47'J DR G. PLARR ON THE DETERMINATION OF 



With the definitions (§ II.) of a?!, y u z x : 



This gives then 







i • J . & 



\//-i = — - 03, + — #, 







+ -V,— z. 







1 v u 



(- 



-Shfn) 



or P„ = -i - — * 



and so on. 



In the case of Q, R 1? R 2) we make some further transformation. We have 



u 3 Q = v?x x — y^z Y 



[it is to be remembered that </> is self-conjugate, therefore we have replaced 



a5i = S/^ _1 A by Sk^j] . 



Applying the formulae 



V^- 1 X0-V = ^0VX A * 



(where w = the first coefficient in the cubic relative to <f>), we get 



w 3 Q = — Sj0/c. 

 m "^ 



Likewise in Ri, R 2 we have respectively 



Thus 



(yf - w 2 u 2 ) = SkiYf-^-H = -Sj0j 



1 m *' w w 



% 3 R, = -Sfc0ife+tt 4 -^ 



In § XIII. of the former paper we have stated the formulas 



(i) y-a, 



(2) z=w-^l 



v u 



P namely being supposed in the plane of j, Jc, we have assumed there 



p =jy + kz 



