AND ITS APPLICATION TO ME. B. TOWER’S EXPERIMENTS. 
27. The Integration of the Equations. 
Integrating equation (50) between the limits 9 0 and. 9 
— A 1 {cos (9— </> 0 )— cos {9 (J -<f > 0 )} 
+ y {sin 2(9—<f) 0 )— sin 2(9 0 —<j> 0 )} 
&c. &c. 
“lbfl^ C0S [( 2w + 1 )(^- < ^o)]- cos [(2n+l)(0o-&)]} 
+^(sm 2n(9—<f> 0 ) - sin 2 n(9 0 —<j> 0 )} . 
whence putting 0=6^ by condition (43) 
Putting 
O=A o 0 1 —Aj sin sin </> 0 +"W sin 20 x cos 2<£ 0 —. &c. 
— sin [(271+1)^] sin (2n+l)<£ 0 
2»+l 
A 
sin 2n^ 1 cos 2«<£ 0 
2jfO 
A. 
E=A X cos 9 1 cos <^ 0 +— 2 cos 2^ sin 2<^ 0 +, &c. 
+ ^fl C0S X )^i] cos [( 2w + 1 )^o 
+ yy 1 cos 2nd 1 sin 2iuf> (J . 
whence from equations (57) and (58) 
^=E+V-A, cos (0-<£„)+f s:n 2 (0-« 
-^ i C 0 S K 2n+1 )^-*» 
