But in this difficulty, small as it seems, we are not left wholly without resource. We are not only able to say that the discrepancy is probably due to a gradual retardation of the earth’s rotation-movement, but we are able to place our finger on a very sufficient cause for such a retardation. One of the most firmly established principles of modern science is this—that where _work is done_, force is, in some way or other, expended. The _doing of work_ may show itself in a variety of ways— in the generation of heat, in the production of light, in the raising of weights, and so on; but in every case an equivalent force must be expended. If the brakes are applied to a train in motion, intense heat is generated in the substance of the brake. Now, the force employed by the brakesman is _not_ equivalent to the heat generated. Where, then, is the balance of force expended? We all know that the train’s motion is retarded, and this loss of motion represents the requisite expenditure of force. Now, is there any process in nature resembling, in however remote a degree, the application of a brake to check the earth’s rotation? There is. The tidal wave, which sweeps, twice a day, round the earth, travels in a direction contrary to the earth’s motion of rotation. That this wave ‘does work,’ no one can doubt who has watched its effects. The mere rise and fall in open ocean may not be strikingly indicative of ‘work done;’ but when we see the behaviour of the tidal wave in narrow channels, when we see heavily-laden ships swept steadily up our tidal rivers, we cannot but recognise the expenditure of force. Now, where does this force come from? Motion being the great ‘force-measurer,’ what motion _suffers_ that the tides may _work_? We may securely reply, that the only motion which _can_ supply the requisite force is the earth’s motion of rotation. Therefore, it is no mere fancy, but a matter of absolute certainty, that, though slowly, still very surely, our terrestrial globe is losing its rotation-movement. Considered as a time-piece, what are the earth’s errors? Suppose, for a moment, that the earth was _timed_ and _rated_ two thousand years ago, how much has she _lost_, and what is her ‘rate-error?’ She has lost in that interval nearly one hour and a quarter, and she is losing now at the rate of one second in twelve weeks. In other words, the length of a day is now more by about one eighty-fourth part of a second than it was two thousand years ago. At this rate of change, our day would merge into a lunar month in the course of thirty-six thousand millions of years. But after a while, the change will take place more slowly, and some trillion or so of years will elapse before the full change is effected.