332 Mr. 0. Heaviside on the Electromagnetic Efects due 



by (27), if /a = cos 6. Performing the differentiation, and also 

 getting out E the tensor of the electric force, we have the final 

 result that the electromagnetic field is fully given by* 



with the additional information that E is radial and H circular. 

 Now, as regards ^, if we bring it in, we have only got to 

 take it out again. When the speed is very slow we may 

 regard the electric field as given by — V^ jo/ms a small cor- 

 recting vector, which we may call the electric force of inertia. 

 But to show the physical inanity of ^, go to the other extreme, 

 and let u nearly equal v. It is now the electric force of inertia 

 (supposed) that equals +V^ nearly (except about the equa- 

 torial plane), and its sole utility or function is to cancel the 

 other — V"^ of the (supposed) electrostatic field. It is surely 

 impossible to attach anj^ physical meaning to ^ and to pro- 

 pagate it, for we require two ^'s, one to cancel the other, and 

 both propagated infinitely rapidly. 



As the speed increases, the electromagnetic field concentrates 

 itself more and more about the equatorial plane, 6 = ^tt. To 

 give an idea of the accumulation, let ^^^/^?^ = •99. Then cE is 

 •01 of the normal value q/r'^ at the pole, and 10 times the 

 normal value at the equator. The latitude where the value is 

 normal is given by 



i/=(v/m)[1-(1-w>2-)§P (^30) 



12. When u = v, the solution (29) becomes a plane electro- 

 magnetic wave, E and H being zero everywhere except in the 

 equatorial plane. As, however, the values of E and H are 

 infinite, distribute the charge along a straight line moving in 

 its own line, and let the linear-density be q. The solution is 

 then t 



, 'K=:Elcv=2qv/r (31) 



at distance r from the line, between the two planes through 

 the ends of the line perpendicular to it, and zero elsewhere. 



To further realize, let the field terminate internally at r=a, 

 giving a cylindrical-surface distribution of electrification, and 

 terminate the tubes of displacement externally upon a coaxial 

 cylindrical surface; we then produce a real electromagnetic 

 plane wave with electrification, and of finite energy. We have 

 supposed the electrification to be carried through the dielectric 

 at speed v, to keep up with the wave, which would of course 



* ( 

 t 



.„„j^ —^ — ..„._, 



' Electrician,' Dec. 7, 1888, p. 148. 

 Ibid. Nov. 23, 1888, p. 84. 



