Kant, who was by no means a mere “abstract philosopher,” but a good mathematician and well versed in the physical science of his time, not only proved this in an essay of exquisite clearness and intelligibility, now more than a century old,[54] but deduced from it some of its more important consequences, such as the constant turning of one face of the moon towards the earth.

But there is a long step from the demonstration of a tendency to the estimation of the practical value of that tendency, which is all with which we are at present concerned.  The facts bearing on this point appear to stand as follow:—­

It is a matter of observation that the moon’s mean motion is (and has for the last 3,000 years been) undergoing an acceleration, relatively to the rotation of the earth.  Of course this may result from one of two causes:  the moon may really have been moving more swiftly in its orbit; or the earth may have been rotating more slowly on its axis.

Laplace believed he had accounted for this phaenomenon by the fact that the eccentricity of the earth’s orbit has been diminishing throughout these 3,000 years.  This would produce a diminution of the mean attraction of the sun on the moon; or, in other words, an increase in the attraction of the earth on the moon:  and, consequently, an increase in the rapidity of the orbital motion of the latter body.  Laplace, therefore, laid the responsibility of the acceleration upon the moon; and if his views were correct, the tidal retardation must either be insignificant in amount, or be counteracted by some other agency.

Our great astronomer, Adams, however, appears to have found a flaw in Laplace’s calculation, and to have shown that only half the observed retardation could be accounted for in the way he had suggested.  There remains, therefore, the other half to be accounted for; and here, in the absence of all positive knowledge, three sets of hypotheses have been suggested.

(a) M. Delaunay suggests that the earth is at fault, in consequence of the tidal retardation.  Messrs. Adams, Thomson, and Tait work out this suggestion, and, “on a certain assumption as to the proportion of retardations due to the sun and the moon,” find the earth may lose twenty-two seconds of time in a century from this cause.[55]

(b) But M. Dufour suggests that the retardation of the earth (which is hypothetically assumed to exist) may be due in part, or wholly, to the increase of the moment of inertia of the earth by meteors falling upon its surface.  This suggestion also meets with the entire approval of Sir W. Thomson, who shows that meteor-dust, accumulating at the rate of one foot in 4,000 years, would account for the remainder of retardation.[56]

(c) Thirdly, Sir W. Thomson brings forward an hypothesis of his own with respect to the cause of the hypothetical retardation of the earth’s rotation:—­