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.
FOOTNOTES:
[Footnote 10: Presidential Address to the British Association,
Johannesburg, August 30, 1905.]
[Footnote 11: _Comptes Rendus_, tom. lii., p. 481.]
[Footnote 12: _Astrophysical Journal_, vol. xi., p. 103.]
[Footnote 13: Moulton, _Astrophysical Journal_, vol. xi., p. 110.]
[Footnote 14: Nolan, _Nature_, vol. xxxiv., p. 287.]
[Footnote 15: _Bulletin Astronomique_, tom. ii., p. 223.]