626 PROCEEDINGS OF SECTION H. 
ode 
ae (2 ae —sin-'(e sing)) 
' +gpah(— a — E(¢) ) 
* 2Et 3aee_. A cos b sing 
erp sing cosg } “804 Bp.” 8 
| h ‘ 
| +92 (4 bg singh) 
+ D ae ; 8 oa (24) 
The complete solution of (24) is 
v= ReosP + Ssinp+T ' (25) 
where #, S are arbitrary constants and J is a particular 
integral of (24) the elements of which, corresponding to 
each term on the right of (24) are given in the table 
below—these are obtained by successive applications of 
the method used for obtaining the particular integral of 
(8) observing that we have identically 
cos ¥{ is (= cosy dy = 1 C0 $e al J ¥cosp.dg (26) 
cos" Cos’ 
Term. eon ey element of Particular Integral. 
a b 
A sing 3 ken al) bsin p+ 
(1-1) r-@—l)al oat] 
sin-'(esin @) = [ « sin-1(esin @) + 
i a boos g+(A—}) sing | 
A cos@ aa L{ (!— 3) F+(1+ 5) = fain g 
+= cos ¢ | 
log (A+ecos @) X. [clog (a +e 0 9) +(1—A) 008 ¢ 
+(F— EF) sin d | 
