518 Dr. J. W. Nicholson on the Bending of 



further the special case of diffraction round the surface of a 

 large sphere. The type of analysis is suitable for all problems 

 of diffraction by large obstructing spheres or circular cylin- 

 ders, with other forms of less importance. Many portions 

 of the analysis are applicable without change to a large class 

 of problems. 



The harmonic series for an oscillator in the presence 

 of a sphere. 



Let C be a radial oscillator in the presence of a sphere of 

 centre 0, where 00 = ^. OC may be taken as axis of z in 



a system of cylindrical polar coordinates, the distance of a 

 point P from the axis being p, and its spherical polar co- 

 ordinates (r, 6, <f>). Let CP = E. 



By considerations of symmetry, the magnetic force in the 

 combined system is distributed in circles having OC for their 

 common axis. Let 7 be its value at P. The magnetic force 

 7i due to the oscillator alone is 



7i = 



dp H 



(i) 



where the strength of the oscillator is unity, and the time 

 factor is ignored. 



But 7 must be a solution of the equation 



where 2tt/k is the wave-length of the oscillation. 



(2) 



Writing 

 Then 



Thus 



fj,= cos 0, p = r sm0, z = r cos 0. 



(V 



\Br 2 



1-/* 2 a 2 



r 2 3 M 2 



+ K>)yp = 0. 



yp = r* sin 2 6 2 j A n J m ( K r) + B«J_ TO (*r) }^ 

 where m = n + ^. 



dfi 



(3) 



