464 Mr. E. Talbot Paris on the Polarization of 



numerical values of these functions tabulated by Rayleigh 

 can be used. From equations (3) and (4) we see that 



s »fo)=(_)»i.3.r..(2 B +i)*»o0> • • ( 9 > 



aDd /^)= ( _ n ,3,5 1 ..(2n + l) E ^- • • ^ 10 > 

 Thns . ^ = J^ (n) 



For N„, since rj = ka and — = & -y- , we have 



ISL = - 



Differentiating 





N== _(» + l)W/)+^^ , t»('/) 



(n + l)B.(,)+,^B^,) 



Now 1/^(77) satisfies the equation 



*2£+«W =(2n + l) | ♦.-ifo)-^?) } . . (12) 



and E„(^) satisfies an equation of the same form. There- 

 fore, 



(2H + l)+n-ifo)-™M*?) n ox 



* '-(2n+l)E n . 1 { v )^nK( v y ' ' { 6} 



By separating E„ into its real and imaginary parts, the 

 values of M n and N n given by (11) and (13) can be calcu- 

 lated without further trouble for any value of tj for which 

 yfr and ^ have been tabulated by Rayleigh. 



Alternatively, the values of M n and N„ for the case of a 

 perfect conductor can be found by putting K = oo , and, in 

 order that K/^ may remain finite, /z,= in the general fixpres- 

 ions for M n and N n . This is analogous to the method used 



