112 



♦ KNOWL.EDGE ♦ 



[ACG. 8, 1884. 



out again into interstellar space. This might happen tens, 

 hundreds, thousands, or even millions of times, a comet 

 either sweeping in a long ellijttical crbit with enormous 

 periods of revolution, aroimd one sun ; or, if its velocity 

 were slightly greater than that supposition implies, rushing 

 first round one sun, then out into the depths of space to 

 visit another sun, then to yet another, and so on, flitting 

 from sun to sun for ever, or until the kind of disturbance 

 in which the holders of the theory we are considering 

 believe, had changed this kind of motion into actual orbital 

 circuit.* 



In either case the minimum velocity with which a comet 

 would be moving, when at any given distance from our 

 sun, would be determinable within a few yards per second. 

 It is well known that the velocity with which a body 

 travelling to the sun from an infinite distance (though one 

 cannot, of course, conceive such a movement) would reach 

 the sun, would not exceed by a foot per second the velocity 

 with which a body would reach him after travelling from 

 the distance of the nearest fixed star. So, also, the 

 velocities of bodies moving in orbits reaching half as 

 far from the sun as the distance of the nearest star, 

 would be the same within a foot or bo per second as 

 the velocities with which bodies coming to the sun from 

 infinity would reach the same distance from him. If 

 such bodies had originally a great inherent velocity, 

 of course they would reach any given distance from 

 the sun with much greater velocity. But this would 

 not aflect our estimate of the least velocity at that dis- 

 tance. Thus we know what the giant planets to which has 

 been attributed the final capture of those comets which now 

 form a part of the solar system, had to do. We can tell 

 the precise velocity in miles per second, or, at least, the 

 minimum velocity, with which our imagined meteoric flight 

 would cross the orbit of Neptume, or Uranus, or Saturn, 

 or J upiter, as the case might he, before its capture. We 

 know, in the case of each comet supposed to have been 

 captured, the precise velocity of the comet at the distance 

 of the planet which captured it, — its special planet-master. 

 The difl'erence is the amount of velocity which the 

 capturing planet had to take away in order to effect the 

 supposed capture. 



Observe that we are here on sure ground, if the theory is 

 sound. It is certain that a comet in coming from remote 

 interstellar space to the solar system would have at the 

 distance, say, of Jupiter, a certain velocity. It is certain 

 that a comet now travelling in a particular orbit, approach- 

 ing at one point very near to the orbit of Jupiter, has at 

 Jupiter's distance a certain velocity, very much smaller. 

 Hence, it is certain that, if Jupiter captured that comet by 

 disturbing it as it approached him on the last of its many 

 free visits to the sun, the giant planet must have deprived 

 the comet of so many miles per second of its former velocity. 

 All we have to do is to find out how the planet could do 

 this ; iu other woids, how near the comet must have 

 apjiroached the planet to be thus effectively disturbed. 



These columns are not suited for the close and exact 

 discussion of the case of any particular comet. I have 

 elsewhere (in a paper which appeared in the "Proceedings" 

 of the Astronomical Society) given the details for certain 

 cases which have been regarded as among the most satis- 

 factory illustrations of the comet-capturing ways of the 

 giant planets, and have shown that the theory is in those 

 cases, and therefore in all, al.)Solutely untenable, though so 

 resolutely held. Still it may be well here to consider an 



* I have here considered only two kinds of cometic orbit, the 

 elliptic and the hyperbolic ; for a true parabolic orbit would be as 

 unlikely, or rather aa impossible, as a truly circular orbit among 

 the planets. 



illustrative general case — the simplest that can be taken, 

 and also the most effective, because the conditions are, in 

 reality, much more favourable than they are in any known 

 case. 



Imagine a flight of meteors to travel from interstellar 

 space toward the sun until it reaches the distance of 

 Jupiter, and that when at that distance it chances to pass 

 very close to the orbit of Jupiter, and at a time when 

 Jupiter himself is very near the place where the meteor 

 flight crosses his track. Observe that the chances against 

 each one of these contingencies are enormous. If we con- 

 ceive a sphere arouud the suu, girdled by Jupiter's orbit, 

 the meteor flight in its course sunwards might traverse the 

 surface of that sphere (or, which is the same thing, might 

 traverse the part of its course where it is at the same 

 distance as Jupiter from the sun) anywhere, and we arfr 

 supposing that it traverses that surface close to a particular 

 girdling circle (technically a " great circle " of the sphere). 

 Suppose that by " close " we mean within a million miles ; 

 then the imaginary girdle of the sphere through which the 

 meteor flight must pass to fulfil the required conditions is 

 two millions of miles broad. The sphere itself has a dia- 

 meter of some nine hundred and sixty millions of miles, and 

 by a well-known property of the sphere,* its surface is four 

 hundred and eighty times greater than that of the 

 girdling strip. The chance is but one in four hundred and 

 eighty than any meteor flight coming from interstellar 

 space toward the sun will be witkin a million miles of 

 Jupiter's orbit when at Jupiter's distance from the sun. 

 Then Jupiter's path has a circuit of more than three 

 thousand millions of miles. Thus the chance that at the 

 moment of the meteor flight's passing the orbit, Jupiter 

 will be within a million miles on either side of the place of 

 passage, is as two in three thousand, or one in one thousand 

 five hundred. But the chances that both these relations 

 hold is only as one in one thousand and five hundred mul- 

 tii)lied by four hundred and eighty, or as one in more than 

 seven hundred thousand. Thus, assuming — though the 

 case is otherwise — that a million miles would be an ap- 

 proach near eiiough for capture, still only one meteor flight 

 out of seven hundred thousand which come from outer 

 space could be captured by Jupiter. 



This, however, is but the mere beginning. We may 

 admit that millions of times as many comets or meteor 

 flights approach our system as the planets have captured ; 

 and if so, we need recognise no special force in any such 

 considerations as have just been presented. I have only 

 advanced them to suggest the conditions which are, as it 

 were, essential for the process of comet capturing by a giant 



planet 



{To ie continued). 



MIND IN 3*IAN AND BRUTE. t 



By George J. Ecmanes. 



IF it is true " The proper study of mankind is man,'' 

 assuredly the study of nature has never before reached 

 a territory of thought so important in all its aspects as that 

 which, in our own generation, it is now for the first time 

 approaching. After centuries of intellectual conquest in 

 all regions of the phenomenal universe, man has at last 

 begun to find that he may apply in a new and most unex- 



* The property is this : that the surface of a sphere exceeds the 

 surface of a girdling strip, such as we are considering, in the same 

 degree (if the strip is relatively narrow) that the diameter ot the 

 sphere exceeds the breadth of the strip. 



t From an article on " Man and Brute," in the yorth American 

 Rei'icir. 



