228 Prof. 0. J. Lodge on the Theory 



These are equations to wave-propagation, and will give 

 stationary waves in finite wires of suitable length, supplied 

 with an alternating impressed E.M.F. 



The solution for a long wire, for the case when r x is small 

 and the frequency big *, is 



V=V <fS* cos 72 (*—) .... (18) 

 where r x , 1 



The velocity of propagation is therefore n h and the wave- 



, , . 27m, 

 len £tn is - — * . 



Now T , for two parallel wires as in the figure, 



h = 4;fj, log- + ^, 



and K 



4 log — 



while ri = the geometric mean between its ordinary value 

 and \ n/n ; 

 where the /ju and K refer to the space outside the substance 

 of the wires, /ul refers to their substance, a is their sectional 

 radius, and b their distance apart. 



The second term of l x is, we have seen, practically zero for 

 these high frequencies. Hence (n x ) the velocity of propagation 

 of condenser-discharges along two parallel wires is simply 

 the velocity of light, the same as in general space ; because 



The pulses rush along the surface of the wires, with a 

 certain amount of dissipation, and are reflected at the distant 

 ends; producing the observed recoil kick at B. They con- 

 tinue to oscillate to and fro until damped out of existence by 

 the exponential term in (18). The best effect should be 

 observed when each wire is half a wave-length, or some 

 multiple of half a wave-length, long. The natural period of 

 oscillation in the wires will then agree with the oscillation- 

 period of the discharging circuit, and the two will vibrate in 

 unison, like a string or column of air resounding to a reed. 



Hence w r e have here a means of determining experimentally 

 the wave-length of a given discharging circuit. Either vary 

 the size of the A circuit, or adjust the length of the B wires, 



* Mr. Heaviside lias treated the problem in a much more general 

 manner, see Phil. Mag. 1888, especially February 1888, p. 146. 



