478 Mr. W. H. L. Russell. [June 16, 



1 



Now, since 



. zy + ^dy xz + ^dz xy = xyz, 

 + ( A iCi) i r dx^iA^ + C^) y(C 2 -A^ 3 ) 



-'"2 



where the limits W/ll^v^ must satisfy the equations — 

 aiV + Z W 5 + c W 3 = 

 a 1 X 3 3 + Zv^ + W 5 = e 2 5 

 a^ 3 + \pi 6 + c 2 ^ 2 3 = e 2 , 

 a 2 A 2 3 + 5 2 ,a 2 3 + c 2 j^ 2 3 = e 2 ; 



from which it appears that one pair of limits may be considered arbi- 

 trary, while the other two pairs are given by these equations. 

 Since — 



+ B 



f dx f dy f dz 1 



)x\jz )xifz J xyz 2 ' xyz 



s r A] dx 



Ma/VCC.+b^^-c^ 3 ) 



(7*1 cfo 



^(B^A^^A.-B^ 3 ) 

 the limits being determined as before ; and since — 



