414 



Archdeacon Pratt on the Fluid Theory 



Second test : the density of the strata supposed to be inter- 

 changed, but their form to remain unaltered. 



8. As a second test, I will suppose the density of one of the 

 shells, as for example the second, to be altered throughout in 

 the ratio oc : 1, and that of the third to be altered in the ratio 

 ft : 1, in such a way as not to affect the total mass. This leads 

 to the condition 



a (E I -E 2 )+^(B 2 -E 3 )=B 1 -E 3 ; 



and the potential of the whole mass is 



U=V-V 1 + a (V 1 -V 2 )+^(V 2 -V 3 )+V 3 , 



-'t¥{*-i.+^»W(*-W 



f m . , N /E, a? maf\ 



E Ea 2 r 



= _+- 



+ 



Now, by the relation connecting a and /?, 



If, then, we put 



TT E Ea 2 f m „"! (\ 9 \ 



■1) 



E i— E s 



E n — E c 



tt-^ 1\/ E i^\ ma ? Ej— E 3 /E 2 « 2 2 m« 2 5 \ 

 ti " la " 1] lE? ei "2/~Vl 3 ll a 262 2 F/ 



eAE a 2 3 2 aVJ ' 



+ 



E, 



and, precisely as in the other case, the increase of gravity in 

 passing from the equator to the poles =3H. 



9. This I will now reduce to numbers. By substituting from 

 paragraph 5, 



H = S(°- 38835 -S x0,l0423+ S x °-° ura ) 



_^_l( .32768-g x 0-07776+ 1| x 0-01024), 



= (a- 1) (0000523 - 0-000262) = (a- 1) x 0-00026. 

 Hence 3H = (a— 1) x 0-00078, and this change in the distribn- 



