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.'
FOOTNOTES:
[Footnote 16: _Mémoires de l'Académie de Montpellier_, tom. i.]
[Footnote 17: _The Tides_, p. 327.]
[Footnote 18: _Mémoires de l'Académie de Montpellier_, tom. viii.]
[Footnote 19: C. Wolf, _Bulletin Astronomique_, tom. i., p. 596.]
[Footnote 20: _American Journal of Science_, vol. xxxviii., p. 3.]
[Footnote 21: G. H. Darwin, _Nature_, vol. xxxi., p. 506.]
[Footnote 22: _Proceedings of the American Philosophical Society_, vol.
xxii., p. 109.]
[Footnote 23: De Vries, _Die Mutationstheorie_, Bd. II., p. 714.]
[Footnote 24: _Formation Mécanique du Système du Monde._ See also _Le
Problème Solaire_, by the Abbé Th. Moreux, p. 63 _et seq._]
[Footnote 25: _Revue des Questions Scientifiques_, January, 1904.]
[Footnote 26: _The Earth's Beginnings_, p. 247.]
[Footnote 27: _Astrophysical Journal_, vol. xi., p. 130.]