fine Lines or transmitted by narrow Slits. 353 



Passing on to the second boundary condition (11), we have 



*V f *V/ 3 , ikc\\ , 99 . 



iCl=W {l-^!( y+ | + log!| c )}, . . (23) 



-G 2 =-^- (24) 



When these values are introduced into (8), we see that the 

 terms in C and Ox are of equal importance. Limiting our- 

 selves to these, we have 



f= -kVe-»"-(^:) i (h + cosd), . . . (25) 



the symbolical expression which gives the effect of the 

 incidence of aerial waves upon a rigid and fixed obstacle 

 ('Theory of Sound/ § 343). Fully to interpret it we must 

 restore the time-factor and finally reject the imaginary part, 

 thus obtaining 



^ = - 2 W"^ +C0S ^ C0S T (a '- , ' _ * x) ' • (26) 



corresponding to the primary waves 



= cos^(a* + a,') (27) 



A, 



In the application to electric or luminous vibrations the 

 present solution is available for the case of primary waves 



c*=e ikx , (28) 



incident upon a perfectly conducting, i. e. reflecting, cylinder, 

 €* denoting the magnetic induction for which the condition to 

 be satisfied at the surface is dc*/dr = 0. Accordingly the 

 secondary waves are given by (25) with c* written for ty. 

 This is the case of incident light polarized in a plane parallel 

 to the length of the cylinder. 



For incident light polarized in the plane perpendicular to 

 the length of the cylinder the primary waves have the 

 expression 



U=e ikx , (29) 



where R denotes the electromotive intensity parallel to z. In 

 this case the secondary waves are given by (21) with R in 

 place of \jr. It appears that if the incident waves in the two 

 cases are of equal intensity, the secondary waves are of 

 different orders of magnitude, R preponderating. Thus if 



