JElolotropic Potential, T43 



potential. The integral of the section which is of the second 

 order in xyz is 



+ y (Cd + Be' + A'6') + # ( B'a + AV + C6') ~j , 

 or p~T j aaA 



40 Jo x/J* 

 We shall show that the second part involving Ua is f o£ the 

 first part, so that the total energy is 



7o°J 75 OH) 



The constructive proof sets out from (87) which gives 



:LX I "f^-sT ^-(Aa 2 +B 7 ' 2 +C^' 2 +2CV + 2B'«^-| 2A'£V) 



Jo V J Jo VJ 



integrating the second section by parts, 



= - 7 -2(Aa+2AV), quoting (86). Thus 

 J o v J 



SA. [" ^y = [" ^j [«S(A«+2AV) +2(A» S + B7"+ ...)], (H*) 



or the integral which is quadratic in a... on the right-hand 

 is reducible to a linear form. Now the integral 



C y=\ dr^+c'y + b'z) {*x+jy+pz)u a 



is of the second order in a..., of the fourth order iwxijz. To 

 effect the volume integrations we have*, with 



35 A:..*.- 1 = 3A 2 , 35A^y = AB + 2C' 2 , 35A5fy = 3AC, 



35A^V=2B'C'+AA' .... (11,0) 

 It will be found that the substitution of these means will 



• These statements are readily proved by transformation from the 

 principal axes to other axes. I have not been able to find these, or 

 ■ I the simpler formula used before for x 2 and xy. 



2 G 2 



