98 Prof. Moseley on the Application of the Principle 



we have 



S2P «P «P S2P 



So.'! dj^ c?z t &.r 2 



82P . 82P n Q . 



-=— = 0, -7— = 0, &c. ; also 



ssp : m> . s^P . s^p n « - 



= 0, 1 a = 0, 1 = 0, -5 — = 0, &c. &c. 



§«! OPj 8 7l 8 «2 



Let l + (Ai + B 1 ^-B 2 ») cosa + (A 2 -B^ + B 3 z) cos 

 + (A 3 +B 2 x — B 3 y) cosy = L. 



.\ L^? + P(-B 1 cos/3fB 2 cosy) + Xw' = 

 L j? +P ( B x cos a-B 3 cos y) + X «" = 

 L 5? + P(-B 2 cos a + B 2 cos/3) + x«?" = 



tt z 



Sin a-s Aj + Bjj/— B 2 ^ + /x cos a > = ~) 

 Sin/3«fA 2 --B 1 ,r + B 3 2: + |«, cos j8\ = >. (6.) 



Sin J A 3 +B 2 ^— B 3 j/ + /x cosy J> = OJ 



Multiplying the first of equations (6.) by cos a, the second 

 by cos /3, the third by cos y, and adding, observing that 



cos 2 a 4- cos 2 /3 + cos 2 y = 0, 

 we obtain 



(Ai + Bjj/— B 2 z) cos a + (A 2 — B^ + Bg*) cos /3 + (A 3 + B 2 # 



— B 3 y) cosy 4-^ = 0; 



.-. L+ju,— 1 =5 0. 



Let A^Bjy-Bg* = K' 



Aa-B^+Bg* = K" 

 A 3 +B 2 *-B 3i , = K'" 

 .'.by equations (6.) 



I* 2 = K' 2 +K" 2 +K'" 2 . 

 Let jw. . L = K, .'.by equations (6.) 

 cos* K' cos/3 K" cosy K^ 



L " X' Tr""""!^ "TT " K* 

 .*. by equations (5.) 



