485 
sn R’WsnW cosWL-cosRWeos RL 
nee, a sin RW sin RL 
_ sin RWsin W cos WL -cos R"W cos R"L 
esi 77) air sin RW sin R'L 
or, substituting for cos RL, cos R”L the values— 
cos RW cos WL - sin RW sin WL cos W, 
cos Rk” W cos WL +sin R”Wsin WL cos W, 
the expression becomes 
cos NA sin W 
sn RL sin R'L 
(cosWL sin? RW+ sinWL sin RWceos RW cos W) 
= cos NR 
sin R” W 
sin RW 
+ ula (cosWL sin? R” W-sinWL sin R" Weos R” W cos w)| 
sin Lt” W ) 
cos NR sin W 
sin RL sin kh" L 
x {2cosWLsinRWsin R’W+sinWL sin (R'W-RW)cosW} 
_ Cos NER sin Wsin WL 
SO Vem PE sm ee, 
x {2 cot WLsin RWsin R"W+sin (R"W- RW) cos W}. 
Or, putting for cot WL its value, which gives 
cot WL sin R Wah R'W = sin? NW tan WR’, 
and putting also 
sin(R”WV- RW) =sn2NW = 2sin NW cos NW, 
the expression becomes 
_2 cos NR sin Wsin WL sin? NW 
sin RL sin RL 
The right-hand side of the equation to be proved is 
sin NW ; 
” / / U 
sin R” LR ——_-~ cos WR’ an NE cos #’U' sin U'," 
(tan WR’ + cot NW cos W). 
and we have 
