54 A NEW METHOD OF DETERMINING 
2 
The value of = found by integrating a(“) = 2e.sin e.dg, is 
2 (1) 2) (3) 
r 
5 1 + 3e — 4J, cos g — 4J,, cos 2g —4-J;, cos 3g — ete. 
2 
(2) 
In terms of the #,; functions, 
(2) 
2 (2) (2) 
“=1+3€—R, cosg — R, cos 2g — R, cos 3g — ete. 
a 
2 
Again, since 
Oj __ @ 
apa oe 
we have 
2 aes Sir V1l—e* dg 
Let 
+0 ee 
F=J + =, Crsin2g ; 
then 
- =1+ ae 7C; C08 219, 
and hence 
(—2) 1. C; 
ki; a V1 Gi 
The coefficients represented by C; designate the coefficients of the equation of 
the centre. 
