444 Mr. 0. Heaviside on Electromagnetic Waves, and the 



tube. The wave-length must be great in order to render it 

 applicable to a wire, because instantaneous penetration is 

 assumed. 



I mentioned that s/y must vanish. This occurs when y=i, 

 or the external dielectric is boundless. But it also occurs 

 when E = at r = x, produced by a perfectly conductive 

 screen. This is plainly allowable because it does not interfere 

 with the E = all over property. What the screen does is 

 simply to terminate the field abruptly. Of course it is 

 electrified. 



58. 5 = and H z = 0. — But with other boundary conditions, 

 we do not have the solutions (331). Thus, let H* =0, instead 

 of E z =0. This makes y = J Xx /G lx in (317), (318). There 

 are at least two ways (theoretical) of producing this boundary 

 condition. First, there may be at r = x a screen made of a 

 perfect magnetic conductor (c/ = ^> ) . Or, secondly, the whole 

 medium beyond r — x may be infinitely elastive and resistive 

 (c = 0, k = 0) to an infinite distance. 



Now choose s = in addition and reduce (317), (318). 

 The results are 



E= e p = _!*5 , l 



l+±x*ep/£7rKa' ~ cp dz 



K332) 

 . TT cpe (r r x 2 \ 



(in) or (out) H ^ - 1 + ^j^Ka \i ° T 2 " %r )' J 



which are at once realized by removing p from the denomina- 

 tor to the numerator. 



Although E is not now zero, it is independent of r, only 

 varying with t and z. 



When s 2 is negative, or n<m/v, the solutions (317), (318) 

 require transforming in part because some of the Bessel 

 functions are unreal. Use (312), because q is now real. 

 There are no alternations in E or H along r. They only com- 

 mence when n>mv. 



59. Separate actions of the two surfaces of curl e. — Since all 

 the fluxes depend solely upon the curl of e and not upon its 

 distribution, and there are two surfaces of curl e in the tube 

 problem, their actions, which are independent, may be 

 separately calculated. The inner surface may arise from e in 

 the — direction in the inner dielectric, or by the same in the 

 + direction in the tube and beyond it. The outer may be 

 due to e in the — direction beyond the tube, or in the + 

 direction in the tube and inner dielectric. 



We shall easily find that the inner surface of curl of e, say 

 of surface density f ly produces 



