Transmission of Electric Waves along Wires, 367 



present experimental case, Lu = 56 x 10 10 and p = 2 X 10 8 in 

 the same units. Hence ^ / =L«S / j p = *037, a=— 00035, 

 a / =--OLiS and A 2 = a 3 + a' 2 = -00036. 



Thus the energy rctlected by the electrometer is of tho 

 order 0'04 per cent, of that incident upon it, and is therefore 

 quite negligible. 



23. Intermediate Resistance. — It seems desirable for the 

 purpose of contrast with the reflexion from a condenser to 

 consider now that of an intermediate resistance. In this case 

 the phase-change introduced does not vary with the amplitude 

 coefficient. But, however the resistance is varied, the phase- 

 change introduced in the reflected wave-train remains con- 

 stant and equal to a lag of it. 



24. Thus, using the same notation as before, we have the 

 following equations as the conditions connecting potential- 

 difference and current where a bridge of resistance W is 

 placed on the line, the line being understood to extend 

 beyond it. 



01-+ 0' = ^!, 



h = 0i/Lw, 

 » V =-07L». 



ii + i'— tj=0j/ii'. 



Whence, on elimination of the z's, we obtain 



and -T- = 



0! ~ 211' + Lv fa ~ 2 It' + Lv ' 



25. Or, we may say that if the incident wave-train be 

 a cosine function of the time, damped or not, the reflexion- 

 coefficient and phase-change are respectively 



A -"W+1S' and a ' = -' K - ' ' (11) 



Similarly, the amplitude-coefficient and phase-change for the 

 transmitted wave-train are seen to be respectively 



B -2TOT»' and *-°- • • • < 12 > 



26. Terminal Condenser. — Let the capacity of the con- 

 denser at the end of the line be S , the previous notation for 

 incident and reflected waves &c. being retained. We then 



