28 A NEW METHOD OF DETERMINING 
From 
(s) 
(e) 
A, ,or A, =$q+ 6, cosg + © cos 2g + ete. 
+ s, sing + s, sin 29g + ete., 
abe (c) (s) 
and similarly, for every other value of x in A;,, A;,, we have a check on the values of 
C,, S, In each series. Thus if in case of sixteen divisions of the cireumference we 
take g = 22.°5 and find the value of the series, the sum of the terms must equal the 
© © 
value of A;,, -A;,, corresponding to g = 22.°5. And this check should be employed 
on each series, using that value of g that gives the most values of c, and s,. If 7 
; (Onn) ‘ 
extends to z= 9, we have ten separate checks for the values of A; ,, A;,., respectively. 
In the equation 
Y=3e + ¢,.cos g + ¢.cos 2g + c;,. cos 3g 4 ete. 
+ s,.sing + s.. sin 2g + s;. sin 3g + etc, 
if the circumference is divided into twelve parts, each division is 30°. Then for the 
special values of Y we have 
¥, = te + & + 6 = ¢ + ete. 
Y, = $q + 4. cos 30° + ¢,. cos 60° + ¢ cos 90° + ete. 
+ s, sin 80°+ s, sin 60° +s, sin 90° + ete. 
Y, = q+ «.cos 60° + c,. cos 120° + c, cos 180° + ete. 
+s, sin 60° + s,. sin 120° + s, sin 180° + ete. 
Y,, = q+ ¢,.330° + ,.cos 800° + ©; cos 270° + ete. 
+ s5,.330° -+s,.sin 300°+ 8, sin 270° + ete. 
In the same way we proceed for any other number of divisions of the cireum- 
ference. 
