334 Mr. 0. Heaviside on the Electromganetic Ejects due 



in telephony through circuits of low resistance and large in- 

 ductance, there may be a wide difference between my V and 

 that of the electrostatic force. Consider, for instance, the 

 extreme case of an isolated plane-wave disturbance with no 

 spreading-out of the tubes of displacement. At the boundaries 

 of the disturbance the difference between V and the electro- 

 static difference of potential is great. 



But it is worth noticing, as a rather remarkable circum- 

 stance, that when we derive the system (32) by elementary 

 considerations, viz. by extending the diffusion-system by the 

 addition of the E.M.F. of inertia and leakage-current, we 

 apparently as a matter of course take V to mean the same as 

 in the diffusion-system. The resulting equations are correct, 

 and yet the assumption is certainly wrong. The true way 

 appears to be that given by me in the paper last referred to, 

 by considering the line-integral of electric force in a closed 

 curve. We cannot, indeed, make a separation of the electric 

 force of inertia from — A^ without some assumption, though 

 the former is quite definite when the latter is suitably defined. 

 But, and this is the really important matter, it would be in 

 the highest degree inconvenient, and lead to much complica- 

 tion and some confusion, to split V into two components, in 

 other words, to bring in "^ and A. 



In thus running down ^, I am by no means forgetful of 

 its utility in other cases. But it has perhaps been greatly 

 misused. The clearest course to pursue appears to me to 

 invariably make E and H the primary objects of attention, 

 and only use potentials when they naturally suggest them- 

 selves as labour-saving appliances. 



13. Returning to the solutions (29), the following are the 

 special tests of their accuracy. Let Ej and Eg be the z and 

 h components of E. Then, by (11) and (13), with the special 

 meaning assumed by p, we have 



1 d j^ dE^ 



^ -77 /lli= —CU—:j—} 



li dli dz 



^^ = -cu'^, orH=c«E2, } (33) 



dz dz 



rfEi d'E>^_ dH dE^_f u^\dE^ 



-dh~'d^~~^''^^' '"'"'dh-V'v'j-dr' 



In addition to satisfying these equations, the displacement 

 outward through any spherical surface centred at the charge 

 may be verified to be 2- ; this completes the test of the accu- 

 racy of (29). 



