16 A NEW METHOD OF DETERMINING 
We can put 
Ay? : 
() = 70 — 71 Cos e’ — By. sine’ + 72. Cos .e’ 
a 
in the form 
(2) = [C—q. cos (¢ — Q)] [1—q- cos ( — @,)], (14) 
in which the factor 1 — q, . cos (e’ — @,) differs little from unity. For this purpose, if 
we perform the operations indicated in the second expression, and then compare the 
coefficients of like terms, we find 
y= C+ ¢q-qsin Q.sin Y, 
v1 =¢.cosQ+q,.Ceos Q, 
¥2=7-M-cos(Q + Q) 
Po=q-snQ+tqu-.CsinQ, 
0=sin(Q+ Q,). 
The last of these equations is satisfied by putting 
Q ==. 
The remaining equations then take the form 
Ne = mee ce > ee | 
| 
a Nn | 
B= (¢—a-C).sing | 
The expressions 
GS OQ) = by sb 2 1) 
q. cos OS ee (16) 
Gh. Csi C) = & | 
Gia C..cos O77) a 
pen the relations expressed by the second and fourth of equations (15‘, where 
— /Yo als Gi 
We haye now to find expressions for the small quantities £, 7, ¢ found in these 
equations, 
