422 Mr. 0. Heaviside on the 



nary conductor. Similarly, if the line consist of a single wire 

 whose circuit is completed through the earth, by regarding it 

 as infinitely conducting we replace the true variably distri- 

 buted re turn- current by a surface-current, and, terminating 

 the magnetic field there, have L 8 = v~ 2 ; but if we allow the 

 magnetic field to extend into it, though with insignificant loss 

 of energy by electric current, we shall no longer have this 

 property. 



The property is intimately connected with the influence of 

 perfect conductivity on the state of the dielectric. For per- 

 fect conductivity will make the lines of electric force normal 

 to the conducting boundaries, will make them cut perpendi- 

 cularly the magnetic-force lines, which lie in the planes z = 

 const, and are tangential at the boundaries, and will make 

 L S = -y -2 , irrespective of the shape of section of the conduc- 

 tors. Now, at the first moment of putting on an impressed 

 force, wires always behave as if they were infinitely conducting, 

 so that, by the above, the initial effect is simply a dielectric 

 disturbance, travelling along the dielectric, guided by the 

 conductors, with velocity v, irrespective of the form of sec- 

 tion. Of course dissipation of energy in the conductors 

 immediately begins, and finally completely alters the state 

 of things, which would be, in the absence of dissipation, 

 the to-and-fro passage of a wave through the dielectric for 

 ever. Except the extension to other than round conductors, 

 this does not add to the knowledge already derived from their 

 study. The effect of alternating currents in tending to become 

 mere surface-currents as the frequency is raised (Part I.) 

 may be derived from, or furnish itself a proof of, the property 

 above mentioned — that at the first moment there is merely a 

 dielectric disturbance. For in rapid alternations of impressed 

 force, we are continually stopping the establishment of the 

 steady state at its very commencement and substituting the 

 establishment of a steady state of the opposite kind, to be itself 

 immediately stopped, and so on. 



When the dielectric is unbounded, not enclosed within 

 conductors, there is also the outward propagation of disturb- 

 ances to be considered; but it would appear, by general 

 reasoning, that this is, relatively to the main effect, or propa- 

 gation parallel to the wires, a secondary phenomenon. 



It is clear that the same principles apply to conductors 

 having other forms of section than circular, when V and 

 are made the variables, provided the functions E/' and K/ 

 can be properly determined. The quantity VC being in all 

 cases the energy-current, its rate of decrease as we pass along 

 the line is accounted for (as in Part III.), thus, by making 



