Auci. 15, 1884.] 



♦ KNOVV^LEDGE ♦ 



127 



velocity with which a body would reach the surface, if 

 brought thitlicr solely by the earth's action from interstellar 

 space, would be a little over seven miles per second, or more 

 than twenty-seven times greater than the velocity of the 

 swiftest cannon-ball. 



But wliilo Jupiter — to keep for the moment to our giant 

 planet — has thus, theoretically, the power of giving or 

 taking away a velocity of thiity-six miles per second, he is 

 not practically able to do anything of the sort. He is not 

 left to draw matter to himself, or to act on the recession of 

 matter from bimself, alone. The bodies which come near 

 to him from outer space have been drawn by solar might 

 within that distance from the sun, and almost the whole 

 velocity they there possess is sun-imparted. We have seen 

 what it is — some eleven miles per second. Now mani- 

 festly this greatly affects Jupiter's power of imparting or 

 withdrawing velocity. Both processes require time, and it 

 is clearly impossible for Jupiter to produce anything like 

 the same effect on a body rushing past him with a sun- 

 imparted velocity of eleven miles per second as he would 

 produce on a body left undisturbed to his own attraction. 

 Jupiter's action at any moment is the same whether the 

 body is moving or at rest ; but the number of movements 

 is very much reduced owing to the swift rush of tlie body 

 past the planet. To use the old-fashioned expression of 

 the first students of gravitation (an expression which has 

 always seemed to me amusingly quaint) the solicitations of 

 Jupiter's attractive force are as urgent on a swiftly rushing 

 body as on one at rest ; but if a body will not stay to 

 hearken to them, much less effect must be produced. In all 

 this part of my reasoning, I may remark, I am not pleading 

 a cause, but indicating what every student of celestial 

 dynamics knows. 



We may fairly regard twenty -five miles per second as the 

 utmost velocity that Jupiter can impart or take from any 

 body coming out of interplanetary space past him, as close 

 as such a body can pass without being actually captured. 

 Moreover, in every possible case, Jupiter can only abstract 

 or add a small portion of this amount ; for this reason, 

 simply, that in every possible case there will be first an 

 action of one kind (abstraction or addition of velocity), and 

 afterward an action of the opposite kind (addition or 

 abstraction respectively). It will be but the difference 

 between these effects, in most cases very nearly equal, 

 which will actually tell on the body's future period of revo- 

 lution around the sun.* This makes an enormous reduction 

 on Jupiter's potency to modify cometic revolution. Cer- 

 tainly ten mUes per second is a very full estimate of the 

 velocity he can abstract or add in the case of a body passing 

 quite close to his apparent sm-face. 



But even this may seem ample. Seeing that a loss of 

 three miles or so per second would cause a body whicli had 

 reached Jupiter's distance from the sun, after a journey 

 from out of interplanetary space, to travel in the same 

 ])eriod around the sun as .Jupiter himself, and since we 

 seem to recognise a power in Jupiter to abstract ten miles 

 per second, it would seem as though Jupiter's capturing 

 power were in fact demonstrated. 



But while, to begin with, the close approach required for 

 this capturing power to exist is something very different 

 from that approach within a million miles which I before 

 considered, there is a much more important difficulty to be 

 considered, in the circumstance that we have thus far dealt 

 with Jupiter's capturing power on one body, not on a flight 

 of bodies, such as a comet approaching from interstellar 



* As distinguished from the orbit. The orbit might be largely 

 affected even in a case where the velocity at Jupiter's distance re- 

 mained absolutely nnchanged; but in this case the period of revolu- 

 tion would remain the same. 



space is held to be, according to the theory I am discussing. 

 Let us take theformer point, though the least important, first. 



At Jupiter's apparent surface the actual maximum 

 velocity which the planet could give to a body approaching 

 from a practically infinite distance would be about thirty- 

 six miles per second, and we reduced the actual maximum 

 effect on a body passing Jupiter very close, under such 

 conditions as actually prevail in the solar system, to ten 

 miles per second. Let us see what would be the corre- 

 sponding numbers in the case of a body passing within a 

 million miles of him, remembering that even that would 

 carry such a body right through Jupiter's system of satel- 

 lites, the span of that system being about four and a half 

 millions of mQes. Since a distance of one million miles 

 exceeds the distance of Jupiter's surface from his centre 

 nearly twenty-five times, it follows (I need not explain why ; 

 mathematicians will know, and for non-mathematicians the 

 explanations would be tedious and difficult) that the velo- 

 cities which Jupiter can give or abstract at the greater 

 distance would all be reduced to little more than one-fifth 

 those determined for Jupiter's surface. So, instead of ten 

 miles per second, we should get but two miles per second, 

 as the greatest Jupiter could abstract from a body approach- 

 ing him within a million miles. And this would not be 

 sufficient reduction to make such a body travel thenceforth 

 in Jupiter's period, still less in one of the much shorter 

 periods observed throughout what has been called Jupiter's 

 comet-family. 



But the other difliculty is altogether more serious. A 

 comet approaches .Jupiter, on the theory we are dealing 

 with, — and indeed the same may be assumed on any 

 theory, — as a flight (jf scattered bodies. Either this flight 

 is so close as to be in effect, because of mutual attractions, 

 a single body, or it is not. If it is, the flight will not be 

 broken up by Jupiter's action ; and, if not so broken up, 

 will remain for ever after a united family. But if, as is 

 more in accordance with observed facts, the cometic flight 

 is so large that the attraction of the flight, as a whole, on 

 the separate members, can be overcome by Jupiter's action, 

 then not only will the flight be broken up, but the orbits given 

 to different members of it by Jupiter's disturbing action 

 will be widely different. Suppose, for example, the extent 

 of the flight to be such that the parts coming nearest to 

 Jupiter approach his centre within fifty thousand miles (a 

 very close approach, indeed, to his surface), while those 

 parts which are remotest from him at the time when the 

 fifght, as a whole, is nearest, came only within sixty 

 thousand miles from his centre. Then, in round figures, 

 the reduction of velocity of the nearer members of the 

 flight will be greater than the reduction for the farther 

 members, as six exceeds five. Supposing, for argument's 

 sake, the former reduction to be three miles per second, as 

 it must be to make those members of the flight travel 

 thenceforth in Jupiter's period round the sun, then the 

 reductiton for the outermost members would be but three 

 and a half miles per second ; or thenceforth one set of 

 meteors -fosmerly belonging to the comet would have at 

 Jupiter's distance a velocity of eight miles per second 

 (eleven less three), while another set would have a velocity 

 of eight and a half miles per second (eleven less two and 

 a half) at that distance. This means that thenceforth 

 the mean distance of the latter set from the sun would 

 exceed the mean distance of the former set about as nine 

 exceeds eight* Since the former set would thenceforth be 



* The simple law is, that for two bodies having different velo- 

 cities at the same distance from the sun, the mean distances from 

 him differ as the squure of those velocities. Now, the square of 

 eight and a half is seventy-two and a quarter; that of eight is 

 sixty-four. 



