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 22 seconds of time in a century from this cause. (Sir W. Thomson, l. c. p. 14.)
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 1 foot in 4000 years, would account for the remainder of retardation. (L. c. p. 27.)
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 : —
" Let us suppose ice to melt from the polar regions (20° round each pole, we may say) to the extent of something more than a foot thick, enough to give 1.1 foot of water over those areas, or 0.006 of a foot of water if spread over the whole globe, which would in reality raise the sea-level by only some such undiscoverable difference as 3/4 of an inch or an inch. This or the reverse, which we believe might happen any year, and could certainly not be detected without far more accurate observations and calculations for the mean sea-level than any hitherto made, would slacken or quicken the earth's rate as a timekeeper by one-tenth of a second per year." (L. c. p. 27.)
I do not presume to throw the slightest doubt upon the accuracy of any of the calculations made by such distinguished mathematicians as those who have made the suggestions I have cited. On the contrary, it is necessary to my argument to assume that they are all correct. But I desire to point out that this seems to be one of the many cases in which the admitted accuracy of mathematical processes is allowed to throw a wholly inadmissible appearance of authority over the results obtained by them. Mathematics may be compared to a mill of exquisite workmanship, which grinds you stuff of any degree of fineness ; but, nevertheless, what you get out depends on what you put in ; and as the grandest mill in the world will not extract wheat-flour from peascods, so pages of formulae will not get a definite result out of loose data.
In the present instance it appears to be admitted : —
1. That it is not absolutely certain, after all, whether the moon's mean motion is undergoing acceleration, or the earth's rotation retardation*. And yet this is the key of the whole position.
2. If the rapidity of the earth's rotation is diminishing, it is not
- It will be understood that I do not wish to deny that the earth's rotation
may be undergoing retardation.
