352 On the Self-induction of Wires. 



Now to make some remarks on the impossibility of joiir'ng 

 on terminal apparatus without altering the normal functions, 

 the terminal arrangements being made to impose conditions 

 of the form V = ZC. It is clear, in the first place, that if the 

 quantity VC at z=0 and z=.l really represents the energy- 

 transfer in or out of the line at those places, then the equation 



A,= 



Uqi— T l 



will be valid, provided u and iv be the correct normal func- 

 tions. But to make VC be the energy-transfer at the ends 

 requires us to stop the longitudinal transfer in the conductors 

 there, or make the current in the conductors longitudinal. 

 This condition is violated when the current function w is pro- 

 portional to cos (mz + 6), as in the previous, except in the 

 special cases, because the radial current y in the conductors is 

 proportional to sin (mz + 0), and 7 has to vanish. Not in the 

 dielectric, but merely in the conductors. 



We can ensure that VC is the energy-transfer at the ends 

 by coating the conductors over their exposed sections with 

 infinitely conducting material and joining the terminal appa- 

 ratus on to the latter. The current in the conductors will be 

 made strictly longitudinal, close up to the infinitely conducting 

 material, and y will vanish in the conductors. But 7 in the 

 dielectric at the same place will be continuous with the radial 

 surface-current on the infinitely conducting ends, due to the 

 sudden discontinuity in the magnetic force. Thus the energy- 

 transfer, at the ends, is confined to the dielectric. 



It is clear, however, that the normal current-functions in 

 the two conductors must be such as to have no radial compo- 

 nents at the terminals, so that they cannot be what have been 

 used, such that d 2 /dz 2 = constant. They require alteration, of 

 sensible amount may be, only near the terminals, but theore- 

 tically, all along the line. It would therefore appear that only 

 the five cases of V = at either or both ends, or C = ditto, 

 or the line closed upon itself, admit of full solution in the 

 above manner. The only practical way out of the difficulty 

 is to abolish the radial electric current in the conductors, 

 making (66) the equation of V, and VC the longitudinal 

 energy-transfer, with full applicability of the V = ZC terminal 

 conditions. With a further consideration of this system, and 

 some solutions relating to it, I propose to conclude this paper. 



