206 DR. T. J. FA. BROMWICH ON THE SCATTERING OF PLANE ELECTRIC WAVES, ETC. 
Our result accordingly becomes 
(7-69) 
X = 
//ca“ 
r 
1 . 
IKT I „t<ta (l+COS 0) COS fl' 
Jo (/ca sin B sin O') sin 0' cos 0' dO'. 
An exact evaluation of the integral would be troublesome; but it can be trans¬ 
formed by integration by parts. This process leads to a series of which the first 
term is 
^ Ji Ua sin O) 
r Ka sin B 
The formula (7’7) will represent (7 ’69) sufficiently accurately if (1 + cos 6)/sin B = cot ^B 
is regarded as small; and this is the correct assumption here, since B is supposed to 
be nearly equal to tt. 
In the special cases Ka = 9, 10 it appears that the approximation (7’7) represents 
the scattered wave sufficiently well within a cone extending to about 10° from the 
axis. 
(77) 
