- 68 A NEW METHOD OF DETERMINING 
we have 
(0) (2) (0) (2) 
=o (+a lene a o Loe les 
(a) Or). qa) (3) 
+26 [ Jar oly | sin (— 29’) + 28’ | J, — J _| cos (— 29) 
(3) 
(2) 
(2) (4) (4) 
+ 8B [ Tye + Sou | sin (— 8g’) + 8’ [ey — Fay | 08 (— 89’) 
+ ete. + ete. 
The value of (Z)’ is found from 
(Ty = “sin (2). 7 sin (f + 0). 
From 
_=l— 2 as, 
a 
we find 
a’ = , \—3 
6) = (= excos ea 
a 
Expanding, 
ANS oil pene ; 
(5) = Se + (de + 22e + ete.) cos g 
+ (%e”-+ Ze* + etc.) cos 29’ 
+ 43e" cos3q’ + 231e cos 49’ + ete.; 
which, for brevity, we write, 
r 
Gy = ~ + 2p; cos g’ + 2 p, cos 2g’ + 2 p; cos 3g’ + ete. 
But 
, ‘sinof (0) (2) Es () (3) 
~ r= [EA +4, |sng+4 Ba + JS, ] sin 2g + etc. 
(2) (1) (3) 
7a (0 3 
“cos f = —e+ [ee pete cosg +4 Jn. — Jn | cos 2g + ete. 
