24. A NEW METHOD OF DETERMINING 
and hence 
s s+2 ,.,8 stl s4+2s5+3 4 
Se SUES BY a os aia Se ne ae G 
i? 3 Lae 2 3 ee 
EE OP eg ae] 
3 $ ep-bi g+9 s @ts ».,8 stil sts sta ., Vee 
youa? st1 242 gy | ee api Sbt Shs std (29 
ath @4® gt s-L4 5-46 
4 eo ee eS Se, Sr +? a + ete, | 
oO 
and generally 
O—® 8 Sarl @=Fe=1 ss 218 Shel Saree 9se ob 4 
b = 2.5 eyo ; ee ae; Pe et te | 
Since s = —, we find from these expressions the values of the 6 coefticients for 
>? 
different values of 7. 
Runxk sz has tabulated the values of 6 in a paper published by the Sm1rrHsonran 
Institution. Thus the value of 
[1 + a? — 2a cos (’e—Q)]~2 
is obtained with great facility. 
The value of [1 + 6° — 2b cos (¢ + Q)}2 is found in the same way. 
We now let 
- aa 2 5 IN a cos *Q ) (30) 
sO=21 WN. B®. sin2.1Q) 
And hence have 
CU TENGE. 
C= NP Be cos. 
Ce) = eo A oO), sin AAG) 
iain i 15°), COS 40) 
ei IN Jina) 
etc.= ete. 
