1 PROCEEDINGS OP THE GEOLOGICAL SOCIETY. 



observed retardation could be accounted for in the way he had sug- 

 gested. There remains, therefore, the other half to be accounted for ; 

 and here, in the absence of all positive knowledge, three sets of hy- 

 potheses 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 pro- 

 portion 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, I. c. p. 14.) 



h. 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 ap- 

 proval of Sir W. Thomson, who shows that meteor-dust, accumula- 

 ting at the rate of 1 foot in 4000 years, would account for the re- 

 mainder of retardation. (X. c. p. 27.) 



G. 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 J 

 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 mathema- 

 ticians 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 ex- 

 tract 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 re- 

 tardation*. 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 iinderstoocl that I do not wish to deny that the earth's rotation 

 may be undergoing retardation. 



