GRAVITATIONAL STABILITY OF THE EARTH. 205 



and by means of the identity 



+ 4) 10 51 120 



(2*+3)(2K+5)(2K + 7)~ 2* + 3 (2/c+3)(2ic + 5) (2K+3)(2K+5)(2+7) 

 we ti'ansfonn the series 



If _j_ tf 8.8s 4 , y (2<c-l)(2*+2)(2*+4)x i - "1 



5|_~ 6.7 2.7.9 2.4.7.9.11" 2.4.6.7.9...(2c+7) 



into 



3.5.9 



which is the same as 



16 

 Hence we have 



Again we find 



(92) 



and 



1 9 "" If f9 f\ \ / 



Hence the equation lim, (AD/--'-B s C^; 2 ) = is 



- ' (94) 



where x is written for ja. A factor v~ l s~* has been omitted in forming the equation, 

 as neither v nor * is supposed to vanish. The terms of lowest degree in the left-hand 



