156 



Now 



sm^ Pi 



hence 



ïtn" P. 



^iii = 



X 



2{—4.cosS.cos{S-P,).cos{S-P,).cos{S—P^) q,'' • 



Putting 



— 4cosS. cos (S-P,) . cos {S-P,) . cos (S-P,) = Q , 



we obtain 



whence 



Vi- 



'?i = 



sin' Pj 

 sin P, 



Further we find, after reduction, 



Q =z I — cos'- Pj — cos' Pj cos' P3 — 2 COS Pj cos P, CO*" Pg, 



consequent!}- 



Q = 1 - ^s' — ^13' - ^12' + - ^3 ^13 »'l2- 



Finally 



^^ ^^ '^^ • .sm^ P, .m^ P, .i,r P, 8>;„ij,,ii33(2 ' 



Introducing the mean errors '^]■^, 1}^ ^»d t]^ of .I'l, .r^ and .^g, which 

 satisfy the equations 



n,' = ^i: 



''^22 ' ^3 '^li 



we find 



sill Pi 

 Qi = ;^ , (i=l,2,3) 



^i.- 1/2 Q 



E 



1 



and 



ir = 



1 

 2Q 



1 -: 



_ '*ii 



23 - 2 

 I ^1 



8 n.' n.' -n,' Q 



23 ' 13 ' 1 



V^Vi 



- §2 Sb — 



(2jr//. ii, .?3 ^3 l/Q 



d'^j.d's^.d'Hj 



