66 



Transactions of the Royal Canadian Institute 



Where the primes indicate differentiation with respect to the arc Sq. 

 Along g = const., we have 



, EiXi 



Xi 3Cii 



dSg=V E dp, x'= ~TW- > ^ = ~^ 



72 ' 



V£~\ E 



Xn El J Xi ±L\i I Xi hji 



\ etc. 



Thus 



(9) -V='"' 



PQ 



£2 



£2 



1 ^ 



* £3 





by virtue of formulae (3) and (4). 

 Again 



1 



Pq" <^Q 



= {x y z )- 



( 



Xi _3^i _ 1 yiE 

 V~E' E ^ £2 



1 i_ rzm _ 3 



£i 1 Zi£r , ZiEi 



£2 



2 £2 + 



m) 



£3 



Now form relations (1) and certain evident elementary properties of 

 determinants, we deduce the relation : 



(-.n.u)=((..^)(.a|^V^3]^^)) + 



\} W ^ ^'^ ^ ^P ^P 



^)) 



= {^^ W ^A ^ '^/ v^"^ "^J ' 



