1887.] On certain Definite Integrals. 479 



[dx Cxdy Cxdz x 



)yz J y 2 z J z*y ~ y* 



C^dx WrV), f y ^g v^Bg + A^) 

 moreover, since 



Jx jx ]x z X 



we shall have JjZa* J/(0 9 — A^) I ^ ^jft+A^) 



1 r Ai y(C 2 + B 1 ^)y(B 2 -C 1 o; 3 ) _ _X, X^ . 



Again, since 



jcfcy 2/ 5 ^ 2 -|-5j^ i/ 4 3 2 a; + 2|z dz xif = xifz 1 , 



2A 1 8B 1 ^(A) 1 J» dx (B 2 + A 1 ^)^(A 2 -B 1 a ; 3 )^ 



+ 5A 1 2 C i 2 ^ / (A 1 ) j dx ^(Aj + C^KOa-Aia 8 )* 



= A^BA 2 ^( A x ) (X 2/ t* 3 S 3 - h/h 5 »i S ) • 

 Similar^, since 



tfo+j (0+3) <%+| (x + y)dz = xy + xz + yz, 

 ^(B^)] <fa {^(C. + B^-^B.-C^ 3 )} 

 + ^(A 1 C 1 )j *" {^(A 2 + C^ 3 )-^(C 2 -V 3 )} 

 + ^(A 1 B 1 )| rfe {^(B. + A^-^CAo-B^ 3 )} 

 = ^(A^CyjSX^ -SX^}. 



VOL. XLII. 2 M 



