis. 
 
 7. Capella, or a Aurigae. 
 
 8. Vega, or a Lyrae. 
 
 9. Procyon, or a CanisJVlinoris. 
 10. Betelgeuse, or a Orionis. 
 
 11. Achernar, or a Eridani. 
 
 12. Aldebaran, or a Tauri. 
 
 13. (t Centauri. 
 
 14. a Crucis. 
 
 15. Antares, or u Scorpionis. 
 
 16. Altair, or a Aquilae. 
 
 17. Spica, or a Virginis. 
 
 1 8. Fomalhaut, or a Piscis Australis. 
 
 19. /? Crucis. 
 
 20. Pollux, or /* Geminorum. 
 
 Some astronomers admit into this class only the first sev- 
 enteen of the above list. Others add to the list Regulus, or 
 a Leonis ; others, a Ursse Majoris and a Andromedas. 
 
 THE HISTORY OF THE CONSTELLATIONS. 
 
 THE question with respect to the time when the stars were 
 first grouped into constellations has been much discussed, but 
 cannot be said to have been settled. Some writers believe 
 that the earliest division of the starry sphere into such figures 
 dates back to fourteen hundred years before the Christian 
 era; but the most ancient reference to them in literature is in 
 Homer and Hesiod, some seven hundred and fifty or eight hun- 
 dred and fifty years before Christ. These poets mention only 
 a few of the more marked stars and asterisms, as Arcturus, 
 Sirius, the Pleiades, the Hyades, Orion, and the Bear. There 
 are references to certain stars or groups of stars in the Bible, 
 Job ix. 9, xxvi. 13, xxxviii. 31, 32; Amos v. 8; but they are 
 probably not more ancient than those in the Greek poets, and 
 the translation of the passages is a matter of dispute. 
 
APPENDIX. 333 
 
 It is pretty certain that nearly four hundred years before 
 Christ all the leading constellations had been formed ; for 
 about that time Eudoxus, of Cnidus, wrote an account of them, 
 which would appear to have become quite a popular work. It 
 has not come down to our day, but we know that it was the 
 basis of the famous " Phaenomena '* of Aratus, written about 
 270 B. C. This was the first attempt, so far as we know, to 
 describe in verse the groups and motions of the stars, and, 
 though it was by no means free from mistakes, it was received 
 with the highest favor, and has been famous even down to our 
 own day. It was translated and praised by Ovid, by Cicero, 
 and by Germanicus. Manilius drew from it in the preparation 
 of his Astronomica^ and Virgil himself borrowed from it in his 
 Georgics. 
 
 Ptolemy, about 140 A. D., enumerates forty-eight constel- 
 lations, twenty-one northern, twelve zodiacal, and fifteen 
 southern. We have described all the northern, except Equu- 
 leus, the Little Horse, which contains only ten stars, all below 
 the third magnitude, between the head of Pegasus and the 
 Dolphin. 
 
 The twelve zodiacal constellations are Aries, Taurus, Gem- 
 ini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricor- 
 nus, Aquarius, and Pisces. They are situated along the line 
 of the zodiac (page 187), and have all been described above. 
 
 Of the fifteen south of the zodiac, we have mentioned eight. 
 The others are Eridanus, Argo Navis, Crater, Centaurus, Lu- 
 pus, Ara, and Corona A us trails. 
 
 Eridanus, or the River Po, winds in an irregular stream 
 through some 130 of the heavens. The portion of it which is 
 visible in the latitude of Boston lies between Orion and Cetus. 
 
 Argo Navis, or the Ship Argo, is one of the largest and most 
 brilliant of the southern constellations. It contains two stars 
 of the first magnitude, four of the second, and nine of the third. 
 Only a small part of it, containing none of the brightest stars, 
 rises above the horizon in our latitude. 
 
 Crater, or the Cup, is on the back of Hydra, south of the 
 hind feet of Leo. It is made up of a few stars, only one of 
 which rises to the third magnitude. 
 
 Centaurus, or the Centaur, is a large and conspicuous con- 
 
334 APPENDIX. 
 
 stellation, but none of its brighter stars are visible in our lat- 
 itude. 
 
 Ara, or the Altar, does not rise above our horizon. 
 
 Lttptts, or the Wolf, is directly south of Scorpio. It con- 
 tains no conspicuous stars. 
 
 Corona Australis, or the Southern Crown, is a small group 
 of stars, only one of which is equal to the fourth magnitude, 
 between the fore legs of Sagittarius and the Milky Way. 
 
 Of the constellations described by us, two are modern, 
 Coma Berenices, added by Tycho de Brahe, about 1603, and 
 Canes Venatici, by Hevelius, in 1690. Fifty or sixty more 
 have been added from time to time, some of which have been 
 rejected by modern uranographers. 
 
 The ancient constellations include all the brighter stars in 
 the heavens, except in a small region about the south pole. 
 The later ones are mainly made up of the small stars not in- 
 cluded in these early asterisms, and, with very few exceptions, 
 are not worth tracing. 
 
 THE MYTHOLOGY OF THE CONSTELLATIONS. 
 
 To the Greeks the starry heavens were an illustrated mytho- 
 logical poem. Every constellation was a picture, connected 
 with some old fable of gods or heroes. We shall give a brief 
 sketch of the more important of these myths, with a few out 
 of the many allusions to them in ancient and modern poetry. 
 
 The two Bears have one story. Callisto was a nymph be- 
 loved by Jupiter, who changed her into a she-bear to save her 
 from the jealous wrath of Juno. But Juno learned the truth, 
 and induced Diana to kill the bear in the chase. Jupiter then 
 placed her among the stars as Ursa Major, and her son Areas 
 afterwards became Ursa Minor. Juno, indignant at the honor 
 thus shown the objects of her hatred, persuaded Tethys and 
 Oceanus to forbid the Bears to descend, like the other stars, 
 into the sea. Hence, Virgil speaks of the Bears as " Oceani 
 metuentes aequore tingi"; and Ovid, as "liquidique immunia 
 ponti." 
 
 According to Ovid, Juno changed Callisto into a bear ; and 
 
APPENDIX. 335 
 
 when Areas, in hunting, was about to kill his mother, Jupiter 
 placed both among the stars. 
 
 Ursa Minor was also called Phcenice, because the Phoenicians 
 made it th-eir guide in navigation, while the Greeks preferred 
 the Great Bear for that purpose. It was also known as Cy no- 
 sura (dog's tail} from its resemblance to the upturned curl of 
 a dog's tail. The Great Bear was sometimes called Helice 
 (winding), either from its shape or its curved path. Ovid says, 
 as Aratus had said before him, 
 
 " Esse cluas Arctos ; quarum Cynosura petatur 
 Sidoniis, Helicen Graia carina notet." 
 
 Bootes (the Herdsman} was also called Arctophylax and Arc- 
 furtts, both of which names mean the guard or keeper of the 
 bear. According to some of the stories, Bootes was Areas ; 
 according to others, he was Icarus, the unfortunate son of 
 Daedalus. The name Arcturus was afterwards given to the 
 chief star of the constellation. 
 
 Cepheus, Cassiopeia, Andromeda, Perseus, and Pegasus are a 
 group of star-pictures illustrating a single story. 
 
 Cepheus and Cassiopeia were the king and queen of Ethi- 
 opia, and had a very beautiful daughter, Andromeda. Her 
 mother boasted that the maiden was fairer than the Nereids, 
 who in their anger persuaded Neptune to send a sea-monster 
 to ravage the snores of Ethiopia. To appease the offended 
 deities Andromeda, by the command of an oracle, was exposed 
 to this monster. The hero Perseus rescued her and married 
 her. 
 
 Milton, in // Penseroso, alludes to Cassiopeia as 
 
 " that starred Ethiop queen that strove 
 To set her beauty's praise above 
 The Sea-Nymphs, and their powers offended." 
 
 According to one form of the story, it was her own beauty, and 
 not her daughter's, of which the "Ethiop queen " boasted. 
 
 Pegasus, the winged horse, sprang from the blood of the 
 frightful Gorgon, Medusa, whom Perseus had slain not long 
 before he rescued Andromeda from the sea-monster. Accord- 
 ing to the most ancient account, Pegasus became the horse 
 of Jupiter, for whom he carried the thunder and IH 
 
336 APPENDIX. 
 
 but he afterward came to be considered the horse of Aurora, 
 and finally of the Muses. Modern poets rarely speak of him 
 except as connected with the Muses. 
 
 The Dragon, according to some of the poets, was the one 
 that guarded the golden apples of the Hesperides ; according 
 to others, the monster sacred to Mars which Cadmus killed in 
 Boeotia. 
 
 Virgil describes the dragon thus (G. i. 244) : 
 
 " Maximus hie flexu sinuoso elabitur Anguis 
 Circum perque duas, in morem fluminis, Arctos." 
 
 The Lyre is said to be the one which Apollo gave to Orpheus. 
 After the death of Orpheus, Jupiter placed it among the stars 
 at the intercession of Apollo and the Muses. 
 
 The Crown was the bridal gift of Bacchus to Ariadne, trans- 
 ferred to the heavens after her death. Virgil speaks of it (G. i. 
 222) as " Gnosia stella Coronae," referring to the Cretan birth 
 of Ariadne. Ovid also calls it (Fasti, iii. 457) "Coronam Gno- 
 sida." Spenser refers to it as follows : 
 
 " Look how the crown which Ariadne wore 
 Upon her ivory forehead that same day 
 That Theseus her unto his bridal bore, 
 When the bold Centaurs made that bloody fray 
 With the fierce Lapiths which did them dismay, 
 Being now placed in the firmament, 
 Through the bright heaven doth her beams display, 
 And is unto the stars an ornament, 
 Which round about her move in order excellent." 
 
 Hercules is spoken of by Aratus as 
 
 " An Image none knows certainly to name, 
 Nor what he labors for " ; 
 
 and again, in another part of the poem, as " the inexplicable 
 Image." Ptolemy refers to it in somewhat the same way. 
 Manilius calls it "ignota fades." When the name Hercules 
 was given to it would appear to be uncertain. 
 
 Aquila fs probably the eagle into which Merops was changed. 
 It was placed among the stars by Juno. Some, however, make 
 it the Eagle of Jupiter.. 
 
APPENDIX. 337 
 
 Cygnus or Cycnus, according to Ovid, was a relative of 
 Phaethon. While lamenting the unhappy fate of his kinsman 
 on the banks of the Eridanus, he was changed by Apollo into a 
 swan, and placed among the stars. 
 
 Sagittarius was said by the Greeks to be the Centaur 
 Cheiron, the instructor of Peleus, Achilles, and Diomed. It 
 is pretty certain, however, that all the zodiacal constellations 
 are of Egyptian origin, and represent twelve Egyptian dei- 
 ties who presided over the months of the year. Thus Aries 
 was Jupiter Ammon ; Taurus, the bull Apis ; Gemini, the in- 
 separable gods Horus and Harpocrates ; and so on. The 
 Greeks adopted the figures, and invented stones of their own 
 to explain them. 
 
 Scorpio, in the Egyptian zodiac, represented the monster 
 Typhon. Originally this constellation extended also over the 
 space now filled by Libra. Thus Ovid (Met. ii. 195) says : 
 
 " Est locus, in geminos ubi brachia concavat arcus 
 Scorpios, et cauda flexisque utrimque lacertis 
 Porrigit in spatium signorum membra duorum" 
 
 Virgil also (G. i. 33) suggests that the deified Augustus may 
 find a place among the stars, 
 
 " Qua locus Erigonen inter Chelasque sequentes 
 
 Panclitur." 
 
 Erigone is Virgo, and Chela are the claws of the Scorpion. 
 The poet goes on to picture the Scorpion as drawing himself 
 into narrower space, to make room for the new-comer: 
 
 " Ipse tibi jam brachia contrahit ardens 
 Scorpios, et caeli justa plus parte reliquit." 
 
 Ophiuchus represents /Esculapius, the god pf medicine. Ser- 
 pents were sacred to him, " probably because they were a sym- 
 bol of prudence and renovation, and were believed to have the 
 power of discovering herbs of wondrous powers." 
 
 Milton (P. L. ii. 709) speaks of 
 
 " the length of Ophiuchus huge 
 In the arctic sky." 
 
 Aquarius, in Greek fable, was Ganymede, the Phrygian 
 boy who became the cup-bearer of the gods in place of Hebe. 
 15 v 
 
338 APPENDIX. 
 
 Capricornus, the god Mendes in the Egyptian zodiac, is the 
 subject of several Greek fables not worth recounting. 
 
 There are various stories also with regard to Auriga. The 
 star Capella takes its name from the goat which he bears on 
 his shoulder. Aratus says (Dr. Frothingham's translation): 
 
 " On his left shoulder rests 
 The sacred Goat, said to have suckled Jove ; 
 Olenian Goat of Jove the priests have named her." 
 
 So Ovid (Fasti v. 112): 
 
 " Nascitur Oleniae signum pluviale Capellae." 
 
 Taurus, as has been staled above, was the Egyptian Apis. 
 The Greeks made it the bull which carried off Europa. The 
 Pleiades are usually called the daughters of Atlas, whence their 
 name Atlantides. Milton (P. L. x. 673) speaks of them as " the 
 seven Atlantic Sisters." The idea that only six of the seven 
 can be seen is very ancient. Aratus says : 
 
 " As seven their fame is on the tongues of men, 
 Though six alone are beaming on the eye." 
 
 And Ovid (Fasti iv. 167) : 
 
 " Quae septem diet, sex tamen esse solent." 
 
 According to one legend the seventh was Sterope, who be- 
 came invisible because she had loved a mortal ; according to 
 another, her name was Electra, and she left her place that she 
 might not witness the downfall o/ Troy, which was founded by 
 her son, Dardanus. Tennyson, in Locksley Hall, alludes to the 
 Pleiades : 
 
 " Many a night I saw the Pleiads, rising through the mellow shade, 
 Glitter like a swarm of fire-flies tangled in a silver braid." 
 
 The H jades, according to one of several stories, were sisters 
 of the Pleiades. The name probably means the Rainy, since 
 their heliacal rising announced wet weather. Hence Virgil 
 speaks of them -as pluviae, and Horace as tristes. 
 
 Cetus is said by most writers to be the sea-monster from 
 which Perseus rescued Andromeda. 
 
 Orion was a famous giant and hunter, who loved the daughter 
 of CEnopion, King of Chios. As her father was slow to con- 
 
APPENDIX. 339 
 
 sent to her marriage, Orion attempted to carry off the maiden ; 
 whereupon (Enopion, with the help of Bacchus, put out his 
 eyes. But the hero, in obedience to an oracle, exposed his 
 eye-balls to the rays of the rising sun, and thus regained his 
 sight. The accounts of his subsequent life, and of his death, 
 are various and conflicting. According to some, Aurora loved 
 him and carried him off; but, as the gods were angry at this, 
 Diana killed him with an arrow. Others say that Diana loved 
 him, and that Apollo, indignant at his sister's affection for the 
 hero, once pointed out a distant object on the surface of the 
 sea, and challenged her to hit it. It was the head of Orion 
 swimming, and the unerring shot of the goddess pierced it with 
 a fatal wound. Another fable asserts that Orion boasted that 
 he would conquer every animal; but the earth sent forth a 
 scorpion which destroyed him. 
 Aratus alludes to the brilliancy of this constellation : 
 
 " What eye can pass him over, 
 Spreading aloft in the clear night ? Him first 
 Whoever scans the heavens is sure to trace." 
 
 And again he speaks of him as 
 
 " In nothing mean, glittering in belt and shoulders, 
 And trusting in the might of his good sword." 
 
 Ovid calls him " ensiger Orion," and Virgil describes him as 
 "armatum auro." We have a vivid picture of him in Long- 
 fellow's " Occultation of Orion " : 
 
 " Begirt with many a blazing star, 
 Stood the great giant Algebar, 
 Orion, hunter of the beast ! 
 His sword hung gleaming by his side, 
 And, on his arm, the lion's hide 
 Scattered across the midnight air 
 The golden radiance of its hair." 
 
 Cants Major and Minor are the dogs of Orion, and are pur- 
 suing the Hare. 
 
 The Twins, Castor and Pollux, the sons of Jupiter and Leda, 
 are the theme of many a fable. They were especially worshipped 
 as the protectors of those who sailed the seas, for Neptune had 
 
34 APPENDIX. 
 
 rewarded their brotherly love by giving them power over winds 
 and waves, that they might assist the shipwrecked. 
 
 Leo, according to the Greek story, was the famous Nemean 
 lion slain by Hercules. Jupiter placed it in the heavens in 
 honor of the exploit. 
 
 The Hydra also commemorates one of the twelve labors of 
 Hercules, the destruction of the hundred-headed monster of 
 the Lernsean lake. 
 
 Virgo represents Astraea, the goddess of innocence and 
 purity, or, as some say, of justice. She was the last of the 
 gods to withdraw from earth at the close of " the golden age." 
 Aratus thus speaks of her : 
 
 " Once on earth 
 
 She made abode, and deigned to dwell with mortals. 
 In those old times, never of men or dames 
 She shunned the converse ; but sat with the rest, 
 Immortal as she was. They called her Justice. 
 Gathering the elders in the public forum, 
 Or in the open highway, earnestly 
 She chanted forth laws for the general weal." 
 
 But when the age became degenerate, 
 
 " Justice then, hating that generation, 
 Flew heavenward, and inhabited that spot 
 Where now at night may still be seen the Virgin." 
 
 Libra, or the Balance, is the emblem of justice, and is usually 
 associated with the fable of Astraea. 
 
 Argo Navis is the famous ship in which Jason and his com- 
 panions sailed to find the Golden Fleece. 
 
 This slight sketch of the leading fables connected with the 
 constellations will serve to show how completely the Greeks 
 "nationalized the heavens." There have been various at- 
 tempts to change into Christian titles the whole nomenclature 
 of the skies. Julius Schiller, in 1627, urged such a revolution 
 in his Coelum Stellatum Christianum, as Bartsch and others 
 had done before him. According to these reformers of the 
 heavens, the Great Bear becomes the skiff of St. Peter ; Cas- 
 siopeia, Mary Magdalene; and Perseus with Medusa's head, 
 David with the head of Goliath. The cross in the Swan is the 
 
APPENDIX. 341 
 
 Holy Cross ; the Virgin is Mary ; and the Water-bearer, John 
 the Baptist. 
 
 In the seventeenth century Weigel, a professor in the Uni- 
 versity of Jena, proposed the formation of a collection of he- 
 raldic constellations. In the zodiac he wished to place the 
 escutcheons of the twelve most illustrious houses of Europe ; 
 and Orion, Auriga, and other leading asterisms were metamor- 
 phosed in the same way. 
 
 Sir John Herschel says : " The constellations seem to have 
 been almost purposely named and delineated to cause as much 
 confusion and inconvenience as possible. Innumerable snakes 
 twine through long and contorted areas of the heavens, where 
 no memory can follow them. Bears, lions, and fishes, small 
 and large, northern and southern, confuse all nomenclature. 
 A better system of constellations might have been a material 
 help as an artificial memory." 
 
 But the habits of four thousand years are not easily changed. 
 Men will still 
 
 " Hold to the fair illusions of old time, 
 Illusions that shed brightness over life, 
 And glory over nature " ; 
 
 and the starry heavens will continue to be for ages to come, 
 as they have been for ages gone by, a picture-book of Greek 
 fable. 
 
QUESTIONS FOR REVIEW AND 
 EXAMINATION. 
 
 MOTIONS AND DISTANCES OF THE HEAVENLY 
 BODIES. 
 
 I. WHAT was the earth once thought to be ? 2. What is 
 the shape of the earth now known to be ? 3. How is this 
 shown by observation of ships at sea? 4. How by the ob- 
 servation of the eclipses of the moon ? 5. How do we know 
 that the sun, moon, and planets are all globes ? 6. What is 
 known of the shape of the stars ? 7. How do the stars rise 
 and set ? 8. What are circumpolar stars ? 9. What is true 
 of the motion of the Polar Star ? 10. What is true of the 
 motion of the stars as we go from the Polar Star? n. How 
 do we know that the stars describe accurate circles about the 
 Polar Star as a centre ? 12. How do we know that the stars 
 move at a uniform rate, and all describe their circles in the 
 same time ? 13. How do we detect the existence of atmos- 
 pheric refraction ? 14. What is the effect of refraction upon 
 all the heavenly bodies ? 15. Explain this effect ? 16. 
 Prove that the earth rotates from west to east in 24 hours ? 
 17. Do the heavens really rotate about the earth from east 
 to west? 18. How do we know this? 19. State the direc- 
 tion of the circles described by the stars, as compared with 
 that of the horizon in different parts of .the earth ? 20. Do 
 the stars as seen in different parts of the earth describe cir- 
 cles which really have different directions ? 21. Show by an 
 illustration that two co-ordinates are sufficient to define the 
 position of a point on a plane surface ? 22. What two co-or- 
 dinates serve to define the position of a point on the sur- 
 face of a globe ? 23. Show that these co-ordinates will serve 
 to define the position of such a point ? 24. What are the 
 most convenient co-ordinates of a star ? 25. Which of these 
 
344 QUESTIONS FOR REVIEW AND EXAMINATION. 
 
 co-ordinates is measured by means of the transit instrument ? 
 26. Explain the adjustment of this instrument. 27. Explain 
 how one of the co-ordinates of a star is measured with it. 
 28. What is a sidereal day? 29. Describe the mural circle. 
 
 30. Explain how the horizontal reading of the circle is found. 
 
 31. Explain how the altitude of the celestial pole is found. 
 
 32. Which co-ordinate of a heavenly body is found by the 
 mural circle ? 33. Explain how. 34. Do the fixed stars ap- 
 pear in exactly the same position in the heavens, from what- 
 ever part of the earth they are observed ? 35. How do we 
 know ? 36. What is the solar day ? 37. How is its length 
 found, and h6w does it compare with that of the sidereal clay ? 
 38. What does the difference of length of these two days 
 show as to one of the co-ordinates of the sun ? 39. By what 
 other observation is this same thing shown ? 40. What is a 
 sidereal year? 41. How do the solar days compare with one 
 another in length ? 42. Why is ordinary clock time called 
 mean time ? 43. What is the ecliptic ? 44. What is the in- 
 clination of the ecliptic to the earth's axis ? 45. What belt 
 of the earth is called the torrid zone ? 46. What belts are 
 called the frigid zones ? 47. What belts are called the temper- 
 ate zones ? 48. What is true of the sun's coming directly 
 overhead, and of its rising and setting in each of these zones ? 
 49. Explain the changes in the relative lengths of day and 
 night. 50. Explain the change of seasons. 51. What is the ce- 
 lestial equator ? 52. Explain declination and right ascension. 
 53. What are the equinoxes ? 54. What is the precession of 
 the equinoxes ? 55. What is the tropical year? 56. How does 
 it compare with the sidereal year ? 57. Which is the year 
 of common life ? 58. What are the solstices ? 59. What does 
 the variation of the sun's apparent diameter prove ? 60. How 
 can the form of the path descried by the sun among the stars 
 be found? 61. What kind of a curve is it? 62. To what 
 does the inclination of the earth's axis to the ecliptic give 
 rise? 63. What is twilight? 64. What causes it? 65. It 
 continues while the sun is within what distance of the hori- 
 zon ? 66. When and where is twilight shortest ? 67. Explain 
 why this is so. 68. In the latitude of Boston how does the 
 twilight in the summer compare with that in the winter ? 
 
QUESTIONS FOR REVIEW AND EXAMINATION. 345 
 
 69. Explain why it is so. 70. Where is the new moon always 
 seen ? 71. What is her motion? 72. When is the moon in 
 conjunction ? 73. When in opposition ? 74. What is true of 
 the moon's declination ? 75. What are the moon's nodes ? 
 76. What is a lunar day, and how does it compare with the 
 solar day ? 77. How do lunar days compare with one another ? 
 78. What is the moon's orbit, and how can it be found ? 79. 
 What is meant by the moon's being in perigee ? 80. What by 
 her being in apogee? 81. What is the line of apsides ? 82. 
 Describe the apparent motion of Venus. 83. The apparent 
 motion of Mercury. 84. Why are these bodies called plan- 
 ets ? 85. What is meant by the greatest elongation of these 
 planets ? 86. Describe the apparent motion of the other plan- 
 ets. 87. How did the ancients attempt to explain the ap- 
 parent irregular motion of the planets ? 88. Give an account 
 of the Ptolemaic system. 89. Explain what is meant by 
 cycles, epicycles, and deferents. 90. What change did Tycho 
 de Brahe introduce into this system? 91. How was this sys- 
 tem further modified by Copernicus ? 92. Did he dispense with 
 epicycles and deferents in his system.? 93. What three facts 
 did Kepler discover about the planetary motions ? 94. Give 
 an account of the method by which he discovered these facts. 
 95. Whose observations did he make use of? 96. What is the 
 sidereal period of a planet ? 97. What is the synodical period 
 of a planet ? 98. How is the sidereal period of the earth 
 found ? 99. How is the synodical period of a planet found ? 
 100. What planets can be in inferior and superior conjunc- 
 tion ? 101. What planets have conjunctions and oppositions? 
 102. What must be known in order to compute the sidereal 
 period of a planet ? 103. Find the sidereal period of an 
 inferior planet. 104. Find the sidereal period of a superior 
 planet. 105. What must be observed in order to find the rel- 
 ative distance of an inferior planet from the sun ? 106. Find 
 the relative distance of an inferior planet from the sun. 
 107. What must be observed in order to find the relative dis- 
 tance of a superior planet from the sun ? 108. Find the rela- 
 tive distance of a superior planet from the sun. 109. When 
 the relative distances of the planets from the sun are known, 
 what must be found in order to ascertain their real distances 
 
346 QUESTIONS FOR REVIEW AND EXAMINATION, 
 
 from the sun? no. By means of what is the distance from 
 the earth to the sun found? in. Find the distance in miles 
 between the chords which two observers see Venus describe 
 across the sun's disc, supposing that we know the distance be- 
 tween the observers in miles. 112. What observation is ne- 
 cessary to find the length of the two chords in degrees and 
 minutes? 113. Explain how we find the length of these 
 chords in degrees and minutes, and of the radius of the sun. 
 114. Find the distance between these two chords in angular 
 measurement. 115. Find the angle which the radius of the 
 earth would subtend at the distance of the sun. 116. Know- 
 ing this angle, find the distance of the earth from the sun. 
 117. Explain how the length of the earth's radius can be 
 found. 1 1 8. Explain how we find what fraction of a whole 
 meridian the arc included between two places is. 119. Ex- 
 plain how we can find the distance between two points by 
 triangulation. 120. Give an account of the measurement of 
 a base line. 121. Why is so great care necessary in the meas- 
 urement of the base line? 122. Explain how a system of tri- 
 angles can be constructed between two points, and how their 
 parts can be computed. 123, Explain how the distance be- 
 tween the two points can be found after the system of triangles 
 has been constructed. 124. How do we know that the earth 
 is not an exact sphere ? 125. Is the exact distance from the 
 earth to the sun known ? 126. How can the real distance of 
 the planets from the sun be found, after their relative distance 
 and the distance of the earth is known ? 127. How did the 
 ancients find the distance of the moon from the earth approx- 
 imately ? 128. What is parallax? 129. Show that we real- 
 ly judge of the distances of ordinary objects by means of par- 
 allax. 130. In finding the parallax of the moon what takes 
 the place of the two eyes? 131. Explain how the difference 
 of direction of two telescopes, when pointed at the moon from 
 different parts of the earth, can be found by measuring the 
 moon's polar distance at each place. 132. Explain how the 
 moon's parallax is found when the difference of direction of 
 the telescopes is known. 133. Explain how this difference of 
 direction can be found by measuring at each place the distance 
 of the moon from a star near which she passes. 134. Why 
 
QUESTIONS FOR REVIEW AND EXAMINATION. 347 
 
 is the latter method preferable to the former? 135. Give a 
 general account of the orbits of the planets. 136. What are 
 nodes ? 137. Explain why the transits of Venus occur so sel- 
 dom. 138. Explain how we estimate the distance of an ob- 
 ject by using only one eye. 139. What is found to be true 
 when a telescope is pointed to certain fixed stars at inter- 
 vals of six months ? 140. What is one way of finding whether 
 the direction of the telescope would be the same at both ob- 
 servatories ? 141. Explain precession. 142. What is nuta- 
 tion ? 143. What is aberration of light ? 144. What is its 
 effect upon the position of a star? 145- Explain the second 
 method of finding the parallax of a star. 146. What is true 
 of the distance of the stars ? 147. Name some of the re- 
 markable nebulae. 148. What has led astronomers to be- 
 lieve that many of the nebulae are systems of stars ? 149. 
 How did Herschel believe our sidereal system would ap- 
 pear at the distance of the nebulae? 150. What is true of 
 the motion of the planets and satellites of our solar system ? 
 151. Are the stars really fixed? 152. Show that our sun is 
 moving through space. 153. Give an example of a double 
 star. 154. What is the difference between a physically and 
 an optically double star ? 155. Give an account of Theta Ori- 
 onis. 156. Of Xi Ursae Majoris. 157. What is true of the 
 length of the periods of the binary stars ? 158. What, of the 
 dimensions of their orbits ? 159. Are the physically connect- 
 ed systems of stars numerous ? 160. Show that the sun is 
 a star. 161. What seems to be true of all the heavenly 
 bodies? 162. How do the velocities with which the stars 
 are moving compare with the earth's velocity in its orbit? 
 
 PHYSICAL FEATURES OF THE HEAVENLY BODIES. 
 
 163. Explain how we may find the diameter of the sun. 
 
 164. How does the sun compare with the earth in size ? 
 
 165. What are sun-spots ? 166. At what intervals are they 
 most frequent ? 167. Give an account of the movements of 
 these spots. 168. Show that these spots are not planets. 
 
 169. Show that the sun rotates on his axis in about 25 days. 
 
 170. Show that the sun's axis is not perpendicular to the 
 
34 8 QUESTIONS FOR REVIEW AND EXAMINATION. 
 
 ecliptic. 171. Describe the appearances of the spots. 172. What 
 are tne dimensions of the sun-spots ? 173. Give an account of 
 the changes which they undergo.- 174. Give an account of the 
 faculae. 175. Give an account of the "pores" and "willow 
 leaves." 176. Give an account of the corona. 177. Of the 
 rose-colored clouds. 178. What were Wilson's observations 
 and conclusions with reference to the sun-spots ? 179. What is 
 Herschel's theory of the sun-spots ? 180. Give some account 
 of the investigations of De La Rue, Stewart, and Loewy. 
 181. How have they shown that the faculae are elevations of the 
 sun's photosphere ? 182. What do they consider to be the na- 
 ture of the photosphere ? 183. What have they found to be the 
 usual position of the faculae? 184. How do they think the 
 spots and faculae are formed ? 185. How have they shown that 
 Venus and Jupiter have an influence on the formation of the 
 spots? 1 86. Why is Mercury seldom seen as a conspicuous 
 object? 187. What is the shape of his orbit? 188. What is 
 its inclination to the ecliptic? 189. How do we know that 
 Mercury is an exact sphere ? 190. How does the diameter of 
 Mercury compare with that of the earth? 191. Explain the 
 phases of Mercury. 192. Is there any evidence of the existence 
 of mountains on the planet ? 193. What led Schroter to think 
 that Mercury rotates on his axis in about 24 hours ? 194. What 
 did Schroter think to be the inclination of Mercury's axis to 
 the plane of his orbit ? 195. What led him to this conclusion ? 
 196. Give an account of Mercury's seasons on the supposition 
 that this inclination is correct. 197. Show that this planet has 
 an atmosphere. 198. What is the second planet from the sun. 
 199. What is the form of her orbit ? 200. How does her di- 
 ameter compare with that of the earth ? 201. By what names 
 is Venus familiarly known ? 202. Explain her phases. 203. In 
 what position is Venus most brilliant ? 204. What indicates 
 that there are mountains on Venus ? 205. According to Schro- 
 ter what is the period of her axial rotation ? 206. Has Venus 
 an atmosphere ? 207. Has she a moon ? 208. Give an ac- 
 count of the Zodiacal Light 209. What have been the suppo- 
 sitions with reference to the nature of this light? 210. What is 
 the third planet from the sun ? 211. What is the inclination of 
 its axis to the ecliptic? 212. What is its diameter? 213. By 
 
QUESTIONS FOR REVIEW AND EXAMINATION. 349 
 
 what is the earth attended ? 214. What is the interval between 
 two successive new moons ? 215. Give an account of the phases 
 of the moon. 216. Explain the moon's libration in longitude. 
 217. Explain her libration in latitude. 218. Explain her paral- 
 lactic libration. 219. Give an account of the earth's phases as 
 seen from the moon. 220. When does the moon appear 
 largest? 221. Show that the moon is nearer when in the 
 zenith than when at the horizon. 222. What is true of the ap- 
 parent size of the moon as compared with her real size ? 
 223. What kind of a path does the moon describe through 
 space? 224. Give an account of the harvest moon. 225. Give 
 an account of the surface of the moon. 226. Show how the 
 height of a lunar mountain can be found. 227. Give an account 
 of Tycho. 228. Of Copernicus. 229. Of Kepler. 230. Of 
 Eratosthenes. 231. Are there active volcanoes on the moon? 
 232. Give an account of the crater Linne*. 233. Show that the 
 moon has no atmosphere. 234. What have some thought to 
 exist on the side of the moon turned from us ? 235. What is 
 the form of the shadows of the earth and moon ? 236. What 
 is the umbra, and what the penumbra, of these shadows ? 
 237. Explain when an eclipse may occur. 238. Explain each 
 of the three kinds of eclipses of the sun ? 239. What are the 
 conditions under which a total eclipse of the sun is possible ? 
 240. Do total eclipses of the sun often occur ? 241. Give 
 Hind's account of the total eclipse of 1851. 242. How many 
 kinds of eclipses of the moon may there be ? 243. What 
 is the fundamental difference between eclipses of the sun 
 and of the moon ? 244. When is a lunar eclipse central ? 
 
 245. Upon what does the magnitude of a lunar eclipse depend? 
 
 246. Does the moon become invisible during a total eclipse ? 
 
 247. After what intervals do the eclipses of. the sun and moon 
 repeat themselves ? 248. What is an occultation ? 249. Ex- 
 plain how longitude at sea is ascertained by the motion of the 
 moon among the stars. 250. What are shooting stars? 
 251. At what season of the year are shooting stars most 
 numerous ? 252. At what intervals is the November shower 
 particularly brilliant? 253. Give an account of the shower of 
 1799. 254. What has led astronomers to attribute the August 
 and November showers to the passage of the earth through 
 
350 QUESTIONS FOR REVIEW AND EXAMINATION. 
 
 meteoric rings at these times ? 255. Do these meteoric bodies 
 ever fall to the earth ? 256. Why is Mars called an exterior or 
 superior planet ? 257. How does the size of Mars compare 
 with that of the earth ? 258. When is Mars situated most 
 favorably for observation ? 259. What are the physical char- 
 acteristics of Mars ? 260. Why does Mars experience about 
 the same change of seasons as the earth? 261. How do we 
 know that Mars has an atmosphere of considerable density ? 
 262. Which planets belong to the inner group, and what are 
 ttheir resemblances ? 263. What led Kepler to suspect that a 
 planet existed between Mars and Jupiter ? 264. What led to a 
 systematic search for the suspected planet ? 265. What is 
 Bode's law of planetary distances ? 266. Give an account of 
 the discovery of Ceres. 267. Of the discovery of Pallas. 
 268. What led Dr. Olbers to think that Ceres and Pallas were 
 fragments of a broken planet ? 269. When and by whom was 
 Juno discovered ? 270. Give an account of the discovery of 
 Vesta. 271. Give an account of the discovery of Astrasa. 
 272. What is this group of planets called ? 273. How many 
 are now known to exist ? 274. How do their orbits differ from 
 those of the larger planets ? 275. What is the first planet 
 outside of this group ? 276. What is true of his brightness ? 
 
 277. How does his size compare with that of the earth ? 
 
 278. Is Jupiter a perfect sphere ? 279. Describe Jupiter's 
 belts. 280. In what time does Jupiter perform his axial rota- 
 tion ? 281. How was this ascertained? 282. How many 
 moons has Jupiter ? 283. When and by whom were they dis- 
 covered ? 284. What is true of their configurations and their 
 axial rotations ? 285. Give an account of the occupations, 
 eclipses, and transits of Jupiter's moons. 286. What is the 
 planet next outside of Jupiter ? 287. How does the bulk of 
 Saturn compare with that of Jupiter ? 288. How many moons 
 has Saturn ? 289. Give an account of the discovery of Saturn's 
 rings. 290. Explain the various appearances of these rings. 
 291. What is true of their number? 292. What are some of 
 the conjectures PS to their nature? 293. Previous to 1781, 
 what planets were known ? 294. What planet was discovered 
 in that year? 295. Give an account of its discovery. 296. How 
 does the size of Uranus compare with that of the earth ? 
 
QUESTIONS FOR REVIEW AND EXAMINATION. 351 
 
 297. Why do we not know the period of its rotation ? 298. How 
 many moons has it ? 299. What is there peculiar about their 
 motion ? 300. What is the most distant planet now known to 
 exist? 301. Is its period of rotation known? 302. What is 
 peculiar about its moon ? 303. Give an account of the dis- 
 covery of Neptune ? 304. Which planets belong to the outer 
 group, and in what do they resemble one another ? 305. What 
 is common to the motions of all the planets and moons ? 
 306. Give a general description of the comets. 307. Give an 
 account of some of the most famous comets. 308. To what 
 is the twinkling of the stars due ? 309. What is the whole 
 number of stars visible to the naked eye? 310. How many 
 stars are there of the first magnitude ? 311. How many of the 
 second magnitude ? 312. How many of the third ? 313. What 
 is the number of the telescopic stars ? 314. What are the con- 
 stellations ? 315. Name the zodiacal constellations. 316. Ex- 
 plain the naming of the stars. 317. What is true of the color 
 of the stars? 318. What are variable stars? 319. Give an 
 account of Algol and Mira. 320. What are irregular or tem- 
 porary stars? 321. Give an account of some of the most 
 famous of these stars- 322. Give an account of the Milky Way. 
 323. What did Herschel believe to be the form of our side- 
 real system ? 324. Mention some clusters of stars that are 
 visible to the unaided eye. 325. Give an account of the tele- 
 scopic cluster in Hercules, and that in Centaurus. 326. What 
 are nebulous stars ? 327. Are the nebulae ever variable ? 
 328. Give an account of the Magellanic clouds. 329. By what 
 other name are they known ? 
 
 GRAVITY. 
 
 330. What is the first law of motion ? 331. How is this 
 law established ? 332. Show that the planets and their moons 
 are acted upon by some force. 333. What is the second law 
 of motion ? 334. How is this law established ? 335. De- 
 scribe Atwood's machine. 336. Show upon what the form of 
 the curve described by a moving body depends. 337. Show 
 that the force which curves the path of the planets is always 
 directed towards the sun. 338. Show that gravity would 
 
352 QUESTIONS FOR REVIEW AND EXAMINATION. 
 
 cause all bodies to fall at the same rate, were it not for the 
 air. 339. Describe the pendulum. 340. Describe the sim- 
 ple pendulum. 341. What are the four laws of the pen- 
 dulum ? 342. Establish each of these laws. 343. What is 
 the formula of the pendulum ? 344. Describe the compound 
 pendulum. 345. Show that the centres of oscillation and sus- 
 pension are interchangeable ? 346. Explain the use of the 
 pendulum in measuring the force of gravity. 347. Show that 
 the intensity of gravity varies directly as the mass of the body 
 acted upon. 348. Show that the moon's path is curved by 
 gravity. 349. Show that the paths of the planets are curved 
 by gravity. 350. Show that the paths of their moons are 
 curved by gravity. 351. Illustrate and explain the resolution 
 of forces. 352. Explain how it is that the planets can recede 
 from the sun after they have approached him. 353. Show 
 that the force which causes a planet to describe an ellipse must 
 vary inversely as the square of the distance of the body from 
 the sun. 354. In what kind of orbits do the comets move? 
 355. Show that the form of these orbits is the result of the 
 action of gravity. 356. Explain the perturbation called the 
 moon's variation. 357. Explain the mutual perturbations of Ju- 
 piter and Saturn due to the inequality of long period. 358. Ex- 
 plain how the amount of the perturbation of the planets can be 
 calculated. 359. Do the observed motions of the planets agree 
 with their computed disturbances ? 360. What do the per- 
 turbations of the moon and planets prove? 361. Show that 
 the theory of gravitation holds good throughout the uni- 
 verse. 362. Give an account and an explanation of the tides. 
 363. Account for the spheroidal form of the earth. 364. Ex- 
 plain the precession of the equinoxes. 365. What do the tides, 
 the spheroidal form of the earth, and the precession of the 
 equinox prove ? 366. Give an account of the Schehallien ex- 
 periment, and show how the weight of the earth was deter- 
 mined by it. 367. Give an account of the Cavendish experi- 
 ment, and show how the weight of the earth was found by it. 
 368. Give an account of the Harton Coal Pit experiment, 
 and show how the weight of the earth was determined by 
 it. 369. Explain how the weight of the sun can be found? 
 370. Explain how a planet attended by a moon can be weighed ? 
 
QUESTIONS FOR REVIEW AND EXAMINATION. 353 
 
 371. How can a planet not attended by a moon be weighed ? 
 
 372. Explain how the weight of the moon can be found from 
 the tides. 373. Explain how the weight of the moon can be 
 found by means of the apparent displacement of the sun caused 
 by the action of the moon upon the earth. 374. About what 
 do all the systems of the heavenly bodies revolve ? 
 
 CONSERVATION OF ENERGY. 
 
 375. Define and illustrate actual and potential energy. 
 
 376. Define mechanical, molecular, and muscular energy. 
 
 377. What are the forces that tend to convert potential into 
 actual energy ? 378. Show that each of these forces tends 
 to do this. 379. Show that mechanical energy may be con- 
 verted into heat. 380. Describe Count Rumford's experi- 
 ment. 381. Describe Sir Humphrey Davy's experiment. 
 382. What do these experiments show? 383. Into what is 
 all mechanical energy ultimately converted ? Show this. 
 384. What is the mechanical equivalent of heat ? 385. Show 
 how this equivalent is found. 386. Into what may heat be 
 converted ? 387. Illustrate this. 388. Show that the same 
 amount of heat, when converted into mechanical energy, always 
 gives rise to the same amount of energy. 389. To what does 
 the energy of affinity always give rise ? 390. Find how many 
 foot-pounds of energy are developed by the burning of a pound 
 of hydrogen. 391. Of a pound of carbon. 392. Show that 
 the energy of affinity sometimes appears as muscular force. 
 393. Can energy be destroyed ? 394. What is the source of 
 all the energy that appears on the earth ? 395. Show that 
 this is so. 396. What is the amount of heat given out by the 
 sun ? 397. How can it be found ? 398. .Why does it seem 
 that the sun's heat cannot be developed by ordinary combus- 
 tion ? 399. Give an account of the meteoric theory of solar 
 heat. 400. Of the nebular hypothesis. 401. Of Helmholtz's 
 theory of solar heat. 402. What is the relation between the 
 theories of Mayer and Helmholtz ? 
 
 w 
 
INDEX. 
 
 3T For concise statements of the leading topics of the book, see the SUMMARIES, 
 which will be readily found by means of the Table of Contents. The references in 
 this Index are only to the fuller treatment of subjects in the body of the work. 
 
 A. 
 
 Aberration of light, 80. 
 Adams, and the discovery of Neptune, 178. 
 Aldebaran, 188. 327. 
 Algenib, 26. 
 
 Algol, a variable star, 188, 326. 
 Alpha Centauri, parallax of, 81. 
 period of, 94. 
 rate of motion of, 96. 
 Alphabet, the Greek, 323. 
 Altitude, 20. 
 Andromeda, 326, 335. 
 
 nebula in, 83. 
 Angle, sine of, 303. 
 
 supplement of, 304. 
 Antares, 188, 325, 330. 
 Aphelion, 42. 
 Apogee, 33, 131. 
 Apsides, 33. 
 
 Aquarius, or the Water-bearer, 326, 337. 
 Aquila, or the Eagle, 325, 336. 
 Ara, or the Altar, 334. 
 Aratus, 333. 
 Arcturus, color of, 1 88. 
 
 distance of, 83. 
 
 proper motion of, 90. 
 
 rate of motion of, 96. 
 Argo Navis, or the Ship Argo, 333, 340. 
 Aries, or the Ram, 327. 
 Ascension, right, 26. 
 Asteroids, 165 (see Minor Planets). 
 Astrasa, discovery of, 165. 
 Atoms, 270. 
 
 Atwood's machine, 204. 
 Auriga, or the Charioteer, 327. 
 Axis, celestial, 8. 
 
 of earth points always in the same 
 direction, 77. 
 
 B. 
 
 Base line measured, 59. 
 Bear, the Great, 5, 323, 334. 
 Beehive, the (see Praesepe). 
 Bode's Law, 161, 179. 
 Bootes, 324, 335. 
 
 Calendar, the, 307. 
 
 the Gregorian, 307. 
 Cancer, or the Crab, 329. 
 
 Canes Venatici, or the Hunting Dogs, 
 
 326, 330, 334. 
 
 Canis Major, or the Great Dog, 329, 339. 
 Minor, or the Little Dog, 329, 339. 
 Capella, change in brightness of, 189. 
 color of, 1 88. 
 rate of motion of, 96. 
 Capricornus, or the Goat, 326, 338. 
 Cassiopeia, 5, 190, 324, 335. 
 Cavendish experiment, 251. 
 Celestial axis, 8. 
 
 poles, 8, 213, 276. 
 Centaurus, or the Centaur, 333. 
 
 cluster of stars in, 194. 
 Centrifugal force, or tendency, 241. 
 Cepheus, 324, 335. 
 Ceres, discovery of, 162. 
 Cetus, or the Whale, 328, 338. 
 Changes of seasons, 24. , 
 
 Coal-Sack, the, 192. 
 Coma Berenices, or Berenice's Hair, 330, 
 
 334- 
 
 Comet, Biela's, 183. 
 Donati's, 184. 
 Encke's, 183. 
 Halley's, 183. 
 Comets, 181. 
 
 parabolic motion of, 225. 
 of 1680, 1811, 1843, and 1861, 184. 
 Conjunction, 22, 33, 46. 
 
 inferior and superior, 45. 
 Constellations, 186, 323. 
 
 zodiacal, 187, 333. 
 
 Co-ordinates of a heavenly body, 13. 
 Copernicus, a lunar mountain, 123. 
 
 system of, 39. 
 Cor Caroli, 325. 
 Corona.Australis, or the Southern Crown, 
 
 334- 
 Corona Boreafis, or the Northern Crown, 
 
 3 2 5. 336. 
 
 Corona in solar eclipse, 112. 
 Corvus, or the Crow, 330. 
 Crater, or the Cup, 333. 
 Cycles and epicycles, 37. 
 Cygnj, 61, parallax of, 82. 
 period of, 94. 
 proper motion of, 90. 
 rate of motion of, 96. 
 Cygnus, or the Swan, 325, 337. 
 
 Day, length of, 24. 
 lunar, 33. 
 
356 
 
 INDEX. 
 
 Day, sidereal, 17. 
 
 solar, 21. 
 Declination, 26. 
 
 Delphinus, or the Dolphin, 327. 
 Denebola, 26, 329. 
 Distance of planets from sun, 49. 
 of sun, 23. 
 polar, 13. 
 
 Dominical letter, the, 308. 
 Draco, or the Dragon, 324, 336. 
 
 Earth, the, 129. 
 
 a molten mass, 240. 
 as r seen from the moon, 132. 
 heV density as found by Cav- 
 endish experiment, 254. 
 her density as found by Har- 
 ton Coal Pit experiment, 
 257- 
 .her density as found by Sche- 
 
 hallien experiment, 250. 
 her distance from 'sun, 53. 
 path curved by gravity, -218. 
 periodic time of, 45. 
 rotation proved by experi- 
 ment, 10. 
 
 . : semi-diameter found, 57. 
 spheroidal form of, 65, 240. 
 unvarying direction of axis of, 
 
 77- 
 
 weight of, 247. 
 Eclipses, cycle of, 150. 
 
 may occur when, 143. 
 of moon, 142, 148. 
 " " used to find her dis- 
 tance, 67. 
 of sun, 145. 
 Ecliptic, the, 23, 29. 
 Ellipse, construction of, 41. 
 Ellipses of the planetary orbits caused by 
 
 gravity, 2-21. 
 Energy, actual, 273. 
 
 mechanical, 273. 
 
 converted into heat, 
 
 275, 278. 
 molecular, 274. 
 
 " converted into heat, 
 
 *...'' 283. 
 " converted into elec- 
 
 'tricity, 284. 
 muscular, 274, 286. 
 of affinity, 274, 284, 286. 
 " cohesion, 274, 283. 
 "gravity, '2 74, 291. 
 potential, 273. 
 source of, 287. 
 
 transmuted, not destroyed, 286. 
 Epact, 312. 
 Epicycles, 37. 
 
 Epicycloid, the moon's orbit an, 134. 
 Equator, ce'estial, 26, 44. 
 Equatorial, the, 6. 
 Equinoxes, 26. 
 
 precession of, 27, 78, 242. 
 Equuleus, or the Little Horse, 333. 
 Eratosthenes, a lunar mountain, 140. 
 
 Eridanus, or the River Po, 333. 
 Eudoxus, 333. 
 
 F. 
 
 Faculas, solar, no. 
 Force, centrifugal, 241. 
 
 curving the planetary orbits, 207. 
 Forces, atomic, 270. 
 
 resolution of, 221. 
 Foucault's experiment, 12. 
 
 G. 
 
 Galaxy, the (set Milky WayX 
 Gemini, or the Twins, 328, 339. 
 Golden number, 310. 
 Gravity, 202, 274. 
 
 causes all bodies to fall at same 
 rate, 209. 
 
 causes bodies to fall 16 feet a 
 second, 215. 
 
 curves the moon's path, 216. 
 
 varies as the mass of bodies, 216. 
 
 II. 
 
 Harton Coal Pit experiment, 210. 
 
 Harvest moon, 134. 
 
 Heat, converted into mechanical energy, 
 
 280. 
 Count Rumford's experiments on, 
 
 275- 
 
 Davy s experiments on, 277. 
 from affinity, 284. 
 " mechanical energy, 273, 278. 
 " molecular " 283. 
 mechanical equivalent of, 280. 
 amount of solar, 289. 
 Helmholtz's theory of solar, 295. 
 meteoric ' 291. 
 
 unit of, 280. 
 Heavens, a dial, 151. 
 Hercules, 325, 336. 
 
 cluster of stars in, 194. 
 motion of solar system to- 
 wards, 91. 
 Horizon, 30, 306. 
 Hyades, the, 327. 
 Hydra, 329, 340. 
 
 Inequality of long period, 229. 
 
 J. 
 
 Juno, discovery of, 164 
 Jupiter, apparent motion of, 35. 
 
 distance, period, size, etc. of, 167. 
 
 moons of, 170, 233, 322. 
 
 path curved by gravity, 218. 
 
 perturbations of, 229. 
 
 physical features of, 168. 
 
INDEX. 
 
 357 
 
 K. 
 
 Kepler, a lunar mountain, 139. 
 laws of, 41. 
 system of, 40. 
 
 Law, Bode's, 161, 179. 
 Laws, Kepler's, 41. 
 
 of motion, 201. 
 
 of pendulum, 211. 
 Leo, or the Lion, 329, 340. 
 Lepus, or the Hare, 328, 339. 
 Le Verrier, and the discovery of Nep- 
 tune, 154. 
 
 Libra, or the Balance, 330, 340. 
 Libration of moon, 130. 
 Light, aberration of, 80. 
 
 interference of, 185. 
 
 velocity of, 83. 
 
 zodiacal, 127. 
 
 Linne, a lunar crater, 140, 317. 
 Lunar day, 33. 
 
 month, 32. 
 
 Lupus, or the Wolf, 334. 
 Lyra, or the Lyre, 324, 336. 
 Lyrae Epsilon, 91. 
 
 M. 
 
 Machine, Atwood's, 204. 
 Magellanic clouds, 196. 
 Mars, 37, 157- 
 
 his distance, size, etc., 157. 
 
 from sun found, 51, 
 physical features of, 158. 
 mass of, 258. 
 Mercury, 37, 45, 120. 
 
 apparent motion of, 34. 
 atihosphere of, 124. 
 distance, size, etc. of, 120. 
 mass of, 259. 
 ' phases of, 121. 
 rotation of, 122. 
 seasons of, 123. 
 
 Meridian, measurement of, 57. 
 Meteoric rings, 1 56; 
 showers, 154. 
 stones, 157. 
 Meteors, 154. 
 Metre, French, 313. 
 Metric system, 312. 
 Milky Way-, 191. 
 
 distance of stars in, 83. 
 Mira, a variable star, 189, 328. 
 Month, lunar, 32. 
 Moon, apparent motion of, 32. ' 
 apparent size of, 1 18. 
 atmosphere of, 141. 
 Moon, 
 
 cycle of, 280. . 
 distance of, 129. 
 
 " . found, 61. 
 disturbed by Venus, 234. 
 eclipses of, 142, 148. 
 
 Moon, harvest. 134. 
 
 her effect in precession, 246. 
 libration of, 139. 
 mass of, 260. 
 of Neptune, 178, 322. 
 orbit of, 33. 
 - parallax of, 71. 
 path curved by gravity, 216. 
 period of, 130, 
 perturbations of, 226. 
 phases of, 130. 
 rotation of, 131. 
 shadow of, 142. 
 size of, 129. 
 surface of, 135. 
 tides caused by, 237. 
 variation of, 227. 
 Moons, 89. 
 
 of Jupiter, 170, 322. 
 " Saturn, 173, 322. 
 , " Uranus, 177, 322. 
 Motion, curvilinear, 206. 
 elliptical, 221. 
 laws of, 201. 
 parabolic, 225. 
 Mural circle, 18. 
 
 < ."- N. 
 
 Nebula, crab, 86. 
 
 dumb-bell, 86. 
 in Andromeda, 83. 
 ring, 86. 
 
 Nebular hypothesis, the, 294. 
 Nebulae, 83, 193. 
 
 distance of, 87. 
 number and nature of, 86, 88. 
 variable, 195. 
 Neptune, discovery of, 178. 
 
 distance, size, etc. of, 178. 
 Nodes, 33, 75. 
 Nubeculae, 196. 
 Nutation, 79. 
 
 O. 
 
 Occultation of stars by moon, 142, 150. 
 Olbers on the origin of the minor plan- 
 ets,. 164. 
 
 Opposition, 33, 46. 
 Ophiuchus, or the Serpent-bearer, 325, 
 
 Orbits of planets inclined to plane of 
 
 ecliptic, 75. 
 
 Orion, 328, 338. . 
 
 Orionis, Theta, 93. 
 
 P. 
 
 Pallas, discovery of, 165. 
 Parabolic motion of comets, 225. 
 Parallax, 68. 
 
 of the fixed stars, 72, 73. 
 
 " " moon, 71. 
 Pegasus, or the Winged Horse, 326, 335. 
 
358 
 
 INDEX. 
 
 Pendulum, the, 12, 201, 210, 252, 255. 
 compound, 213. 
 formula of, 213. 
 laws of, 211, 212. 
 reversible, 214. 
 simple, 211. 
 
 used to measure force of grav- 
 ity, 214. 
 
 Perigee, 33, 131. 
 Perihelion, 41. 
 Period, sidereal, 46, 47. 
 
 synodic, 46. 
 Perseus, 326, 335. 
 
 cluster of stars in, 194. 
 variable star in (see Algol). 
 Perturbations of the moon, 226. 
 
 moons of Jupiter, 233. 
 planets, 229. 
 
 " how comput- 
 ed, 232. 
 
 Pisces, or the Fishes, 327. 
 Piscis Australis, or the Southern Fish, 
 
 326. 
 
 Planets, apparent motions of, 34. 
 curved orbits of, 207. 
 inclination of the orbits of, 75. 
 inferior and superior, 46. 
 inner group of, 160. 
 mean distances from sun, 65. 
 minor, 161, 319. 
 
 move in ellipses because of grav- 
 ity, 221. 
 
 orbits curved by gravity, 220. 
 perturbations of, 229. 
 relative distances from sun, 53. 
 secular perturbations of, 236. 
 synodic periods of, 45. 
 Pleiades, a cluster in Taurus, 193, 327, 
 
 338. 
 
 Poles, celestial, 8, 213, 276. 
 Praesepe, a cluster in Cancer, 193, 329. 
 Ptolemaic system, 35. 
 
 R. 
 
 Refraction, 8, 73. 
 
 in lunar eclipse, 149. 
 Resolution of forces, 221. 
 Retrograde motion defined, 177. 
 Right ascension, 26. 
 
 S. 
 
 Sagitta, or the Arrow, 327. 
 Sagittarius, or the Archer, 325, 337. 
 Scorpio, or the Scorpion, 325, 330, 337. 
 Serp'ens, or the Serpent, 325. 
 Satellites 89 ( see Moons). 
 Saturn, distance, period, size, etc. of, 172. 
 
 moons of, 173, 322. 
 
 perturbations of, 229. 
 
 rings of, 173. 
 
 Schehallien experiment, 247. 
 Seasons, the, 25. 
 Sector, zenith, 58, 248. 
 Secular changes, 236. 
 Shadow of the earth, 3, 142. 
 
 Shadow of the moon, 142. 
 Shape of the earth, 3. 
 
 " sun, moon, and planets, 4. 
 Sine of angle defined, 303. 
 Sirius, 329. 
 
 color of, 1 88. 
 distance of, 83. 
 name of, 187. 
 proper motion of, 90. 
 rate of motion of, 96. 
 Solar system, motion of, 90. 
 
 position of, 192. 
 Solstices, 27. 
 Star, Polar, 5, 16, 324. 
 Stars, apparent motions of, 5. 
 circumpolar, 5, 323. 
 clusters of, 193. 
 color of, 187. 
 double, 91. 
 
 periods of, 94. 
 physical and optical, 92. 
 revolve about common centre of 
 
 gravity, 262. 
 fixed, 185. 
 
 ' distance of, 76. 
 " proper motion of, 90, 95. 
 magnitudes of, 186. 
 names of, 187. 
 nebulous, 195. 
 number of, 185. 
 of first magnitude, 332. 
 temporary, 190. 
 twinkling of, 185. 
 variable, 188. 
 Style, old and new, 307. 
 Sun, apparent diameter of, 27. 
 
 path of, 28. 
 
 appearances in total eclipse of, in. 
 as a fixed star, 95. 
 axial rotation of, 103. 
 distance of, 51. 
 eclipses of, 145. 
 Hind's description of total eclipse 
 
 of, 147- 
 
 planetary orbits curved towards, 207. 
 "pores," "willow leaves," etc. on 
 
 the, no. 
 
 position of axis of, 104. 
 revolves round centre of gravity of 
 
 solar system, 262. 
 size of, 99. 
 spots, 101. 
 
 ' appearances of, 105. 
 " changes of, 108. 
 1 dimensions of, 107. 
 " motion of, 102, 105. 
 " nature of, 113. 
 weight of, 257. 
 System, metric, 282. 
 
 of Copernicus, 39. 
 
 " Kepler, 40. 
 
 " Ptolemy, 35. 
 
 " Tycho de Brahe, 40. 
 
 T. 
 
 Taurus, or the Bull, 327, 338. 
 Theodolite, 63. 
 
INDEX. 
 
 359 
 
 Tides, 237. 
 
 neap, 239. 
 
 spring, 239. 
 
 weight of moon found from, 259. 
 Transit instrument, 15. 
 Transits of Venus, 54, 65, 76, 126. 
 Trial and error, method of, 40, 72. 
 Triangle, right, 303. 
 
 oblique, 303. 
 
 computation of parts of, 304. 
 Triangulation, 59. 
 Triangulum, or the Triangle, 327. 
 Twilight, 29. 
 
 duration of, 30. 
 Tycho, a lunar mountain, 136. 
 
 U. 
 
 Universe, gravity acts throughout the, 234. 
 Uranus, discovery of, 176. 
 
 distance, period, size, etc. of, 177. 
 
 moons of, 177, 322. 
 
 perturbations of, 178. 
 Ursa Major, or the Great Bear, 323, 334. 
 Minor, or the Little Bear, 324, 334. 
 Ursae Majoris, Xi, 93. 
 
 V. 
 Vega, 6, 324. 
 
 parallax of, 82. 
 rate of motion of, 96. 
 Venus, 36, 38, 45, 124. 
 
 apparent motion of, 34. 
 
 atmosphere of, 126. 
 
 distance from sun, 124. 
 
 disturbs our moon, 234. 
 
 her distance from sun found, 49. 
 
 Venus, mass of, 258. 
 
 period of revolution and rotation, 
 125. 
 
 seasons of, 126. 
 
 size of, 124. 
 
 transits of, 54, 65, 76, 126. 
 Vesta, discovery of, 164. 
 Via Lactea (see Milky Way). 
 Virgo, or the Virgin, 330, 337, 340. 
 Volcanoes, lunar, 135, 140. 
 
 W. 
 
 Weight of earth, 257. 
 
 " moon, 259. 
 
 " planets, 258. 
 
 " sun, 257. 
 Weights, metric system of, 282. 
 
 Y. 
 
 Year, civil, 307. 
 Julian, 307. 
 leap, 308. 
 sidereal, 22, 27. 
 tropical, 27, 308. 
 
 Z. 
 
 Zenith sector, 58, 248. 
 Zodiac defined, 187. 
 
 constellations of, 187, 333. 
 
 signs of, 187. 
 Zodiacal light, 127. 
 Zone, torrid, 24. 
 Zones, frigid, 24. 
 
 . temperate, 25. 
 
 THE END. 
 
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