218 FIGURE OF THE EARTH. [11 



T7 / \ 4 ./ \/\* l \ 



V, = 2irp, (/c 2 3 - *, 2 ) - - w/vei (e 2 - e,) X - - , 



o \ d/ 



77" o / 2 2 \ 2 / \ I \ \ 



\ *J / 



In addition to V there is the term 



Now F+-o>y 2 (l X 2 ) is constant; equate to zero the coefficient of X 2 - 



Zi o 



in it ; we get the equation 



fj . Mj 4 pj 4 , ,4 , \ljsn 



(I) e, - - TT ^ Kj'e, - - Tr/o./c, 2 (e, - e,) - ^ w/yc,- (e, - e,) - - o> K, = 0, 



4 

 where M,=-yye, s , the mass of the inmost fluid. This is the condition of 



o 

 equilibrium of the first stratum. 



For the second stratum, any point of it is external to two fluids and 

 internal to the third ; 



T7 4 1 4 c,/.. l\ 4 1 /., 1 



Pi = o .V>i - + o T, 3 P. ~ X - 3 ) - 5 ^^ ' - X " - 3 



o /t 2 o K., \ O/ i) /C 2 \ O 



F 3 = 2Trp 3 (x 3 2 - K/) - - ir/D 3 /c 2 2 (c, - e,) ( X 2 - - ; 



\ O/ 



in addition there is the term 



Then, as before, these give the condition of equilibrium of the second stratum 

 (II) (M t + 1T 2 ) - - - irp^fa - - - - irp, (/c 2 6 e 2 - K/eJ , - - irp 3 (c, - e 2 ) K 2 2 - - w 2 K 2 2 = 0, 



where M 2 = ~ 77p 2 (*./ K*), the mass of the second layer, 

 o 



Lastly, for the exterior surface 

 PI = o v Pi K i I- o ^P^ ~ { ^ ~ o ) ~" "c '"'Pi^i ~s ( ^ ~ o ) > 



S K 3 6 K, \ O/ *C, \ O/ 



c, d 



