70 POPULAR LECTURES AND ADDRESSES. 



we may 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 time-keeper by one- 

 tenth of a second per year. 1 



Again an excellent suggestion, supported by 

 calculations which show it to be not improbable, 

 has been made to the French Academy by M. 

 Dufour, that the retardation of the earth's rotation 

 indicated by M. Dclaunay, or some considerable 

 part of it, may be due to an increase of its moment 

 of inertia by the incorporation of meteors falling 

 on its surface. If we suppose the previous 

 average moment of momentum of the meteors 

 round the earth's axis to be zero, their influence 



1 The calculation is simply this. Let E be the earth's whole 

 mass, a its radius, k its radius of gyration before, and k' after the 

 supposed melting of the ice, and W the mass of ice melted. Then, 

 since \a2. is the square of the radius of gyration of the thin shell of 

 water supposed spread uniformly over the whole surface, and that of 

 either ice-cap is very approximately \(- (sin 20)'-', we have 



E/fc'-' = E/t 2 + Wa- [1 - i(sin 20) ]. 



And by the principle of the conservation of moments of momentum, 

 the rotatory velocity of the earth will vary inversely as the square 

 of its radius of gyration. To put this into numbers, we take, 

 as above, J^-=\a l and # = 21x10. And as the mean density 

 of the earth is about 5 A times that of water, and the bulk of a globe 

 is the area of its surface into .', of its radius, 



K : \\ : : **" : '066 



