



Light scattered by Spherical Metal Particles. 471 



can be shortened a little in the following manner. In the 

 general expression for M n and N» the -^-functions with r/ as 



argument only occur in the form yn '" ,\ . Dividing (16) 



by ^ n (7]') and rearranging the terms we have 



where <3>« is written for ■ , ~ / * Thus two values of -^n(V) 



TH 7 ? ) 

 can first be found from (15), for example -v/r 5 and ijr 6 when 

 17 = 1. These give the value of <t> 6 , and <X> 5 , <3> 4 , &c. can be 

 obtained by using (17). 



It is convenient to tabulate <!>«, and 



r »={^i^' 2 - 1 ) + *"}- 



We then have, omitting the arguments, 

 numerator of M n = yjr )l _! — <£>« . -^r n , 



denominator of M»= 1 x numerator — ^ u -i 4- <X>n • ^». 



And 

 numerator of N»=nt' 2 ^r,i_i- F« . tyn, 

 denominator of N»=iX numerator — m'*ty n ~i 4- r» . ^n. 



The following values of S^n and yjr are required, in addition 

 to those given by Rayleigh, to enable the polarization to be 

 calculated for 77 = 1"25, winch was very near to some of the 

 values of 77 obtained experimentally. 



n. 



¥»■ 



| 





1= 



1-25. 







... 



0*25226 





0-75919 





1 ... 



2 3064 





085222 





2 ... 



19720 





0-S9312 





... 



39006 





091622 





4 ... 



14932 





0-93108 





5 ... 







0-94145 





G ... 







0-94910 





