Transmission of Electric Waves along Wires. 375 



the condenser and oscillator and passed to and fro along 

 the line. 



44. Let curves be imagined with l 2 , the distance between 

 electrometer and condenser, as abscissas, and F, G, and H as 

 ordinates. It is then seen by inspection of (36) that the curve 

 for F is practically a straight line parallel to the axis of 

 abscissas. This was to be expected on physical grounds, for 

 it represents the effect at the electrometer due to all the 

 positively-travelling waves. And they are almost independent 

 of any change in the value of l 2 when that change is small 

 compared with l 1 . 



45. Similarly, on inspection of (37), we see that, apart 

 from the small terms in k and the slight change of r with l 2 , 

 the curve for G is a logarithmically drooping one. But the 

 droop is very slight for s q = A 9 e~ ill ' T . This again is what 

 might be expected from physical considerations, since this 

 term , Gr, is due to the return of the w ave-train reflected at 

 the condenser apart from interference effects. 



4(i. Turning finally to equation (38), we see that the main 

 features of H are those represented by the first term. This 

 term consists essentially of two factors, one exponential and 

 the other trigonometrical. The exponential factor here gives 

 a much quicker droop than that in G, for we now have se~ ke 

 instead of s 2 simply as before. 



47. The essential nature of H will be made clearer if we 

 write the chief parts of its first term in full. Thus 



2Ae-2W cos (%& -a\=h (say). . . (39) 



Let now a curve be plotted with h as ordinates and l 2 as 

 abscissae, and call this the interference curve, since it repre- 

 sents the essential features of the electrometer-throws due to 

 interference of waves reflected by the condenser with those 

 incident upon it. Then by inspection of (39) and comparison 

 with equation (27), representing the incident wave-train, we 

 have the following results : — 



(1) The interference curve is of damped wave-form. 



(2) The wave-length of the interference curve is half that 



of the incident wave-train. 



(3) The logarithmic decrement per wave of the interference 



curve is equal to that of the incident wave-train. 



(4) The amplitude of the interference curve is double the 

 amplitude factor introduced by the condenser on 

 reflexion. 



(5) The phase change exhibited in the interference curve 



compared with the incident wave-train is equal in 

 magnitude but opposite in sign to that introduced by 

 the condenser on reflexion. 

 2 D 2 



