﻿50 Dr. J. G. Leathern : Effect of a Long 



of the differential equation 



Of course g(x) and h(x) can differ from BesseFs functions 

 only by constant factors, but we can use them without any 

 knowledge o£ the formulae expressing properties of Bessel's 

 functions ; our great gain in simplicity depends upon our 

 recognizing the fact that it is unnecessary to evaluate the 

 constants A and B. 



3. Transmission of Waves by a Single Wire. 



Cylindrical coordinates r, 0, z are employed, the surface 

 of the wire is taken to be r=a, the specific resistance and 

 the magnetic permeability of the material of the wire are 

 represented by a- and //, respectively, the dielectric is supposed 

 to be non-magnetic and to have specific inductive capacity K, 

 the velocity of radiation in free sether is denoted by c, that 

 in the dielectric by v, the electromagnetic system of units is 

 used, and the displacement current in the wire is neglected. 

 The magnetic force is in circles round the axis of z and is 

 denoted by w, the electric intensity is in planes through the 

 axis of z, and has components R parallel and P perpendicular 

 to that axis. Suffixes (]) and ( ) refer to the metal and to 

 the dielectric respectively. 



From the equations of the electromagnetic field the follow- 

 ing facts are deduced in the usual manner, it being assumed 

 that all components of electric and magnetic intensity depend 

 on the time t and on z only through the factor eK mzJ \-vt) . 



_^KdR p _^ IW^Rq 



Vo -cWlJr~' ~""^lW 



Or 2 r or 

 where tc 2 = m 2 — Kp 2 /c 2 = m 2 —p 2 /v 2 ; 



_ 4-7T BR-x p_ im'd'Ri 



Or* r or 



> • • (3) 



« 



wh ere n 2 — m 2 + ATr/tip/a, 



= 4z7r(jLip/o~ very approximately for 

 oscillations less rapid thau those of light. 



