and the Dynamical Theory of Diffraction. 423 



currents are in circles, and magnetic induction in planes 

 passing through the axis. 



Let us consider the first case. We shall find it much more 

 convenient to continue with the imaginary form, remembering 

 that a similar term with i changed in sign is always to be 

 added except where it has already been done. We shall then 

 have : — - 



Components of the vector potential, 



©o= S^T Krc + l)C„_ 1 +nC n+1 ^-™ 



c(2n + l)p < ' 



_ <n + l)C 

 Magnetic induction, 



Components of the electric current, 



\ _ . n(n + 1)0 vt) 



AlTfJU 4:7T/J,p 2 



Components of the electric displacement, 



K d& __ VKsinflQ'» , , - * p , ( W) 



Itt^T" 47r(2^ + l) / >'^ + 1)U - 1+nU+1 ! € ' > 



_ K cffo = YKn(n + l)0 w , } 



4tt eft ' 47rcp 2 Hn ' 



where /jl is the magnetic permeability and K the inductive 

 capacity, and we have the well-known relation of Maxwell, 



V 2 = ~. 



Should a perfectly conducting sphere exist, the electric 

 density on its surface will be 



K d rfM_! K ^P 



4tT/> 2 6^ rf/,6 47T C& 



YKn(n + l)C n o ( vo 

 *~ 4ttc P 2 "^ € 



This is the same as the radial component of the electric dis- 

 placement at this point. 



