Damped Electrical Oscillations along Parallel Wires. 297 



by supposing sufficient leakage to counteract the distortion 

 produced by the resistance of the leads, whereas in Dr. Barton's 

 circuit the leakage was negligible. 



It is probable that the nearness of the wires has an appre- 

 ciable effect on the phenomenon. The discrepancy would be 

 diminished if the actual resistance of the wires was greater 

 than that calculated by Dr. Barton from Lord Rayleigh's 

 high-frequency formula. Now the effect of the neighbourhood 

 of two wires carrying rapidly oscillating currents in opposite 

 directions is to make the currents concentrate towards the 

 inner sides of the wires*; and this would cause an increase 

 in the effective resistance. 



I have examined the effects of (2) and (3), viz. of the 

 damping and the want of balance in the constants of the 

 circuit. The investigation is perhaps of some interest owing 

 to the fact that these elements are always present in the 

 ordinary experimental conditions ; although, as will be seen, 

 we are led to the conclusion that in all actual cases their in- 

 fluence on the phenomena is of quite negligible order. The 

 method is the same as that used by Mr. Heaviside. 



General Theory. — Let the inductance of the circuit be L, its 

 capacity 8, its resistance (of double wires) R, and its leakage- 

 conductance K, all per unit length. An important part is 



played by the ratios j- and -^ ; we shall call these p and cr. 



When p and a are equal we have the " distortionless " circuit 

 above referred to. 



Now if V be the difference of potential between the wires 

 and C the current in the positive wire, we have the equations 



-S=( R+I 4) C > « 



-§=(*<>> w 



giving 



since LSt> 2 =^l, where v is the velocity of radiation. 

 To simplify the algebra we shall work first withV= Y Q e~ mz+ni . 



* Cf. J. J. Thomson, ' Recent Researches/ p. 511. 



