GRAVITATIONAL STABILITY OF THE EARTH. 199 



and therefore the terras of adP'i/da which are of the first order in h* and If are 



P 



OV 



where p,, ...have the above values, that is to say, these terms are 



, 



4 a* /I .1, 



r 



2.4...(2*-2)7 9 



,_ 

 - 



_ _ 



151/1.2.5 2.4.7 -l ' 2.4...(2K-2)(2ic+l) 



It follows that the terms of the first order in h* and * in 



" 



are 



A/t 



/tVfl a 8 j^a 4 /_\.J^L 

 15v L* 2 2.4~ ^ 2.4...2K"*J 



2AWfl^_lsV / x.^i 1 *"'" 1 

 * 15^ L5 2 72.4 2c+32.4...2c"'J' 



or they are 



2APa a /lg a a 8 _l s 4 a 4 \ 

 15*V \5 2 ~72.4 



AJfcV - 



15 



Again, when we put /t 2 and F equal to zero, we find 

 2A 



E ._2 _sa / y.+i__ 



El -5?L~ "2~ 2T1 4 2.4...2K 



p/ 2A^ra* ji^ y'a* /_v.+ij^ 1 f^_ 



15U? 8.4 2.4.6 ' V ; 2.4...2ie*"J > 



, 2A* 4 f a- 1 a 4 1 sW / v ^"^ 



1= T5^L~5? 7 "2 92.4"' 1 ; (2K+3)2.4...(2/c-2)" 



and therefore the terms of the first order in h 3 and If in 



are 



1., ,P 2A _ |A , jZA fV sV /_y+i_ **!?*- 



~3 L 5? g 5^12.5 2.4.7 -V ; 2. 4...2*(2K+3)'" J J' 



Hence the terms of A, which are of the first order in A* and A.* are 



lAPa^-j^ 



and 



A,_ Ao' e -i^ 



