THE CURVE ON ONE OF THE COORDINATE PLANES. 485 



fiW = u V W~ 1 *)+- f^Vtyi 



Treating first i/> (<^') by S.£ l5 the coefficient of S&z will be 



1 W 



= — S<j>i.i<h~ l i= H • 



a T r U 



Then, remarking that we have 



S^k = x a y x - x^ = + W 3 , 



we get 



W W 



u v 



-^JS-foM*- 1 *). 



W 



We will at once eliminated by z^ = , 



taking 

 Thus 



W 



w 



+ ^[Si0- 1 i0^+s^- 1 ^]. 



w 



As <£ _1 is self-conjugate we have for the coefficient of — - 

 Also 



+ S.YijV<p- 1 kcj>i 

 =xj$i<p- l i — xfii^i + Siipi.x^ — SjipiSi^-^^k 

 = SJc ( f>jSi(f>- 1 i- Si<j>jSk<f>- 1 i 

 = S.YMV<p-H<f>j 



We have thus, first, 



W 



1 v 



