FOOTNOTES:

FOOTNOTES:[3]Quoted by Dr. Hastie in the preface to his translation of Kant'sCosmogony, Glasgow, 1900.[4]Sur l'Origine du Monde, 3eéd., p. 136.[5]This also was pointed out by M. Faye,loc. cit., p. 150.[6]Nature, July 9, 1903.[7]Rutherford,Radio-activity, p. 342.[8]Philosophical Transactions, vol. lxxxi., p. 85.[9]Herschel met Laplace during a visit to Paris in July, 1801, but what passed between them is unrecorded. In the sixth edition, however, of theExposition du Système du Monde, Laplace referred to Herschel's observations of nebulæ as confirmatory of his own genetic scheme.

[3]Quoted by Dr. Hastie in the preface to his translation of Kant'sCosmogony, Glasgow, 1900.

[4]Sur l'Origine du Monde, 3eéd., p. 136.

[5]This also was pointed out by M. Faye,loc. cit., p. 150.

[6]Nature, July 9, 1903.

[7]Rutherford,Radio-activity, p. 342.

[8]Philosophical Transactions, vol. lxxxi., p. 85.

[9]Herschel met Laplace during a visit to Paris in July, 1801, but what passed between them is unrecorded. In the sixth edition, however, of theExposition du Système du Monde, Laplace referred to Herschel's observations of nebulæ as confirmatory of his own genetic scheme.

CRITICISMS OF THE NEBULAR HYPOTHESIS

Laplace'stheory was a perfectly definite conception. In this lay its distinctive merit; in this also its special susceptibility to attack. Here was no question of condensation round nuclei arising at discretion amid the large possibilities of boundless elemental confusion; but of an orderly succession of occurrences, rendered inevitable by the steady operation of mechanical laws, and harmonizing, in their outcome, with the array of ascertained phenomena visible in the planetary system. These accordingly ceased to be regarded as arbitrary or casual; they became linked together in the present, and with the past, as joint products of one grand scheme of development. The mode of origin of the bodies exhibiting them accounted, its inventor claimed to have shown,simply and entirely for them all; and at least the fundamental propositions laid down by him could not be gainsaid.

Clearly, the unanimity of planetary movements is no result of chance; it represents quite obviously a survival of the general swirl of an inchoate mass, occupying primitively the whole recognised sphere of solar influence. Ambiguities set in only when details come to be considered. The engendering nebula devised by Laplace was provided with a vast endowment of heat and a slow movement of rotation; hence cooling, contraction, and acceleration advancedpari passu, the last as a consequence of the mechanical law by which the algebraic sum of the areas described by any number of bodies round a given axis, multiplied by their several masses and projected upon a single plane, remains constant to the end of time. In other words, to repeat what has been stated a few pages back, the moment of momentum of a congeries of particles can neither increase nor diminish through the effects of their mutual interactions, however varied and prolonged.

The nebula then quickened its pace until astage was reached at which centrifugal speed could no longer be controlled by gravity; separation became inevitable, and an equatorial ring was abandoned, which thenceforward revolved on its own account in the period conformed to by the undivided mass at the epoch of its secession. This was the first of many subsequent crises of instability, each eventuating in the detachment of a nebulous ring. These rings, however, were regarded as merely transitional forms. They survived, just for illustrative purposes, in the Saturnian system; elsewhere they broke up into fragments, which ultimately coalesced into globes, and the globes were embryo planets. There was, indeed, a hitch in the line of argument which did not escape the acumen of the French geometer. The direction of the axial movement imparted to the members of the solar family depended essentially upon the relative velocities of the portions of matter brought together for their construction. If the inner sections of the self-shaping mass moved faster than the outer, the resulting rotation should have been retrograde; if slower, direct rotation would have ensued. Now, in a ring like thatof Saturn, composed of discrete particles, linear speed decreases continuously outward, each of its minutest constituents obeying independently Kepler's law of periods and distances. Such a formation, since it would necessarily have yielded backward-spinning planets, would have been unfit for the purpose in view, and Laplace accordingly substituted an annulus endowed with a considerable amount of cohesion, and capable of rotating, like a solid, in a single period. It is true that such unanimity of movement was incompatible with the other postulated conditions; but the anomaly escaped notice for above half a century.

Professor Darwin has moreover pointed out[10]that a ring of matter distributed with any approach to uniformity must concentrate, if at all, round its own centre of gravity. It should accordingly collapse upon, and become re-absorbed by, the parent-body. If markedly unsymmetrical and ill-balanced, its materials might certainly collect at an interior point more or less remote from the centre; but inno case could the focus of condensation be situated in any part of the annular circumference, where it was located by Laplace.

Whether workable or not, the genetic plan traced out by him was a strictly regulated one; its steps were marked with characteristic precision. Yet by this very determinateness it gave hostages to the future. It challenged the application of tests which designs more vaguely sketched might have evaded. The primary criterion of its truth was the prevalence of concordant motion throughout the solar domain. Counter-currents were formally excluded; their possibility was not even contemplated. Hence, the discovery of the retrograde systems of Uranus and Neptune flatly contravened its pretensions to unconditional acceptance. With less evidence, but equal certainty, Laplace's hypothesis, strictly interpreted, involves the consequence that each planet circulates in the identical time occupied by the rotation of the undivided nebula just before instability toppled over into separation. Each of the planetary periods should accordingly bear a certain ratio, prescribed by inexorable mechanical law, to the actual period of the sun'srotation. In point of fact, however, the periods in question are much shorter than comports with the necessity for the conservation from age to age of the system's moment of momentum. The discrepancy was adverted to nearly half a century ago by M. Babinet.[11]He showed in March, 1861, that the axial movement of the solar mass, when distended to fill the sphere of Neptune, should have been, by the law of areas, so excessively slow that more than 27,000 centuries would have been needed for the completion of a single rotation; while the period, even when the shrinking nebula had come to be bounded by the terrestrial orbit, must still have been protracted to 3,181 years. Under these circumstances, centrifugal force would never have overbalanced central attraction; no rings could have separated, and no planets could have been formed.

Quite recently, Mr. F. R. Moulton, of Chicago,[12]has reconsidered the subject in the course of a careful and candid discussion of the difficulties besetting the nebular cosmogony as viewed from the standpoint of modernscience, and he comes to essentially the same conclusion. His calculations, though founded on data expressly chosen so as to give the classic theory the benefit of every doubt, made it perfectly clear that the moment of momentum of the embryo planetary system should have exceeded its present value no less than 213 times if, when it extended to the distance of Neptune, it rotated in what is now the period of Neptune. But moment of momentum is a constant. The lapse of millions of years makes no difference to it; it is not, like energy, subject to 'dissipation'; it can neither have gained nor lost value since the sky was first flecked with the 'breath-stain' appointed to condense into our sun, which, in this respect at least, must at every stage of its subsequent evolution have maintained immutability. On the other hand, this being so, its primeval wheeling motion would have been much too leisurely to permit the occurrence of accesses of instability. Gravity would have steadily kept its supremacy over the forces tending to disruption until the nebula had contracted to less than the compass of the Mercurian sphere, and its overthrow at that epoch would havebeen too late for the origination of any of the sister orbs of the earth. These results, it is true, depend in part upon the mode of variation in density ascribed to the progressively shrinking nebula; but the law adopted by Mr. Moulton has a consensus of authorities in its favour. Nor could its deviation from exactitude—if it be inexact—possibly suffice to account for the enormous discrepancies which calculations based upon it have brought to light.

The nebular hypothesis stipulates further that satellites must revolve more slowly than their primaries rotate. The reason is patent. In the periodic time of a body detached by centrifugal acceleration the rate of gyration of the original mass is, if the theory be valid, perpetuated. Subsequent contraction tends to quicken, and very greatly to quicken, the rotation of the planet, while the period of the satellite survives unaltered as a standing record of what the joint period was. This relation may indeed be modified by the effects of tidal friction, but it is more than doubtful whether it can ever be reversed. It is, then, a characteristic feature of the mode of evolutiondescribed by Laplace that no month—so to call it—can be shorter than the corresponding day. And the rule is conformed to in nearly every part of the solar system. Nevertheless, two flagrant violations of it have lately obtruded themselves upon notice, and can scarcely be explained away by supplementary hypotheses. The first ascertained anomaly of the kind was met with in the swift circulation of Phobos, the inner satellite of Mars, which completes three revolutions and enters upon a fourth while the planet attended by it wheels once on its axis. The fact is most perplexing, and the confident persuasion that solar tidal friction would avail to remove the difficulty has not proved well grounded. Solar tidal friction, it may be remarked, acts as an external force upon subordinate systems submitted to its influence. Within their precincts moment of momentum may be destroyed by it; it tends, so far, to abrogate the law of conservation; and the supposition was hence feasible that the rotation of Mars had, in the course of ages, greatly slackened through the retarding effect of sun-raised tides. But the agency was demonstrably inadequate to the task assigned to it.

The reduction of the rotational moment of Mars to about one twenty-fifth its primitive amount[13]would have brought other consequences in its train, at least one of which did clearly not ensue. At an early stage of the process Phobos should have been re-engulfed in the mass of its primary.[14]For the pull of the small tidal wave raised by it on the surface of that body would have been backward from the instant that the balance of periods became inclined, through solar compulsion, in a direction contrary to that it would have naturally taken; and the ensuing loss of velocity must have entailed the descent of the little satellite along a spiral path towards an inevitable doom. Its continued existence, then, closes this way of escape from the difficulty raised by the shortness of its period. M. Wolf had recourse to a different explanatory subterfuge.[15]He believed that Phobos might have owed its origin to one of Roche's 'elliptic sheddings' of nebulous matter dropped downward from near the polar regions of the distended Martianspheroid, and rotating, owing to its low rate of linear speed, in the immediate vicinity of the cooling planet. The explanation, though ingenious, is too recondite to be satisfactory. The mind takes no grip of it; it evades distinct apprehension.

The Saturnian system exhibits a case of the same kind, but still more perplexing to speculative prepossessions. Saturn's ring-system has always appealed to thinkers as a striking object-lesson in nebular development. It forcibly arrested Kant's attention, and he sketched its birth-history on lines anticipatory of those adopted by Laplace for the solar system in its entirety. Laplace himself regarded the formation as the one surviving relic of the annular stage of planet-building—as a witness from the dim past to a condition of things elsewhere transitory. Yet the witness has turned king's evidence, and betrayed the whole situation. The innermost Saturnian ring has a period far too short to be compatible with the requirements of theory. For its meteoric constituents, known on spectroscopic testimony to revolve each on its own account, complete their circuits in betweenfive and six hours, while the planet needs just ten hours and a half for its axial rotation. Moreover, tidal friction is here far less available than on Mars; yet no other retarding agency has been invented. The deadlock appears final and hopeless.

An objection quite as formidable, and even more fundamental, was raised by Kirkwood in 1869. The nebulous material of the uncondensed sun must have been, at the outset, of the utmost tenuity. Atmospheric air is, by comparison, a dense and massive substance. Yet no reasonable person could ascribe to aerial matter the least power of resisting strain. We know perfectly that a rotating globe of air, and,à fortiori, a globe of matter thousands of times less compact than air, would unintermittently disintegrate at the surface with the progress of acceleration. The disturbance and restoration of equilibrium would be virtually simultaneous. There could be no accumulation of internal stress, and consequently no definitely separated epochs of instability. At the first solicitation, at the first instant that centrifugal velocity gained the upper hand over gravity, nebulous wispswould have become detached, and their detachment would have gone on without pause. Space would have been strewn with the débris of the condensing nebula, and there should have resulted a vast cloud of cosmic dust, not a majestic array of revolving spheres.

Further, the possibility of their emergence from pre-existent annuli is by no means assured. Even if the nebulous material had possessed the fabulous cohesion indispensable for its division into voluminous rings with wide intervening empty gaps, their ultimate agglomeration into planetary globes would probably never have been effectually accomplished. Kirkwood long ago questioned the feasibility of the process. Mr. Moulton has gone far towards demonstrating that it must have had an abortive outcome. Professor Darwin pronounces its very inception, apart from very special conditions, to be impracticable.

Another grave objection to Laplace's scheme is founded on the marked deviations visible in the solar system, from conformity to a fundamental plane of motion. Unless acted on by influences difficult to imagine or explain, allthe planets should circulate along the level of the sun's equator, and rotate on axes perpendicular to it. How far this is from being realized in nature we have only to look around us to perceive. We owe the changes of our seasons to the tilted fashion of the earth's spinning. Yet it is by no means easy to understand how the pole of its equator comes to be situated in the tail of Ursa Minor, while the pole of the ecliptic is involved in the folds of Draco. They should have coincided if the simple rules of the nebular prescription had been followed in the making and modelling of the planets. Nor are the terrestrial arrangements exceptional. The Saturnian equator and the Saturnian rings have a still higher inclination; while in the systems of Uranus and Neptune—if we may thus interpret their retrograde revolutions—the angle exceeds the limit of a quadrant. These and other similar discrepancies prove the solar mechanism to have originated by a more complex method than that imagined by Laplace, and an hypothesis which invokes the aid of a multitude of auxiliary devices for its extrication from accumulating embarrassments falls thereby underthe suspicion of not being worth the trouble of extricating. It forfeits, at any rate, all claim to commendation for directness and simplicity.

The cosmogony turned out at Paris has thus proved vulnerable on a number of points; but all the blows aimed at it have not told with such deadly effect as those just referred to. Some have fallen harmlessly, or glanced aside. One hostile argument in particular, which for a time seemed irresistible, has been completely overthrown by the logic of facts, and deserves mention only as a historical curiosity. Towards the middle of the nineteenth century the progress of sidereal astronomy seemed to take the direction of showing all nebulæ indiscriminately to be of stellar composition. With Lord Rosse's great reflectors a good many such objects were genuinely, and some besides were deceptively, resolved into stars, the illusory effects being confirmed by Bond's observations with the deservedly celebrated 15-inch refractor then recently built by Merz for Harvard College. Hence the rash inference was drawn that resolution was wholly a question of optical power, and that no real distinction existed between the stellar and the nebular realms. Herschel's 'shining fluid' assumed a mythical air; 'island-universes' came into popular vogue; and all but a few careful thinkers held nebulæ and clusters to be differentiated merely by degrees of remoteness. But if space contained only full-grown stars and no stars in the making—no star-spawn, no star-protoplasm—then the imagined evolutionary history of our system was left in the air, destitute of even the most fragile prop of observed fact.

From this precarious position it was rescued, partly by the cogent reasonings of Whewell and Herbert Spencer, finally and triumphantly by Sir William Huggins's spectroscopic discovery of the cosmic gas 'nebulium.' Since August, 1864, there has been no possibility of denying that the heavens contain ample stores of just the kind of material Laplace wanted, though whether it played just the part he assigned to it in the manner that he supposed is a question to be answered with profound and growing reserve.

An objection of late urged against the nebular theory from the standpoint of thekinetic doctrine of gaseous constitution is of much speculative interest. A gaseous nebula equal in mass to the sun and planets, and distended sufficiently to fill the orbit of Neptune, would have been, supposing the prevalent opinion correct, subject to a rapid leakage into space of its lighter ingredients. Of hydrogen and helium, we are told, it should infallibly have become depleted; yet there is no lack of either in the sun of the twentieth century. Their retention, it must be admitted, is, on the hypothetical conditions, difficult to account for. The 'critical velocity' at the limiting surface of the supposed nebula would have been 4·8 miles a second. This is, in fact, at the distance of Neptune, parabolic speed. The planet itself, if it could attain to it, would break the bonds that bind it to the sun, and seek its fortunes under some different allegiance. Similarly, any particle of the primitive nebula thus accelerated should have become an irreclaimable vagrant.

Now, the velocity of hydrogen molecules at the zero of Centigrade is, in the mean, about 1-1/6 miles a second, but attains in the extreme to above seven miles. Hydrogen could not thenhave been permanently retained by the solar nebula, and the escape of helium would have more slowly ensued. Yet these results, though seemingly inevitable, did not actually come to pass, either because the generating body was differently constituted from what has been supposed, or because countervailing influences were brought to bear. It is, for instance, amply possible that the dynamical condition of gases may be essentially modified by rarefaction carried to a degree transcending the range of experimental enquiries. The progress of science affords many warnings against trusting implicitly to the rule of continuity. Curves of change seldom preserve indefinitely a uniform character. Their unexplored sections may include quite unlooked-for peculiarities of flexure, and the possibility seriously undermines confidence in inferences depending upon 'extrapolation.' The presence of hydrogen and helium in our system cannot, then, be ranked among facts incontestably contradictory of the nebular hypothesis.

The concerted advance of mathematical astronomy during the eighteenth century was effected with the confident serenity of irresistible power. One after another the obstacles barring its path went down before repeated and skilful onslaughts, the unbroken succession of which lends a certain exultant sameness to the story of the heroic age of analysis. TheMécanique Célesteattested 'victory all along the line.' There were no more worlds to conquer that Laplace knew of; the reign of gravitational law was firmly established throughout the solar dominions; menaced revolts had been appeased; anomalies removed; no extant observations any longer impaired the perfect harmony between what was and what had been foreseen. Nature for the moment submitted readily to the trammels put upon her by human thought; her intricacies had apparently ceased to defy unravelment; her modes of procedure looked straightforward and intelligible. As they were judged to be in the present, so they might be presumed to have been in the past; and the temptation was irresistible to adventure backward speculation, inferring initial conditions from the elaborated product laid open to scrutiny.

It was an epoch of peremptory renewals. The formula of equality promised to regeneratesociety; a political panacea had been found by the creation of a republic 'one and indivisible'; and the success of the guillotine in securing its supremacy was almost outdone by the triumphs of the calculus in vindicating the unimpeded sway of gravitation.

Humanity had made a fresh start; science should do likewise. The sanguine spirit of a rejuvenated world animated all forms of human endeavour. It has long since evaporated. The buoyant hopes of a century back have been crushed; the future of civilization looks dim; and its uncertainty compromises the future of knowledge. But we, at any rate, no longer delude ourselves with the idea that he who runs may read the secrets of the universe. We have learned by convincing experience how much, and how variously, 'the subtlety of nature transcends the subtlety of sense and intellect'; we are vividly aware that there is no single and simple recipe for the 'cosmification' of chaos.

That devised by Laplace has ceased to be satisfactory. Its simplicity, at first sight so seductive, leaves it at a disadvantage compared with the intricacy of the effects it was designedto elicit. The relations claiming explanation have multiplied with the progress of research. Those of the dynamical order were alone attended to by the geometers of the eighteenth century, and even they have grown recalcitrant; while those of a physical and chemical kind have proved wholly unmanageable. It has, indeed, become abundantly clear that the series of operations described by Laplace could scarcely, under the most favourable circumstances, have been accomplished, and in a thin nebulous medium would have been entirely impossible. The nebular cosmogony has not, then, stood 'Foursquare to all the winds that blew.'

Its towers and battlements have crumbled before the storms of adverse criticism. It survives only as a wreck, its distinctive features obliterated, although with the old flag still flying on the keep. In the next chapter we shall attempt a survey of the works set on foot for its reconstruction.

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.

[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.

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'sNatural History of the Heavens; the long-discarded and despised Cartesian vortices reappear, with the éclat of virtual novelty, in others; nor are there wantingtheories 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 than2·44 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 wasseriously 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 oftrainées elliptiquesnot 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 aconsequence, 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, thelimiting 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 beenby 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 waswhich 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 itsgoal. 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 thesolvitur ambulandoprinciple cannot but prove convincing. But how if the ringscannot 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 divisionbetween 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 beof 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 theallowance of æons was unstinted. Because the rate of change was indeterminate, they might be permitted to elapsead 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 amuch 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 tospeculation 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 reducedpostulates 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. Theplanetary 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. Themodus operandiemployed, 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 gradualpropagation 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 coincidencesand 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, ofthe 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.'

Back to Index Next