THE CURVE ON ONE OF THE COORDINATE PLANES. 475 



We have now two equations, the one giving the sum of vy and ivz, the other giving 

 (when multiplied by yz) the product vy x wz. 



Let us put for abbreviation, 



u V 2 = t 



y 2 z 2 = s 

 — (S^+m 2 ) = L 



we have 



Then we may put 



where 



vy+wz = — 2 (t + L ) 



vy x wz = — — (t + L + Lj) . 





We will now deduce two other expressions of v, w, from the equations (1), (2). But 

 for this we must now have recourse to the hypothesis 



b 2 = c 2 , 



which constitutes the ellipsoid as a figure of revolution, the axis having the direction of a. 

 In § I. of the former paper we have assumed by definition 



Making b 2 = c 2 , and remarking 

 we get 



As 



becomes 



, aSaca f3S8w , ySyw 

 /SS/3(o + ySyo> = — w — aSaw , 



^co = aSaa)^— 2 -pj- 



'p' 



1 



m= — 



a 2 b 2 c 2 



1 

 ~a 2 ¥ 



Likewise we have 

 From these we deduce 



^ = aSa<ob 2 (a 2 - b 2 ) + coa 2 b 2 . 

 <f>~ 1 co = aSaa)(a? — b 2 ) — wb 2 . 

 ^^[^co + ^ + b 2 )]. 



m 



