Figure of the Earth, 

 Fiir. 1. 



483 



Taking potential to be X , the potential of this ring at P 



= K7r^%{a 2 (l-^) + r 2 -2^+ i /2 j " 



= TLirp<ra*hy {b%l + 2e)U-^\+r 2 --2yr+f} "'nearly 



= K>7rp<Ta 2 8y{r 2 -2yr + b 2 + 2e(b 2 -y 2 )\-* 



= ^paa 2 hy{r 2 -2yr + b 2 )^ { 1- ^fg^y } 



where only the first power o£ e has been retained. The 

 potential o£ the whole shell 



{ (f - 2yr + b 2 ) "*— e(b 2 ~y 2 ) (r 2 - 2yr + b 2 ) ~*}dy 



J- 



r 1 x b 2 ~\ +b 



= K7rpva 2 \ -±(r 2 -2yr + b 2 y-e r ( r *-2yr + b 2 )-*] 



-r eKirpaa 2 \ y 2 (r 2 — 2yr + b 2 ) " %dy . 



Now j y 2 (f - 2yr + 6 2 )<fy 



= ^(r 2 -2yr + b 2 ) "* + ^(r»-2yr + ^)*+ ^r(r*-Sty*+P)t 



