Transmission of Electric Wares alone/ Wires. 361 



end; alternated with (2) electrometer-readings with a con- 

 denser on the line at an intermediate position, as well as the 

 absorbing-bridge at the end. The mean ratio of the readings 

 under the different conditions constitutes the experimental 

 estimate of the effect produced by the condenser in question 

 when in that position. 



12. In order, however, to interpret the experimental results 

 and compare them with theory, we need to trace the history 

 of the wave-train reflected by the condenser until it is, 

 practically, extinguished by its losses through repeated re- 

 flexion and attenuation. The effect at the electrometer when 

 no condenser is on the line may be represented by a single 

 time-integral which, without sensible error, owing to the 

 damping of the wave-train, may be taken from the com- 

 mencement of the time to infinity. The effect at the 

 electrometer when a condenser is on the line requires, how- 

 ever, an infinite series of integrals. 



13. To construct this series we must first determine the 

 various elements of which it consists. We must accordingly 

 treat the case of a condenser on the line, not at the end. This 

 will be referred to as an intermediate condenser. We have 

 here to determine the coefficients of reflexion and transmission 

 and the phase-lags of both the reflected and transmitted 

 portions. The c<ise of a terminal condenser must also be 

 treated, since the oscillator at the beginning of the line falls 

 under this category. Here, only two constants are required, 

 the amplitude and phase of the reflected portion. These 

 points will now be dealt with in order, together with subsidiary 

 matters that crop up by the way and are included for the sake 

 of completeness. 



14. We shall treat the circuit throughout as what Mr. 

 Oliver Heaviside terms a " distortionless circuit/'' not that it is 

 strictly distortionless, but because it is very nearly so ; and this 

 treatment, while sacrificing nothing of material accuracy, 

 considerably simplifies the analysis. Prof. W. B. Morton* 

 has shown that for the circuit in question the errors thus 

 involved are less than one in a thousand. 



15. Intermediate Condenser. — At the place of attachment 

 of the condenser let <p x denote the potential-difference of the 

 two wires of the line due to the arrival there of the incident 

 wave-train. Then <£ x is a function of the time. Similarly 

 let <j>' and <f> 2 correspond to the reflected and transmitted 

 wave-trains respectively. Then by consideration of potential 

 and Heaviside's theory of the distortionless circuit, assumed 



* Phil. Mag., March 1899. 



