FOOTNOTES:
[10] Presidential Address to the British Association, Johannesburg, August 30, 1905.
[11] Comptes Rendus, tom. lii., p. 481.
[12] Astrophysical Journal, vol. xi., p. 103.
[13] Moulton, Astrophysical Journal, vol. xi., p. 110.
[14] Nolan, Nature, vol. xxxiv., p. 287.
[15] Bulletin Astronomique, tom. ii., p. 223.
[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]
That hypothesis, in its original form, as explained in the last chapter, produced planets with retrograde rotation—that is, spinning in an opposite sense to that of their circulation. For the purpose of abolishing the anomaly, Kirkwood, in 1864,[20] had recourse to solar tidal friction, and he was followed, doubtless independently, by Roche, and by Roche's interpreter, C. Wolf of Paris. Objections to any particular mode of planetary formation, on the ground that its outcome must have been inverted axial movement, lost their validity, they remarked, through the consideration that solar tidal friction would have availed to redress the incongruity. For its retarding action would have ceased only when synchronism with the revolutionary period was attained—that is, when the planet wheeled in its orbit, as Mercury seems to do, turning always the same face inward; and then already direct rotation would have set in, and, becoming accelerated by contraction, should permanently retain the direction impressed upon it by the friction of sun-raised tides. A certain air of plausibility is given to this view by the fact that the only two retrograde planetary systems are situated entirely beyond the possible range of any such manner of influence, and may accordingly be supposed to have preserved unaltered their primitive fashion of gyration.
The late M. Faye was less loyal to tradition than the savant of Montpellier. The appearance in 1884 of his work, Sur l'Origine du Monde, gave the signal for renewed activity and a larger license in cosmological speculation. Conservative opinions on the subject are now rarely held; the old groove has been by most definitively quitted; inquiry becomes continually more individual and less constrained by tradition. Faye's reform, however, was not avowedly of a revolutionary character. He did not make a clean sweep of the work of his great predecessor, by way of preliminary to setting forth his own more perfect plan. Yet his emendations of it went very deep.
Laplace's nebula was of a gaseous consistence, and it stood in a genuine atmospheric relation to the central condensation—that is to say, its strata gravitated one upon the other; they were subject to hydrostatic pressure. Faye ruled things otherwise. The nebulous matrix which he postulated was a vast congeries of independently moving particles, forming a system governed by a single period, in which both gravity and velocity increased in the direct ratio of the distance from the centre. Now, globes formed by the method of annulation (admitting its practicability) out of materials thus conditioned, should have possessed, ab initio, a direct rotation; their axial spinning would have been in the same sense as their orbital circulation. And this it was which recommended to Faye the adoption of a meteoric structure for the inchoate solar system. But the simple law of force regulating it at first would, by degrees, have undergone essential alteration. That of inverse squares, familiarized to ourselves by long habits of thought, would have begun to supersede it so soon as a sun, properly so called, could be said to exist. The retrograde planets, Uranus and Neptune, must, however, by Faye's supposition have taken shape under the modern regimen; they were formed subsequently to the earth and all the rest of her sister orbs. This unexpected inversion of the recognised order of planetary age involved the further consequence that the ante-natal offspring of the sun—thus paradoxically to designate them—must have drawn closer to him as his attractive power developed, Uranus and Neptune alone among the entire cortège preserving the original span of their orbits.
Faye's scheme, if it did not meet all the arduous requirements of the problem it confronted, served, at any rate, to illustrate very forcibly the devious variety of tracks by which nebular evolution might advance towards its goal. The particular one chosen was certainly not clear of impediments. In his preoccupation with the removal from Laplace's hypothesis of the flaw relating to planetary rotation, M. Faye had discarded its cardinal merit of explaining secessions of material by the growth of centrifugal force. He alleged no sufficient reason, and none could be alleged why the remodelled nebula should have separated into rings.[21] The process implies definite and special conditions; it testifies to a rhythmically acting cause. Laplace brought such a cause into play. Faye abolished it, and his annuli, accordingly, wear a fictitious aspect. It is, indeed, true that an annular structure is commonly visible in nebulæ, but it is begging a most arduous question to assume that nebular spires have anything in common with planet-forming rings.
These would probably never have been heard of save for the Saturnian example. A pattern is easily copied; an idea palpably feasible is tempting to adopt; a demonstration on the solvitur ambulando principle cannot but prove convincing. But how if the rings cannot be made to coalesce into globes? And the difficulty of the transformation becomes more apparent the more clearly its details are sought to be realized. Reversed in direction, it might better find a place in the order of Nature. 'Analysis seems to indicate,' Kirkwood wrote in 1884,[22] 'that planets and comets have not been formed from rings, but rings from planets and comets.' Nor is this mode of procedure merely possible according to theory; it is also vividly illustrated by facts. Meteoric swarms can be observed, decade by decade, to disperse under the scattering influence of the sun and planets, and unmistakably tend to become more or less uniformly distributed along the entire round of their orbits. Their advance is directed, not towards condensation, but towards disaggregation; and they pursue it with surprising rapidity.
Faye's theory was disfigured by a still more glaring incongruity. Nothing in the planetary economy seems more evident than that the zone of asteroids marks a division between two strongly dissimilar states of the solar nebula. It is a visible halting-place. One series of events came to an end, and there was an interlude before the next began. During that interlude, during the partial suspension of activity which ensued upon the production of the Ajax among the planets, the crowd of planetoids were launched to fill the blank space. Here, if anywhere, Nature changed her hand and tried a fresh method. Faye's shifting of the scene of change to trans-Saturnian regions is then, as M. Wolf justly perceived, non-natural, and undermines the credit of a plan to which the device is essential.
On the other hand, it had the merit of being elastic enough to include the great cometary family. Kant had also, although in an unsatisfactory manner, made room for them; but Laplace had no choice save to regard them as casual intruders from space, the admission of which as natives of his well-ordered domain would have led to the subversion of all its harmonious regulations. Modern inquiries, however, prove comets decisively to be no such stray visitors as Laplace supposed, but to be of the same lineage—however remotely traceable—with the planets, and to own the same allegiance. Drifting with the sun, they form part of its escort on the long, irrevocable voyage it is engaged upon, and cannot, save by accidents of perturbation, be driven finally to part from its company. The problems of planetary and cometary origin are then inseparable; the two classes of body are fellow-citizens of one kingdom. Comets become only by compulsion cosmopolitan wanderers from star to star.
There was yet another motive and semblance of justification for Faye's reform of the nebular hypothesis. The discovery of the conservation of energy supplemented, as we have seen, very happily the mechanics of a condensing nebula by satisfactorily solving the enigma of solar radiation. Helmholtz was thus able, in 1871, to sketch cosmic development as, in its essence, a thermodynamic process on the grandest scale. Yet the alliance entered into, fruitful and fortifying though it was, had an attendant embarrassment. Time had now to be reckoned with. In the cosmogonies of Kant, Herschel, and Laplace the allowance of æons was unstinted. Because the rate of change was indeterminate, they might be permitted to elapse ad libitum. But it was otherwise when the driving-power came to be defined. 'Conservation of force' implies the measurableness of force. Equivalence cannot be ascertained where no limits are determinable. Knowledge, accordingly, regarding the source of the sun's heat brought with it the certainty that the source was by no means inexhaustible. The stock of energy rendered available by shrinkage from a primitively diffuse to its present compact state was enormous, but not boundless. The task then became incumbent upon cosmogonists of proving its sufficiency, or of eking out its shortcomings.
The problem is both retrospective and prospective. We look back towards the birth of the sun, we look forward to its demise; and each event has, if possible, to be located on our time-scale. Helmholtz assigned terms of twenty-two millions of years in the past and seventeen millions in the future for the shining of our luminary with its actual intensity. Geologists and biologists, however, claimed a much more extended leisure for the succession of phenomena on this globe, and efforts on the part of physicists to meet their demands barely availed to tone down without removing the discrepancy. M. Faye then came to the rescue. His suggestion that the earth took separate form while the sun was still nebulous was designed to conciliate the demands of those who needed all but eternity for the slow accumulation into specific differences of infinitesimal variations. In this way a start was gained upon the sun; the preparations for vitality on our planet were going forward long before the lavish radiative expenditure designed to nurture its development had begun. The earth, in fact, was shaping itself for its destiny in advance of the epoch when time began to count for the sun.
This supposed relation of precedence cannot, indeed, be insisted upon; it was imagined to save a difficult situation, and intimates a design more or less academic. Yet the expedient was significant as regards the effect of the introduction into modern thought of the principle of the conservation of energy. It gave definiteness and a kind of solidity to speculation by widening the basis upon which it was made to rest. At the same time it necessitated adjustments between the exigencies of the various sciences, and brought into prominent view apparent incompatibilities only to be removed by prolonged investigations of wide scope and intricate bearings. Modern cosmogony, in short, while disposing of enlarged means, has to meet multiplied requirements. Quite lately, nevertheless, some authoritative exponents of geological and biological science manifest a satisfactory disposition to 'hurry up their phenomena,' quite independently of the inadequate age of the sun.[23] On neither side, accordingly, are the irreconcilable claims of the past any longer insisted upon, and a compromise has become easily possible.
A theory of planetary evolution marked by some novel features was ably expounded by M. du Ligondès in 1897.[24] Designed to improve, by simplifying, Faye's plan, it reduced postulates to a minimum, and left the freest possible play to 'original indetermination.'[25] The embryo world of M. du Ligondès was a tumultuous mêlée of particles moving anyhow. Their jostlings, however, did not, and could not, exactly balance, and the inequality, small though it might be, sufficed to afford a basis for harmonious growth. Motion became regularized by collisions; counter-currents of velocity were gradually eliminated; and the particles pursuing eccentric or retrograde courses, brought sooner or later to a stand, fell towards the centre and accumulated into the sun, while the remnant that travelled in the prevalent direction along circular paths finally constituted the planets. They were formed, not at haphazard, but through the medium of zones of maximum density, due to the variations of gravity within the disc towards which the primitive spheroid finally collapsed; and each, as it took shape, became a source of perturbative influence on its subsequently developed neighbours, by which the inclinations of their orbital planes and of their axes of rotation were in various ways altered. The planetary zones, too, contracted with the advance of condensation, so that the matured planets occupied positions much nearer to the sun than those assigned to their inchoate materials. The modus operandi employed, in short, adapted itself with praiseworthy readiness to the diversities of nature.
Sir Robert Ball is at one with M. du Ligondès in regarding the origin of the solar system chiefly under its mechanical aspect. Like Helmholtz and Faye, he chooses pulverulent materials to work with; his nebula is a 'white nebula.' But looking still further back, he discerns as its parent an irregular 'green' nebula, the confused movements of which falling into a settled order as the result of encounters, it slowly flattened down into the 'plane of maximum areas'—the fundamental plane conformed to more and more closely as the energy of a system inevitably wastes. He dispenses with the troublesome process of annulation, and starts his planets virtually by Kant's method of accidental nuclear condensation.[26] A spiral structure, moreover, would be imparted to the entire nebula by the gradual propagation outward of the central acceleration due to contraction.
But would it have contracted? It had, by supposition, reached the stage of approximate unanimity in movement. The great bulk of its constituent bodies circulated in the same direction, in nearly the same plane, and presumably in orbits not deviating much from circularity. Their aggregate condition might then be regarded as permanent and stable. The central mass would, accordingly, no longer be fed by the engulfment of particles brought to rest by their mutual impacts; motion being unimpeded, heat could not be evolved; and the imagined transformation of a disc-like meteoric formation into a sun and planets would fail to come to pass.
What, then, we may ask ourselves, is the upshot of these various efforts at reconstruction? They establish, certainly, the unassailable unity of the solar world; and the solar world must be understood to embrace comets and cometary meteors. The arguments favouring this unity have gained enormously in cogency through modern discoveries. For those depending upon structural coincidences and harmonies of movement have been reinforced by others of a totally different nature, furnished by the doctrine of the conservation of energy and the teachings of spectrum analysis. The sun is hot because it was anciently expanded; the energy of position formerly belonging to its particles incontestably provided a large part, if not the sum total, of its present thermal energy, and this amounts to saying that a sphere indefinitely great was once filled by our inchoate system. The conclusion that it arose from an undivided whole through the gradual differentiation of its parts is further ratified by the identity of solar and terrestrial chemistry. The earth is thus strongly averred to have once made an integral part of the substance of the sun, and what is true of the earth is no less true of its sister planets.
Regarding the mode and manner of cosmic change there is, nevertheless, no consensus of opinion. Faye made a noteworthy effort to elaborate a process that might endure modern tests of feasibility, yet his theory has been well-nigh torn to pieces by adverse criticism. M. du Ligondès escapes some, but not all, of the objections which proved fatal to his predecessor. That there was in the beginning a solar nebula, all are agreed; but whether it was gaseous or pulverulent, whether it shone with interrupted or continuous light, how it became ordered and organized, how it collected into spheres, leaving wide interspaces clear, the wisest are perplexed to decide.
Mr. Moulton concludes, from his careful examination of the subject, that 'the solar nebula was heterogeneous to a degree not heretofore considered as being probable, and that it may have been in a state' resembling that exhibited in recent photographs of spiral nebulæ.[27] But, even if all the facts do not chime in with this tempting analogy, there can be little reason to dissent from his intimated opinion that 'the Laplacian hypothesis is only partially true, and that we do not yet know the precise mode of the development of the solar system.'