[CHAPTER V]
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.