202 



So also j = 4>a 



THE ROYAL SOCIETY OF CANADA 

 Sj<t)a 



(c/>a)2 



+ ..+ 



^ Si4>aSj(pa Si(j)l3Sj(f)l3 Si(t)ySf(f)y 



{4>ay 



im- 



{4>iy 



So also 



Again 



_ Si(f>aSj4)a 



{T<t>af 

 Sj(f)aSk4>a 



_ Sk4)aSi4>a 



{T4>ay 



Si(t>a 



+ ..+ . 



t =<pa 



i<i>o.y 



Si<j>^ Si<t>y 



. — 1 = 1- = — — -_ — + 



So also 1 = 



1 = 



(4>ay 



Si(t)ay 



T^ay 



iSj4>ay 

 (Sk(})ay 



or 1 = ^^i^ + 



(nay 



(<t>^y 

 (Sict>^y 



(Sim' 



{n^y 



+ ... + .. 



(</>7)' 

 {Sici>yy 

 (4>yy 



(si^y 



(T<pyy 



+ ...+ 



{T<t>ay 



Then tangent plane is 



SiriSia , SwjSja , SirkSka , 



STr(t)a=l, or + -^ -I = 1 



a" b- c- 



or STriSi(l)a-\-SirjSj(t)a-\-STrkSk(t)a= —1, from (1). 



1 



T(f)a 



or Sirt —^ I-Sttj — — -^-Swk 



T4>a T(t)a T(t)a 



(3) 



(4) 



Si(l>l3 Sjct>l3 SH^ 



So also OTT/ +'J7r7 +07r/? 



r0/3 r<^^ T4>^ 





Squaring and adding, obse'rving result (3) and (4) 



{STTiy+{Sirjy-^{STvky=a~+h''+c\ 



