483 
1 sin ft” 
- WW LAGE LW a LE et W (cos RW-cos LR cos LW) 
sin R 
— SLR? in RW (cos W-cos LR cos LW)}. 
sin 2” sin R 
ainLB’ anLR” 2 each equal to 
Or, observing that 
aa LR 
tan Ron” this becomes 
1 
“sin R’R 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-sn RW sin LW cos WV, 
cos R”V cos LW+sin R”Wsin LW cos W, 
the foregoing expression becomes, 
lub ee s0: na As 
sin RR sink LW 
x {sn R’W(cseRkRWsintLW+snkRWsinLWeos LW cos W) 
-sin RW (cos Rk’ Wsin? LW-sin R"Wsin LW cos LWeosW)}, 
= ao {sin R”Vcos RW-sin RWeoos R"W 
+2cotLWsin RW sin R”Weos W} 
ape bee 
sin RR 
x {sin (R”W- RW)+2cot LWsin RWein R’W cos W)} ; 
and, putting R”WV- RW=2NMW, and substituting also for 
cot WL its value, which gives cot LWsin RW sin R’W 
= sin’? NW tan WR’, the expression becomes, 
1 - - 
= RP sn 2NW+ 2sin? NW tan WR’ cos W} ; 
but we have 
