TIDAL FRICTION AS AN AGENT IN COSMOGONY
The effects of tidal friction are of almost infinite complexity. How it
will act in each particular case cannot be predicted offhand; it is a
matter for detailed inquiry. Mutually countervailing influences have to
be taken into account, nor is the balance easy to strike. The manner of
its inclination may, indeed, often depend upon qualities and relations
of the bodies concerned which lie outside the range of what can be
distinctly ascertained. All that may be hoped for, then, is to arrive
at estimates neither misleading by their ostensible precision, nor yet
so vague as to be wholly uninstructive, of the part played by tidal
forces in moulding the history of connected globes.
The assumption that they attract one another as if the mass of each
were collected at its centre, is one of those convenient fictions
without which the advancing feet of science would be impeded by tangled
thickets of illusory refinements and superfluous elaborations. The
fiction would correspond with fact only if the globes were truly
spherical, and they could be truly spherical only if they were ideally
rigid. Cosmic bodies, however--suns and planets alike--are actually
plastic spheroids; they can, to be sure, be treated without sensible
error as attractive points when their distances are very great
relatively to their diameters; but upon a closer approach inequality
of action supervenes. The component parts of the gravitating masses
respond, each individually, and in a measure independently, to the
graduated pulls exercised upon them, and tidal strains begin variously
to take effect.
Their historical significance was in part divined by Kant. His
penetration of so recondite a secret is truly astonishing. A struggling
young pedagogue in a remote Prussian province, profoundly learned,
though no more than half skilled in technical acquirements, saw by
intuition what escaped the acumen of all the great geometers of the
eighteenth century--namely, that the moon turns one perpetual face
towards the earth, because its primitive rotation was stopped by the
friction of earth-raised tides. He perceived besides that a reciprocal
action of the same kind must affect the earth, and will continue to
affect it until the day coincides in length with the month. Nor did he
fail to point out that, in a molten state of the globes, the process
would advance with comparative rapidity. To one solitary thinker, then,
it became apparent, already in 1754,[28] that oceanic tides are, in
cosmogony, of negligible importance compared with bodily tides.
There is no substance in nature that will not change its shape through
prolonged stress, and the more readily the nearer it approaches to the
fluid condition. The heaping-up of the waters on the earth's surface at
the bidding of the moon is thus a differential effect. Continents heave
and subside as well as oceans, though not nearly to the same extent.
The measurable rise of water serves to gauge the relative mobilities
of the solid globe and of its liquid envelope. If the former did not
yield at all to the pull so readily obeyed by the latter, the tides
would, in fact, be greater than they actually are in the proportion of
about three to two, the ratio indicating for the earth an effective
rigidity at least equal to that of steel.[29] Were there no discrepancy
in rigidity between the various parts of our terraqueous world, tides
would fail to be perceptible. The ocean and the bed of the ocean would
rise and fall together, and to the same extent. In the far past there
_was_ no discrepancy. The viscous earth took, as a whole, the form
momentarily impressed upon it by the unequal attractions of the sun and
moon on its variously distant sections, with the upshot of bringing the
year, month, and day into relations so familiar as to appear inevitable.
Tidal friction does not merely act as a check upon rotational speed.
One element of motion in a system cannot be altered without some
counter-change in the others. They are coupled up together like a train
of geared wheels. From the principle of the conservation of moment of
momentum, we know with certainty that a loss in one direction must
be compensated by a gain in some other. Tidal friction had, then,
reactive consequences. They were first adverted to by Julius Robert
Mayer in 1848,[30] and were brought prominently into view in the series
of investigations begun by Professor Darwin in 1879. The rotational
momentum removed from the earth by the drag of a circulating wave of
deformation must assuredly have reappeared in some other part of the
system. It was restored, all but the percentage wasted as heat, by the
widening of the lunar orbit.[31] Concomitantly with the slackening of
the earth's axial rate, the moon retreated from its surface, pulled
forward by the tidal crest continually in advance of its position. This
redressed the balance by augmenting orbital momentum, while at the same
time diminishing the moon's linear velocity. The importance of this
secondary frictional effect in the history of the earth-moon system was
the virtual discovery of Professor Darwin.
That system occupies a critical situation in the solar cortège. The
planets interior to it have no satellites; the planets exterior to it
(Neptune making probably only an apparent exception to the rule) have
two or more. The earth alone is truly binary; and the moon is not only
its solitary companion, but it is by far the largest companion-body,
relatively to the mass of its primary, to be found within the precincts
of the solar domain. These circumstances are certainly not disconnected
one from the other, and they obviously depend upon a single cause.
Solar tidal friction was here the determining factor. The apportionment
of satellites to the various planets was, beyond doubt, in great
measure prescribed by the degrees of retarding power exerted on their
axial movement through the agency of sun-raised tides in their still
plastic bodies. Hence, the disruptive rate of spinning needed for
the separation of satellites was never attained by either Mercury or
Venus; they remained moonless for all time, and exposed, through the
cutting down of their rotational velocity, to uncompensated extremes
of temperature. How the earth was to fare in both respects long hung
in the balance. Rightly to forecast its destiny would, indeed, have
demanded no common perspicuity in an intelligent onlooker from some
other sphere. Although the solar brake acted upon terrestrial rotation
with no more than one-eleventh the power brought to bear upon that
of Venus, it nevertheless sufficed during uncounted ages to hinder
acceleration from reaching the pitch involving instability.
Our embryonic planet had long ceased to be nebulous, and had, in fact,
shrunk by cooling nearly to its present dimensions before the die was
cast. Then, at last, the hurrying effects of contraction prevailed
over the slowing down due to tidal resistance, axial speed overbore
equilibrium, and the spheroid divided. Now globes thus far advanced
in condensation are apt to split less unequally than globes in a more
primitive stage; and the moon, because late-born, was of large size.
Its mass is 1/81 that of the earth; the masses of Titan and Saturn are
as 1 to 4,600; while Jupiter's third and greatest satellite contains
only 1/11300 part of the matter englobed in the parent-body. Moreover,
Professor Darwin has made it clear that the satellites of Jupiter and
Saturn revolve now in orbits not widely remote from those at first
pursued by them; while the moon, on the contrary, started on its career
almost, if not quite, from grazing contact with its primary. Owing to
these two exceptional circumstances--its considerable relative mass
and its close initial vicinity--the moon wielded over the earth tidal
influence incomparably more powerful than that exerted by any of its
compeers in the sun's realm.
The lunar-terrestrial system offers, accordingly, an example unique
among those in solar subordination of a pair of globes, the mechanical
relations of which have been settled on their present basis by the
predominating agency of bodily tides. It holds forth, too, the one
case in which origin by fission was possible. Professor Darwin's
communication to the Royal Society in 1879 occasioned on this point a
remarkable diversion of ideas. Saturn's rings were at last, through
the reasonings contained in it, perceived to be illustrative of only
one among many feasible modes of cosmic growth. It became clear that a
single cut-and-dried method would not answer all the infinitely varied
purposes of creative design. Annulation might have served its turn,
but there were alternatives. A fresh standpoint was virtually attained,
and the wide prospect commanded by it begins already to spread out
invitingly before the gaze of investigators.
But whether the moon emerged from the earth as a protuberance, or was
abandoned by it as an irregular equatorial ring, it was revolving,
when our theoretical acquaintance with it begins, in a period of
not less than two and not more than four hours, quite close to the
earth's surface; while the nearly isochronous rotation of the earth
was conducted with all but disruptive rapidity. The situation is so
suggestive that it needs only a short and tolerably safe leap in the
dark to reach the conclusion that the two masses had very recently
been one. With their division, at an epoch estimated to have been
about sixty million years ago, the process began by which the moon was
pushed back along a widening spiral course to its present position,
the vanished rotational momentum of the earth cropping up again in the
augmented orbital momentum of the moon. And the transformation is, at
least in theory, still going on.
Tidal friction has further capabilities. The transference of momentum
from one part of a system to another is only the most obvious among
the crowd of its results. Scarcely an element of movement escapes its
influence. It increases, as a rule, orbital eccentricity. The smallest
initial deviation from circularity develops, through the inequality of
accelerative action thence ensuing, into pronounced ovalness. That of
the moon's path can in this way be accounted for. Moreover, its plane
was, in all probability, shifted simultaneously and under compulsion
of the same power, from its original coincidence with the earth's
equatorial plane to the level it now occupies. The obliquity of the
ecliptic, too, is partially explicable on the same principle. 'The
present motion of the two bodies' (to quote Professor Darwin's words),
are 'completely co-ordinated by the theory that tidal friction was the
ruling power in their evolution.' Holding this clue, we are enabled to
trace them back to the start of their dual existence, and to follow
the insensible modifications by which their state was moulded to its
actual form.
In no other satellite-system is this possible. No moon besides our own
possesses a stock of orbital momentum large enough to intimate for it
an analogous history. Planetary attendants elsewhere travel nearly in
their original tracks; the fluid ripples raised by them on the surfaces
of their primaries lacked power to displace them sensibly. Their own
rotation, indeed, seems to have been completely destroyed. Destroyed,
that is, relatively to the destroying body. There is a certainty that
some, there is the strongest likelihood that all, of the Jovian and
Saturnian satellites turn unchangingly the same face towards their
primaries. They rotate in the period of their several revolutions,
just as our moon does, and as a consequence of the same cause. Tidal
friction, however, appears to have been otherwise of subordinate
importance in shaping their dynamical relations.
The agency will not, then, serve in all cases for a _deus ex machinâ_.
It is not indiscriminately efficacious. The modes of its action have,
in each of the systems considered, to be delicately distinguished.
The stage of development arrived at by the bodies affected, their
degree of viscosity, their comparative mass and bulk, their modes of
motion, all avail profoundly, and it may be incalculably, to modify the
outcome. The facility of error in estimates of the kind is illustrated
by Professor Darwin's remark that the magnitude of the tide-raising
force is only one factor of the product.[32] The other is relative
movement. Now, in the case of the moon the former continually augmented
retrospectively, while the latter fell off. Tidal generative power
varies inversely as the cube of the distance; in antique times, then,
when the earth and moon revolved contiguously, the bodily distortions
they mutually produced were beyond question on an extremely large
scale. Yet, because of the near coincidence of the periods of the
globes, they must have been almost inoperative for frictional purposes.
The travelling of the piled-up matter over their surfaces was too slow
to lend it much power as a friction-brake. The insignificant waves
raised by the sun were, we are led to believe, because of their swift
relative motion, more influential at that early epoch in checking
terrestrial rotation than the colossal, but nearly stationary waves due
to the moon.
Numerical calculations, where they are practicable, afford the only
safe guide to this intricate field of inquiry. It does not suffice to
show that tidal action would have been of the kind required--would
have taken the right direction--for bringing about some apparently
anomalous result. Proof must, besides, be forthcoming that the action
would have been of adequate power. Plausible guesses on the subject
may be entirely fallacious. The machine, even if properly constructed
for the end in view, may work too feebly for its attainment. We are,
for instance, assured that no difficulty connected with the sense of
planetary rotation need impede acceptance of the theory of planetary
origin from separated rings, since even if the embryo globes gyrated
the wrong way at the outset, solar tidal friction would promptly have
reduced them to conformity with the general current of movement. This
is true in principle, but will it bear quantitative investigation?
Many promising hypotheses have broken down under the weight of
figures; whether this particular one is strong enough to survive their
application remains to be seen. We are, indeed, sure of its validity as
regards Mercury, but the efficacy of tidal friction decreases as the
sixth power of increasing distance, and the actual rotation of Venus
furnishes an enigma sufficiently perplexing to discourage scrutiny of
its dimly discerned antecedent conditions. As regards the earth and the
exterior planets, the question could only be answered with the help of
information which is not forthcoming.
The unexpected circumstance that the newly-discovered ninth Saturnian
moon circulates from east to west can thus be no more than tentatively
explained by invoking this agency of change. Admitting (as we seem
bound to do) that satellites are the offspring of the planets they
attend, there is no evading the conclusion that the small body under
discussion was thrown off from a primary endowed with a rotation
opposite to that now possessed by it. And the reversal must have been
completely brought to pass before the eighth satellite, Japetus, came
into existence. The crux is most arduous; there is no other resource
for meeting it but to consider the effects on planetary rotation of
solar tides, and this Professor W. H. Pickering, the discoverer of
Phœbe, has done.[33] But a cause may be true without being sufficient;
and close calculation will be needed to determine, in this instance,
how the matter stands.
Professor Darwin's researches were fruitful just because they were
definite. They demonstrated, once for all, the diverse faculties of
tidal friction as a cosmogonic agency, and indicated clearly the
departments of cosmogonic change in which its competence lay. They
availed, moreover, to determine for the earth-moon system the amount of
work actually done by tidal friction in these several departments, and
to prove its large excess over the corresponding output in any other
sub-system falling within the sphere of observation. This memorable
result suggests that our terrestrial home may be singular, not only in
its evolutionary history, but in the innumerable adjustments fitting it
to be the abode of life.
The relations of the earth and moon adumbrate, and scarcely more
than adumbrate, the physical influences mutually exerted upon each
other by numerous twin-globes in stellar space. Tidal friction is of
maximum power in systems formed of equal masses; and those of double
stars are seldom widely disparate. Most, if not all of them, were,
besides, primitively very near neighbours, so that their symmetry must
have been marred by conspicuous tidal deformations. The results upon
their development have been expounded in detail by Dr. See. One of
the most remarkable is the high average eccentricity of their orbits.
Visual binaries, with few exceptions, travel in considerably elongated
ellipses, while spectroscopic binaries as a rule pursue approximately
circular paths. Dr. See's argument that the eccentricity of the more
spacious systems was acquired under the influence of tidal friction,
during the long course of progressive separation, is well-nigh
irresistible.
True, this line of explanation is not wholly clear of obstacles and
incongruities. Yet they may probably be described as of a complicating,
rather than of a contradictory kind. The theory of tidal friction
is not a universal solvent of the difficulties encountered in the
study of double stars. That the mode of action it deals with had a
contributory share towards regulating their mechanical arrangements
may, nevertheless, be regarded as certain, while the potency and
perhaps even the manner of its operation varied extensively from system
to system. What precisely it effected in each lies beyond our range of
determination. For the data available regarding the viscosity, density,
and axial movements of embryo star-pairs must always be too scanty and
insecure to provide a basis for rigorous computations. The mystery of
the fore-time can never be entirely dissipated. Enough if we can look
at it through a glass which darkens, without distorting, the objects
presented in its field of view.
FOOTNOTES:
[Footnote 28: _Sämmtliche Werke_, Bd. VI., pp. 5-12, 1839.]
[Footnote 29: G. H. Darwin, _Encyclopædia Britannica_, article on
'Tides.']
[Footnote 30: _Dynamik des Himmels_, p. 49.]
[Footnote 31: Darwin, _Philosophical Transactions_, vol. clxxii., p.
528.]
[Footnote 32: _Philosophical Transactions_, vol. clxxi., p. 876.]
[Footnote 33: _Harvard Annals_, vol. liii., p. 58.]