The eclipse occurred later than calculation warrants. Now this would have happened from either of two causes, either an acceleration of the moon in her orbit, or a retardation of the earth in her diurnal rotation—a shortening of the month or a lengthening of the day, or both. The total discrepancy being, say, two hours, an acceleration of six seconds-per-century per century will in thirty-six centuries amount to one hour; and this, according to the corrected Laplacian theory, is what has occurred. But to account for the other hour some other cause must be sought, and at present it is considered most probably due to a steady retardation of the earth's rotation—a slow, very slow, lengthening of the day.
The statement that a solar eclipse thirty-six centuries ago was an hour late, means that a place on the earth's surface came into the shadow one hour behind time—that is, had lagged one twenty-fourth part of a revolution. The earth, therefore, had lost this amount in the course of 3600 × 365¼ revolutions. The loss per revolution is exceedingly small, but it accumulates, and at any era the total loss is the sum of all the losses preceding it. It may be worth while just to explain this point further.
Suppose the earth loses a small piece of time, which I will call an instant, per day; a locality on the earth will come up to a given position one instant late on the first day after an event. On the next day it would come up two instants late by reason of the previous loss; but it also loses another instant during the course of the second day, and so the total lateness by the end of that day amounts to three instants. The day after, it will be going slower from the beginning at the rate of two instants a day, it will lose another instant on the fresh day's own account, and it started three instants late; hence the aggregate loss by the end of the third day is 1 + 2 + 3 = 6. By the end of the fourth day the whole loss will be 1 + 2 + 3 + 4, and so on. Wherefore by merely losing one instant every day the total loss in n days is (1 + 2 + 3 + ... + n) instants, which amounts to ½n (n + 1) instants; or practically, when n is big, to ½n2. Now in thirty-six centuries there have been 3600 × 365¼ days, and the total loss has amounted to an hour; hence the length of "an instant," the loss per diem, can be found from the equation ½(3600 × 365)2 instants = 1 hour; whence one "instant" equals the 240 millionth part of a second. This minute quantity represents the retardation of the earth per day. In a year the aggregate loss mounts up to 1⁄3600th part of a second, in a century to about three seconds, and in thirty-six centuries to an hour. But even at the end of the thirty-six centuries the day is barely any longer; it is only 3600 × 365 instants, that is 1⁄180th of a second, longer than it was at the beginning. And even a million years ago, unless the rate of loss was different (as it probably was), the day would only be thirty-five minutes shorter, though by that time the aggregate loss, as measured by the apparent lateness of any perfectly punctual event reckoned now, would have amounted to nine years. (These numbers are to be taken as illustrative, not as precisely representing terrestrial fact.)
What can have caused the slowing down? Swelling of the earth by reason of accumulation of meteoric dust might do something, but probably very little. Contraction of the earth as it goes on cooling would act in the opposite direction, and probably more than counterbalance the dust effect. The problem is thus not a simple one, for there are several disturbing causes, and for none of them are the data enough to base a quantitative estimate upon; but one certain agent in lengthening the day, and almost certainly the main agent, is to be found in the tides.
Remember that the tidal humps were produced as the prolateness of a sphere whirled round and round a fixed centre, like a football whirled by a string. These humps are pulled at by the moon, and the earth rotates on its axis against this pull. Hence it tends to be constantly, though very slightly, dragged back.
In so far as the tidal wave is allowed to oscillate freely, it will swing with barely any maintaining force, giving back at one quarter-swing what it has received at the previous quarter; but in so far as it encounters friction, which it does in all channels where there is an actual ebb and flow of the water, it has to receive more than it gives back, and the balance of energy has to be made up to it, or the tides would cease. The energy of the tides is, in fact, continually being dissipated by friction, and all the energy so dissipated is taken from the rotation of the earth. If tidal energy were utilized by engineers, the machines driven would be really driven at the expense of the earth's rotation: it would be a mode of harnessing the earth and using the moon as fixed point or fulcrum; the moon pulling at the tidal protuberance, and holding it still as the earth rotates, is the mechanism whereby the energy is extracted, the handle whereby the friction brake is applied.
Winds and ocean currents have no such effect (as Mr. Fronde in Oceania supposes they have), because they are all accompanied by a precisely equal counter-current somewhere else, and no internal rearrangement of fluid can affect the motion of a mass as a whole; but the tides are in different case, being produced, not by internal inequalities of temperature, but by a straightforward pull from an external body.
The ultimate effect of tidal friction and dissipation of energy will, therefore, be to gradually retard the earth till it does not rotate with reference to the moon, i.e. till it rotates once while the moon revolves once; in other words, to make the day and the month equal. The same cause must have been in operation, but with eighty-fold greater intensity, on the moon. It has ceased now, because the rotation has stopped, but if ever the moon rotated on its axis with respect to the earth, and if it were either fluid itself or possessed any liquid ocean, then the tides caused by the pull of the earth must have been prodigious, and would tend to stop its rotation. Have they not succeeded? Is it not probable that this is why the moon always now turns the same face towards us? It is believed to be almost certainly the cause. If so, there was a time when the moon behaved differently—when it rotated more quickly than it revolved, and exhibited to us its whole surface. And at this era, too, the earth itself must have rotated a little faster, for it has been losing speed ever since.
We have thus arrived at this fact, that a thousand years ago the day was a trifle shorter than it is now. A million years ago it was, perhaps, an hour shorter. Twenty million years ago it must have been much shorter. Fifty million years ago it may have been only a few hours long. The earth may have spun round then quite quickly. But there is a limit. If it spun too fast it would fly to pieces. Attach shot by means of wax to the whirling earth model, [Fig. 110], and at a certain speed the cohesion of the wax cannot hold them, so they fly off. The earth is held together not by cohesion but by gravitation; it is not difficult to reckon how fast the earth must spin for gravity at its surface to be annulled, and for portions to fly off. We find it about one revolution in three hours. This is a critical speed. If ever the day was three hours long, something must have happened. The day can never have been shorter than that; for if it were, the earth would have a tendency to fly in pieces, or, at least, to separate into two pieces. Remember this, as a natural result of a three-hour day, which corresponds to an unstable state of things; remember also that in some past epoch a three-hour day is a probability.
If we think of the state of things going on in the earth's atmosphere, if it had an atmosphere at that remote date, we shall recognize the existence of the most fearful tornadoes. The trade winds, which are now peaceful agents of commerce, would then be perpetual hurricanes, and all the denudation agents of the geologist would be in a state of feverish activity. So, too, would the tides: instead of waiting six hours between low and high tide, we should have to wait only three-quarters of an hour. Every hour-and-a-half the water would execute a complete swing from high tide to high again.