February, 1913. 



KNOWLEDGE. 



73 



Now, the sphere of the Earth's influence extends to 

 a distance of over nine hundred thousand miles, so 

 that any small body revolving within this distance 

 would be entirely under the Earth's control, and 

 since the Moon is less than two hundred and forty 

 thousand miles away, its position, and the circularity 

 of its orbit, could most easily be accounted for by 

 this supposition. The same remark applies to all 

 the known satellites of the other planets, which are 

 in every case well within the space controlled by 

 their respective primaries, and which, with the 

 exception of the outer ones of Jupiter and Saturn, 

 have remarkably circular orbits. 



Owing to the unique nature of the Saturnian 

 system it has frequently been typified as an example 

 of cosmical evolution. Thus, at the time when 

 Kant and Laplace framed their theories, the rings 

 were thought to consist of gas, and, therefore, to 

 corroborate them. The rings have since that time 

 been conclusively proved to be formed of vast 

 numbers of independent particles revolving round 

 their primary, but were still considered to be a 

 satellite in course of formation. Edouard Roche, 

 a French mathematician, has, however, shown that 

 it is impossible for a satellite to exist within 

 2-44 radii of its primary, owing to the strain 

 imposed by the attraction of the latter. It is, 

 therefore, probable that if a resisting medium exists 

 in the solar system, a satellite may have actually 

 been brought by its influence within the pro- 

 scribed area and been torn to pieces, the rings thus 

 being an example of the end rather than the birth 

 of a world. 



The thesis of possession by capture would con- 

 sequently account for the presence of the satellites 

 under the control of their various primaries in the 

 most likely manner. Indeed, were it not for the 

 conflicting testimony offered by our Moon, there could 

 be but little diversity of opinion on the subject. It 

 will be as well, therefore, to examine the evidence 

 regarding our own domestic system somewhat more 

 fully. There is, of course, only one other possible 

 way to account for the present position of our 

 satellite, which, if it has not been captured, must 

 have been formed by fission of the Earth, and this 

 latter theory seems to have met with almost 

 universal acceptance ever since the time of Anaxa- 

 goras, 500 B.C. Now, there is one unusual feature 

 about the Earth- Moon system favourable to this 

 hypothesis, namely, the relative sizes of its two 

 constituents, which are in the ratio of eighty-one to 

 one. If we except Neptune and his satellite, about 

 which some doubt exists, the nearest approach to 

 equal masses in the other planetary systems is to be 

 found in that of Saturn. His largest satellite, 

 Titan, is but the one four thousand seven-hundredth 

 part of his mass, and there is a still greater dis- 

 crepancy in the relative sizes of all the other 

 satellites to their primaries. This peculiarity of 

 our Moon might, therefore, seem to imply a different 

 origin from that of other satellites^although, if it ever 

 revolved against resistance, there is no dynamical 



reason why our Earth should not have captured such 

 a comparatively large globe. 



There are, however, several objections to the fission 

 theory. In the first place, it would be necessary for 

 the Earth to have attained a sufficiently rapid 

 rotation to have overcome the force of gravity by 

 centrifugal force. The alternative to this would 

 be to assume that the rupture was caused by tidal 

 strains, in the same way as that suggested in the 

 evolution of the solar system. Now, if this had 

 happened, two streams of matter would have been 

 ejected and formed a small spiral nebula. It is 

 extremely unlikely that all the meteorites forming the 

 coils would have only condensed into one other body, 

 since we should expect a miniature solar system of 

 our own, with some satellites considerably nearer 

 than the lunar orbit, and others further off. More- 

 over, the presence of the disturbing element would 

 have to be accounted for. Unlike the strange star 

 which is supposed to have caused the birth of the 

 primordial nebula, this second sphere would pro- 

 bably be unable to escape from the control of the 

 Sun, and as it would necessarily be of considerable 

 size to cause the requisite amount of damage, its 

 presence could almost certainly be detected ; for even 

 were it now beyond the range of our telescopes, we 

 should in all likelihood notice its perturbing effect on 

 the outer planets. As we know of no such body, 

 we are forced to discard this surmise and fall back 

 upon a rapid rotation as the only cause of fission. 



It has been calculated that, in order to overcome 

 the adhesion of its particles by centrifugal force, our 

 planet would have to possess an axial rotation of 

 two hours and forty-one minutes. The only means 

 of obtaining this enormous velocity would be by 

 contraction from a nebulous condition. To appreciate 

 this process it is necessary to understand what is 

 involved in the term " moment of momentum." It 

 is well known that momentum is the product of the 

 mass and velocity of a body, and " moment of 

 momentum " denotes its rotary power round an 

 axis. If we neglect outside influence it is manifestly 

 impossible to alter its amount in a rotating body, 

 however much the latter expands or contracts. 

 Whatever it loses, therefore, in decreasing size, is 

 compensated by an increase in angular velocity, or 

 in other words, in a contracting body, rotating freely 

 in space, the angular velocity varies inversely as the 

 square of the radius. 



Now, this increase is considerably in excess of the 

 additional speed required by the particles of a body 

 to counteract the increase of centripetal force, due 

 to their nearer approach to the centre of gravity. 

 Thus, although the Earth is thirty times nearer the 

 Sun than the planet Neptune, its angular orbital 

 velocity is only one hundred and sixty-five times 

 that of the latter, whereas the contraction of a rota- 

 ting sphere to one-thirtieth of its original diameter 

 would result in an increase of 30 2 or nine hundred 

 times its initial angular speed. 



If, therefore, the Earth were sufficiently diffuse, and 

 its original rotational velocity were rapid enough, it 



