483 
1 sin 
a W(cos RW - cos LR cos LW) 
sin ; 
~ LR" sin RW (cos Rk” W - cos LR” cos L w)}. 
sin R” sin R 
nL’ anLp’ each equal to 
Or, observing that 
sn R’LR .. 
gnk’R” this becomes 
1 
“sin RR sin? LW 
-sin RW (cos R”W-cos LR’ cos LW)}; 
{sin R” W (cos RW-cos LR cos LW) 
and, substituting for cos LR, cos LR”, the values 
cos RW cosLW-sin RW sin LW cos W, 
cos Rk” W cos LW+sin R"Wsin LW cos W, 
the foregoing expression becomes, 
ab see ld 
sin R’ RA sin? LW 
x {sin R”W(cosoaRWsin?LW+sin RWsinLWeos LW cos W) 
-sin RW (cos Rk” Wsin? LW-sin R"Wsin LW cos L WcosW)}, 
ae {sin R”Wcos RW —-sin RWeos R"W 
+2cot LWsin RW sin R’Weos W} 
1 
~ sin RR 
: x {sin(R”W- RW)+2cot LWsin RWsin R” W cos W)} ; 
and, putting R’W- RW=2NM,, and substituting also for 
_ cot WL its value, which gives cot LWsin RW sin R"W 
= sin? NW tan WR’, the expression becomes, 
— {sin 2NW+ 2 sin? NW tan WR’ cos W} ; 
but we have 
