[Footnote 17:  Sir W. Thomson, loc. cit. 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 one foot in 4,000 years, would account for the remainder of retardation.[18]

[Footnote 18:  Ibid. 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 deg. 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 three-fourths 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."[19]

[Footnote 19:  Ibid.]

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 process 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 upon 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.[20] And yet this is the key of the whole position.

[Footnote 20:  It will be understood that I do not wish to deny that the earth’s rotation may be undergoing retardation.]

2.  If the rapidity of the earth’s rotation is diminishing, it is not certain how much of that retardation is due to tidal friction, how much to meteors, how much to possible excess of melting over accumulation of polar ice, during the period covered by observation, which amounts, at the outside, to not more than 2,600 years.