IV. The Diffraction of Electric Waves Round a Perfectly Reflecting Obstacle. 



By H, M. MACDONALD, F.R.S., Professor of Mathematics in the 

 University of Aberdeen. 



Received August 13, Read November 4, 1909. 



IN a previous communication*" it was verified that the effect at a point on a perfectly 

 conducting sphere due to a Hertzian oscillator near to its surface was negligible in 

 comparison with the effect that would have been produced at that point but for the 

 presence of the sphere, when the point is at some distance from the oscillator and the 

 radius of the sphere is large compared with the wave length of the oscillations. In 

 what follows it is proposed to find the effect at all points produced by a Hertzian 

 oscillator placed outside a conducting sphere whese radius is large compared with the 

 wave length of the oscillations. For simplicity the axis of the oscillator will be 

 assumed to pass through the centre of the sphere, but this assumption will not 

 affect the generality of most of the results. An Appendix is added in which the 

 more important mathematical relations required are established. 



1. Let O be the centre of the conducting sphere of radius a, and let the oscillator 

 be at a point O 1( the direction of the axis of the oscillator being OCX, and the distance 

 i being r t . In this case the lines of magnetic force are circles which have the line 

 for common axis. If y denotes the magnetic force at any point P, p the 

 distance of P from 00^ and z the distance of P from the plane through 

 perpendicular to 00^ yp satisfies the differential equation 



(7p} ~ - ~ (yp}+ 



where 2-ir/K is the wave length of the oscillations. Ti^ansforming to polar co-ordinates 

 (r, 6), where r is the distance OP and 6 the angle P00 1; z = r cos 6 and p = r sin Q ; 

 hence, writing cos 6 = //., the differential equation becomes 



* 'Roy. Soc. Proc.,' vol. 72 (1904), p. 59. 

 VOL. COX. A 462. Q 28.2.10 



