50 Lord Rayleigh on the Incidence of Aerial 



notwithstanding. Thus, if the axis of the disk be parallel 

 to #, that is to the direction of primary propagation, we have 

 (21), (25), 



T - 4R3 T -0 (129) 



In spite of its thinness, the plate being a perfect conductor 

 disturbs the electric field in its neighbourhood ; but the 

 magnetic disturbance vanishes, the zero permeability having 

 no effect upon the magnetic flow parallel to its face. If the 

 axis of the disk be parallel to y {see (24)}, 



. . (130) 









T 



N 



4R 3 



~ 3vr' 



T 





2R 3 





4-7T — 



M 



" 3tt' 



and 



if the 



axis 



be 



parallel to 



T 



N=°> 



Z 1 



T 





= 0, . 





47T — 



M 



. . (131) 

 so that in this case the obstacle produces no effect at all. 



Circular Aperture in Conducting Screen. 



The problem proposed is the incidence of plane waves 

 (h = e ikx ) upon an infinitely thin screen at.a?=0 endowed with 

 perfect electric conductivity and perforated by a circular 

 aperture. In the absence of a perforation there would of 

 course be no waves upon the negative side, and upon the 

 positive side the effect of the screen would merely be to 

 superpose the reflected waves denoted by h =—e~ ikx . We 

 wish to calculate the influence of a small circular aperture of 

 radius R. 



In accordance with the general principle the condition of 

 things is determined by what happens in the neighbourhood 

 of the aperture, and this is substantially the same as if the 

 wave-length were infinite. The problem is then expressible 

 by means of a common potential. The magnetic force at a 

 distance from the aperture on the positive side is altogether 

 87rV, and on the negative side zero ; while the condition to 

 be satisfied upon the faces of the screen is that the force be 

 entirely tangential. The general character of the flow is 

 indicated in fig. 1. 



The problem here proposed is closely connected with those 

 which we have already considered where no infinite screen 

 was present, but a flat finite obstacle, which may be imagined 

 to coincide with the proposed aperture. The primary 



