96] Stability 95 



where / stands for A% 2 + Brf + Of 2 1, and G is given by 



G = A {- 3 ^A 3 a 3 + J^A 2 Ba 2 /5 + ^A 2 Ca 2 7 + 

 + f AC 2 a 7 2 + M ABCa/3 7 



- Jj A 2 C (Zy + 2-ma) 

 (Ma + 2/i/S) - ^AC 2 (Na + 2nj) - ^ABC (la + m/3 + ny) 



21/5) - ^BC 2 (^ + 2Z 7 ) 

 + j5 A 2^ + _3_ B2 j^ + ^ C2 ]^ +i i_ BC i +i ^ ACm + T 3_ ABn ......... (257). 



With this value for < 3) let us put 



f /^ 



I ^d\ = x (C n 4 + 088^+ C 33 ^ 4 + C 12 a? 2 i/ 2 + C 3 i^ 2 a; 2 + Ca^+ ^+ lT 2 2/ 2 + & 3 * 2 + 1 4 ) 



...... (258). 



The value of V b the potential at the boundary is 



V b = - TT^a&c f [/+ e^ + e 2 2 4- e 3 c 3 ] ^- ; 

 Jo A 



the condition that the figure (253) shall be a figure of equilibrium is, as in 

 equation (240), 



F 6 + H 2 + e 2 S 2 ) (^ 2 + y 2 ) = - ^&^ 



\df C , / 



...... (259). 



On equating coefficients of terms independent of e, and of terms in e and 

 e 2 in this equation we obtain precisely the systems of equations which have 

 been already obtained and discussed ; on equating terms in e 3 we obtain 



&,* 4- & 4 ) 



On equating coefficients, this is found to be equivalent to the separate 

 equations : 



e - (260) ' 



(262), 



