442 Mr. R. Hargreaves on 



while 



The part of Vg%i which is due to implicit differentiation 

 through A is 



VJ (U+ " + ^ :) ISA'S +' Ty + '} SJ 



~diU ,d\ d\ ■ ,dX\ , ~dii a ( ,dX , ,d\ , d\\ 1 



which by (78) is p{*x-\-yy+0z)ly/5. The part of Vj^i 

 which is due to explicit differentiation with regard to a?ys is 



'-5JT^[{f'- + 'V + ^S+fr , -+«'+^S ! 



+ (./cc+p'r/ + r0) ^° } + (ax + </y + 0z) X 0» + 2pV)] • 

 The coefficient of a? in { } is 



which by (80) is —2a, t. e. { } is — '2(ax + y y + ft' z) ; also 

 by (86) %{p* + 2p'* , )=J/J. 



Hence the second part of V*^, is 



f»J"^{«+yy+/S'*-J(<w+7 / y+/8'«)/j} 



Thus outside the ellipsoid, where both parts occur, the terms 

 are cancelled and Vf ^ = ; while within, where only the 

 latter part appears, V 2 e ^ l + p(ax + c , y + b / z)=:0, because the 

 use of A = for the lower limit makes J=l, a = a, y' = c 



The energy in this case is 

 P g J ^\dT i {ax + c'y + b'z)( O LX + yy+0z)(l--it a ), 

 viz. : the volume-integral of half the product of density and 



