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Theory of the Optical Properties of Metals. 663 



Now we know that 



d<f> 



i 1+ 2^\ * 



■jon/ TO . 



sin cos </> 



7T 

 ^0 V M 



') 





sin 2 # cos 2 $ 



which integrates by a well-known method and gives 

 &r(l + ^s) 



v/(i + ^) a 



y/™ 2 ,. 





The integral with respect to 6 is then 

 cos 2 6 sin 6 d6 



9 r 1 7T cos^ sm 



jW . 



sin 2 



which by the transformation 



jtmZ, 



cos 



// iplm\ 2 p 2 nHm 2 . , 



is directly evaluated in the form 



2tt 



7 1+ !MA 



pht 2 i 



p 3 n% 



sm 



e 



[V(i + ^) a + ^ a 

 (l +;*£>* } 



Calling this expression 



we have then on insertion in the last integral. 



iplm\' 2 p' 2 n' 2 lm- 





