GRAVITATIONAL STABILITY OF THE EARTH. - 185 



% 



and thus the equation for Q. becomes 



r d 



^L (i f J^\ + 2 ( n 2) _<L (I ^L- VI 



__ _ 



2n+l i<h*\i' dr r dr\r dr 



1 V([d*_ A rfEjA , 2_(n+ 2) ^ /I </E.\ . _rf /I dE. 



2n+ I A'.U^ \r 3r"/ / rfr \r rfr / dr \r dr 



1 [fP /I rfE.\ + 2(n+2) rf /I ffi.\ +p /I rfjE. 

 2n+ 1 [_d>* \r dr I r dr -r dr / ' \r dr 



by the equation (40). Hence we have 



where Q'. satisfies the equation 



11. To find the form of P' H , we assume 



^A(^ + ^+^ + ...) ....... (51) 



Then equations (48) and (37) give 



2.4...2K(2n+3)(2n+5)...(2+2t-l) 



VOL. CCVII. A. 2 B 



