[CHAPTER IV]
THE NEBULAR HYPOTHESIS VARIED AND IMPROVED
'Restorations' often go very far. Things may be improved beyond recognition, nay, out of existence. So it has happened to the nebular hypothesis. Stat nominis umbra. The name survives, but with connotations indefinitely diversified. The original theme is barely recalled 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 submerged. Some of the schemes proposed by modern cosmogonists are substantially reversions to Kant's Natural History of the Heavens; the long-discarded and despised Cartesian vortices reappear, with the éclat of virtual novelty, in others; nor are there wanting theories or speculations reminiscent even of 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 had 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. Under cover of the intellectual vagueness thus fostered, a backward drift of thought is, indeed, discernible towards the view-point of the Königsberg philosopher. It is recommended, not so much by the favourable verdict of science as by the wide freedom of the prospect which it affords. 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 Édouard 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 Lycée of his native town. The waters of oblivion have grown, perhaps, more turbid than of yore. Anyhow, Roche 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.[16] Nearer to the ruling planet than 2·44 of its mean radii, it could not—setting aside 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 pulverulent condition. Professor Darwin accordingly regards knowledge of that condition as dating from 1848, the year in which Roche published the law involving it as a corollary.[17]
Roche was the precursor of Poincaré and Darwin in those profound investigations of the figures of equilibrium 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[18] constituted a reinforcement of first-rate importance to the strength of Laplace's position. He was perhaps its most effective and timely defender; he came to the rescue just when its safety was seriously compromised, repaired its breaches, and threw 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 attain. They were arrived at laboriously, legitimately, by long-drawn analytical operations; and the reasonings survive in full credit, even although the initial conditions they started from now wear an aspect of unreality. Thus, the invention of trainées elliptiques not only usefully met an argumentative emergency, but still remains as a supplementary adjunct to cosmic processes. Undeniably, polar annulation may have played a part in planetary formation; the possibility cannot be gainsaid.
The 'ellipsoidal trains' investigated at Montpellier were huge nebulous strata detached from the polar regions of the primitive spheroid, which, bringing with them the low rotational velocity proper to that situation, tended, 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 quickening 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 circumstances 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. What he called the 'limiting surface' 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 fixed at the distance just outside of which a satellite could freely circulate in the axial period of its primary. Now the limiting surface, if contraction had proceeded equably, should have retreated continuously, as axial movement quickened, its withdrawal being attended by the shedding of slender rivulets of superfluous matter. But by the introduction of 'elliptic trains,' stability, artificially maintained (so to speak) throughout long spells of time, was overthrown only by catastrophic downrushes from the shoulders of the nebulous spheroid, when, with the prompt abridgment of the axial period, the limiting surface as promptly shrank inward, and there was left, outstanding and self-subsistent, the tenuous ring destined to coalesce into a planet. A singular and unexplained felicity of Roche's analysis consisted in the symmetry of time-relations established by it. The successive births of his planets followed each other at equal intervals. A species of translation of Bode's law of distances (extended by him to satellite-systems) in terms of the nebular hypothesis thus appeared to be rendered feasible.[19]