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THE 
 SOLAR SYSTEM 
 
 DELIVERED AT THE MASSACHUSETTS 
 
 INSTITUTE OF TECHNOLOGY 
 
 IN DECEMBER, 1902 
 
 BY 
 
 PERCIVAL LOWELL 
 
 NON-RESIDENT PROFESSOR OF ASTRONOMY AT THE 
 MASSACHUSETTS INSTITUTE OF TECHNOLOGY 
 AND DIRECTOR OF THE LOWELL OBSER- 
 VATORY, FLAGSTAFF, ARIZONA 
 
 BOSTON AND NEW YORK 
 HOUGHTON, MIFFLIN AND COMPANY 
 
 1903 
 
Copyright, 1903, 
 BY PERCIVAL LOWELL, 
 
 ALL RIGHTS RESERVED 
 
 Published May, fgoj. 
 
CONTENTS 
 
 CHAP. PAGB 
 
 I. OUR SOLAR SYSTEM i 
 
 II. MERCURY 27 
 
 III. MARS 47 
 
 IV. SATURN AND ITS SYSTEM 72 
 
 V. JUPITER AND HIS COMETS 94 
 
 VI. COSMOGONY n6 
 
 ELEMENTS OF THE SOLAR SYSTEM 
 
 TABLE 
 
 I. ORBITAL ELEMENTS facing 134 
 
 II. BODILY ELEMENTS Joeing 134 
 
 ERRATA. 
 
 Page 23, line 8. 
 
 m 
 Por rn read 
 
 Page 74, line 18. 
 
 For Pierce read Peirce. 
 Page 104, second line under diagram. 
 
 For P read O. 
 Page 123, line i. 
 
 After momentum insert projected at right angles 
 to it. 
 
 154155 
 
Copyright, 1903, 
 BY PERCIVAL LOWELL, 
 
 ALL RIGHTS RESERVED 
 
 Published May, igoj. 
 
J?. 
 
 CONTENTS 
 
 CHAP. PAGE 
 
 I. OUR SOLAR SYSTEM i 
 
 II. MERCURY 27 
 
 III. MARS 47 
 
 IV. SATURN AND ITS SYSTEM 72 
 
 V. JUPITER AND HIS COMETS 94 
 
 VI. COSMOGONY 116 
 
 ELEMENTS OF THE SOLAR SYSTEM 
 
 TABLE 
 
 I. ORBITAL ELEMENTS facing 134 
 
 II. BODILY ELEMENTS Joeing 134 
 
 ! 54155 
 
LIST OF ILLUSTRATIONS 
 
 PACK 
 
 INNER PLANETS 4 
 
 OUTER PLANETS 5 
 
 DIAGRAM 7 
 
 METEOR STREAMS 14 
 
 CONSPICUOUS COMETS 19 
 
 MERCURY TRIAD OF DRAWINGS .... 30 
 
 LIBRATION IN LONGITUDE 31 
 
 PERTURBATIVE ACTION EXEMPLIFYING THE ORIGIN 
 
 OF THE TIDES 36 
 
 MAP OF MARS 57 
 
 DRAWINGS SHOWING IDENTITY BETWEEN CANALS AND 
 
 RIFTS IN THE POLAR CAP 63 
 
 SATURN'S RINGS 79 
 
 POSITION OF MASSES IN SATELLITE SYSTEMS . . 85 
 INCLINATIONS OF SATELLITE ORBITS TO PRIMARY'S 
 
 EQUATOR 87 
 
 JUPITER'S FAMILY OF COMETS 100 
 
 RELATIVE ORBITS 104 
 
 ACTION OF JUPITER 107 
 
 COMET APHELIA 114 
 
 DIAGRAM 123 
 
 FAYE'S LAWS OF ATTRACTION IN CONDENSING NEBULA 125 
 SUCCESSIVE CURVES OF ATTRACTION IN CONDENSING 
 
 NEBULA 126 
 
 DIAGRAM 127 
 
 Axis INCLINATIONS OF THE MAJOR PLANETS . . 131 
 
THE SOLAR SYSTEM 
 
THF" \ 
 
 { UNIVERSITY 1 
 
 \X 
 
 THE SOLAR SYSTEM 
 
 OUR SOLAR SYSTEM 
 
 IN the long perspective of knowledge, which Its position in 
 begins with the close at hand and stretches to the knowledge!" 
 infinitely remote, the solar system marks a middle 
 distance. Between the intimacy possible with 
 objects on this Earth and the distant recognition 
 of the universe of suns, it furnishes an acquaint- 
 anceship combining something of the interest of 
 the one with the grandeur of the other. 
 
 Our knowledge about the solar system has its constitu- 
 greatly increased during the last quarter of a cen- 
 tury ; and first in the recognition of what makes 
 part of it. To our solar system we now know 
 belongs every heavenly body we see except the 
 fixed stars and the nebulae. Not only are the 
 Sun, Moon, and planets members of it, but me- 
 teors, shooting-stars, and comets we have found 
 to be so, too. That all of these bodies are part 
 and parcel of what the Sun controls, I shall first 
 
The Solar System 
 
 proceed to show you ; for it is proper that we 
 should recognize the members of the system be- 
 fore considering the system's constitution and the 
 several characters of its constituents. 
 
 obsolete In many text-books you shall find it still stated 
 
 that these flaming portents, the cometae or long- 
 haired stars, for the ancients saw tresses where 
 we prosaically see tails, one of which, on the 
 average, startles a generation into wonder, are 
 visitors to us from other stars. So also we were 
 taught that the strange stones that fall to us from 
 the sky, and we call meteorites, were bits of some 
 body from far interstellar space. Such knowledge 
 belongs now to the history of science, not to sci- 
 ence itself ; for these bodies carry with them their 
 badge of membership : it shows in the orbits they 
 describe. So, when we pass through a comet's 
 tail, or pick up a piece of meteoric iron, we now 
 recognize that we have to do, not with a stranger, 
 but with our own kith and kin. Man may gaze 
 at matter beyond the solar system, but man has 
 never yet touched it. 
 
 Path the Proof of community lies in the character of the 
 
 proof of one- 
 ness, paths. Planet and particle alike turn out to 
 
 travel in ellipses, and ellipticity betrays association. 
 How the orbit labels the occupant we shall see, 
 on finding the paths the planets pursue and why 
 
Our Solar System 
 
 they pursue them. The orbits of the planets are 
 then the first point to consider. 
 
 To begin with the Sun. Observation shows not Earth travels 
 
 ... in an ellipse. 
 
 only that the Sun changes its place in the hea- 
 vens, but changes its size as well. To measure- 
 ment through a smoked glass, it seems to contract 
 in summer and expand in winter. Plotting the 
 directions it successively takes in the form of a 
 spider, and taking the legs inversely proportion- 
 ate to the diameters at the times, we find an 
 ellipse, in one of whose foci lies the Sun. The 
 Earth, then, goes round the Sun in an ellipse. 
 
 To find the path of a planet, we first get its So do the 
 
 , . . , . , . , , 10 other planets, 
 
 synodic period, or period with regard to the Sun. 
 
 Then, from a sufficient number of observations of 
 synodic periods to give their mean, we obtain the 
 sidereal period, or period with reference to the 
 stars. 
 
 By considering the angular motions, the two 
 periods are easily seen to be connected by the fol- 
 lowing equation : 
 
 i _ i i 
 S ~ T ~E"' 
 Where E = the Earth's period ; 
 
 S = the Planet's synodic period ; 
 P = the Planet's sidereal period. 
 
 From two bearings separated by a sidereal 
 
The Solar System 
 
 period, we get a quadrilateral, of which, knowing 
 parts enough to solve, we derive the planet's dis- 
 tance from the Sun at the moment. We now 
 
 Distance to 
 
 Nearest Fixed Star 
 
 275 000 A U. 
 
 MARS 
 
 Distance to 
 
 Boundary of Sun's Domain 
 114000 A.U. 
 
 FIG. I. INNER PLANETS. 
 
Our Solar System 
 
 Distance to 
 
 Nearest Fixe.d Star 
 
 275000 A U. 
 
 NEPTUNE 
 
 Distance to 
 
 Boundary of Sun's Domain 
 II4000A.U. 
 
 FIG, II. OUTER PLANBTS. 
 
 have for the planet what we had for the Sun, 
 direction and distance at a given time. Dotting 
 these data upon the apparent path, Kepler proved 
 
6 The Solar System 
 
 that the orbit of Mars was an ellipse. Mars was 
 the first of the planets thus to have its orbit found ; 
 following it the others yielded similarly to the 
 genius of the man. All the planets, then, move 
 in ellipses about the Sun. 
 
 Thus we have obtained the accompanying plan 
 of the system. 
 
 Kepler's laws. Kepler discovered two more relations : first, 
 that the radius vector of any planet swept over 
 equal areas in equal times ; and, second, that the 
 cubes of the major axes of the orbits of any two 
 planets were as the squares of their periodic times. 
 The latter is not exactly true, but becomes so if 
 we take the masses at work into account. 
 
 From these three "laws," Newton showed that 
 the force governing the motions of the planets 
 was in each case directed to the Sun, and was as 
 the inverse square of the distance from him. Re- 
 versely he showed that such being the law of 
 gravitation, the orbits must all be conic sections. 
 Ellipses and But conic sections are of two kinds, ellipses 
 or closed curves, and hyperbolas or curves that do 
 not return into themselves. Clearly permanent 
 members of a system must travel in the first of 
 these two classes of curves, visitors only in the 
 second. Here, then, we have an instant criterion 
 for distinguishing bodies that belong to our system 
 from those that visit it from without. 
 
Our Solar System 
 
 Which of the two orbits a body is pursuing may 
 be determined either by actually finding the body's 
 path or by finding the distance of the body from 
 the Sun and its speed at the moment. For an 
 interesting equation connects the speed with the 
 distance, giving the major axis of the orbit, upon 
 which alone the class of curve depends. This 
 equation is 
 
 in which the sign betokens the ellipse, the -}- sign the 
 hyperbola. 
 
 Suppose a body at p moving along the curve whose tan- 
 gent is pt with acceleration f always directed to s. Then 
 z/, the resolved part of the acceleration along the tangent, 
 is f cos ^. 
 
 
8 The Solar System 
 
 The resolved part of the velocity v along sp is r, 
 and r = i> cos /> ; 
 
 whence 
 
 can be determined from the actual velocity at some 
 point in the orbit (at the end of the minor axis, for instance, 
 in the ellipse), and from this we can find that 
 
 where a is the semi-major axis of the curve, the upper sign 
 referring to the ellipse, the lower to the hyperbola. 
 
 The velocity in the hyperbola thus exceeds that 
 in the ellipse, and the dividing line between the 
 two classes of curves is clearly when the second 
 term is zero. 
 
 Consequently 
 
 7/2=^ 
 
 r 
 
 is the velocity which at any given distance r sepa- 
 rates the bodies moving in ellipses from those 
 moving in hyperbolas, the sheep from the goats. 
 
 ffeA 
 
 r 
 
 is called the parabolic velocity, but the student 
 should be careful to remember that the parabola 
 is a mathematical conception, not a physical fact. 
 
Our Solar System 
 
 It is a conceptual dividing line between ellipses 
 and hyperbolas, the paling between the sheep and 
 the goats. 
 
 Now the planets all move in ellipses. They 
 are therefore under the Sun's control and form 
 part of his system. 
 
 Occasionally stones fall out of the sky on to Meteors. 
 the earth. Suddenly a flash occurs overhead, a 
 detonation follows, and then if the observer be 
 near enough, a mass of stone or iron is seen to 
 bury itself in the ground. This is a meteorite, 
 aerolite, or bolide, a far wanderer come at last 
 to rest. 
 
 The flash, the report, and the fused exterior of 
 the mass found are due to the meteor's striking 
 against our air. The bodies enter the upper at- 
 mosphere at speeds of from ten to forty miles a 
 second, and such speeds are equivalent to immers- 
 ing them in a blow-pipe flame of a temperature 
 of many thousands of degrees. For the tempera- 
 ture of a gas is as the mean velocity-square of its 
 molecules, and the rush of the meteor produces 
 the same effect as if the molecules of the air were 
 moving and the air therefore very hot. 
 
 Its outward condition is a consequence of the Previously 
 last stage in its journey, but its inner state at c< 
 times continues to bear witness to a previous con- 
 
io The Solar System 
 
 dition. If the mass be large, time does not suffice 
 to fuse more than its exterior, and the interior re- 
 tains the cold of interplanetary space. As Young 
 tells us, one of the fragments of the Dhurmsala 
 meteorite in India was found in moist earth, half 
 an hour or so after its fall, coated with ice ! 
 
 Their orbits But their speed is the real tell-tale upon their 
 ellipses. past An j n g en j ous investigation by the late Pro- 
 fessor Newton, whose specialty was these very 
 things, proved that ninety per cent., and probably 
 all of the meteorites for which we have sufficient 
 data, were traveling, before their encounter with 
 the earth, in orbits not parabolic, but elliptic, like 
 those of the short-period comets, and were moving 
 direct. They come to us, therefore, not from the 
 stars, but from the Sun's own domain. They, 
 too, then are members of the system. 
 
 Their origin. Most interesting is their constitution in its bear- 
 ing upon their origin. Some are stone, some iron - 
 meteoric iron joined with nickel. Now the iron 
 meteorites are saturated with occluded gases, 
 which can be extracted from them by suitable 
 processes, and which cannot have been occluded 
 originally except in the molten interior of a sun, 
 intense heat and excessive pressure being neces- 
 sary ; and as they are now ungathered in remnants 
 of our own once nebulous mass, they must betray 
 
Our Solar System 1 1 
 
 what that nebulous mass was to begin with ; for 
 in their subsequent history there has been no- 
 thing to make them what they are. They cannot 
 have come from our present sun, since it became a 
 sun, as their orbits conclusively show. They must 
 have come from the sun our system had before 
 the catastrophe, which caused the nebula which 
 caused our Sun, occurred. They antedate the 
 creation of the nebula itself which our nebular 
 hypothesis posits as the beginning of things. 
 They are old with an age which staggers imagina- 
 tion ; older in cycles of evolution, if not in years, 
 than anything we see in the countless spangles 
 of a winter's night in the blue-black firmament of 
 sky. Before the silent tale they tell, history 
 shrinks into yesterday, the Earth's career into 
 the day before, and the evolving of the solar sys- 
 tem itself into modernity. Through that strange 
 Widmannstattian fretwork that marks their sur- 
 face like the lacing of frost-work on a window- 
 pane, we seem to be gazing past the iron bars into 
 the immensity, not of space alone, but of eternity. 
 
 Next to meteors, and doubtless close to them Shooting- 
 in kind, come shooting-stars. Superficial distinc- 
 tions have caused them to be classed apart, but in 
 all likelihood size alone separates the two. 
 
 In the case of shooting-stars, we have the flash, 
 
12 The Solar System 
 
 the lingering scarf of light left when the body it- 
 self has eluded us, but no sound is heard, and 
 nothing reaches the earth. 
 
 Meteor- The visitants come, too, in swarms. They have 
 
 their times and seasons. Different nights of the 
 year are consecrate to special flights ; and the suc- 
 cessive years bring back the same flights like 
 birds that honk overhead at the same recurrent 
 season of the year. 
 
 Such regularity has caused them to be noted 
 and studied, and we have now a score of well- 
 recognized congeries of shooting-stars or meteoric 
 streams, known, for example, as the Leonids, the 
 Perseids, the Andromedes. Each swarm has its 
 radiant or perspective point from which all its 
 members seem to come. From this radiant it 
 derives its name, the Leonids seeming to come 
 from a point in the constellation Leo, the Orionids 
 from the constellation of Orion, and the Lyrids 
 from the Lyre. 
 
 Their speeds. Each of these swarms enters our atmosphere 
 with cosmic speed, all the shooting-stars of one 
 swarm traveling at the same rate ; but each swarm 
 has its own distinctive velocity. The Andromedes 
 move relatively slowly, eleven miles a second, 
 and are reddish. They overtake us ; this accounts 
 for their sluggishness, and their sluggishness ex- 
 
Our Solar System 1 3 
 
 plains their color. They are only red-hot. The 
 Perseids move with medium velocity. They strike 
 us on the quarter at twenty-five miles a second, 
 and they are yellow. The Leonids, or November 
 meteors par excellence, meet us head on at forty- 
 three miles an Hour, "their swiftness giving them a 
 bluish-green tint or a white heat. 
 
 To Professor Newton again we owe our first Their orbits 
 step to knowledge of them. After the shower of 
 the Leonids in 1866, he determined, from all the 
 observations upon them, five orbits which they 
 might have pursued; and then Adams, of Nep- 
 tunian fame, from the motion of their node, showed 
 that only one of the five, an orbit with a period 
 of thirty-three years, would satisfy the problem. 
 Thus was explained the similar shower of 1833 
 and the yet earlier one of 1799, seen by Hum- 
 boldt. We should have had them again in 1900, 
 but that Jupiter probably interfered. 
 
 In the same way, the Andromedes prove to 
 travel in an orbit whose period is thirteen years, 
 and whose aphelion lies just outside the orbit of 
 Jupiter. So, also, the Perseids pursue a closed 
 orbit, but a much larger one, which takes them 
 far beyond the orbit of Neptune. 
 
 Shortly after Newton and Adams had worked 
 out the path of the November meteors, Schiapa- 
 
The Solar System 
 
 Association relli attacked the orbit of the Perseids, or August 
 
 of meteor- .. 
 
 streams with meteors, and to the astonishment of the scientific 
 world brought -out the surprising fact that they 
 
 I Andro'medes and Biela's Comet -1772. 
 D Leonids and Tempel's Comet- 1 8 66-1 
 (Retrograding Comet of shortest period). 
 
 m Perseids and Tunic's Comet - 1862-m. 
 IV Lyrids and Comet- I86I-I. 
 
 FIG. III. METEOR STREAMS. 
 
 traveled in an orbit substantially coincident with 
 that of the great comet of 1862, known as Tuttle's 
 comet (1862 III.). About the same time, Leverrier 
 published his orbit of the Leonids, and nearly 
 
Our Solar System 1 5 
 
 simultaneously Oppolzer, the great comet com- 
 puter, published his of Tern pel's comet of 1866 
 (1866 I.), and the two were found to be practically 
 identical. Here were two identities which could 
 hardly be the result of chance. Researches since 
 have added to the number of such comet-meteor 
 associations. Professor Herschel catalogues 
 seventy-six ; and four pairs the Leonids and 
 Tempel's comet, the Perseids and Tuttle's comet, 
 the Andromedes and Biela's comet, and the Lyrids 
 and the comet of 1861 (1861 I.) are shown in 
 the diagram on the opposite page. 
 
 Thus are comets and meteors connected. But Comets 
 
 . .... become 
 
 we know more about their connection than this meteor- 
 simple fact of association. We know that the sl 
 one becomes the other, for we have seen the pro- 
 cess of transformation take place practically under 
 our very eyes. Biela's comet was for many re- 
 turns a well-ordered member of Jupiter's comet- 
 family, of which family we shall have more to say 
 in the fifth chapter. Up to 1839 ft na ^ returned 
 with due regularity and without incident. In 
 1846, it again appeared on time, but thereupon 
 proceeded to do something very strange and then 
 unheard-of. In mid-career it split. It was first . 
 seen on November 28, and presented the appear- 
 ance of the usual comet. By December 19 it had 
 
1 6 The Solar System 
 
 become pear-shaped, and on January 13 it divided, 
 the two halves at first separating, and thenceforth 
 traveling side by side at a distance of one hundred 
 and sixty thousand miles for the subsequent four 
 months during which they continued visible. A 
 bridge of light sometimes spanned the interval 
 between them. 
 
 In 1852 the two returned. The distance be- 
 tween the pair had now increased to one million 
 five hundred thousand miles, and they traveled 
 thus during the time of their visibility. 
 
 Neither has ever been seen since; but in 1872, 
 just when the Earth was passing the track of the 
 lost heavenly twins, on November 27, occurred a 
 brilliant star-shower. The German astronomer, 
 Klinkerfues, was so impressed with the belief 
 that this must be the remains of the comet, and 
 that the comet itself, or what was left of it, would 
 be seen exactly opposite the radiant, that he tele- 
 graphed at once to Pogson, the government as- 
 tronomer at Madras, India : " Biela touched Earth 
 November 27 ; search near Theta Centauri." Pog- 
 son looked. Clouds at first prevented, but on 
 the third morning it was fair, and he saw in the 
 predicted place a comet with a round head and a 
 faint tail moving as it should have done. The 
 next morning he observed it still better, and in its 
 
Our Solar System 1 7 
 
 proper place. Oppolzer, by assuming the major 
 axis, showed that this may have been Biela's comet. 
 
 Since then, other comets have been observed to 
 split up, due to the action of the planets near 
 which they chance to pass ; and Callandreau has 
 shown that the event ought not to be so very 
 uncommon. 
 
 Another point connected with these meteor Meteor 
 
 , ,-, , r , . streams 
 
 streams must be noticed. Each of them is asso- attendant 
 ciated with the orbit of some particular planet. upon P lanets - 
 The planet in some sense shares with the Sun a 
 control over the stream.* It cannot cause the 
 stream to circle round itself, but it can, and does, 
 cause it to pay periodic obeisance to its might. 
 The stream's perihelion remains at the Sun, but 
 its aphelion becomes its periplaneta. It sweeps 
 about the planet at the one end of its path some- 
 what as it sweeps round the Sun at the other. 
 
 The Andromedes are thus dependent on Jupi- 
 ter, the Leonids on Uranus ; while the Perseids 
 and the Lyrids go out to meet the unknown planet 
 which circles at a distance of about forty-five as- 
 tronomical units from the Sun. 
 
 It may seem to you strange to speak thus con- 
 fidently of what no mortal eye has seen, but the 
 finger of the sign-board of phenomena points so 
 clearly as to justify the definite article. The eye 
 of analysis has already suspected the invisible. 
 
i8 
 
 The Solar System 
 
 Conspicuous 
 comets. 
 
 Parabolic 
 comets. 
 
 In our identification of the members of our sys- 
 tem we have thus got steadily farther and farther 
 away. We began with the planets. Then we 
 attacked the less evident and more erratic bodies, 
 and we found that the nearest of them, the mete- 
 orites, were after all fellow-members, and circled 
 quite near us, their orbits being comparable with, 
 and possibly not alien to, the short-period comets. 
 
 Next we found the shooting-stars, the meteor 
 streams, to be sun-controlled but traveling farther 
 yet out into space, and connected with comets 
 known to be periodic. We have now to take an- 
 other step outward to the comets non-periodic, 
 among which the most conspicuous of those visit- 
 ants are numbered. 
 
 Non-periodic we may call them pending investi- 
 gation. For their orbits are so vast that we know 
 but vaguely what their major axes are. 
 
 Some four hundred of these stars with tresses 
 have been seen from the earliest times of which 
 we have records to the present day. Not a year 
 passes that several are not discovered, but conspic- 
 uous ones are not over-common. In the last 
 forty years there has been but one of superlative 
 mien, and that was twenty years ago. The pre- 
 sent generation has no conception of what a comet 
 worthy the name can be. One of my first recollec- 
 
Our Solar System 
 
 FIG. IV. CONSPICUOUS COMETS. 
 
2O The Solar System 
 
 tions, if not my very first, is of such an one, and 
 the memory of it has never been approached by any 
 celestial phenomenon since. A total eclipse of the 
 Sun is commonplace beside it. Of the four hun- 
 dred up to now observed, the greater part move 
 in orbits differing so little from the parabolic for 
 the small fraction of their paths we are privileged 
 to mark that to all intent they travel in parabolas. 
 They lean, however, to the side of the ellipse. 
 Most of them frankly do so, although so slightly 
 that to determine their major axes to any degree 
 of accuracy is not possible. Very few, three or 
 four perhaps, hint at hyperbolas. Not one is such 
 beyond question, however slightly. In my notes 
 on Galle's catalogue, I find the following gloss at 
 the end of the list : " There is not a single undis- 
 puted hyperbolic orbit ; nor is there one in which 
 the computed non-hyperbolic orbits are not in the 
 majority." 
 
 Their orbits. From this fact of a practical parabolicity of 
 path many astronomers have argued the exterri- 
 toriality of these bodies, and early in the last cen- 
 tury Laplace set himself the problem of finding 
 the probability of hyperbolic to elliptic orbits on 
 the theory that they all came to the Sun from 
 stellar space. In spite of several mistakes in his 
 work, first pointed out by Gauss, he reached a 
 
Our Solar System 
 
 21 
 
 conclusion which is correct in quality : that the 
 number of hyperbolic orbits to elliptic should be 
 very small, less than one in the whole number 
 already seen, on the tacit assumption that the Sun 
 was at rest. 
 
 But the Sun is not at rest. It is traveling at Conclusion as 
 the rate of eleven miles a second towards a point with 
 in the constellation Hercules, carrying its retinue s y stem - 
 with it ; and this motion quite alters the result. 
 Instead of a great preponderance of elliptic orbits, 
 the solution shows in this case a large excess of 
 hyperbolic ones. And in most of the orbits the 
 hyperbolicity would be marked, not faint and 
 doubtful. To Schiaparelli we owe the first sug- 
 gestion of this fact, and, in 1895, to Fabry, of the 
 observatory of Marseilles, a very elegant and con- 
 clusive memoir on the subject. 1 
 
 In view of this we see that comets behave not 
 as they would, did they come to us as visitors from 
 other stars, but just as they should, considered 
 as distant members of our own system. Comets, 
 then, are also all co-members of the system. 
 
 That there is quite room enough within the The sun's 
 Sun's paramount domain for their gigantic orbits 
 becomes evident when we consider the distance 
 to which that domain extends. Measured even 
 
 1 Annales de la Faculte des Sciences de Marseille, 
 
22 The Solar System 
 
 on the vast scale of our solar system, the gap 
 which sunders it from the nearest fixed star is 
 something enormous. Two hundred and seventy- 
 five thousand times our distance from the sun is 
 the space that divides us from the next sun, the 
 star a Centauri. This distance is found by not- 
 ing the shift in the star's position due to the ex- 
 treme swing of the Earth in her orbit called the 
 annual parallax. It is a very minute displacement 
 at most, and requires perhaps the most delicate of 
 all astronomical refinement to detect. Inciden- 
 tally it affords conclusive evidence of itself that 
 the Earth goes round the Sun, not the Sun round 
 the Earth. 
 
 a Centauri. Fortunately a Centauri, our nearest stellar 
 neighbor, is a double star, a binary system, and 
 thus of itself affords us information of the region 
 over which it exercises control. Assuming that 
 gravity acts there just as it does here, any other 
 possible assumption implies that the force de- 
 pends on the orientation, which does not seem 
 rational, 1 we can deduce from the motion of the 
 
 1 Binaries move in apparent ellipses. Parallel projection keeps 
 an ellipse an ellipse and the centre the centre. From the general 
 polar equation of a conic and the differential equation of the orbit, 
 
 /=*("+) 
 
 it appears that the only laws of force which do not depend on 
 
Our Solar System 23 
 
 pair their united mass. It comes out twice that of 
 our Sun. Now, as gravity is as ^-, we have, call- 
 
 ing the whole distance from us to them a, the 
 following quadratic to give us d, the boundary dis- 
 tance between the two domains, our Sun's and 
 a Centauri's, 
 
 m m 
 
 from which we find the dividing line between the 
 Sun's domain and a Centauri's to be 114,000 
 astronomical units. 
 
 Neptune, the farthest known planet at present, 
 is but thirty astronomical units away, or about 
 loVo om *y f tne distance to the limit of the Sun's 
 domain. How nestled we all are under the Sun's 
 protecting wing is evident. It is no wonder that 
 the remotest comets seem almost infinitely distant 
 at their aphelion, though part and parcel of the 
 brood. 
 
 Coming back now from these chill outer con- The several 
 fines of the Sun's territory to the inner family F 
 circle gathered about the hearth or focus of all 
 these ellipses, occupied by the Sun, for such is 
 
 9, that is, on the orientation, are/= cr, which is negatived by 
 the fact that no star has yet been found in the centre of the 
 apparent ellipse, and/= -^., which is thus the only law possible 
 which is rational. It is thus ably put by Moulton (Celestial 
 Mechanics, 1902). 
 
! 
 
 24 The Solar System 
 
 the literal meaning of the word " focus," we 
 must note how the main bodies and yet smaller 
 particles are severally ranged about it. 
 
 Terrestrial Humboldt divided the planets into two groups : 
 P?a d n^ts. J r the terrestrial planets and the major planets, and 
 this classification one shall still find in many a 
 text-book. But it has long since ceased to con- 
 tain even a specious distinction. The so-called 
 terrestrial planets differ among themselves quite 
 as much as any of them do from the major planets. 
 From our present knowledge it would be much 
 nearer the mark to divide the eight into pairs, 
 Mercury and Venus, the Earth and Mars, Jupiter 
 and Saturn, Uranus and Neptune ; yet even be- 
 tween the members of each pair are notable dif- 
 ferences, to say nothing of the asteroids which 
 throng the space betwixt Jupiter and Mars. 
 
 Of the differences, it will be the province of the 
 
 succeeding chapters to speak ; but before doing 
 
 so, let us take a bird's-eye view of the whole. ' 
 
 Solar System Our own Solar System has one characteristic, 
 
 one" 8 r a general family trait, which distinguishes it from 
 
 many that lie round about it in space ; for we may 
 
 not doubt that the stars are centres to systems of 
 
 their own. We have not only analogy to guide 
 
 us to this deduction, but we already have glints of 
 
 evidence of the fact. Our system differs, how- 
 
Our Solar System 25 
 
 ever, from many of its neighbors in being a single- 
 sun system. This is a very important and funda- 
 mental distinction. To begin with, it makes 
 cosmic principles much easier to understand. We 
 think celestial mechanics abstruse enough as they 
 are, but ours are child's play to the complications 
 which two suns, to say naught of three or four, 
 would introduce into any system over which they 
 jointly held sway. It is problems of this nature 
 which Professor Darwin and other modern analysts 
 are trying to unravel. Difficult as the concep- 
 tions are, it is a question whether life itself would 
 not be quite as difficult, under such conditions. 
 Take our nearest stellar neighbor, a Centauri, for 
 instance, and consider what a planet circling round 
 either or both of its suns would be called upon to 
 undergo. Certainly our orderly succession of 
 phenomena would be seriously disturbed to the 
 consequent inconsequency of development upon 
 its surface. Day and night would become mean- 
 ingless terms, and organisms would have to put up 
 with variations which make imagination stare. 
 
 For fashioning worlds like the terrestrial, a 
 single-star system is, in general, a prerequisite. 
 
 This oneness is due to the system's original Due to 
 small moment of momentum. A minimum mo- ^ 
 ment of momentum is caused by the centralization momentum 
 
26 The Solar. System 
 
 of the mass ; a maximum by its equal division into 
 two or more. If we calculate the moment of mo- 
 mentum of the Solar System to-day, and compare 
 it with that of any binary system, we shall find it 
 in comparison almost vanishingly small. 
 
 The system, 61 Cygni, with only one fifth of its 
 mass, has a moment of momentum two hundred 
 and fifty times as great, and that of a Centauri, 
 which has twice the mass, has two thousand times 
 the moment. 
 
 This means that in the region of space, which 
 made room to the solar nebula, the individual mo- 
 tions must have been either small or equally large 
 in all directions, the negative motions almost 
 exactly canceling out with the positive ones. 
 
II 
 
 MERCURY 
 
 NEAREST to the Sun of all the bodies of the 
 system, excepting only the swarm of particles 
 which give us the Zodiacal Light, is Mercury. 
 
 Till very lately, we knew next to nothing about Till lately 
 
 . . , 11. very little 
 
 this planet. Its doings, as represented by its known of it. 
 
 path, were well determined, but its self not at all. 
 
 Part cause of this was its nearness to the Sun ; a 
 
 part, its being an inferior planet, and thus being 
 
 but ill seen when most observable ; for when at 
 
 its greatest apparent distance from the Sun, 
 
 at one of its elongations, as it is called, half of 
 
 it alone is illuminated, and that half but poorly. 
 
 Secondly, when it appears to the naked eye, and 
 
 when in consequence it is generally looked for 
 
 with the telescope, it is deep sunk in the vapors 
 
 of the horizon, and the air through which it is 
 
 seen is so tremulous that its disk, in consequence, 
 
 is ill-defined. As this was supposed the best time 
 
 for observation, the disk was deemed inscrutable. 
 
 But the obvious is to be avoided. Acting upon Markings 
 
 ..,,. ,,. . nn detected in 
 
 this principle, Schiaparelli, in 1889, took a new 1889. 
 departure by systematically observing Mercury by 
 
28 The Solar System 
 
 day. He was before long rewarded. Markings 
 began to show themselves upon the little disk, 
 difficult of detection, indeed, but still visible 
 enough to enable him to be satisfied of their per- 
 manency ; and then the markings disclosed of 
 themselves a very singular fact. From the sta- 
 bility of their positions, it became evident that 
 the planet rotated upon its axis in the same time 
 that it revolved about the sun. 
 
 Rotation and Let us consider a moment how it was the mark- 
 iTodlronous. m g s disclosed this fact. Suppose, for simplicity, 
 a body revolving round its primary in a circle and 
 made visible by the light received from it. Fur- 
 thermore, suppose the revolving body to have 
 markings upon it, and to rotate once upon its axis 
 as it makes one revolution round its sun. Clearly 
 it will always present the same face to the central 
 attracting and illuminating body, and therefore 
 the markings will maintain an invariable position 
 with regard to the illuminated face. To an out- 
 sider, the planet, if inferior, will present the phases 
 of the Moon. Unlike the Moon, however, the 
 illumination will not sweep over an invariable face, 
 but lighting and lighted will rotate together ; for 
 in the case of the Moon, we are the attracting, but 
 not the illuminating, body ; in the case of a planet, 
 the Sun is both. 
 
Mercury 29 
 
 Schiaparelli was the only one to see these mark- Flagstaff 
 
 . corroborates 
 
 ings till 1896, when the subject was taken up at Schiaparelli. 
 Flagstaff. The planet was at the time coming 
 out from inferior conjunction, and was at first no 
 easy matter to find ; for in relative visibility Mer- 
 cury behaves like the Moon. Size of disk does 
 not begin to compensate for phase, as calculation 
 would lead one to expect ; because obliquity of 
 illumination greatly enfeebles its amount. The 
 planet presented so faint a contrast with the sky 
 that on one occasion an assistant, coming to look 
 at it through the telescope, could not see it until 
 its exact position was pointed out to him ; and I 
 always picked it up myself by trailing it across 
 the field, an object in motion being much more 
 evident than one at rest, as every hunter knows. 
 Nor could I at first make much out of it ; it was 
 only a pretty little moon nearly lost in the vast 
 blue sky. To my surprise, however, as it left 
 elongation to return to the Sun, it grew brighter 
 and brighter, and distinct dark markings came out 
 upon its disk. The best views occurred when 
 popular almanacs inform their readers : " Mercury 
 invisible during the month." In the clear. sky 
 and steady air of Arizona and Mexico the mark- 
 ings were not especially difficult objects, though 
 more difficult than the canals on Mars. They 
 
30 The Solar System 
 
 were narrow, irregular lines and very dark. They 
 were not in the least like the markings on Mars. 
 There were no large patches of shade on the one 
 hand, nor fine, regular pencilings on the other. 
 Its lines were fairly straight, but broken and of 
 varying width. " Cracks " best explains their ap- 
 pearance, and probably their nature. 
 
 Their positions were unmoved, even after as 
 much as five hours' interval. 
 
 
 Nov. 1 21h 16m. Nov. 2 Oh 38m-45m. Nov. 2 2h 40m. 
 
 FIG. V. 
 
 TRIAD OF DRAWINGS, Nov. 1-2, 1896. 
 No shift in markings during sh 24m. 
 
 Markings As I continued to map them, I marked that 
 iteration in while their relation to the terminator was un- 
 longitude. cnange( j ^y the hours, it was slowly shifting with 
 the days. The lines were gradually passing over 
 its edge, and it dawned on me what I was witness- 
 ing : the swaying, or libration, of the planet in 
 longitude due to the eccentricity of the planet's 
 orbit. 
 
Mercury 
 
 o 'J 
 
 
 Si 
 
 3 I 
 
 5 II 
 2 3 
 
 5 3 
 
 < r- 
 
 IG 
 R 
 
32 The Solar System 
 
 Cause of Libration in longitude is a necessary conse- 
 
 libration in r , , -, . , , r -, 
 
 longitude, quence of the planet s moving in a focal conic. 
 The moment of rotation of a body of Mercury's 
 mass is so great that it would take more than the 
 Sun's might to suddenly alter it. The planet 
 turns upon its axis, therefore, with a uniform spin. 
 But its angular speed in its orbit is not uniform. 
 Since the radius vector sweeps out equal areas in 
 equal times, the angular velocity near perihelion 
 exceeds that near aphelion. The revolution gains 
 on the rotation here, and at the end of a certain 
 time reaches its maximum ; after which the rota- 
 tion gains on the revolution, and the deficiency is 
 made up again at aphelion. 
 
 Maximum To determine what the maximum is, and where, we 
 
 Hbration in ^ ave : tnat t ^ ie mean angular velocity of revolution in the 
 
 longitude, ellipse is the angular velocity of a body supposed to be 
 
 describing a circle in the time occupied by the planet in 
 
 the ellipse. The area of the ellipse being irab, and the 
 
 period J 1 , the areal velocity in the ellipse, which is con- 
 
 stant, is 
 
 T ' 
 
 This is the areal velocity in a circle of radius *J a b sup- 
 posed described in the same time. 
 
 To find, therefore, the point on the ellipse where the 
 radius has the value corresponding to the mean angular 
 velocity, we must take the expression for r of the ellipse 
 referred to its focus as a pole, 
 
Mercury 33 
 
 -- COS V 
 
 and equate it to that of the circle supposed described 
 about that focus with the length of radius */ab. This 
 geometrically is the point of intersection of the two curves, 
 since the value of r is common to both. 
 Consequently for the point sought 
 
 whence, since 
 
 and 
 
 e 
 
 In the case of Mercury, e = .205605 ; v, the true anomaly 
 of the point of maximum libration, is therefore 98 55'. 13. 
 
 But 
 
 where E is the eccentric anomaly ; and E e sin E = M, 
 where M is the mean anomaly ; whence v M =. C, which 
 is the amount of the maximum libration, is 23 40' 38". 
 
 The gain or loss of the rotation over the revo- 
 lution is the same thing as the equation of the 
 centre. 
 
 We have, then, in the libration, a most conclu- 
 sive and interesting proof of the isochronism of 
 rotation and revolution. 
 
 The next point to consider is what caused this 
 
34 The Solar System 
 
 New branch isochronism. This question raises a wholly new 
 mechanics. set f problems in celestial mechanics from those 
 in which celestial mechanicians were wont to en- 
 gage. Until recently, mathematical astronomy 
 dealt almost entirely with solids, entirely so out- 
 side the consideration of the Earth. But no solid 
 is absolutely rigid, and the action of one body 
 upon another must cause mutual deformation of 
 figure and give rise to tides in the two masses. 
 Darwin has shown 1 that this tidal action is an im- 
 portant cosmic factor, one which has played as 
 constructive a part in the evolution of things as 
 gravitation itself. 
 
 Not only were the planets not rigid in the past ; 
 they are not rigid to-day. So far as we can judge, 
 all the planets behave as plastic bodies at the 
 present moment. So great are the masses that, 
 even in the case of the denser and cooler ones, 
 deformation of figure seems to be what fluidity 
 and rotary conditions would require. They are, 
 therefore, fit subjects for tidal action. 
 Tides Owing to the great importance of the subject, 
 
 how caused. 
 
 and to the fact that the explanation given of it 
 in almost all the text-books is erroneous, I shall 
 present it to you with some pains, the more so 
 that the action may, I think, be outlined quite 
 
 1 Pro. Roy. Soc. 1878-81. 
 
Mercury 35 
 
 simply. The prestige of Sir Isaac Newton's name 
 is responsible for the inertia which still carries 
 the usual explanation rolling down the ages. He 
 attempted to explain the tides statically, and the 
 account he gave has been blindly copied and per- 
 petuated. But the problem is not a static, but a 
 kinematic one ; the body acted on is in motion at 
 the time of the action, and this entirely changes 
 the result. Let me give you an analogous in- 
 stance of the impossibility of treating a problem 
 of motion as if it were one of rest. The preces- 
 sion of the equinoxes is a case in point, and may 
 be seen in a gyroscope. If a weight be hung on 
 the axis of the wheel while the latter is at rest, the 
 wheel instantly turns into the horizontal plane 
 and stays there. This is a case of statics. If 
 now the wheel be set in motion, however slightly, 
 the wheel, instead of lying down in the plane of 
 the pull once and for all, simply rotates in space 
 without any change of inclination whatever. This 
 is a case of kinematics. Kinematic questions 
 always thus differ from static ones. 
 
 Nor can the motion be tacked on afterward, as 
 simultaneity is of the essence of the problem. If 
 the effect of the Earth's rotation was merely to 
 carry forward the crest of the tide through fric- 
 tion, it is the deep-water tides, those in water 
 
The Solar System 
 
 Disturbing 
 force. 
 
 over 1 2| miles deep, not the shallow, that would 
 be nearest under the Moon. 
 
 Consider a body revolving freely around an- 
 other in a circle, and disturbed in this motion by 
 a third. This is the case with any particle of the 
 ocean when we neglect pressure and friction. 
 Connect the three bodies by lines, and, keeping 
 their directions, increase their lengths inversely 
 
 C Centre of the Earth. 
 
 PA Particle at the Surface. 
 
 PERTURBATTVE ACTION 
 EXEMPLIFYING THE ORIGIN OF THE TIDES. 
 
 FIG. VII. 
 
 as their squares, and join the ends. The disturb- 
 ing force will be represented by the connecting 
 line, on the principle of the composition of forces. 
 CM* _PM 
 
 PM* ~ NM ; 
 
 whence PN represents in amount and direction 
 the disturbing or tide-raising force. 
 
Mercury 37 
 
 If M be far away compared with CP, 
 BN2CB = 2p, say; 
 for since P M = BM = D 
 
 and CB=p, 
 
 NM 
 whence 
 whence BMNM=BN = 2p. 
 
 The tide- raising force /Wmay be resolved into 
 a normal disturbing force PL and a tangential 
 disturbing force LN. From the fact that BN is 
 always twice CB, we find for the vanishing points 
 of the normal force a and b, those where the angle 
 BCP = 54 44'. .The whole disturbing force is 
 there tangential. 
 
 Now consider the action of the two compo- 
 nents ; first, that of the tangential factor. At F, 
 the whole force is normal and acting inward. 
 From its minimum here the tangential force rises 
 to a maximum at a, where it comprises the whole 
 force. It then subsides to zero at A. During this 
 quadrant it has been urging the particle onward 
 in its own direction of movement FA. At A, it 
 changes sign and becomes a retarding force, which 
 attains its maximum at b, and then sinks to zero 
 again at E. 
 
 In consequence, the velocity of the particle due 
 
38 The Solar System 
 
 to the disturbing force is a maximum at A be- 
 cause the force has been adding increments to it 
 up to this point and a minimum at F and E. 
 The particle, by traveling fast, lessens the curva- 
 ture of its path about C, since the pull from C has 
 less time to act ; and reversely by traveling slowly 
 it increases this curvature. In consequence, then, 
 of this component, the path is flattened at A and 
 bulged at E. 
 
 The normal component acts inward at Fand is 
 proportional to CP. It helps the central force at 
 F, and curves the path the more. At a it van- 
 ishes, and is then reversed, acting outward or 
 against the gravity of C. It thus lessens the 
 curvature from a- to b. It thus conspires com- 
 pletely with the tangential component ; and the 
 two together squeeze the orbit into an ellipse with 
 its longer diameter at right angles to the line 
 joining C to M. 
 Tide analo- The tidal action on a particle of the ocean is 
 
 gous to 
 
 moon's varia- thus precisely the same, neglecting pressure and 
 friction, as that of the Sun upon the Moon's orbit. 
 This deformation of the Moon's orbit was de- 
 tected, probably by Aboul Wefa, nine centuries 
 ago. It is called the Moon's variation. Thus the 
 tidal wave and the variation are analogous exhibi- 
 tions of the same force. 
 
Mercury 39 
 
 Friction now comes in to modify the result. At Effect of 
 F, in consequence of the tide-raising force, the l 
 particle is traveling less rapidly than the rest of 
 the Earth. Friction, therefore, urges it on and 
 increases its tangential velocity up to some point 
 P' t where its speed becomes equal to the mean 
 speed of the earth. After this, its speed being 
 greater than the Earth's, friction retards it, until 
 it again becomes the mean at P. Then friction 
 begins again to accelerate it. 
 
 In consequence, the particle is accelerated from 
 Q to P', retarded from P 1 to P, and then acceler- 
 ated again. From A on, friction thus helps the 
 retarding tangential force, and the Earth causes 
 the particle to turn the corner of the ellipse at E 
 sooner than it otherwise would. The tangential 
 force thus reaches its maximum earlier, and the 
 crest of the tide is thus shifted from E backward 
 to some point P. 
 
 On the Earth, in the case of the ocean, we are 
 dealing with superficial tides. In celestial me- 
 chanics, it is the substantial tides, or tides of the 
 whole body, with which we are concerned. The 
 latter are immensely the more potent. As the 
 tidal crest lies ahead of the line joining the two 
 bodies, the Sun or the Moon is constantly trying 
 to pull it back into this line, while the Earth is 
 
ing force. 
 
 40 The Solar System 
 
 striving by friction to set it at right angles to the 
 line. The bulge, therefore, acts as a brake upon 
 the Earth's rotation, and must continue so to act 
 until the Earth's rotation and revolution coincide. 
 Tide-gen erat- Now let us determine the tide - generating 
 force 1 : 
 
 Let M= mass of the Earth ; 
 m = mass of the Moon ; 
 x,y,z = ihe coordinates of the Moon re- 
 ferred to the Earth's centre ; 
 r=its distance; 
 
 g,rj, = the coordinates of the particle re- 
 ferred to the Earth's centre ; 
 p = its distance. 
 
 Then the Earth describes an ellipse round the 
 centre of inertia of the Earth and Moon, and its 
 
 acceleration is n \ toward this centre. 
 
 To bring it to rest, we must apply to it an ac- 
 celeration, ^r> of which the accelerations along 
 
 the coordinates are, 
 
 m x my m z 
 
 "a' r > ~ r z' r ' ~r* ' r' 
 
 Now cos^ = ^.l+-> / .^ + ^.- C 
 
 r p ^ r p^ r p 
 
 and r p cos z = x | -f- y t\ + ^ f / 
 
 1 After G. H. Darwin. Article in the Encyclopedia Britannica 
 on "Tides." 
 
Mercury 41 
 
 but - ^ is the diff. coefficient of - "-^r with re- 
 gard to that is the diff. coefficient of - - ^/ cos z. 
 
 The potential necessary to bring the Earth to 
 rest is then - - 7 ~ cos 2. 
 
 The potential of M with regard to the particle 
 is , while the potential of m upon the particle is 
 
 plus a constant. This con- 
 
 \r 2 + p' 2 2 r p cos z 
 
 stant we determine by the condition that the poten- 
 tial at the planet's centre shall be zero, since we are 
 seeking the motion of the particle relative to this 
 
 m M 
 
 centre, and it becomes . . . 9 
 
 V' T~ P" 2 r P cos % 
 
 Since r is very large compared with p, we may 
 advantageously expand the last in powers of -- 
 which gives : 
 
 - cos 2- + etc.]. 
 
 The first term cancels with the potential for 
 bringing the Earth to rest, and we have for the 
 whole potential urging the particle, 
 M m 
 
42 The Solar System 
 
 Of this, the first term is the potential of gravity ; 
 the subsequent ones the tide-raising potential. 
 
 To get the forces, we must differentiate this 
 expression with regard to the position of the par- 
 ticle. 
 Tide-raising In order to compare the tide-raising forces on 
 
 force for .... . _. ... 
 
 different different bodies, we will assume z = o ; whence 
 the tide-raising force at its maximum may be ex- 
 pressed in a rapidly converging series, of which 
 
 the first two terms are ^p*+ ^- 
 
 If the affected body be distant compared with 
 its size, the first term is enough, and we see that 
 then the tide-raising force is directly as the radius 
 of the second body, and inversely as the cube of 
 its distance from the first, while also directly as 
 the latter's mass. 
 
 But the work done by a force is the product of 
 the force into the space through which it acts, 
 as, for instance, the lifting a weight a certain dis- 
 tance, and in a given time the space is itself 
 proportional to the force, whence the work in that 
 time is as the square of the force. 
 
 >o*.*, 
 
 whence // 2 = s. 
 
 Whence if the time remain constant the force must 
 
 vary as the space. For the proportionate work 
 
Mercury 43 
 
 done in a given time by tide-raising forces, we have, 
 then, {^f -f ~ir) > or for most cases sufficiently 
 well, taking only the first term, 4 ^ 6 P . That is, 
 
 it is as the square of the attracting mass and the 
 square of the radius of the affected body directly 
 and inversely as the sixth power of the latter's 
 distance. 
 
 WORK DONE BY TIDE-RAISING FORCE IN UNITY OF 
 TIME IN RATIO TO SUN'S ACTION ON THE EARTH 
 TAKEN AS UNITY. 
 
 By Sun on : 4**V (app rox ^ 
 
 Mercury ........ 43-26 
 
 Venus ........ 6.60 
 
 Earth ........ i.oo 
 
 Mars ...... ... 0.023 
 
 Jupiter ........ 0.006 
 
 f 2 m p . 3 m p 2 ! 2 
 On Earth by : [^ + ^f- J 
 
 Sun ..... . i.oo 
 
 Moon ........ 4-97 
 
 On Satellites by their Primaries : - [ 2 -^- -f ^-^_ 
 
 lapetus ........ 27.6 
 
 Callisto ....... 32,549- 
 
 Ganymede . ..... 1,385,600.0 
 
 Moon ........ 2,374.4 
 
44 The Solar System 
 
 Professor G. H. Darwin has calculated the rela- 
 tive effect of tidal retardation by the Sun on each 
 of the several planets, that upon the Earth being 
 taken as unity, with the accompanying result : 
 
 Planet. 
 
 Number to which Tidal 
 
 Retardation is Proportional. 
 
 Mercury 
 
 Venus 
 
 Earth 
 
 Mars 
 
 Jupiter ...... 
 
 Saturn ... . 
 
 Supposing, then, all the bodies to have started 
 in the race for rotary retardation at the same time, 
 the isochronism of rotation and revolution of Mer- 
 cury is what was to have been expected. For 
 the previously known facts were : first, that the 
 Moon showed this state of things. Now the rela- 
 tive tide-raising effect in a given time of the Earth 
 on the Moon is 2374 ; that of the Sun on the 
 Earth being unity. Second, that lapetus did the 
 same ; for this satellite is always much brighter 
 on the western side of Saturn than on the eastern. 
 Such a periodic change of brilliancy would be 
 accounted for by isochronism of rotation and revo- 
 lution. Now the relative tide-raising effect of 
 Saturn on this satellite is 28. 
 
Mercury 45 
 
 On the other hand, the Earth's rotation and 
 revolution do not coincide ; and the relative effects 
 of Sun and Moon on it are : 
 
 Sun i.oo 
 
 Moon 4.97 
 
 5-97 
 
 Assuming, therefore, that the retardation began 
 synchronously for all, Mercury, upon whom the 
 effect was 43, should have reached the isochronous 
 condition. 
 
 We may note incidentally that Venus on this 
 assumption falls in the debatable ground, since 
 the effect on it is 6.60. 
 
 Bat we do not know either the time of the birth 
 of the Moon nor the relative age of the Earth and 
 Venus. It is quite possible, for aught we know, 
 that Venus may have been subjected to the pro- 
 cess practically much longer than the Earth. 
 
 It is certainly significant that isochronism ceases 
 just where a first approximation would put it. 
 
 Since the date of the detection of Mercury's 
 isochronism by Schiaparelli, the third and fourth 
 satellites of Jupiter, Ganymede and Callisto, have 
 been added to the isochronous list by Mr. Doug- 
 lass at Flagstaff. These, then, agree with theory. 
 We may safely predict that all the other satellites 
 
46 The Solar System 
 
 of Jupiter and Saturn will be found to behave 
 similarly. 
 
 Consummation of tidal effect marks the last 
 stage in the planetary career. So soon as identity 
 of rotation and revolution is effected, the planet 
 is placed in a changeless, or largely changeless, 
 state, which, so far as we can conceive, means as 
 a world its death. It now turns the same face, 
 except for libration, in perpetuity to the Sun, 
 Day and night, summer and winter, have ceased 
 to exist. One half of it is forever being baked, 
 the other half forever frozen ; and from this con- 
 dition there is no escape. The planet must remain 
 so until the Sun itself goes out. 
 
 Mercury, therefore, represents planetary de- 
 crepitude ; and the symptoms of this old age are : 
 loss of air ; isochronous rotation and revolution ; 
 rotundity. 
 
Ill 
 
 MARS 
 
 MERCURY presents us one phase of planetary Mercury old; 
 development ; Mars another, quite different. The middle age. 
 two represent stages in world-life as distinct as 
 those of gray hair and brown in human life. 
 
 Whatever the absolute ages of the several plan- 
 ets, their relative ages, as measured intrinsically, 
 decrease pretty steadily with their distance from 
 the Sun. Mercury is old ; Mars, middle aged ; 
 Jupiter young. 
 
 World-life has its earmarks of time as human 
 life has, and betrays them quite as patently. 
 
 Lack of atmosphere, colorlessness, changeless 
 attitude toward the Sun, are the signs of old age 
 in a planet. Mercury shows all these tokens of 
 senility. Mars presents a very different picture. 
 
 Color is a telltale trait ; for it is a sign that sur- Color a 
 
 r , , ... T r conclusive 
 
 face development still goes on. Lack of atmos- criterion. 
 phere alone prevents vegetation, and this, coupled 
 with unalterableness of face presented to the Sun, 
 weathers the surface to a neutral gray. Such a 
 
48 The Solar System 
 
 body shows but the bleached bones of a once living 
 world. 
 
 Now color is conspicuously wanting on Mer- 
 cury. The disk of the planet is a chiaroscuro of 
 black and white, tones devoid of tints. 
 
 Mars a life- Mars is an opal. Colors comparable only to 
 
 wor?d. r " that stone variegate its disk. At top and bottom, 
 collars of pearl-white contrast vividly with light 
 areas of rose-saffron and darker ones of robin's-egg 
 blue. Daylight reveals these colors much better 
 than night, because the contrast of the blue-black 
 sky clothes the disk with yellow it does not really 
 possess, diluting the true tints. 
 
 Mars has The markings enable the rotation of the planet 
 
 to be found - The markings move under the ob- 
 server's eye and yet keep their relative configura- 
 tions the same, day after day and year after year. 
 They thus reveal the fact that the planet rotates, 
 and by the course of their motion disclose the 
 axis about which the rotation takes place. From 
 the observed data, spherical trigonometry enables 
 us to fix this axis in space and determine its tilt to 
 the plane of the planet's orbit. We thus find that 
 it is inclined to the Martian ecliptic by an angle of 
 25, and that the solar day there is 24 hours and 40 
 minutes long. Thus Mars has both days and sea- 
 sons, and both days and seasons are practically 
 
Mars 49 
 
 counterparts of our own. The days are a little Seasons 
 
 i i i accentuated 
 
 longer and the seasons nearly twice as long, reck- much like 
 oned either by Earthly or by Martian days. The f ur ^ a 
 orderly succession of day and night, spring, sum- length. 
 mer, autumn, and winter, are the same there as 
 here. 
 
 Now this is no accident. It is a direct conse- 
 quence of the planet's size and of its position in 
 the solar family. That, however, the circum- 
 stances of the Earth and Mars should chance to 
 agree so nearly in quantity as well as quality, we 
 as yet lack the data to explain. 
 
 Size, or rather lack of it, has done something Scant 
 else for Mars. It has reduced the atmospheric 
 blanket that covers the planet's body. It did this 
 both at the start and subsequently. If the planets 
 set out with atmospheres in proportion to their 
 masses, a small planet having a greater surface in 
 proportion to its mass would not have this surface 
 so thickly covered, and its lesser gravity would 
 further spread this out skywards. 
 
 Surface being as 4 v r 2 , while mass is as 4 IT r*, the one 
 is to the other, surface to mass, as 
 
 The ratio of surface to mass increases, therefore, inversely 
 as the radius of the body. 
 
50 The Solar System 
 
 In the hext place, its gravity could control only 
 a much smaller velocity at its surface, thus mak- 
 ing the critical velocity beyond which a particle 
 would pass off into space much less. By the kin- 
 etic theory of gases, a certain number of particles 
 will in a given time attain the critical velocity, and 
 the more the lower the critical velocity. Thus, 
 from the planet that hath not shall be taken away 
 even that which it hath. 
 
 In consequence, on Mars the density of the air 
 at the surface of the planet at the start was prob- 
 ably not denser than one-seventh of our own, or 
 more rare than that at the top of our loftiest 
 mountains, and now probably is rarer even than 
 this, owing to the greater speed with which it has 
 been lost. 
 
 Rate of loss The rate at which the different gases would be 
 
 different lost differs. The curve of probability shows that 
 
 they would disappear much more rapidly than the 
 
 ratio of their speeds. Water vapor would go long 
 
 before atmospheric air. 
 
 MAXWELL'S LAW. 
 
 The possible values which the components of the mo- 
 lecular velocities can assume are distributed among the 
 molecules in question, according to the same law by which 
 the possible errors of observation are by the method of 
 least squares distributed among the observations. 
 
Mars 5 1 
 
 The number of molecules traveling at speed u is given 
 by the equation, 
 
 just as the probability of an error is given by the equa- 
 tion, 
 
 VALUES OF THE SPEEDS. 
 
 G mean value of speed in metres per second. 
 G mean value of speed in miles per second. 
 
 G G' 
 
 Hydrogen ..... 1838 1.14 
 
 Water vapor ..... 614 0.38 
 
 Nitrogen ..... 492 0.31 
 
 Atmospheric air .... 485 0.30 
 
 Oxygen ...... 461 0.29 
 
 Carbon dioxide .... 392 0.24 
 
 Cyanogen ..... 361 0.22 
 
 These speeds are got from the consideration that the 
 energy, from which follows the temperature, is the same in 
 the two gases ; and, therefore, that 
 
 and, therefore, the speed of the molecule is inversely as 
 the square root of the atomic weight. 
 
 So far theory. Now it is not a little interesting Air on Mars - 
 that observation supports this. That air still ex- 
 ists on Mars, oxygen, nitrogen, and carbonic acid, 
 
The Solar System 
 
 Change in 
 polar caps. 
 
 Pre-Schiapa- 
 rellian know- 
 ledge and 
 ideas. 
 
 is certain because of the changes which we can 
 see going on in the surface markings ; for without 
 air no change could take place, and changes are 
 indisputable. Water is relatively scarce. 
 
 That change goes on upon the planet's surface 
 has been known for a long time. The polar caps 
 were the first telltale. Sir William Herschel, at 
 the end of the eighteenth century, observed that 
 they waxed and waned periodically, and that their 
 period was timed to that of the planet's year. 
 They were therefore seasonal phenomena. 
 
 They behaved like ice and snow, and this they 
 are generally supposed to be. Some astronomers 
 find difficulty in conceiving of enough heat on 
 Mars to permit them to be water, and carbonic 
 acid has been suggested instead. But certain 
 phenomena connected with the melting prove that 
 carbonic acid cannot be the substance. The evi- 
 dence is now very strong that they are what they 
 look to be, and that the necessary heat will some- 
 how be explained. 
 
 Up to the time of Schiaparelli, not much be- 
 yond this behavior of the polar caps and the gen- 
 eral permanency of the dark and light markings 
 was known about the planet. Its physical con- 
 dition was likened to the Earth's, the white 
 patches being polar snows, the dark markings 
 oceans and seas, and the light markings land. 
 
Mars 53 
 
 In fundamentals, indeed, Mars shows a general Mars intrinsi- 
 similarity to the Earth ; but in subsequent char- ^an the** 
 acteristics it betrays a most interesting dissimilar- Earth - 
 ity. It is the dissimilarity that modern study has 
 specially brought out 
 
 The cause of the dissimilarity springs from the 
 planet's size. The less mass of Mars did not 
 permit it initially to present so fertile a field for 
 development. Mere size entirely alters physical 
 possibilities. In the next place, its dwarfing 
 caused it to age quicker than the Earth. 
 
 Our knowledge of the planets, and especially of Schiapareiii's 
 Mars, has advanced greatly within the last quar- 
 ter of a century. The first steps of this advance 
 we owe, not to instruments, but to the genius 
 of one man, the Italian astronomer Schiaparelli. 
 In 1877 he began to observe Mars, and at once 
 showed a keenness of vision surpassing that of 
 any previous observer and a susceptibility to im- 
 pressions surpassing even his acuteness of sight. 
 It was not so much a matter of eye as of brain. 
 For it turns out now, after the fact, that several 
 of his phenomena had been dimly seen and re- 
 corded before, but without that understanding 
 which made of them stepping-stones to further re- 
 sults. 
 
 His object was to map the planet micrometri- 
 
54 The Solar System 
 
 cally. But in the course of his mapping he be- 
 came aware of some curious markings : dark 
 bands seaming the surface of the light areas, or 
 so-called continents. These he named canali, or 
 channels ; for he, in company with every one else, 
 at the time believed the dark regions to be seas. 
 
 Having got the hint, for it was scarcely more 
 than that, during his first season, the opposition 
 of 1877, he then showed that element of genius 
 without which very little is ever accomplished, 
 the persistence to follow up a clue. As Mars 
 came round again he attacked the planet in the 
 light of what he had already learnt, and first con- 
 firmed and then extended his discovery. This he 
 continued to do at each succeeding opposition. 
 The more he studied, the stranger grew the phe- 
 nomena he detected. And it is to his everlasting 
 credit that he did this in the face of the skepti- 
 cism and denial of practically the whole astro- 
 nomic world. He won. The voices that ridiculed 
 him are all silent now. To-day the canals of 
 Mars are well-recognized astronomic facts, and 
 constitute one of the most epoch-making astro- 
 nomic discoveries of the nineteenth century. 
 
 Through a complete cycle of oppositions, that is, 
 from the nearest to the most remote and round to 
 the nearest again, a period of fifteen years, Schia- 
 
Mars 55 
 
 parelli continued to study these curious phe- 
 nomena, having them practically all to himself,, 
 Indeed, his grand isolation in the quest makes 
 one of the finest and saddest chapters in the his- 
 tory of discovery. In the course of these solitary 
 years he came to see the canals better, and they 
 grew, on improving acquaintance, steadily more 
 strange. He found that they were far more reg- 
 ular than he had at first thought, and he noted 
 that they were dependent in appearance upon the 
 season of the planet's year. So, likewise, were 
 the large dark markings, and he attributed the 
 behavior of both to a seasonal shift of water over 
 the surface. 
 
 His theory of the planet's physical condition, 
 derived from his observations, was as follows : 
 that the polar caps were ice and snow ; that the 
 blue-green areas were seas and the reddish-ochre 
 ones land; that the canals were natural water- 
 channels or straits honeycombing the land and 
 cutting it up into a patchwork of large islands, a 
 sort of natural Venice on a world-wide scale ; and 
 finally that the surface was subject to annual or 
 semiannual inundations and dryings-up, timed to 
 the melting of the polar caps. 
 
 Schiaparelli retired practically in 1892, though 
 not formally till a little later. His work was taken 
 
56 The Solar System 
 
 up by other hands, and the impetus he gave the 
 matter has resulted in a knowledge of Mars which 
 has quite revolutionized even the conception he 
 bequeathed of the planet. 
 
 Methods of Before proceeding to post-Schiaparellian work, 
 iervation. . interest you to know how the phenomena 
 
 in question have been detected, and what they 
 look like when seen. 
 
 Contrary to what the layman thinks, the size 
 of the instrument is the least important factor in 
 the process. As in most things, the man is the 
 essential machine ; and next in desirability to the 
 presence of man is the absence of atmosphere. 
 In good air, with fair attention, the canals are not 
 very difficult objects. Indeed, the surprise is that 
 they were not detected long ago. Under suitable 
 atmospheric conditions a four-inch glass will show 
 them perfectly. Steady air is one essential ; 
 steady study another. 
 
 The canals. In appearance they are unlike any other phe- 
 nomena presented in the heavens. Pale pencil 
 lines, deepening on occasion to India ink, seem to 
 cobweb the continents. Their tone depends on 
 the seeing, in the first place, and on the season, 
 in the second. Their width is invariable through- 
 out, and their directness something striking. 
 Measurable width they have not ; it is only by 
 
m 
 
58 The Solar System 
 
 depth of tint that their importance is inferred. 
 But their most amazing attribute is their geomet- 
 ric character. They seem to be generally arcs of 
 great circles drawn from certain salient points on 
 the planet's surface to certain other equally salient 
 ones. 
 
 Their number appears to be legion. Schiapa- 
 relli discovered 104. But the better the planet is 
 seen the more of them come out. About 350 
 have now been mapped at Flagstaff, and the num- 
 ber is only limited by our penetration. Like the 
 asteroids, the larger ones have already been de- 
 tected. Each opposition now brings out smaller 
 and smaller specimens. 
 
 Their But now comes a most interesting fact con- 
 
 character necte d with them which was discovered by Schia- 
 parelli and found equally true at Flagstaff. They 
 are not always equally visible. Sometimes they 
 are conspicuous, sometimes scarcely discernible 
 even to a practiced eye. And this is not mere 
 matter of distance. The best time for seeing the 
 planet is not the best time for detecting the 
 canals. 
 
 At certain oppositions we pass the planet at 
 close quarters, at certain others a good way off. 
 The close approaches are called favorable opposi- 
 tions, the distant encounters unfavorable ones. 
 
Mars 59 
 
 But the latter are not so unfavorable as they are 
 thought. For another factor beside nearness af- 
 fects the reckoning. The planet's axis is tilted to 
 the plane of its orbit at an angle of 25, and is so 
 faced that the southern hemisphere is presented 
 to us at the time of closest approach. Now the 
 canals lie chiefly in the northern hemisphere. In 
 the next place, it is then the northern winter, 
 and careful comparison reveals the fact that the 
 conspicuousness of a canal is a function of the 
 Martian time of year, becoming pronounced in 
 summer and fading out in winter. 
 
 This is one reason why the canals so long 
 eluded astronomers. They were not looked for 
 at the proper time. 
 
 The first important post-Schiaparellian advance s e as " not 
 was made in the dark regions of the planet. 
 
 For two centuries the dark regions were held 
 to be seas. It became evident, however, from 
 Pickering's observations in 1892 that the great 
 part of them could not be such. In 1894, at 
 Flagstaff, it further became evident that no part 
 of them could be water. From the way in which 
 the clarification of the dark regions progressed 
 with the planet's seasons, it had become patent 
 that the bodily transference of substance, such, 
 for instance, as water, from one place to another, 
 
 seas. 
 
60 The Solar System 
 
 could not account for the phenomena. For the 
 decrease in one locality was not offset by the in- 
 crease in others. As the quantity of the change, 
 positive and negative, did not balance, the change 
 could not be due to a shift of matter. It must, 
 therefore, be ascribable to a transformation of 
 matter. And the only thing of suitable conduct 
 and proper local color to show the phenomena 
 was vegetation. The " seas " were not seas, but 
 probably areas of vegetation. 
 
 Oases. The next significant discovery was the detec- 
 tion of the oases, or small round black spots that 
 dot the planet's surface. These were initially seen 
 as such by W. H. Pickering, at Arequipa, in 1892. 
 Pickering called them lakes, but for a reason 
 which will appear later it seems more proper to 
 consider them oases. Quite as singular a feature 
 as the canals, they prove to be as universal a one. 
 They are the more difficult of detection ; which 
 is the reason they were recognized later. Schia- 
 parelli told the writer that he had himself sus- 
 pected them, but could not make sure. 
 
 Just as the canals form a mesh over the disk, 
 so the oases make the knots where the lines of 
 the network cross. To them, in short, the canals 
 rendezvous. The number of lines which thus 
 come together at one and the same point is some- 
 
Mars 6 1 
 
 times considerable. Nine meet at the Phoenix 
 lake, eleven at the Trivium Charontis, and no less 
 than seventeen at the Ascraeus Lacus at the top 
 of Ceraunius. Nor, so far as can be seen, is any 
 important junction without its spot. Their bear- 
 ing upon the explanation of the canals is at once 
 evident. 
 
 In character the oases are, when well seen, very 
 small and very dark. Too small to disclose dis- 
 tinctive color, they are the most deeply complex- 
 ioned detail upon the disk, and presumably blue. 
 It is only in poor air that they show large and 
 diffuse. About three degrees in diameter and 
 seemingly quite round as a rule, they must be 
 100 miles across, and, for all their minuteness, 
 cover a goodly area of ground. 
 
 They seem to share the same seasonal transfor- 
 mation with all the other markings. 
 
 The next step was the discovery of canals in Canals and 
 
 , , , , . r A , , ~ 1-1 oases in the 
 
 the dark regions of the planet. Streaks in these dark regions, 
 regions were seen in 1892 at Arequipa and at the 
 Lick Observatory, much as Dawes had seen 
 streaks in the light ones thirty years before. But 
 in 1 894, at Flagstaff, Mr. Douglass found that the 
 streaks were not irregular markings, but a sys- 
 tem of lines possessing the same singular char- 
 acteristics which distinguish and differentiate the 
 
62 The Solar System 
 
 "canals" in the light regions from other celestial 
 phenomena. In short, he detected in the dark 
 regions what Schiaparelli had detected in the 
 light. Counterparting exactly the network over 
 the light areas, a mesh of similar lines overspread 
 the blue-green areas. The lines were of uniform 
 width, of unswerving directness, and went from 
 definite points to other equally determinate ones. 
 These points were always of geographic impor- 
 tance. They were at the ends of " seas," at the 
 bottom of "bays," or at points on the "coast- 
 line" where canals debouched. The lines con- 
 nected these topographical centres, crossing one 
 another in the process, and at the junctions there 
 showed, just as in the light areas, dark round 
 spots. 
 
 Instantly to be deduced from such engraving 
 was that the " seas " were not bodies of water. 
 We knew this already, as I have shown ; but the 
 evidence was valuable in completely convincing 
 those who require more than mediate proof. Per- 
 manent lines cannot be writ on water. The seas 
 lost their character forever. 
 
 The absence of any bodies of water outside of 
 the temporary polar sea introduces a far-reaching 
 difference between Mars and the Earth. On 
 Earth three quarters of the surface is water ; on 
 
Mars 63 
 
 Mars all is land. Instead of having more sea 
 than it can use, the planet must be in straits for 
 the article. Its whole supply comes from the 
 annual melting of the polar caps. 
 
 The canal system of the dark regions not only 
 
 " 
 
 ir< /loRTh PoLAR CAP. JA/H 1*5)01 CABALS JU/HE 
 
 \*r ~\~i* 
 
 8HOW1/1Q THE !De/1TITY OF THE TYYO.. 
 
 FIG. IX. 
 
64 The Solar System 
 
 Two systems, resembles the system in the light ; the one joins 
 on to the other. The points where the system in 
 the light areas strike the dark are the points from 
 which the canals in the dark regions set out. The 
 two are thus but parts of one world-wide whole. 
 Whatever purpose the one subserves is thus taken 
 up and extended by the other. 
 
 Nor does the communication come to an end in 
 the dark regions. From the southern portions of 
 these, in the southern hemisphere, other canals 
 run straight into the polar cap ; in the northern 
 hemisphere, similarly, canals penetrate to the most 
 northern limit of the snow. 
 
 Lastly, the rifts which appear in the caps during 
 the process of melting turn out to be where 
 subsequently are seen canals. Now, as there 
 are no mountains on Mars, differences of level 
 cannot be a cause of melting ; areas of vegetation 
 could. 
 
 Summation. We may sum up our present knowledge of the 
 surface conditions of the planet as follows : 
 
 (1) Change takes place upon the planet's sur- 
 face ; this proves the presence there of an atmos- 
 phere. 
 
 (2) The limb-light, the apparent evidence of a 
 twilight, and the albedo, all point to a density for 
 this atmosphere very much less than our own. 
 
Mars 65 
 
 (3) The polar caps melt in their summer and 
 accumulate in their winter, thus showing them- 
 selves to be seasonal in character. 
 
 (4) As they melt, they are bordered by a blue 
 belt, which retreats with them. This negatives 
 carbonic acid as the substance composing them, 
 and leaves to our knowledge only water as a possi- 
 ble explanation. 
 
 (5) Their extensive melting shows their quan- 
 tity to be inconsiderable, and points to a dearth of 
 water. 
 
 (6) Comparison with previous observations 
 shows the melting to occur in the same consecu- 
 tive places year after year. The melting is thus 
 a thing which can be locally counted on. 
 
 (7) The greatest local melting is just south of 
 the largest dark (blue-green) regions, the bays in 
 the polar sea in these longitudes being the largest. 
 
 (8) The dark regions are subject to a wave of 
 seasonal changes ; 
 
 (9) which follows upon the melting of the cap. 
 They darken in early summer and fade out in 
 their autumn. 
 
 (10) The dark regions are not seas : first, be- 
 cause in Professor W. H. Pickering's experiments 
 their light showed no trace of polarization, while 
 that of the polar sea did ; 
 
66 The Solar System 
 
 (n) second, because the quantity of the dark- 
 ening is not offset by the synchronous lightening 
 elsewhere. It cannot therefore be due to shift of 
 substance ; 
 
 (12) third, because they are seamed by a canal 
 system counterparting that of the light areas, 
 permanent in place. 
 
 (13) Extension of this shows that there are no 
 permanent bodies of water on the planet. 
 
 (14) All the phenomena are accounted for by 
 supposing them to be areas of vegetation. 
 
 (15) The polar sea being a temporary affair, the 
 water from it is fresh. 
 
 (16) Observations on the terminator reveal no 
 mountains on Mars, the details of the observa- 
 tions being incompatible with such supposition ; 
 
 (17) but do reveal apparently clouds, which, 
 however, are rare, and are chiefly visible at sunrise 
 and sunset, 
 
 (18) and seem connected with the heat equator. 
 
 (19) The bright areas look and behave like 
 deserts. 
 
 (20) In their winter, the south temperate light 
 regions are covered by a white veil, which may be 
 hoar-frost or may be cloud. 
 
 (21) Very brilliant patches appear also in the 
 equatorial light regions that last for weeks, and 
 seem independent of diurnal conditions. 
 
Mars 
 
 67 
 
 Conclusions 
 as to 
 physical 
 
 (22) They appear always in the same places. 
 
 (23) A spring haze surrounds the polar caps 
 during certain months, outside of and distinct from 
 the cap itself. 
 
 (24) A progressive change of darkening sweeps 
 over the planet's face from pole to pole semi- 
 annually, beginning with the cap, and developing 
 as vegetation would down the disk. 
 
 These phenomena lead to the conclusion that 
 the polar caps are masses of snow and ice ; that 
 the light areas are deserts ; that the blue-green condition 
 areas are tracts of vegetation ; that there are no 
 permanent bodies of water on the planet, and 
 very little water in any form ; that the surface is 
 remarkably flat ; that the temperature is moder- 
 ately high by day but low at night ; that it is 
 fairly warm in summer but cold in winter ; and 
 that the seasonal change of the vegetation is 
 marked even at our distance away. 
 
 To these conclusions we are led by the general 
 aspect and behavior of the planet's disk. We 
 have reached them without reference to the canals 
 considered in themselves, and we should continue 
 to put faith in them were the canals, with all 
 their strange characteristics, blotted from exist- 
 ence. Unbeholden, then, to the canals for this con- 
 clusion, we are the more impressed to find that the 
 
68 The Solar System 
 
 supposition that the "canals" are not the result 
 of chance falls completely in line with our result. 
 
 Water is very scarce on the planet, and is abso- 
 lutely essential to life. Vegetation exists there, 
 and it is therefore highly probable that organic 
 life is to be found there, too. This becomes a 
 posteriori probable, when we behold a system of 
 lines inexplicable on any other ground and pre- 
 cisely what would be needed for the diffusion of 
 water over the planet's surface. 
 
 What we find is this : 
 
 (25) A network of fine dark lines meshing the 
 deserts. 
 
 (26) The lines are uniform throughout and from 
 five to thirty-five miles in width, 1 
 
 (27) and hundreds, sometimes thousands of 
 miles long, 
 
 (28) usually, if not always, following arcs of 
 great circles, 
 
 (29) starting from topographically important 
 points in the dark regions, 
 
 (30) and traveling to other equally conspicuous 
 points ; 
 
 (3 1) both terminals show dark spots, a caret in the 
 coastline and what seems around spot in the desert ; 
 
 1 Tests by the writer on telegraph lines show that a line can 
 be seen, owing to its length, when its width is 2".$, to the naked 
 eye. This would mean about 5 miles on Mars. 
 
Mars 69 
 
 (32) all the way from three to seventeen 
 " canals " will converge upon the same spot ; 
 
 (33) the spots are perhaps a hundred miles in 
 diameter, and their number is very great ; 
 
 (34) the dark regions are meshed by a similar 
 network ; 
 
 (35) the points of departure of both are the 
 same; 
 
 (36) similar centring spots show in the dark 
 areas, darker than their background ; 
 
 (37) with the dark network "canals" others 
 connect, running to the edge of the extreme melt- 
 ing limits of both caps ; 
 
 (38) the lines are seasonal phenomena, develop- 
 ing after the melting of their respective polar cap 
 and fading out later ; 
 
 (39) those in the polar regions occupy the place 
 of earlier rifts in the snow-field, as if the ground 
 were there thawed by vegetation. 
 
 They are of uniform width ; that is, they waste 
 nothing in breadth. Whatever breadth is neces- 
 sary is used, and no more, and that is retained 
 throughout. They go directly from certain con- 
 spicuously probable points to certain others. If 
 we were obliged to connect the planet by a sys- 
 tem of intercommunication, it is precisely those 
 points we should ourselves select. 
 
70 The Solar System 
 
 In addition to the departure points on the bor- 
 ders of the dark regions which are provided by 
 nature are a host of others not apparently so origi- 
 nated. These are the round black dots, the 
 oases. They are found at the intersections of 
 the lines. How important they are in the planet's 
 economy is to be inferred from the host of canals 
 each of them receives. Four, very rarely three, 
 is the minimum number of approaches or depar- 
 tures from them, and this number rises in the case 
 of Ceraunius to seventeen. Even London hardly 
 has this number of railway lines entering and 
 leaving it. It is not too much to suppose, though 
 as yet we cannot count it more than a conjecture, 
 that the oases serve some such purpose as our 
 cities and are centres of population. 
 
 From this, we add to our list of conclusions, 
 that the canals are artificial, and therefore imply 
 organic intelligent life upon the planet. 
 
 Our synthesis leads, then, to the conclusion 
 that Mars is circumstanced like ourselves in the 
 midway of planetary existence, but that the planet 
 has advanced further on the road to old age and 
 death than we have yet done. 
 
 That its world-life was, in any but the broadest 
 sense, an analogue of our own, is certainly not the 
 case. Its career began under different physical 
 
Mars 71 
 
 conditions, owing to its size, ran more rapidly 
 through its successive stages, again owing to its 
 size, and will come to an end sooner for the same 
 reason. 
 
 As a detail of this, life on Mars must take on 
 a very different guise from what it wears on 
 Earth. It is certain that there can be no men 
 there ; that is as certain as anything well can be. 
 But this does not preclude a local intelligence 
 equal to, and perhaps easily superior to, our own. 
 We seem to have evidence that something of the 
 sort does exist there at the present moment, and 
 has made imprint there of its existence far exceed- 
 ing anything we have yet left upon mother Earth. 
 
 In conclusion, let me warn you to beware of 
 two opposite errors ; of letting your imagination 
 soar unballasted by fact, and, on the other hand, 
 of shackling it so stolidly that it loses all incentive 
 to rise. You may come to grief through the first 
 process ; you will never get anywhere by the 
 second. Take general mechanical principles for 
 compass and then follow your observations. Im- 
 agination is as vital to any advance in science as 
 learning and precision are essential for starting 
 points. 
 
IV 
 
 SATURN AND ITS SYSTEM 
 
 Saturn. SATURN marked to the ancients the outer bound- 
 
 ary of the solar system. From its slow motion, 
 they rightly conjectured it to be the farthest away 
 of all the "wanderers," and wrongly to be sinister 
 in intent. Our word "saturnine" expresses the 
 feeling it inspired. 
 
 In the telescope, Saturn is undoubtedly the 
 most immediately impressive object in the hea- 
 vens. Few persons can be shown the planet for 
 the first time without an exclamation. To see it 
 sail into the field of view, its great ball diademed 
 by an elliptic ring, and carrying with it a retinue 
 of star-points set against the blue-black back- 
 ground of the sky, gives the most prosaic a sensa- 
 tion. 
 
 Saturn's self we shall leave till we come to 
 speak of Jupiter (in the next chapter) ; and shall 
 here consider the two systems of bodies dependent 
 on it, its rings and its satellites. 
 
 The Unique, so far as we know, is that appanage 
 
 of Saturn which makes the planet so superb a 
 
Saturn and its System 73 
 
 sight, the ring system. It baffled Galileo with 
 his opera-glass, who first saw the planet triform, 
 and then, to his surprise, marked the two smaller 
 bodies disappear, as if Saturn had indeed eaten 
 his offspring. 
 
 Crowning the planet's equator are several con- 
 centric flat rings of light. Three are usually 
 distinguished, known as A, the outer ring ; B, the 
 middle ring ; and C, the inner or dusky ring. The 
 outer, A, has an extreme radius of about 85, 700 
 miles. It is 12,000 miles across, and is separated 
 from B by a dark space 3400 miles wide, known 
 as Cassini's division. B, the broadest and bright- 
 est of the rings, is 17,000 miles in width, and is 
 joined without perceptible interval by C, which is 
 much fainter, resembling a crepe veil stretched 
 from the inner edge of B, 9500 miles toward the 
 planet, from whose limb it is sundered by a gap of 
 between 7000 and 8000 miles. 
 
 Two thirds way from the outer to the inner 
 edge of A is another division or dark line, much 
 narrower than Cassini's, and sometimes nearly 
 invisible, known as Encke's division, though sus- 
 pected before by Short. 
 
 Edward Roche, in 1848, was the first to show Constitution 
 
 of the rings. 
 
 that the rings were composed of discrete par- 
 ticles, mere dust and ashes. He drew this con- 
 
74 The Solar System 
 
 sequence directly from his investigations on the 
 minimum distance a small fluid satellite may safely 
 approach a fluid primary ; for within a certain dis- 
 tance the differential or tidal pull of the planet 
 must disrupt the satellite. This distance is called 
 Roche's limit. 
 
 For equal densities of planet and satellite, 
 Roche's limit is 2.44 times the planet's radius ; 
 
 for unequal densities, as \ x 244, where d is 
 
 the density of the primary ; d' of the satellite. 
 
 Saturn's system offers the only instance where 
 matter circulates within the limit, and Roche 
 stated distinctly that the rings, therefore, must 
 be mere meteoric stones. 
 
 Even Laplace had shown that the rings must 
 be broken up for stability's sake into several nar- 
 row ones, each revolving at its own rate. Pierce 
 proved that they could in no case be solid. Max- 
 well then demonstrated that they could not be so 
 much as liquid, as disrupting waves would be set 
 up, but must consist of a swarm of small bodies, - 
 brickbats he likened them to, each pursuing its 
 own path. What the spectroscope in Keeler's 
 ingenious hands made visible to the eye had 
 thus been known to mechanics from the time of 
 Laplace. 
 
Saturn and its System 75 
 
 These flights of small bodies are so exactly in AH in the 
 one plane that they vanish when the rings are s 
 turned edgewise to the Earth. Their lustre shows 
 them to be relatively densely packed, so that colli- 
 sions among them must be not infrequent. In 
 consequence of this, Maxwell predicted that they 
 would eventually be forced both out or in, and in 
 part fall upon the ball, in part be driven farther 
 from the planet. Certainly such must ultimately 
 happen ; but the evidence is not conclusive that 
 either process has yet been observed. 
 
 The spectroscope shows that, unlike Saturn, No air about 
 they carry no air with them. This, from their 
 minute size, was to be expected on the kinetic 
 theory of gases and the clever deduction from it 
 as to the atmosphere a body may retain, made by 
 Johnstone Stoney. 
 
 To attempt to account for their dimensions and Gaps in them, 
 divisions might at first seem hopeless. Why A is 
 made up of an outer and an inner portion parted 
 by Encke's streak ; why B is sundered from A by 
 Cassini's division ; and why C is sharply con- 
 trasted with B at its inner edge, sound like difficult 
 questions. But nothing in celestial mechanics is 
 the outcome of chance, and this is no exception to 
 the rule. 
 
 To begin with, Roche's limit falls just at the 
 
76 The Solar System 
 
 Roche's limit, outer edge of the system, supposing the density 
 of the satellite to be f of the primary's. Now 
 the satellites of Saturn are certainly a little denser 
 than the planet. From our present values of its 
 mass and volume, Titan's density comes out .24. 
 This, then, is what has limited the system ex- 
 ternally. 
 
 For the rest of it, another force has proved 
 fashioner. 
 
 Commensu- Our mathematics do not permit us to solve 
 rate periods. 
 
 rigorously the problem of three bodies ; that is, 
 
 the motion of a first revolving round a second and 
 perturbed by a third. We have to have recourse 
 to approximations in series. We can thus deter- 
 mine to any degree of accuracy the result. Now 
 the perturbative effect produced by a third body 
 upon the major axis of a second revolving in its 
 own plane may be expressed by a series developed 
 in terms depending on powers of the eccentricity 
 and cosines of multiple arcs of the mean motions. 
 The typical form of one of these terms is 
 
 COS - ~ 
 
 where P is a function of a and a', the radii vectores. 
 From this, it appears that if / and q are nearly in 
 the inverse ratio of the mean motions, 
 pn qn' is nearly o, 
 
Saturn and its System 77 
 
 and the term has a large coefficient, and therefore 
 a large value. 
 
 If, then, the mean motions, and therefore the 
 periods, of perturber and perturbed are commen- 
 surable, the disturbing effect upon the major axes 
 of each will be great. The major axes will be 
 altered until the periods cease to be commensura- 
 ble, and it will be long before perturbation brings 
 them back to commensurability again. 
 
 Furthermore, the least value / -f- in can have is Greatest 
 p q, while the period of the action of the term t h e smallest 
 
 ratio. 
 
 is . _ , ; whence the greatest term is when/ 
 
 and q are both as small as possible, since conjunc- 
 tions will occur oftener in proportion as q is small. 
 
 Geometrically, the effect can be seen in the Effect 
 
 r n /-i i ^ j- 4. -u- 11 geometrically 
 
 following way. Clearly, the disturbing pull is considered, 
 greatest when the two bodies are in conjunction, 
 and so long as the periods are incommensurable, 
 conjunctions will occur in different parts of the 
 orbit successively, and thus neutralize one an- 
 other's effect upon the major axes. But if the 
 periods of the two bodies be commensurable, con- 
 junctions will occur in the same place over and 
 over again, and the major axes will be altered 
 there without compensatory alterations elsewhere ; 
 and this will go on until the major axes are so 
 
78 The Solar System 
 
 altered that commensurability of period, which 
 depends on the major axis, ceases. Then the 
 bodies will cease to affect each other forcibly. 
 They will gradually meet each other elsewhere, 
 finally oppositely to what they did at first, and 
 the action first produced will be as gradually un- 
 done ; but it will be very long before the major 
 axes attain their original value again ; then they 
 will pass rapidly through them once more in the 
 reverse way. 
 
 If, then, the periods of the two bodies are com- 
 mensurable, they will not appear to be so, since 
 their major axes will stay commensurate but a 
 brief time compared with the time they are out. 
 Gaps due to Now, if we have a swarm of bodies revolving 
 at var i us distances round a central mass, and 
 disturbed by a third, the third will seem, in con- 
 sequence of this, to sweep out spaces where other- 
 wise bodies would revolve in times commensurate 
 with its own. Jupiter has done this very thing in 
 the case of the asteroids, striping the zone with 
 vacant belts. Calculation alone reveals this, as 
 the asteroids are too few to disclose the fact to 
 the eye. But in the rings of Saturn we can ac- 
 tually see the empty places. The gaps in the 
 rings are shown in the following table and in the 
 accompanying picture of the ring system : - 
 
Saturn and its System 
 
 79 
 
 FIG. X. SATURN'S RINGS. 
 
 Outer radius outer ring A 
 Encke's division . . 
 
 Inner radius outer ring A 
 Cassini's division . . 
 
 Outer radius ring B . . 
 
 Inner radius ring B . . 
 
 Outer radius ring C . . 
 
 Inner radius ring C . . 
 
 Planet radius . 
 
 Old 
 Determination. 
 
 54000 
 74000 
 
 72400 
 56200 
 56200 
 46700 
 37500 
 
 New 
 Determination. 
 
 80000 
 
 73200 
 
 85700 
 75300 
 
 71900 
 54700 
 54700 
 43900 
 37000 
 
 SlOIO 
 
 73620 
 
 Let us note these gaps and edges and then cal- Gaps 
 culate what perturbing effect the satellites would 
 exert. The satellites which would have the great- 
 
8o The Solar System ' 
 
 est perturbative action on the rings is Mimas, his 
 effect being more than three times that of Encel- 
 adus and more than twice that of Tethys. 
 The equations of motion are for x 
 
 d^x _ x , m' (x' x] m' x' 
 
 ~dp r -73- (r' r}' 6 ' ~~r^' 
 
 of which the first is the direct force of the central body, 
 
 whose mass is taken as i, upon mj and the other terms 
 
 are the perturbing force of m' on m. 
 
 Assuming the three to be in conjunction, this last be- 
 comes m' { g ~j7s)i where p = r' r. Supposing m 
 
 to be 74,000 miles from the centre of Saturn, and Mimas, 
 Enceladus, and Tethys at 117,000, 150,000, and 186,000 
 miles respectively, and taking the masses as proportionate to 
 their volumes, their radii being taken as 400, 400, and 600 
 miles, we find for their relative perturbative effects : 
 
 Mimas 299 
 
 Enceladus ....... 82 
 
 Tethys . . . . . .no 
 
 The action of the others is smaller still. Now 
 the major axis of a part of the ring which has a 
 period commensurate with that of Mimas may be 
 found from the formula - 
 
 r 2 _ a^ 
 
 77 ~ a? 
 
 Kepler's third law. Beginning, then, with the 
 simplest, and therefore the most potent ratio, J, 
 we find 73,600 miles for the major axis of a particle 
 
Saturn and its System 
 
 81 
 
 whose period is J that of Mimas. This distance 
 falls almost exactly in the centre of Cassini's 
 division. 
 
 Proceeding to the next simplest ratio, \ of Mi- 
 mas's period, the corresponding distance comes 
 out 56,170 miles. This is the distance from the 
 centre of the planet to the inner edge of ring B. 
 
 Again, \ of the period of Mimas gives 46,370 
 miles. This is not far from the radius of the inner 
 edge of the dark ring. So much for the action of 
 Mimas. 
 
 The major axis of one half the period of Encel- ByEnceladus. 
 adus falls without the system, but the major axis 
 of one third the period occurs at 72,090 miles. 
 This is not far from the inner edge of Cassini's 
 division. But the striking coincidence with Encel- 
 adus is that the distance corresponding to -f of his 
 period lies at 81,400 miles, or at Encke's division. 
 
 For Tethys, the only commensurable ratio is \. To Tethys. 
 This makes the distance fall at Cassini's division. 
 
 Thus Mimas, aided by Tethys, has been the 
 divider of the rings into A, B, and C ; while Encel- 
 adus has subdivided A. 
 
 Not less interesting mechanically is Saturn's 
 satellite system. Eight of these bodies are posi- 
 tively known, distanced from Saturn and diame- 
 tered as follows : 
 
 Satellites. 
 
82 The Solar System 
 
 RELATIVE SIZE AND 
 
 POSITION OF THE SATELLITES. 
 
 No. 
 
 Name. 
 
 Diameter 
 in Miles. 
 
 Distance from Saturn 
 in Miles. 
 
 I. 
 
 Mimas . . 
 
 . 800 
 
 .... 117,000 
 
 II. 
 
 Enceladus . . 
 
 . 800 
 
 . . . . 150,000 
 
 III. 
 
 Tethys . . 
 
 . I,2OO 
 
 . . . . 186,000 
 
 IV. 
 
 Dione . . 
 
 . 1,100 
 
 . . . . 238,000 
 
 V. 
 
 Rhea . . 
 
 . 1,500 
 
 .... 332,000 
 
 VI. 
 
 Titan . . 
 
 3,500 
 
 .... 771,000 
 
 VII. 
 
 Hyperion . . 
 
 . 500 
 
 .... 934,000 
 
 VIII. 
 
 lapetus . . 
 
 . 2,000 
 
 .... 2,225,000 
 
 Relative ^ w ^ ^ e seen tnat tne l ar g est Titan OCCU- 
 
 the 6 P^ es a centra ^ position in the line. This might 
 satellites. seem accidental until one recalls the fact that 
 Jupiter, the largest of the planets, holds the same 
 relative place in the solar system : for the plan- 
 etary system tabulated in the same way is as 
 follows : 
 
 SOLAR SYSTEM. 
 
 ,, ,. T Diameter in Distance from Sun in 
 
 No. Name. MUg ^ Millions of Miles. 
 
 I. Mercury . . . 3,300 ..... 36 
 
 II. Venus . . . 7,630 ..... 67 
 
 III. Earth . . . 7,918 ..... 93 
 
 IV. Mars . . . 4,220 ..... 141 
 V. Asteroids . . . 10-500 ..... 250 
 
 VI. Jupiter . . . 86,500 ..... 483 
 
 VII. Saturn . . . 72,500 ..... 886 
 
 VIII. Uranus . . . 31,900 ..... 1,782 
 
 IX. Neptune . . . 34,800 ..... 2,792 
 
Saturn and its System 83 
 
 With the hint given by this, at least singular, 
 coincidence, let us examine the other satellite 
 systems. Two others available for comparison 
 present themselves, that of Jupiter and that of 
 Uranus. Jupiter's system is this : 
 
 fj A/ Diameter Distance from Jupiter 
 
 in Miles. in Miles. 
 
 V. (Nameless). . . 100 .... 112,500 
 
 I. lo ... 2,500 .... 261,000 
 
 II. Europa . . . 2,100 .... 415,000 
 
 III. Ganymede. . .3,550 .... 664,000 
 
 IV. Callisto . . . 2,960 .... 1,167,000 
 
 Here, again, the largest body fills the centre 
 of the field. 
 
 With Uranus, we have : 
 
 jj AT Diameter Distance from Uranus 
 
 No - Name - in Miles. in Miles. 
 
 I. Ariel . . . 500 ..... 120,000 
 
 II. Umbriel . . . 400 167,000 
 
 III. Titania . . . 1,000 273,000 
 
 IV. Oberon . . . 800 365,000 
 
 The same relative agreement of position and 
 mass ! 
 
 Now consider the probability that this coinci- Position of 
 dent arrangement should be due to chance. The largest mass * 
 greater mass might be found either at the begin- 
 ning, in the middle, or at the end of the line. 
 Take, as starting point, that it is found to occupy 
 
84 The Solar System 
 
 the middle of the line in the Saturnian system. 
 The chance, if chance arranged it, that it should 
 occupy the like position in the solar system is one 
 out of three, or two to one that it did not. That 
 it should also do so in the Jovian system is \ of J, 
 or eight to one against it. That furthermore the 
 Uranian system should show the same is \ x J x i. 
 In other words, it is twenty-six to one that the 
 largest satellite would not be found to occupy in 
 all the same position. And it does. Twenty-six 
 to one in betting is very much better than cer- 
 tainty odds. 
 
 Of second This is not all. Consider the four systems 
 more carefully. It will be seen that the second 
 largest mass is in each of them found outside the 
 first and in three out of the four next to it. In 
 the fourth, it comes next but one. Now the 
 chances against this being accident are much 
 greater than for the first coincidence ; while the 
 chance that the two chances should occur together 
 as they do is the product of both. You will see 
 that we are getting outside any chance in the 
 matter at all, and have come face to face with 
 some cause working to this end. 
 
 Of second But we are by no means done with the analo- 
 
 maxima. . Tr f . . , 
 
 gies yet. If we construct a curve of positional 
 sizes, we discover that it has two maxima, not one. 
 
Saturn and its System 
 
 A second lies inside the first. In the solar system, 
 our Earth occupies this place ; in the Jovian, lo ; 
 in the Saturnian, Tethys ; in the Uranian, Ariel. 
 Plotted in curves, the profiles of the four sys- 
 tems show a striking family resemblance, as can 
 be seen from the diagram ; and from what we 
 have noted of the probabilities in the case, we 
 cannot doubt that this betokens a law of system 
 development. 
 
 JITII/E ATTRACTIVE 
 
 FORCE OF 
 
 PRIMARY ON 
 
 RCEST SECONDARY 
 
 Sun on Jupiter t 
 
 taken as unify 
 
 M 
 
 URANIAN SYSTEM 
 
 DISTANCE: FROM PRIMARY 
 POSITION OF MASSES IN SATELLITE SYSTEMS 
 FIG. XI. 
 
86 
 
 The Solar System 
 
 Inclinations 
 of orbits to 
 planet's 
 equator with 
 increase of 
 
 A second point connected with the system is 
 the relative inclinations of the orbits to the plane 
 of the planet's equator. The inclinations to the 
 
 distance from planet's equator of the rings and of the several 
 planet. 
 
 satellites proceeding outward are as follows : 
 
 Same in 
 
 Jovian 
 
 system. 
 
 SATURNIAN SYSTEM. 
 
 Ecliptic. 
 o / n 
 28 10 22 
 28 10 10 
 28 10 10 
 28 10 10 
 
 Inclination of Orbit to 
 
 Planet's Equator. 
 
 Planet's equator . . 
 
 Rings 
 
 Mimas 
 
 Enceladus .... 
 
 Tethys 28 10 10 
 
 Dione 28 10 10 
 
 Rhea 28 10 10 
 
 Titan 27 38 49 
 
 Hyperion 27 4.8 
 
 lapetus 18 28.3 
 
 o o 
 o o 
 o o 
 o o 
 o o 
 o o 
 
 31 
 
 1 5 
 
 12 
 12 
 12 
 12 
 12 
 12 
 
 33 
 34 
 
 It thus appears that the inclinations of the 
 planes of the orbits to the plane of the planet's 
 equator increase as the distance from Saturn in- 
 creases ; furthermore, that the increase is regular. 
 A smooth curve represents them all. 
 
 Now let us turn to the Jovian system. 
 
 The inner satellite, or Benjamin of the family, 
 moves apparently in the plane of its primary's 
 equator. 
 
Saturn and its System 
 
 JOVIAN SYSTEM. 
 
 Inclination of Orbit Plane to 
 Planet's Equatorial Plane. 
 
 I. lo o o' o" 
 
 II. Europa o i' 6" 
 
 III. Ganymede o 5' 3" 
 
 IV. Callisto o 24' 35" 
 
 Here, again, the inclinations increase as we go 
 out, and the smooth curve representing them is, 
 
 INCLINATIONS OF SATELLITE ORBITS TO PRIMARY'S EQUATOR 
 
 JOVIAN SYSTEM 
 
 ! Tethys 
 
 ; M'l'mas ; ,0ione 
 
 SATURN IAN SYSTEM 
 
 Hyper 
 
 Titan 
 
 flings Enceladus 
 
 FIG. XII. 
 
 Callisto. 
 
 'lapetus 
 
 when reduced in scale, almost the counterpart of 
 the Saturnian. 
 
 Clearly some force has operated to compel the Force occa- 
 
 ,,. . . , . sioning this 
 
 satellites to travel in the planet s equatorial plane, due to planet, 
 and this force has emanated from the planet, since 
 it grows less potent as one departs from him. 
 
88 The Solar System 
 
 What this force may be, we shall now proceed to 
 ascertain. 
 
 Combination In order to make the action in the case, com- 
 plicated at best, as understandable as possible, I 
 shall begin by considering what causes the preces-, 
 sion of the equinoxes, or that slow rotation of the 
 pole of the Earth round the pole of the ecliptic. 
 
 Effect of pull Were the Earth a sphere, its axis would main- 
 
 spherofcT 5 " 7 tam an invariable position in the heavens, since 
 any other body would act upon it as if all its 
 matter were collected in its centre ; but with a 
 spheroid the case is different. We may consider 
 the equatorial protuberance as a ring of matter 
 fastened after the manner of a life-preserver around 
 the Earth's waist. Now suppose the Earth tilted 
 up from the line joining its centre and the centre 
 of the attracting body. That body would tend to 
 pull the nearer part of the ring down into its plane 
 and the more distant portion of the same up into 
 the same plane, and the result would be, if the 
 Earth were not rotating, a swing round an axis at 
 right angles to the line joining the centres of the 
 two bodies, which would, after a few oscillations, 
 bring the equatorial bulge to rest in the orbital 
 plane of the outside body. 
 
 Upon rotating Now suppose the Earth to be rotating at the 
 
 spheroid. . 
 
 time the pull is applied ; then the simultaneous 
 
Saturn and its System 89 
 
 rotation and pull entirely alters the problem. 
 From being a statical, it becomes a kinematical 
 one, and the outcome is utterly different from 
 what we might expect. Instead of bringing the 
 plane of the equator into the plane of the ecliptic, 
 it swings the pole of the equator round the pole of 
 the ecliptic in a direction at right angles to the 
 pull, and opposite to the rotation, but without 
 changing the inclination of the two planes perma- 
 nently at all. If the axis be in such position that 
 the pull is perpendicular to the rotation, no change 
 of inclination, even temporarily, occurs. If the 
 axis be so circumstanced that the pull is at any 
 other angle to it, then the change of axis being 
 always perpendicular to the pull, one component 
 of the change rotates the axis as before, the other 
 alters its inclination. 
 
 Now if, as is the case with the attracting bodies Precession 
 of the solar system, the body which exerts the 
 pull revolve about the other, either really or vir- 
 tually, the axis will be presented to the force under 
 varying angles. The axis will then alternately 
 approach and recede from the pole of its small 
 circle while going round it. But at the end of its 
 orbital revolution it will come out again at the 
 point on the celestial sphere from which it started. 
 And this will happen whether the orbit be a 
 
9O The Solar System 
 
 circle or an ellipse. Even if the nodes of the 
 ellipse or its line of apsides regress or progress, 
 this will only postpone the reentrance of the curve 
 into itself to the time when the nodes or perihelia, 
 or both, shall have completed their revolutions. 
 No perma- No permanent change in the inclination of the 
 
 foaxfe 11 * 1186 axis to tne orbit can ever result from tne P U U of 
 a second body upon the first's equatorial bulge. 
 
 Since action and reaction are equal and oppo- 
 site, the equatorial protuberance is equally impo- 
 tent to make the satellite travel permanently in 
 its plane. 
 
 Same analyti- This appears also analytically in the expressions 
 for the effect produced in the line of nodes and the 
 effect upon the inclination, the former having in ad- 
 dition to its periodic terms a term which increases 
 with the time, while the latter has no such term. 
 
 Error in It may be worth pointing out here an error which has 
 
 crept into Young's excellent text-books, in which he states 
 that " Laplace and Tisserand have shown that the equa- 
 torial protuberance of a planet, due to its axial rotation, 
 compels a near satellite to move nearly in the equatorial 
 plane." Neither Laplace nor Tisserand has ever shown 
 this or ever could. 
 
 Laplace and What they did show was that the expression for the per- 
 turbative action of the equatorial bulge of a planet denotes 
 that the inclination of the satellite to the plane of the 
 planet's equator remains constant under the action of that 
 
Saturn and its System 91 
 
 force. Now this could be true, either because the force 
 had a restraining effect to this end, or because it had no 
 effect upon the inclination at all. Laplace jumped to the 
 conclusion that the first was the case, for he tells us, apro- 
 pos of Saturn and his next to outer satellite, that we see 
 " that Saturn's action can retain this satellite in very nearly 
 the same plane ; and much more so those satellites which 
 are inferior to it, as well as the rings." * He made the mis- 
 take of post hoc ergo propter hoc. Tisserand is more 
 guarded when he says: "Ainsi, 1'inclinaison de 1'orbite 
 d'un satellite sur 1'anneau demeure constante et toujours 
 tres petite si elle Fa ete' seulement a un moment donneV' 
 This is so ; but it is true, not because the force has an ef- 
 fect upon the inclination, but precisely because it has none. 
 The spherical ellipse found by Tisserand, t. iv., ch. vi., 
 to represent the change of inclination in the case of the 
 satellites of Saturn, is the curve of the combined preces- 
 sions due to each of the perturbing forces, the equatorial 
 protuberance, the ring, the sun, and the other satellites. 
 
 Impotent on the inclination as the equatorial Effect of tidal 
 protuberance is, there is another protuberance C1 
 which is not so impotent. For consider what 
 effect the tide-raising force of an outside body 
 would have upon the plastic matter of another ro- 
 tating in a plane tilted to the orbital plane of the 
 first. As we saw in Chapter II., the effect would 
 be to raise two bosses or ansae in the equatorial 
 
 1 See Laplace, Book IV., 26. At the time, Hyperion was 
 undiscovered and the " next to outer satellite " in consequence 
 different. 
 

 92 The Solar System 
 
 plane of the rotating planet, one preceding the 
 position of the tide-raising body, the other dia- 
 metrically opposite. 
 
 The action of these ansae upon the attracting 
 body would be analogous to, but in one vital re- 
 spect different from, that of an equatorial protu- 
 berance. Like that, they would tend to alter the 
 position of the axis of rotation at right angles to 
 the pull upon them, but the pull being always 
 backward the axis is constantly solicited forwards 
 toward the attracting body. Consequently the 
 axis of rotation, while rotating round the axis of 
 the orbit, would generally seek the satellite. For 
 the force here, when the axes are perpendicular, 
 is at its maximum. The axis, therefore, continues 
 to tend toward the orbital plane. 
 
 Same Analytically, in this case, unlike that of an 
 
 equatorial bulge due to axial rotation, the expres- 
 sion for the change of inclination contains a term 
 dependent on the time and increasing with it. 
 
 This term causes the inclination of the equato- 
 rial to the orbital plane to diminish until the axis 
 of rotation lies in the plane of the orbit. 
 
 imr 
 
 inclination of The tidal force varies as 7r , approx., and its 
 
 satellite's 
 
 orbital planes , c . A . 4?/zV 2 
 
 to planet's work for any given time as ^ 6 , approx. 
 
 It should therefore be much more potent upon 
 
Saturn and its System 93 
 
 a near satellite than upon a far one, and we 
 should expect the line expressing the action to 
 prove a curve concave to the axis of x, when the 
 bodies acted on are not too dissimilar in size. 
 Such is precisely the opposite of the curve the 
 diagrams present. 
 
 Nevertheless tidal action is probably the cause 
 of the law of inclinations shown in the orbits of 
 satellites to the equatorial plane of their primary. 
 But it would seem to imply that the farther ones 
 were given off first, and very much the first. 
 

 JUPITER AND HIS COMETS 
 
 Jupiter exem- CHAOS describes Jupiter at present ; the seeth- 
 
 plifies chaos. . . . . , _, 
 
 ing something between sun and world, i he 
 planet is either a sun in its senility or an earth in 
 its babyhood, as you are pleased to regard it. For 
 the one state passes by process of development 
 into the other. 
 
 A semi-sun. Viewed as a sun, it lacks little except light ; 
 viewed as a world, it wants everything except that 
 lack of luminosity. It is, as Virgil described an- 
 other giant, informe ingens cui lumen ademptum. 
 Its density is almost exactly that of the Sun itself. 
 Either, therefore, its bulk is chiefly atmosphere 
 round a kernel of planet, which is Professor Dar- 
 win's conclusion, or its smaller mass is offset by 
 its lesser heat, causing a like condensation of the 
 two globes. On the latter supposition, though not 
 luminous, it is still hot. This would bear out and 
 confirm the inference, from the brick-red color 
 between its belts, that its surface is at a red heat. 
 Almost precisely the same is true of Saturn ; 
 the body of that planet, too, being a faint cherry 
 
Jupiter and his Comets 95 
 
 red. Jupiter, however, we see much the better of 
 the two, and we may describe it as typifying both. 
 
 Both are bulky ; their masses to their volumes 
 being such that their mean densities are respec- 
 tively somewhat greater (1.2856) and somewhat 
 less than water (.69 Jo}. Both are in rapid rota- 
 tion ; particles on their equators traveling with 
 speeds comparable with their orbital velocities. 
 Both, in consequence, are strikingly flattened into 
 oblate spheroids whose elliptic curves instantly 
 strike the eye. In the disks of both we look only 
 upon atmosphere and cloud. Lack of solidity, 
 speed of self-movement, cloudy condition, are all 
 so many signs of youth. In relative if not 
 in absolute age, both planets are still very 
 young. 
 
 Semi-suns in several 'senses, the two planets 
 are three-quarters way in their journey from neb- 
 ula to world. In their traits both more closely 
 resemble the Sun than the Earth. Indeed, with 
 the trifling exception of not shining, the disk of 
 Jupiter or of Saturn bears a very remarkable 
 analogy to the solar. 
 
 In a large telescope and in good seeing, Jupiter Ruddy glow, 
 is a color-picture as beautiful as it is marked. A 
 deep pink flush suffuses the planet's equatorial 
 regions. It probably betokens the parts of the 
 
96 The Solar System 
 
 true surface that are laid bare. For that the color 
 is due to the selective absorption of the higher 
 regions of the planet's air is negatived by the 
 spectroscope, which shows dark bands in the red. 
 Rotation* In spite of its enormous bulk, Jupiter turns on 
 its axis with such speed that its figure is flattened 
 by JTT. Its mean time of rotation is g k $$ m . We 
 are forced to say its mean time, not because the 
 markings cannot be accurately timed, nor because 
 of any change in the planet's moment of momen- 
 tum, but because the planet does not rotate as a 
 whole. Different parts of it go round at different 
 rates. Speaking broadly, the nearer the equator 
 the greater the speed. Between the equator and 
 latitude 30 there is a difference of six minutes in 
 the rotation period. But the several belts have 
 each its own period, and this does not always 
 accord with the latitude. In addition, particular 
 spots on the same longitude have particular spins, 
 and pass by each other at speeds from seven miles 
 to four hundred miles an hour. White markings 
 travel faster than dark markings close beside them. 
 Thus the white masses around the great red spot 
 drift by it. The spot itself has changed its rate 
 by six seconds in as many years. It is pretty evi- 
 dent that Jupiter is chaotic. 
 
Jupiter and his Comets 97 
 
 The same is the case with Saturn. Stanley Rotation of 
 Williams, in 1893, found for the Saturnian regions " 
 between 6 N. and 2 S., io 7 ' i 3, and for those be- 
 tween 17 N. and 27 N., io 7 ' 15'". Not only did 
 latitudes differ in rate, but different longitudes 
 went each at its own pace. 
 
 Something similar is true of the Sun. At the Sun's 
 solar equator the spin is swifter than on either 
 side of it ; and the rate decreases steadily from 
 the equator towards the poles. Spots near the 
 equator go round in 25 days (25.23 days), spots in 
 latitude 30 in 26^ days, in latitude 40, 27 days, 
 while in latitude 45 they take fully two days 
 longer than in o. Now Willsing and Professor 
 Sampson, of Durham University, have shown that 
 such a state of things should result in the process 
 of condensing from nebula to star. In the neb- 
 ula, if the density varied from place to place, 
 which, on the doctrine of chances, would certainly 
 be the case, the several parts would revolve round 
 their common centre of gravity at various rates. 
 As the nebula condensed, such parts as held to- 
 gether would tend to equalize their individual mo- 
 tions through friction, until a common rotation 
 was brought about. But this would consume a 
 long time ; in the mean while, the equatorial parts 
 would outstrip the others. In the midst of the 
 
98 The Solar System 
 
 equalizing process the Sun, Jupiter, and Saturn 
 now seem to be. 
 Jupiter has Jupiter, however, has progressed beyond the 
 
 :loud layers, g^ in that the outer j^ of hig SUDS tance 
 
 have cooled down enough to condense into cloud, 
 due, possibly, to the planet's smaller mass. On 
 the surface of the Sun things are still kept largely 
 uniform by the terrific heat, and the slower rota- 
 tion lets us perceive no latitudinal layers. On the 
 contrary, Jupiter's disk is striated with belts of 
 various tone and tint, according almost exactly 
 to the parallels ; while the albedo, or relative 
 brightness of the disk, 62 per cent, of absolute 
 whiteness, indicates that most of it is cloud. 
 Jupiter's- These clouds are quite unlike our terrestrial 
 
 raised, not" ones - Jupiter's clouds are riot Sun-raised, but 
 Sun-raised, self-raised condensations. On the one hand, the 
 Sun's action there, only ^V f what it is here, is 
 impotent to produce the effect we see ; on the 
 s other, the cloud zones show a persistence quite 
 disregardant of the Sun. They are not ephem- 
 eral like ours, but long-lived, lasting for weeks, 
 months, and even years. They must, therefore, 
 be Jove-caused. 
 
 Disk darkens In another feature Jupiter resembles the Sun. 
 Its disk darkens to the limb. None of the 
 smaller planets do this. The only thing capable 
 
Jupiter and his Comets 99 
 
 of producing such effect is a layer of atmosphere 
 surrounding the disk of considerable depth. Ju- 
 piter's atmosphere is dense, and the absorption to 
 which a ray of light would be subjected in pass- 
 ing in from the Sun and then out to us would in- 
 crease from centre to circumference, and thus dim 
 the edges of the disk. 
 
 Jupiter has two families of bodies connected Comets 
 
 associated 
 
 with him ; one an own one of satellites, the other with Jupiter, 
 an adopted one of comets. With his satellites 
 we made acquaintance in the last chapter; we 
 must now be introduced to his comets. 
 
 Thirty-two comets circle near the planet and 
 agree in the following distinguishing character- 
 istics : 
 
 1. Their aphelia hug Jupiter's orbit. 
 
 2. Their ascending nodes occur close to it. 
 
 3. Their motion is direct. 
 
 At some time in the past, therefore, each of Association 
 these comets must have passed close to Jupiter, 
 the comet and the planet chancing to arrive to- 
 gether at the node. At that epoch the comet 
 must have suffered great disturbance at the hands 
 of the planet, and its previous orbit have been rad- 
 ically changed. 
 
 D'Alembert, accordingly, suggested that Ju- 
 piter had captured these comets, and Laplace 
 
100 
 
 The Solar System 
 
 \jupjI5.?- 
 
 ^ - 
 
 FIG. XIII. JUPITER'S FAMILY OF COMETS. 
 
 extended the idea ; but to Professor H. A. New- 
 ton we owe the most important research in the 
 matter. In two striking memoirs (1878 and 1893), 
 he showed that Jupiter was quite capable of such 
 capture ; but he started with the assumption that 
 
Jupiter and his Comets 101 
 
 comets were not denizens of the Sun's domain, so 
 he considered only parabolic comets. 
 
 We now know that all comets probably that Comets all 
 
 belong to the 
 
 man has ever seen are part and parcel of the Sun s solar system, 
 retinue. They do not come to us from outer 
 space, but are stable, if erratic, members of the 
 solar system. In the light of this fact, we may 
 profitably reconsider the subject. 
 
 Picture a comet, coming in to the Sun from Jupiter's 
 
 sphere of 
 
 space, to pass close to the planet in its journey, influence. 
 Within a certain distance of Jupiter, the planet's 
 pull becomes so great that it is mechanically more 
 exact to regard the comet as obeying Jupiter and 
 perturbed by the Sun ; and if the approach be 
 very close, we may neglect in a first approximation 
 the Sun's effect during the passage. This region 
 is called Jupiter's sphere of influence, and is of 
 the general shape of an ellipsoid, whose longest 
 diameter follows the planet's path. The mean ra- 
 dius of the ellipsoid is three tenths of the Earth's 
 orbit, no inconsiderable distance, and the extreme 
 radii differ as i to 1.19. 
 
 As the comet is traveling, when it enters the Relative orbit 
 
 , . , about planet 
 
 planet s sphere or influence, with bun-imposed a n hyper- 
 velocity, its speed, even if the orbit be elliptic of 
 small major axis, will exceed what Jupiter could 
 cause. It will, in general, approach Jupiter with 
 
IO2 
 
 The Solar System 
 
 Comet accel- 
 erated or 
 retarded ac- 
 cording as it 
 passes behind 
 or before the 
 planet. 
 
 Jovian hyperbolic velocity, and its relative orbit 
 about the planet will be an hyperbola. Jupiter, 
 therefore, cannot completely possess itself of the 
 comet. 
 
 The general equation of the relative motion I 
 shall not bother you with. But certain deductions 
 from it I think you will find of interest. In the 
 first place, it appears that the comet will be ac- 
 celerated or retarded, according as it passes behind 
 or in front of the planet. This may be seen 
 directly from the consideration that if it pass in 
 front of the planet, it accelerates the latter, and 
 since action and reaction are equal and opposite, it 
 must itself be retarded ; contrariwise, if it pass 
 behind the planet. 
 
 Suppose now the comet to have been pursuing 
 a parabolic path before the encounter ; then the 
 least retardation will make of its orbit an ellipse ; 
 for whether a body move in an ellipse, a parabola, 
 or an hyperbola is a question simply of its speed 
 at a given distance, shown by the well-known 
 equation, 
 
 * =(*_!). 
 
 \r a) 
 
 Into hyper- Similarly, the least acceleration will throw it into 
 
 bola by 
 
 acceleration, an hyperbola, and it will pass out of the solar sys- 
 tem, never to return. 
 
 Parabola 
 made into 
 ellipse by 
 retardation. 
 
Jupiter and his Comets 103 
 
 For an original elliptic orbit, this is not necessa- 
 rily the case. A comet pursuing such a path may 
 have its velocity increased and yet not pass out of 
 the system. In many cases, however, it would so 
 result, and we can thus perceive how comets might 
 come to us from other systems from purely inter- 
 nal forces there. 
 
 The maximum effect in retarding the comet's Jupiter's 
 
 , ,, , T maximum 
 
 motion occurs when the comet approaches Jupiter effect in short- 
 in such a direction and with such a relative speed ^a^ c ^ x e 
 as to be turned back upon the planet's path, and 
 to leave the planet in the direction of the planet's 
 quit, with a relative speed equaling the planet's 
 own. It is then left stock-still to fall into the Sun. 
 
 Jupiter can do more than this. Though to Jupiter's abso- 
 leave a comet stock-still to drop into the Sun, thus effect. ' 
 shortening the major axis to one half its own, is 
 its maximum effect in the way of contracting the 
 orbit, its power over the comet exceeds such limit. 
 The planet can actually prevent a comet bound 
 round the Sun from attaining its object. It can 
 cause the comet to make itself in place of the Sun 
 the goal of its pilgrimage, and sweeping round the 
 planet, to go back into space without visiting the 
 Sun at all. 
 
 Consider the hyperbola the planet causes the 
 comet to describe. What the planet does is to 
 
104 
 
 The Solar System 
 
 Jupiter's bulk swing the incoming asymptote of this hyperbola 
 
 limits his A , , . . 
 
 power. through a certain angle. Clearly, the closer the 
 
 perijove of the relative orbit, the greater this angle 
 
 tl 
 
 V- 
 
 A 
 
 3& '_ . 
 
 B 
 
 A 
 
 X / 
 
 >;S 
 
 1 
 
 The comet's direction may be turned from OA to OB ; or OA' to OB' ; or OA" 
 to OB", according as it approaches along OA, OA', or OA'', P being the planet. 
 
 FIG. XIV. RELATIVE ORBITS. 
 
 of swing, as the planet gets a greater pull upon 
 the particle. If the comet were not coming too 
 fast and Jupiter's own body did not get in the 
 way, the comet could be turned straight back 
 
Jupiter and his Comets 105 
 
 whence it came. Practically, Jupiter's bulk does 
 get in its way, and the limit of the planet's power 
 lies below such direct reversal ; nevertheless, it is 
 sufficient in many positions to cause the comet 
 to sweep round and dart away from the Sun 
 with a speed such as to carry it beyond the Sun's 
 control. 
 
 The planet's greatest effect in turning the comet 
 is shown in three different conditions of approach. 
 The comet enters along the unbroken lines and 
 leaves by the broken ones. 
 
 You will notice that Jupiter's power is solely Deflective 
 one of deflection. He cannot vie with the Sun } 
 directly in a tug of war ; but he can deflect the 
 comet and thus use the very speed imparted by 
 the Sun against the Sun's attraction. It is like 
 the Japanese jiu-jitsu, or scientific wrestling, of 
 which the art consists in so adroitly turning an- 
 other's strength against himself as to make the 
 man's own momentum cause his fall. 
 
 Considering the case in this wise, we shall have Triangle of 
 the key to all of Jupiter's control. Form a tri- vel< 
 angle of velocities, of which the one side shall 
 represent Jupiter's motion in amount and direc- 
 tion, a second the comet's, and the third the rela- 
 tive motion of the one body about the other ; then 
 draw a circle with the last for radius from the 
 
io6 The Solar System 
 
 meeting-point of the planet's and comet's true 
 motions, and join any other point of it to its centre. 
 This second radius will represent the outgoing 
 asymptote of the relative orbit, according to the 
 planet's pull, while the line joining its peripheral 
 end to Jupiter will be the comet's subsequent 
 motion in amount and direction. 
 
 From this you will perceive that the comet's 
 subsequent career depends upon the actual speed 
 with which, the angle under which, and the near- 
 ness to which, it approaches the planet. If it 
 creep upon the planet from behind, it is more 
 likely to be captured than if it meet it head on ; 
 and if it be traveling slowly, it is more likely to 
 be caught than if it were going fast. 
 
 Direct orbits Any one of many things may happen. If it pass 
 grade/ 6 behind the planet, its actual speed is increased, 
 and either it is sent clean out of the system, or it 
 is at least put farther from capture than before. 
 If it pass before the planet and in such a way that 
 its relative speed about the planet exceeds the 
 planet's own motion, and it is turned round 
 through a sufficient angle, it may, from a pre- 
 viously direct path about the Sun, be diverted 
 into a retrograde one. In this case, it will com- 
 1 monly have a small velocity after the encounter 
 and retrograde in a small ellipse. 
 
Jupiter and his Comets 
 
 107 
 
 FIG. XV. ACTION OF JUPITER. 
 
 F represents in amount and direction the comet's actual velocity 
 in space. V\ similarly denotes that of the planet, the two bodies 
 meeting one another under the angle VO V\. VQ will then re- 
 present the relative motion, in amount and direction, with which 
 the comet approaches the planet. 
 
 The action of the planet is to turn the relative motion of the 
 comet through an angle, say AO, OA representing the in-coming 
 asymptote of the relative orbit, OE the out-going one. EP or V 
 will then represent the absolute motion in space of the comet 
 after the encounter. Similarly, if the comet passed behind the 
 planet and was turned through the angle AOI, PI would be the 
 new absolute velocity of the comet on leaving the planet. 
 
io8 The Solar System 
 
 The critical It however, its entering speed and approach- 
 ing angle, which we will call o>, are such that 
 
 I fj 
 
 cos w < -, where v is its actual velocity, v^ that 
 
 of the planet ; then its relative velocity , z/ , can 
 never be greater than v v and the resulting orbit 
 never can become retrograde. This angle we will 
 call the critical angle, and designate it by the 
 symbol \. 
 
 Now w we can calculate for each of the comets 
 of Jupiter's family from their known present paths. 
 Furthermore, since Jupiter's only effect is to swing 
 the outgoing asymptote of the relative orbit round, 
 v can never be changed, and the future possible 
 values of o> have a superior limit o>', which they 
 can never pass. This also we can calculate. 
 Doing this, and calculating also the value of x for 
 each comet, we find the table on the opposite 
 page, 
 w and ' both From the table, it appears that in every one of 
 
 aTcomets X of n tne comets of Jupiter's family, w is within the 
 Jupiter's crit ; cal angle _ 
 
 Furthermore, that c/, the maximum value which 
 w may attain under the perturbative effect of the 
 planet, owing to the swing of the asymptotes of 
 the hyperbolic relative orbit of the planet, is also 
 always within ^. 
 
Jupiter and his Comets 1 09 
 
 OO w sO -i 
 
 4- d n tx d> ood 
 
 vO t^\O SO sO \D O 
 
 w' 
 
 mum val 
 ible for w 
 
 o' rood >-,' 
 cottoxj- 
 
 o o oo 
 \o d- vd rood 
 ro N - ro ro 
 
 ax 
 pos 
 
 ro 00 O 00 
 in N od in 
 m ro co M 
 
 
 O * O 
 
 M (> * tx O in roOO O tx N CxN H \O rot^~ rovO ro O CT> -*OO "f H ; f J l f> 1 - | O^ N 
 
 -too ooiOONNNiHi-iOON O^O t^OOO row IONOO t^O tx rooO O vO O N ro ro 
 
 Incli 
 of o 
 ecl 
 
 q>ONq\q M M\O tvq -*ONONN in-^-m t^oo ^-fric>qNooooNvqqcot>qN q^ 
 
 +4-4-4-+++++++++++++++++4-+++++4-++++ " 
 
 
 i ro tvoo OO C OOfOO -cooo ooo - 
 
 'U 
 
no 
 
 The Solar System 
 
 o> nearly 
 ahnost all" 1 
 
 Potential rela- 
 
 re V ma V ins OClty 
 unchanged. 
 
 Comets of 
 
 the 
 disappear. 
 
 Therefore, of the comets of Jupiter's comet- 
 family, not only is none now retrograde, but none 
 can ever become so unless some other body inter- 
 fere with it. 
 
 A singular coincidence characterizes the values 
 ^ w anc * <>' In a ^ but two cases, <o nearly equals 
 a/, as if for some reason o> were always trying to 
 attain this maximum as a condition of stable equi- 
 librium. In ten cases out of twenty, or in one 
 half of the whole, the approach is within less 
 than J. 
 
 It is to be noticed that in orbits potentially 
 retrograde, the potential direct velocity is also 
 greatest ; so that both on the score of retrograda- 
 tion and of greater direct velocity, comets pursuing 
 such orbits are more subject to expulsion. 
 
 In course of time, comets possessing a high 
 potential velocity must be weeded out of the sys- 
 tem . f or> sooner or later, they must meet the 
 planet under conditions of approach which con- 
 vert their high potential velocity into an actual 
 one. This will happen the sooner for comets 
 in proportion to their velocity possibilities. It 
 therefore will occur more speedily for originally 
 parabolic comets than for elliptic ones of short 
 period ; but it will require some time even for 
 them. 
 
Jupiter and his Comets 1 1 1 
 
 Either, then, Jupiter's present comet family has 
 been of very slow growth, and each comet remains 
 for a long time in the family, or it is made up only 
 of short-period comets drawn from the immediate 
 neighborhood. 
 
 Now, comets appear to be ephemeral things, Comets 
 being easily disintegrated into meteor swarms, and thi 
 never abiding long in one stay. Thus the latter 
 supposition seems on the face of it the more likely. 
 We may conclude provisionally that Jupiter's 
 comet family came from the neighborhood. 
 
 It is certain that Jupiter has swept his neighbor- Jupiter has 
 hood of such comets as do not fulfill the criterion neighbor- 8 
 of the angle x; that is, of all the comets actually or l 
 potentially retrograde. If we consider the comet 
 aphelia of short-period comets, we shall notice 
 that they are clustered about the path of Jupiter 
 and the path of Saturn, thinning out to a neutral 
 ground between, where there are none. Two 
 thirds way from Jupiter's orbit to Saturn's, space 
 is clear of them, the centre of the gap falling at 
 8.4 astronomical units from the Sun. 
 
 Let us consider the mean comet ; that is, a 
 comet having the mean inclination of parabolic 
 comets, the mean perihelion distance of the comets 
 of Jupiter's family, such being the distance 
 most likely to disclose them to us, and let this 
 
Mean 
 
 inclination of 
 comets : 
 theoretical. 
 
 112 
 
 The Solar System 
 
 mean comet have successively aphelion distances 
 from Jupiter's orbit to Saturn's. 
 
 The mean inclination we may take either as the 
 mean of comets coming to us from all parts of 
 space indifferently or as the mean of such para- 
 bolic comets as have actually been observed. 
 
 If we suppose the inclinations of the cometary 
 orbits to be equally distributed through space, 
 then the poles of the orbits will likewise be strewn 
 uniformly over the celestial sphere. If a be the 
 angle made by a pole with the pole of the ecliptic, 
 the mean inclination of the poles can be found by 
 multiplying the number of poles at any inclina- 
 tion, which is as the strip of surface yielding it, 
 by that inclination, and then dividing the integral 
 of this for the whole sphere by the surface of the 
 sphere. The strip of surface at any inclination a 
 is 2 TT r 2 sin a . da. Whence the average inclina- 
 tion in radians is 
 
 r v 
 
 2vr 2 sin a. a. 
 Jo 
 
 r v 
 
 I 2 IT r 2 sin a. do. 
 Jo 
 
 or 
 
 = 57 u -3. 
 
 Mean mcima- The second mean inclination or actual mean of 
 
 tion observed. . 
 
 all the parabolic orbits observed is z = 52 .4. 
 
Jupiter and his Comets 113 
 
 It is worthy of notice how near the two are, 
 showing that the parabolic comets come to us, 
 practically, indifferently from all parts of space. 
 
 Calculating w and x for the successive aphelia, 
 we find that, on the first supposition, w passes x at 
 8.4 astro, units ; on the second, at 8.75 ditto. 
 
 It is Jupiter, then, that has swept this space of 
 comets. 
 
 Only a small fraction of Jupiter's comet family Family larger 
 
 ... i r tban we see - 
 
 can ever come within our ken ; tor any comet 
 
 whose perihelion lay outside of two astronomical 
 units must, perforce, escape recognition. Invisi- 
 bility would be caused both by the comet's dis- 
 tance from us and by its distance from the Sun, 
 
 J 
 for the commotion set up in these bodies, as they 
 
 near the Sun, is chiefly responsible for the display 
 they make. 
 
 The family undoubtedly consists of many more 
 comets with greater perihelion distance. 
 
 Jupiter is not the only planet that has a comet- 
 family. All the large planets have the like. 
 Saturn has a family of two, Uranus also of two, 
 Neptune of six ; and the spaces between these 
 planets are clear of comet aphelia ; the gaps prove 
 the action. 
 
 Nor does the action, apparently, stop there. 
 Plotting the aphelia of all the comets that have 
 
The Solar System 
 
 been observed, we find, as we go out from the 
 Sun, clusters of them at first, representing, re- 
 spectively, Jupiter's, Saturn's, Uranus', and Nep- 
 
 FIG. XVI. COMET APHELIA. 
 
 tune's family ; but the clusters do not stop with 
 Neptune. Beyond that planet is a gap, and then 
 at 49 and 50 astronomical units we find two more 
 
Jupiter and his Comets 1 1 5 
 
 aphelia, and then nothing again till we reach 75 
 units out. 
 
 This can hardly be accident ; and if not chance, 
 it means a planet out there as yet unseen by man, 
 but certain sometime to be detected and added 
 to the others. Thus not only are comets a part 
 of our system now recognized, but they act as 
 finger-posts to planets not yet known. 
 
 We have thus examined the case of an old 
 planet, Mercury ; of a middle-aged one, 
 Mars ; of a youthful one, Jupiter ; and we have 
 ended by envisaging the yet unchristened. 
 
VI 
 
 COSMOGONY 
 
 Present the AFTER the present, the past. The forces that 
 the C past we h ave f un d to be moulding the system to-day 
 must be those that fashioned it earlier. Given, 
 therefore, the condition at the moment, if we 
 apply to it the forces now at work reversed, we 
 shall get the condition that was. 
 
 Similarly, we can cast its horoscope for the 
 future, by Taylor's theorem. 
 
 Unfortunately, the problem is so complicated 
 that no solution, even approximately satisfactory, 
 has yet been obtained; but that the mystery 
 baffles us renders it all the more fascinating. 
 Striking reia- In the solar system, as we find it to-day, are 
 solar system severa -l remarkable congruities which are quite in- 
 dependent of gravitation, and bespeak a cause. 
 
 I. The central body is much larger than its 
 attendants. 
 
 II. The planets move in orbits nearly circular. 
 
 III. They travel nearly in one plane. 
 
 IV. And in the same sense (direction). 
 As for the planets themselves 
 
Cosmogony 117 
 
 V. Their planes of rotation nearly coincide with 
 their orbital planes (except Uranus and Neptune). 
 
 VI. They rotate also in the same direction that 
 they revolve, counter-clockwise, all of them (except 
 Uranus and Neptune). 
 
 VII. Their satellites revolve nearly in the planes 
 of their primaries' equators (so far as we can see). 
 
 VIII. And in the same direction. 
 
 IX. They rotate in the same plane (so far as 
 we can see). 
 
 X. In the same direction (so far as we can see). 
 Immanuel Kant was the first to suggest some- Kant's 
 
 thing approaching a rational explanation of this hypothesis, 
 very curious and elegant state of things. He 
 made the error, however, of supposing that rota- 
 tion of the whole could be produced by collisions 
 of its parts ; but no moment of momentum can 
 be caused by the interaction of parts of a system, 
 since internal forces occur in pairs and their mo- 
 ments round any line are equal and opposite. We 
 will consider this in detail a little further on. La- 
 place, who appears not to have known of Kant's 
 writing, himself some years later developed a 
 somewhat similar theory, but with more mathe- 
 matical foundation. He assumed an original rota- 
 tion and got the credit for the nebular hypothesis. 
 He had a faculty of getting credit for things 
 which was only second to his ability. 
 
1 1 8 The Solar System 
 
 Laplace's To account for so orderly an arrangement La- 
 
 nebular . , 
 
 hypothesis. place supposed : 
 
 a. That the matter now composing our solar 
 system was once in the form of a nebula. 
 
 b. That this original nebula was very hot, a 
 fire-mist. 
 
 c. That it possessed initially a slow rotation. 
 
 d. That as it contracted under its own gravity 
 and thus, from the principle of conservation of 
 moment of momentum, rotated faster as it shrank, 
 it rotated always like a solid body with the same 
 angular velocity throughout, until its outer por- 
 tions, which went the fastest, came to go so fast 
 that the centrifugal tendency overcame the cen- 
 tripetal force and they were left behind as a ring. 
 
 e. That this ring revolved as a whole until it 
 broke, rolled back upon itself and made a planet ; 
 the outer parts of the ring having the swiftest 
 motions, the resulting planet rotated in the same 
 sense that it revolved. 
 
 f. The planet thus formed gave birth in like 
 manner to its satellite system. 
 
 Physical error The prestige of Laplace gave this explanation 
 hypothesis. 8 a mental momentum which has carried conviction 
 nearly to the present day. But it is erroneous for 
 all that, nor can it be made to work by any addi- 
 tions or slight alterations as some text-books will 
 
Cosmogony 1 1 9 
 
 tell you. For it was founded on what it has now 
 foundered on : one fundamental mistake. Laplace 
 assumed that his nebula would revolve, as he saw 
 the air around the Earth to revolve, of a piece. 
 But he forgot that friction due to the pressure 
 alone produces this, and that in particles moving 
 freely no pressure exists. Under the pull of a 
 central mass each layer of the nebula would re- 
 volve at its own appropriate rate, or as r~ * So 
 that his beautiful explanation of the agreement in 
 direction of the rotations and the revolutions - 
 the vital point of the theory falls to the ground. 
 
 Faye first definitely pointed out this fatal fal- Faye's nebu- 
 lacy in Laplace's hypothesis in 1886, in his " Ori- s is. 
 gine du Monde," in which, after reviewing the 
 previous history of the subject, he brought for- 
 ward a new theory of his own, both elegant and 
 ingenious. 
 
 He begins by assuming a nebulous mass of par- 
 ticles, roughly uniform throughout, but with local 
 condensations. He supposes this nebula cold, for 
 the heat can be trusted to come of itself. With 
 uniform density throughout, the speed of rotation 
 would also be uniform, thus giving the same re- 
 sult that Laplace got, but for a very different rea- 
 son. In a spherical mass of matter of uniform 
 density, a particle at any point is attracted only 
 
1 20 The Solar System 
 
 Force origi- by the sphere within it. It is therefore pulled by 
 
 nally as 5r. m 8r s 
 
 the force - 2 = ? = 8 r, where 8 is the density. 
 
 Since the force is thus linear it may be resolved 
 into two harmonic motions and becomes motion 
 in an ellipse with the acceleration directed to the 
 centre, or elliptic harmonic motion whose equa- 
 tion is expressed in vector coordinates : 
 
 f p = a cos (nt 4- e) + b sin (nt + e\ 
 whence < p'= n\a sin (nt-}- e) b cos (nt-\-e}~\, 
 
 [ p"= n 2 [a cos (lit + e) + b sin (nt -f e}~\ u 2 p. 
 
 The form of the ellipse depends upon the amount 
 and direction of the initial velocity of the par- 
 ticle. 
 
 This equation shows, first, that the period of 
 rotation is the same for all the particles ; and sec- 
 ond, that the angular speed in such different neb- 
 ulae is as the square root of their densities. 
 Subsequently When the mass has practically collected in the 
 
 m 2jrf 
 
 centre, the force is ^, or the ordinary law of grav- 
 itation, giving elliptic motion with acceleration 
 directed to the focus, or elliptic motion par excel- 
 lence. 
 
 At any intermediate stage of the process he sup- 
 
 a 
 
 poses the force to be represented byf= a r -+- ^> 
 a gradually dying out and ft increasing as central- 
 ization goes on. 
 
Cosmogony 121 
 
 Planets given off under the first state of things 
 would rotate in the same direction in which they 
 revolved ; under the last in the opposite way. 
 He, therefore, supposes the terrestrial planets to 
 be the older ; the outer planets the younger mem- 
 bers of the system. His theory makes the order 
 of birth the exact contrary of Laplace's. 
 
 More recently Lieutenant-Colonel R. du Ligon- 
 des 1 has evolved another cosmogony. Ligondes's 
 general theory is ingenious, but to me not convin- 
 cing. His first point is unqualifiedly good. He 
 starts out by calling attention to the evidence 
 offered by the moment of momentum of the solar 
 system upon the early history of that system. He 
 shows that to produce a single star system like 
 ours, the original motions of the several parts of 
 the nebula must have been nearly balanced, the 
 plus motions almost canceling the minus ones. 
 
 It now becomes of interest for us to consider Moment of 
 
 , . . ,. ^ r r momentum. 
 
 this question. Conservation of moment of mo- 
 mentum is as fundamental in mechanics as the 
 conservation of energy. The momentum of a 
 body is its mass into its velocity, and the moment 
 of momentum is this mass-velocity multiplied by 
 the perpendicular upon its direction from the point 
 
 1 Formation Mecanique du Sysftme du Monde, Gauthier-Villars 
 et Fils, Paris, 1897. 
 
122 The Solar System 
 
 or line around which the moment is taken. The 
 moment of momentum is thus twice the area 
 swept out by the moving body about the fixed one 
 in unit time. 
 
 When two bodies collide, the amount of motion 
 is not changed. This truth is the result of experi- 
 ment, and was first determined by Newton. If 
 the two are perfectly inelastic, they move on after 
 the collision as one mass with a loss of kinetic 
 energy. If perfectly elastic, they rebound in such 
 a manner that not only the amount of motion, but 
 the kinetic energy remains unchanged. Now 
 probably no bodies are perfectly inelastic, just as 
 no bodies are perfectly elastic. In the case, there- 
 fore, of the bodies in nature, while the amount of 
 motion is never altered, a part of the kinetic energy 
 is lost by the shock. It is transformed into heat 
 energy. 
 Moment of Now the moment of a velocity, and therefore of 
 
 momentum , . 
 
 constant. a momentum, clearly remains constant when un- 
 acted upon by any force, for its direction continues 
 the same, and a perpendicular upon it from any 
 point measures out the same area in the same 
 time, as the perpendicular, too, is constant. 
 
 The like is true, if it be acted upon by a force 
 constantly directed to the same point ; for in that 
 case the force can generate no velocity except 
 along the perpendicular upon the line which repre- 
 
Cosmogony 123 
 
 sents the body's momentum, and therefore cannot 
 change the area swept out. 
 
 When two bodies collide, therefore, they each 
 bring an eternal definite amount of motion to the 
 collision ; this amount is unaffected by the shock. 
 
 Nor can the mutual attraction of the two bodies 
 themselves alter it ; for, since a force is measured 
 by the amount of velocity it can generate in a 
 given time, the velocities generated must be as 
 the opposite masses, and therefore the momentum 
 produced in each be the same. 
 
 Let m and m r be the masses. 
 
 Then / w t = m^ m , 
 
 and f mi t = viv mi , 
 
 and = ' j 
 
 whence in-^u m jnv mi 
 
 or Aa = Bb 
 
 where Aa = and Bb = 
 
 FIG. XVII. 
 
1 24 The Solar System 
 
 Moreover, it is directed in both cases along the 
 same line. Whence its moment in the two cases 
 about any point is the same in amount, the per- 
 pendicular from the point being common to both, 
 but opposite in direction. The two moments thus 
 destroy one another. From which we see that 
 the internal forces of a system are unable to 
 change the moment of momentum of the system. 
 Similarly they are incapable of having created it 
 to begin with. 
 
 The present moment of momentum of the solar 
 system can be calculated. It is found to be nearly 
 the least possible. It must, therefore, always 
 have been so. It was predestined by internal 
 motions to make a single star. 
 
 So far, he is admirable, but from this point I 
 lose him ; I cannot see the cogency of all his suc- 
 ceeding steps. They lead him to the conclusion 
 that everything is as it should be, and incidentally 
 that Jupiter or Neptune is the oldest planet, 
 Uranus the next, then Saturn, Mars, the Earth, 
 Venus, and Mercury. The importance of the 
 order will appear shortly. 
 Trowbridge's With regard to the retrograde rotations of the 
 
 explanation . 
 
 of direct and outer planets and the direct rotations of the inner 
 ones, Trowbridge suggested that uniform density, 
 or a density increasing toward the centre, would 
 
Cosmogony 
 
 125 
 
 account for it. Suppose, first, the density uniform, 
 or nearly so. Then the inner parts of the mass 
 that went to form the planet would be traveling 
 fastest, and their momentum would prevail over 
 that of the outer particles and give a retrograde 
 rotation to the whole. Suppose, however, that 
 the density increased toward the inner side of the 
 mass. Then the centre of inertia would be so far 
 shifted toward the inner edge, say to N, that the 
 sum of the moments about it of the particles from 
 without would, owing to their distance from it, 
 surpass that of those within and a direct rotation 
 result. 
 
 The attraction, and thence the velocities in the Laws of force 
 different parts of the nebula, may be well shown 
 graphically. 
 
 Faye's laws of attraction 
 in condensing nebula. 
 
 x 
 FIG. XVIII. 
 
126 
 
 The Solar System 
 
 Faye's equation holds only when a and are 
 functions of r as well as of t. It, therefore, fails 
 to give a good representation of what occurs 
 throughout at a given moment. Furthermore, 
 the equations do not hold up to the axis of y, as a 
 discontinuity occurs so soon as we enter the cen- 
 tral mass. 
 
 A better picture is the following, somewhat 
 changed from Ligondes. As the matter gets 
 drawn into the central mass, the attraction at the 
 outer parts of the original nebula grows less and 
 less, therefore C sinks to F, and the successive 
 curves of the attraction become OC, DD, EE, FF. 
 
 Successive curves of attrac- 
 tion in condensing nebula. 
 x= radius of point. 
 y = attraction at the point. 
 
 x 
 FIG. XIX. 
 
 The velocities at different distances follow a 
 similar law. 
 
 This shows, as Ligondes points out, that there 
 
Cosmogony 
 
 127 
 
 is a maximum velocity somewhere in the centre of Effect on 
 the nebula, which degrades on both sides, so that r 
 we should have a plan of velocities for outside 
 and inside portions of the nebula, thus : 
 
 Maximum 
 velocity. 
 
 FIG. XX. 
 
 Supposing the density either the same through- 
 out or to increase toward the centre, we should 
 have, if the various planets were formed simul- 
 taneously, a retrograde rotation for the outer, a 
 direct rotation for the inner ones. 
 
 In addition to the ten congruities known in the New congrui- 
 time of Laplace, we must now add others from { 
 knowledge acquired since, to wit : 
 
 XL All the satellites turn the same face to 
 their primaries (so far as we can judge). 
 
 XII. Mercury and probably Venus do the same 
 to the Sun. 
 
 XIII. One law governs position and size in the 
 solar system, and in all the satellite systems. 
 
 ace. 
 
128 The Solar System 
 
 XIV. Orbital inclinations in the satellite sys- 
 tems increase with distance from the primary. 
 
 XV. The outer planets show a greater tilt of 
 axis to orbit-plane with increased distance from 
 the Sun (so far as detectable). 
 
 XVI. The inner planets show a similar rela- 
 tion. 
 
 Tidal friction Tidal friction explains xi. and xii. ; xiii., xiv., xv., 
 
 explanation. an( ^ xy i- are as vet unexplained. 
 
 Tidal friction Tidal friction would account for xiv., but only 
 
 fails with A . , J _. ,_, ,, L ,,., 
 
 axial inclina- on the supposition that the outer satellites were 
 given off first. This is contrary to Faye's theory, 
 largely so to Ligondes's, and is not championed by 
 any other, for Laplace's supposition with regard 
 to this point cannot stand. 
 
 Not only must the outer satellite have been 
 given off the first, but very long before the next 
 inner one, and so on for all ; for tidal friction is 
 potent as the inverse sixth power of the distance. 
 A similar objection holds against the attempt 
 to explain the increased tilt of rotation axis to 
 orbit planes, as distance from the Sun increases 
 both for the outer and the inner planets. This 
 increased tilt with increased distance is well worth 
 particular notice. It may be seen in the follow- 
 ing table. 
 
Cosmogony 129 
 
 Inclination of Equator 
 Planet. to Orbit-plane. 
 
 Neptune - HS ^) 
 
 Uranus 98(?) 
 
 Saturn 27 
 
 2 
 
 Jupiter 
 
 Mars 2 5 
 
 Earth 2 3i 
 
 Venus ( ? ) 
 
 Mercury 
 
 We cannot be certain of Uranus and Neptune 
 because we cannot see their surfaces well enough 
 to be sure of the position of their axes, but the 
 planes in which their satellites revolve makes the 
 value given altogether likely. 
 
 The tidal friction explanation of this would 
 make Neptune very much the oldest planet, Ura- 
 nus very much the next so, and so on. But the 
 explanation is not satisfactory. 
 
 Our solar system has, as I have said, a very 
 small relative moment of momentum ; only the of 
 one thousandth part of what it might have as 
 exemplified in the system of a Centauri. 
 
 One supposition will account for the small mo- ^^ O a n bl e f 
 ment of momentum of the system, without sup- two suns. 
 posing the individual motions so nearly balanced 
 at the start. The moment of momentum would 
 be small if the principal mass were initially col- 
 lected in the centre of the nebula. Now this 
 
1 3 o 
 
 The Solar System 
 
 
 Physical 
 condition of 
 meteorites 
 sustains this 
 idea. 
 
 Distribution 
 
 would be the case if the present system had been 
 formed by the collision of two bodies. For, when 
 dealing with such masses, the elasticity may be 
 considered small, and, in default of elasticity, the 
 matter after the collision would be found chiefly 
 near the scene of the catastrophe if the impact 
 were in the line joining their centres. The col- 
 lision in space of two bodies happening head on 
 is, of course, one of which the chances are very 
 small, and, were it not for another fact, might be 
 dismissed from reasonable consideration. 
 
 This fact is the present constitution of the un- 
 attached particles of the system, the meteorites. 
 As we saw in a preceding lecture, these fragments 
 betray a previous habitat. Their character shows 
 that they came from the interior of a great cooled 
 mass which once had been intensely heated. 
 They are therefore proof of the prior existence 
 of a great sun, and that they should be now 
 strewn in space makes the theory of a subsequent 
 collision far less improbable. 
 
 If such a collision occurred, the fragments 
 would be scattered more sparsely according to 
 their distance from the scene of the catastrophe, 
 and we may perhaps assume the law governing 
 this sparseness to be the curve of probability, 
 

 132 The Solar System 
 
 Then the probable amount of matter lying be- 
 tween x and x + dx is -^e h ***dx, and considering 
 
 x to be y, and y, x, we have similarly for the prob- 
 able amount of matter lying between y and y + dy, 
 
 *..-** 
 
 The probable amount, therefore, in the rect- 
 angle dxdy is e-(*+rtdxdy=~e~-**a> where 
 
 adxdy, and r denotes its distance from the ori- 
 gin, or, in this case, the centre of the Sun. 
 
 For the amount in a ring at distance r, we have 
 a r dr. 
 
 Effect on Consequently it is evident that there is less 
 
 relative variation in the density with the distance 
 as one goes out. A fortiori, therefore, when the 
 planetary masses do not increase in like propor- 
 tion, the two ends, the outer and the inner, of the 
 strip or bunch of matter that went to make each 
 up, vary less in density inter se. In the result- 
 ant rotation, the speed of the separate particles 
 counts for more, relatively, than their density, 
 and, in consequence, for the outer planets we 
 should get a retrograde rotation ; for the inner, a 
 direct one. 
 
 Inner planets That the inner planets were not formed early in 
 later formed. ^ svs t e m's development seems pointed at pretty 
 
Cosmogony 133 
 
 conclusively by their several masses. Present 
 mechanical conditions of the matter inside Jupi- 
 ter's orbit appear to point to the pre-existent in- 
 fluence of Jupiter upon it before birth. Not only 
 do the amounts of matter in the several terrestrial 
 planets indicate this, but the lack of formation of 
 a planet in the gap occupied by the asteroids 
 seems well-nigh conclusive on the point. 
 
 A glance at the axial inclinations of the outer shown by 
 and the inner planets betrays a break in the "rial rotation, 
 symmetry of their arrangement. Each, taken by 
 itself, evinces a gradual righting of the axis as one 
 approaches the Sun. This appears strikingly 
 from the table of the inclinations of the equators 
 of the several planets to the planes of their orbits. 
 
 This, too, seems to point to the action of Jupi- Jupiter's 
 ter. On the whole it appears probable that Jupiter j|j e n the 
 existed before any of the small planets within its 
 orbit, and profoundly modified them prenatally. 
 
 We thus come to a conclusion in which nothing Conclusion, 
 is concluded : but we need not regret that. The 
 subject becomes the more exciting for remaining 
 yet a mystery. We now know of relations so 
 systematic and singular that we are sure some law 
 underlies them, and it is rather pleasant than oth- 
 erwise to have that law baffle our first attempts 
 at discovery. 
 
1 34 The Solar System 
 
 Future of the But though we cannot as yet review with the 
 
 system. 
 
 mind s eye our past, we can, to an extent, foresee 
 our future. We can with scientific confidence 
 look forward to a time when each of the bodies 
 composing the solar system shall turn an un- 
 changing face in perpetuity to the Sun. Each 
 will then have reached the end of its evolution, 
 set in the unchanging stare of death. 
 
 Then the Sun itself will go out, becoming a 
 cold and lifeless mass ; and the solar system will 
 circle unseen, ghostlike, in space, awaiting only 
 the resurrection of another cosmic catastrophe. 
 
. 
 
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