190 Mr. F. L. Hitchcock m 



Furthermore, because \/' 2 v is a vector, 



svvv^o 



= -(P + Q + R) 



~HP+;r;+0),bjr(S)and(3j, 



a in 

 whence we have for the value of F r 



P— £ (5) 



am 



It remains to get an expression for r' . Identically we have 



VVVf^(?-/)x+(?-? / > + (**-*•>; - ■ (6) 



operate by Sv and put for r its value from (3), 



but bv the ordinary expansion 



S . v\7(cfi) — cSi/S7p — -7-7 ; 

 whence by equating yalues 



r^cSvtffjL. ...... (7) 



To sum up results, 



1 am at 



or more compactly 



dc \ 



y]rdp=\&dpt ^ — e&v\//j,,/j — cc 1 v\ — /j,SdpSJc + cvSdpxfJ>. 



The quantity r may be expanded thus 

 = eSvV(-Xv) 

 = c(SVA--c) (9) 



