758 Dr. J. W. Nicholson on the Bending of 



The first approximation to u is *S/C*, and in terms of this 

 approximation, by (160) and (164), 



where 8 = \ + Jft/i/, so that finally, v being z cos <j> — h\ 



2=vws(i+f);^' ir+,aC , 



where 



S=(3 + 8S 2 )/12C 3 , (166) 



and S is of the same form as before, with 4> for 6. 

 The magnetic force is therefore given by 



7P = ffW2 



_ 2ism6 d_ ffl tdcj> 



ka 2 7T ddJ Q </2)/C08<l>—G0Sd 



= 2k srn^ e _ lIcr _ h7r d C9 #sinj> j ± i(3 + 8rin»0)\ $ _ ika coa , 

 sjirka ' ddj <y C os<j> — coa 6\ 12ka cos* <j> J 



. . . (167) 

 Now if \i is the integral, 



J \/cos<£— cos# 

 Then with cos <j> = cos # + w> 2 , 



I 1 - = 2^ acQS0 j dwe lJcaw \ 



and 



^ = - 2tta sin 6 e ika cos dw e lkaw -f 2* cos \Be l % 



the second term arising from differentiation of the limit of 

 integration. 



But to a second approximation, by the usual formula for 

 an integral of Fresnel's type, 



sm±0 i /_\i , ^(1 — cos0) 



7 ika.ii) 1 L / vr \ 2 iiir e v 



if 2 sin \6 is not small. On substitution of this value, the 

 second term of d\ x jd0 is removed, and to the second order 

 of (ka)~\ 



^=-i(>jrkaf sin0 e l * acose +T. . . (170) 

 do 



