FOOTNOTES:
[3] Quoted by Dr. Hastie in the preface to his translation of Kant's Cosmogony, Glasgow, 1900.
[4] Sur l'Origine du Monde, 3e éd., 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 the Exposition du Système du Monde, Laplace referred to Herschel's observations of nebulæ as confirmatory of his own genetic scheme.
[CHAPTER III]
CRITICISMS OF THE NEBULAR HYPOTHESIS
Laplace's theory 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 advanced pari 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 a stage 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 that of 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 in no 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's rotation. 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 modern science, 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 have been 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 evolution described 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 Martian spheroid, 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 between five 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 wisps would 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, all the 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 under the 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 the kinetic 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 then have 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. The Mécanique Céleste attested '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 regenerate society; 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 designed to 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.