3^2 Mr. S. P. Owen on Radiation 



Putting «sin# = £sin<£, this reduces to 



IT 



p A5 2 sin 2 ^ 6cos^.^j> 



= Aft 2 p sin 2 </>. ^ 



. V • (2) 



b 

 (* sin -1 a T)p> 



Taking the part I cos 6 . sin 2 . tan" 1 — cW, 



Jo ^ ; 



, b 



?. <?. I cos <9 sin 2 . tan" I — - }• "A 



«7 G \ 



and putting a cos # -f \//> 2 — ft 2 sin 2 0=//, 



the integral reduces to 



Similarly I cos 6 sin 2 . tan" 1 .</# 



Jo * 



('"-* ,y 2 + a 3 -& 8 / y 2 + a 2 -l 2 \ 2,v ^ 



J V^ V4a 2 ^^/ -Hx 2 ^^ 2 ) 2 V ~ % ~ / <® 2 +f) ' ' lJ ' 

 b 

 i^sin 2 . tan " ] ^=~sin 2 . tan" 1 ^jcos 6 . d<9 



= i C" h 2,xy(y 2 + a 2 -b 2 ) 



2 J a+b a(^ 2 +/)v / 4aV 2 --(/ + ^-^) 2 



-i f "'* ^(r+^-^) 2 d 



2 J a+ i ay(w 2 +y 2 )\/Ia 2 f--(y 2 — a 2 + b 2 )'' ' " 



