202  Mr.  J.  W.  Nicholson  on  the  infraction  of 
For  the  integral  I1? 
,         izx  /r2        2 
^=2^/1-  .r  -  2*  cos-1  .r  +  —  -  y  -2  -  * 
and  r  =  6+^+coS-icS. 
1  2  r 
Thus  at  both  limits  x=l,  a=  e2"1, 
-f^cos-1 f-c/.r 
r 
'  =  7r  +  0  — sin-1- 
similarly, 
VJ  =  77-6  -sin-1- 
r 
vs'  =  w  —  sin-^  +  fl, 
r/^Tr-sin-1--^ 
(34) 
Moreover, 
(35) 
Again, 
\  rjtkcv,  _ 
U 
ethCl-  =  e    2  .  exp 
{ 
.ikcld  +  7r—  sin"] 
V?-} 
at  both  limits 
^^=exp.-^{^-7r+sin-^  +  yJ-l}7         ^     (36) 
^J*—s=-exp.-ikc  |tt+0-  sin"1^-^  ^-1}' 
^ie^4==g~2.exp.^c{«7r—  0-  sin"1^  —  \/ \i  ~1  J  '- 
