102 Method of determining the Thickness of the Earth 1 *s Crust, 



u and /3 being known quantities independent of the crust and 

 fluid, 



Let P, C, A be the values of P, C, A when the whole earth is 

 solid. Then 



C fC-~A , S7ra 3 ef(a)\ 



P"""C^A V C 



15C 



If we substitute for A, C, A, C* and neglect the square of ellip- 

 ticities, we have 



P 



C^d.a't, r*,d.a*e'. 3 C^d.a'*, 



V r*,d,a' 5 Af 



y~w da 



Now evidently 



f a d, a 1 * 2 C a d . «'V 



p' * , da! is greater than I p'— '-p — da 1 , 

 ~ yi JO 



since a and e are greater than any other value of a! and e'. 

 Hence the second factor in the value of P-hP is greater than 

 unity; and the first factor is evidently greater than unity. 

 Hence P is greater than P, or the crust has more precessional 

 motion during the time my equations hold than the whole earth 

 supposed solid. It follows, then, that even if at any instant the 

 whole arrangement and motion of the "crust and fluid nucleus 

 are the same as if they were one solid (which really cannot have 

 occurred) , nevertheless that state could not continue ; and it is 

 a mistake to say that the motion of the crust will be the same 

 whether the interior is fluid or solid. 



7. It will be observed that the above formula of Precession 

 does not coincide exactly with Mr. Hopkins's. For when p is 

 constant P does not =: P, as he says it does. The fact is, that 

 my calculation above is purposely made on the hypothesis of M. 

 Delaunay's view being true, and that, at least for a time, the 

 instantaneous axis of rotation of the fluid coincides with the axis 

 of the crust ; and I show that the hypothesis immediately breaks 

 down ; whereas Mr. Hopkins assumes from the beginning the 

 correct state of things, that the instantaneous axis of rotation of 



* Mechanical Philosopy, p. 534. 



