July, 190B.] 



KNOWLEDGE. 



149 



by many of the variations played upon it. Entire license 

 of treatment prevails. The strict and simple lines of 

 evolution laid down by Laplace are obliterated or sub- 

 merged. Some of the schemes proposed by modern 

 co^mof^onists are substantially reversions to Kant's 

 " Natural History of the Heavens " ; the long-discarded 

 and despised Cartesian vortices reappear, with the I'clat of 

 virtual novelty, in others ; nor are there wanting theories 

 or speculations reminiscent even oE Buffon's cometary 

 impacts. Moreover, the misleading fashion has come into 

 vogue of bracketing Kant with Laplace as co- inventor of 

 the majestic and orderly plan of growth commonly 

 designated the " Nebular Hypothesis." This has been, 

 and is, the source of much hurtful confusion. Save the 

 one fundamental idea — and that by no means their 

 exclusive property — of ascribing unity of origin to the 

 planetary system, Kant's and Laplace's evolutionary 

 methods Lad little in common. Their postulates were 

 very far from being identical ; they employed radically 

 different kinds of " world-stuff " ; and the " world-stuff " 

 was subjected, in each case, to totally dissimilar processes. 

 Yet it is often tacitly assumed that to defend or refurbish 

 one scheme is to rehabilitate the other. TJnder cover of 

 the intellectual vagueness thus fostered, a backward drift 

 of thought is indeed discernible towards the standpoint of 

 the Konigsberg philosopher. It is recommended, not so 

 much by the favourable verdict of recent science as by 

 the wide freedom of the prospect which it aflbrds. The 

 imperative guidance of Laplace, reassuring at first, led to 

 subsequent revolts. But Kant is highly accommodating ; 

 one can deviate widely from, without finally quitting the 

 track of his conceptions ; they are capacious and indefinite 

 enough to comport with much novelty both of imagination 

 and experience, and hence lend themselves with facility to 

 the changing requirements of progress. 



A noteworthy attempt was made, in 1873, by the late 

 fidouard Roche, of Montpellier, to reconstruct, without 

 subverting, Laplace's Hypothesis. This remarkable man 

 lived and died a provincial ; only a few scattered students 

 have made acquaintance, at first hand, with his works ; 

 his fame, always dim, now already begins to seem remote. 

 Yet a score of years ago he was still lecturing at the 

 Lycce of his native town. The waters of oblivion have 

 grown, perhaps, more turbid than of yore. Anyhow, 

 Eoche of Montpellier is only vaguely remembered, and 

 that by a specially educated section of the public, as having 

 fixed a limit within which a satellite cannot revolve intact.* 

 Nearer to the ruling planet than 2'44 of its mean radii, it 

 could not — apart from improbable conditions of density — 

 maintain a substantive globular status under the disruptive 

 strain of tidal forces. In point of fact, all the moons so 

 far discovered in the solar system circulate outside 

 " Roche's Limit " ; and Saturn's rings, which lie within it, 

 owe to that circumstance, it may plausibly be asserted, 

 their ])ulveruleut condition. Professor Darwin, atxordingly, 

 considers knowledge of that condition to date from 1848, 

 the year in which Roche published the law involving it as 

 a corollary. t 



Roche was the jirecursor of Poiucarc and Darwin in 

 those momentous investigations of the figures of equi- 

 librium of rotating fluid bodies which have opened up new 

 paths and disclosed untried possibilities in evolutionary 

 astronomy. His researches, moreover, into the origin of 

 the solar system I constituted a reinforcement of primary 

 account to the strength of Laplace's position. He was 



• " Memoires de I'Acad. Montpellier," t. I. 

 t " The Tides," p. 327. 



t " M.Mimiirs dc VAoad. MoiitiH-lliov," t. VIU. 



l)erhaps its most effective defender, repairing breaches, and 

 throwing up skilfully constructed outworks. Adopting the 

 same premisses, he drew virtually the same conclusions as 

 Laplace, ingeniously modifying them, however, so as to 

 evade certain objections, and temporarily to silence the 

 less obstinate cavillers. His results were, indeed, almost 

 as difficult to disprove as they had been to obtain. They 

 were arrived at laboriously, legitimately, by long-drawn 

 analytical operations ; and the reasonings survive in f^ll 

 credit, even although the initial conditions they started 

 from now wear an aspect of unreality. Thus, the invention 

 of trainees elMptiques not only usefully met an argumen- 

 tative emergency, but still remains as a supplementary 

 adjunct to cosmic processes. Undeniably, polar annula- 

 tion may have played a part in lalanetary formation ; the 

 possibility cannot be gainsaid The '■elliptic trains" 

 investigated at Montpellier were huge nebulous strata 

 detached from the polar regions of the primitive sphei'oid, 

 which, bringing with them the low rotational velocity 

 l)roper to that situation, tende 3, some to constitute interior 

 equatorial rings, others to become agglomerated with the 

 central mass. But their incorporation should have had as 

 its consequence — since the " law of areas " is inviolable— a 

 (juickening of angular rotation throughout the nebula. 

 The " law of areas," it may be explained, is merely a short 

 title for the "law of conservation of moment of momentum," 

 which prescribes— as we know — that the sum-total of the 

 areas described in a given time on a given plane by the 

 members, or constituent particles of a rotating system, 

 multiplied by their several masses, remains constant under 

 all conceivable cii'cumstances of re-arrangement or mutual 

 disturbance. Hence, approach towards the centre, because 

 it narrows the circle, must quicken the speed of rotation. 

 A short line having to sweep over the same space as one 

 of greater length, its moving end must proportionately 

 hurry its pace. An engulfment, accordingly, by the 

 embryo sun of one of Roche's "elliptic trains" would 

 have "occasioned an immediate shortening of the period of 

 revolution of both nucleus and atmosphere, an accession 

 of centrifugal force producing sudden instability, and, as 

 a consequence, the separation of an equatorial ring. By 

 this subtly-devised expedient. Roche sought to explain 

 away the difficulty connected with the wide intervals 

 between the planets. For they originated, he conceived, 

 not in the regular course of condensation, but through 

 complications arising abruptly, and exceptionally. The 

 " limiting surface "—as he called it — of the nebula might 

 also be described as the atmospheric limit. It corresponds 

 to the widest possible extension of a true atmosphere. Its 

 boundaries are at the distance just outside of which a 

 satellite could freely circulate in the axial jieriod of its 

 primary. Now the limiting surface, if contraction had 

 proceeded equably, should have retreated continuously, its 

 withdrawal being attended by the shedding of slender 

 rivulets of superfluous matter." But by the introduction 

 of "elliptic trains," stability, artificiaily maintained (so 

 to speakj throughout long spells of time, was overthrown 

 only by catastrophic downrushes from the shoulders of the 

 nebulo'us spheroid, when, with the prompt abridgment of 

 tlie axial period, the limiting surface as promptly shrank 

 inwards, and there was left, outstanding and seU'-subsistent, 

 the tenuous ring destined to coalesce into a phuiet. A 

 singular and unexplained felicity of Roche's analysis con- 

 sisted in the svmmetry of time-relations established by it. 

 The successive births of his planets appeared to follow 

 each other at equal intervals. Bode's law of distances 

 (extended by hiin to satellite-systems) was thus translated 

 in terms of the Nebular Hypothesis.* 



• Wolf, Hull. A.-lr.. 1. 1., ).. 50il. 



