THE CURVE ON ONE OF THE COORDINATE PLANES. 479 



Hence, as a/3 = y, ya = /3, fiy = a, we get generally 



S\0X0- X X, = $a\8/3\Sy\ x A, 



where 



va 8 W \c 2 



. W a 2 \ (a* \ fc W\ 



It is evident that, if we add and subtract unity, the second member will repre- 

 sent the development of 





( 



'c 2 in/a 2 ' c\tw « 2 \ 

 .a 2 a* Ah* wAc 2 cV 







= (^W 2 ) (a2 - &2)(c2 - a2)(62 - c2)= 



We have thus 





W^SaiSfliSyi.A 

 W 2 = SajS/3jS 7 /.A 



Introducing the notation 



W 3 = SakS/3kSyk.A. 

 a — m x -\-ja % + ka 3 







fi = ib x +jb 2 + k\ 



we finally get 





7 = * c i +jc 2 +&c 3r 



W 2 = — a 2 6 2 c 2 .A, 

 W 3 = -a 3 & 3 C3-.A. 



wfjf = [ j« 3 & 3 c 3 + /ca 2 & 2 e 2 ] x A 



We put generally 



for h = 



1,2,8: 



then 





W»' = aAc R , 



and 





W*=-W A 'A 



m«^=-(;W 3 ' + ^W 3 ')A. 



§IX. 



If we treat the fundamental equation 



^'(Vidp) = 

 by S . £, we get 



S . ty'Yidp) = S . Vid/*K= ; 

 and, as 



we get 



= W 3 S .j Yidp + W 2 S . kYidp , 



