60 
Similarly, in the case of 
is (i) , 
But a cos f’ = cose’ — €, 
Hence 
Now 
From the values of cos é’ 
- COS ni 
Pe snin i/” 
; COS @ 
We now 
A NEW METHOD OF DETERMINING 
r’ sin f’ 
pon. we have 
cos g 
a (G sin i Poesia if 
dg” \a' cos ¢ 7? cos ¢’ 
r sin f’ . 
and * f = sine’. 
a’ cos ¢ 
a G cos f” ) 7 @.cose 
Sk, a 12 cos T ee 12 9 
dq” 2 : dg” 
2 (7 sin f’ 
1? (S =) _.  @? Sin 7” __ &. sine 
dg” > 7? cos ¢ dg 
COS &’ 
sin ¢’ 
2) 
Bec 
0) (2) 
[woot oh 
assume 
Me 
jh + Ee) cos g’ + tlio = Te cos 2g’ + ete. 
i (1) OA. 
[ee = ee sing’ + | Av + “he | sin 29’ + etc. 
and sine’ we have 
"| cos 9’ + 2 eee abt cos 2g’ + 3 [ Ja — Say_| cos Bg’ + ete. 
| sin g’ + 2 lez + i | sin 29’ + 3 [wee ++ Toe | sin 3g’+ ete. 
(i—1) pte 1 i—1) a, 
x ae a Jin ik 0; =i ees Si ] 
1 (v’—1) (7’+1) 1 (v/—1) fh +1) 
(/ 
i [. va —Siny ii ver | Jim +m i 
Comparing these expressions for y’;, 6’), with those found in the expression for 
sin fe 
“cos 
, given above, 
we see that the relation between them is 7” 
