﻿224 Note on the Rigidity of the Earth. 



mean densities p contained in VII., they are all to be 

 taken inferior to the mean density of the Earth. Now the 

 formula VII. changes to 



3 _ 2 x 4-68 x u* 



7 5-5x0-0011 [l9- + 2#It] 



u = 46,500 centim. per sec, 

 11=637,000,000 centim., 

 <7 = 981 centim. per sec. 

 p = 4'68 [Prof. Newcomb's effective mean density]. 



With these data, 



n=1615 xlO 9 . 



This coefficient of rigidity is nearly twice as great as the 

 coefficient of rigidity of steel after Everett [819 X 10 9 ] . By 

 certain combinations of the chosen effective mean densities 

 in the numerator and denominator of VII., also putting again 

 ■f instead of -f- in the left-hand member, we may render the 

 coefficient of rigidity smaller. But it remains much greater 

 than the coefficient for steel. 



The proof of the rigidity of the Earth from the tidal pheno- 

 mena was subject to certain doubts *, but now it is strongly 

 supported by the test of the phenomenon of Variation of 

 Latitudes. 



M. Grylden f has presented some objections to the views 

 of Lord Kelvin and Prof. Newcomb. Without discussing 

 his paper, we remark only that we can interpret his analysis 

 as corresponding to the case of an absolutely rigid earth with 

 certain fluid or generally mobile parts. Of course he has 

 found that these mobile parts must be greater than the 

 Oceans. We have taken the Earth as incompressible. It is 

 known that this assumption has a very little influence on 

 the final results. In a quite similar case, that of the tidal 

 problem, Mr. Love J has obtained nearly the same results on 

 the hypothesis of compressibility [m = 2n] as on the hypo- 

 thesis of perfect incompressibility [m = oo ]. 



* See Prof. Darwin's paper, Proc. Roy. Soc. London, Nov. 1886. 



t Comirt. ?'endus, vol. cxvi. (1893), pp. 476-479. 



% Transactions Cambr. Phil. Soc. vol. xv. pp. 107-118. 



