OF ARTS AND SCIENCES: MAY 11, 1869. 107 



Mr. Lesley from the observed geological phenomena, involves a prob- 

 able cooling of the whole earth of not less than two thousand degrees 

 centigrade, which would require that its original temperature should be 

 higher than would be consistent with the solidity of these shrunk 

 strata. 



Another source of change of form, which would produce shrinkages 

 in different directions in different parts of the earth, is to be found in 

 the diminution of oblateness arising from the diminished velocity of 

 rotation upon the axis. Such diminution of the velocity of rotation 

 has several years ago been shown by Mr. Ferrel to be caused by the 

 action of the moon in producing the tides ; this is, therefore, a true 

 cause, and it is only necessary to examine how great its amount can be 

 under any circumstances. This is all which is proposed in the present 

 investigation, and the application to facts is reserved for geologists. 



It is sufficient, for the present object, to regard the earth as homo- 

 geneous. Under this condition Laplace has shown that the time of the 

 earth's rotation could not be less than about one tenth of a day, which 

 corresponds to a ratio of the axis of the equator to that of the 

 pole, equal to 2.7197, and an equatorial circumference 94 per cent 

 greater than the present one. Such is then the amount of shrinking 

 which might have taken place, if any cause could be assigned capable 

 of producing so great a reduction of the earth's velocity. The whole 

 surface of the earth would have been about 130 per cent larger than 

 at present. 



But the only cause at present known which would produce a sensi- 

 ble reduction of the earth's velocity is the lunar action upon the tides. 

 But in this mutual action between the moon and the earth, the common 

 rotation area of the earth and moon must remain unchanged. The 

 question then arises, How great a reduction of the rotation area of the 

 earth would have passed into that of the moon ? In this inquiry it 

 may be assumed that the moon revolves in a circular orbit in the plane 

 of the earth's equator. Now the moon's rotation area is 3.716 times the 

 earth's. But if, in the origin, it had revolved just in contact with this 

 earth, its rotation area would not have been less than 0.480 times the 

 earth's, so that it could not have absorbed a rotation area from the earth 

 greater than 3.236 times the earth's present rotation area, and therefore 

 the earth's rotation area could never have exceeded 4.236 times that 

 which it has at present. But, with the maximum velocity of rota- 

 tion given by Laplace, the earth's rotation area would have been 



