Transmission of Electric Waves along Wires. 391 



where 



™__ "1 k "| 



~~ i_ r a — jj (sin 2t — r 2 sin 2i — 2/e), 



and ^ (5?) 



G = 5 * { iZ^s - J} (sin 2t + 2« -»- 2 sin 2t + 2«-2*), | | 



/o and t being defined by (55). 



62. It is to be noted that these formulae in two respects 

 over-correct the original approximate expressions. First, they 

 assume that the trigonometrical coefficient of the exponential 

 term is a maximum for every successive incidence; and second, 

 they assume that for each condenser t+ @ =0, which necessi- 

 tates a different t for each case, whereas the wave-train 

 launched along the line must have the same shaped head in 

 each case. Thus the truth on the long-wave theory may be 

 expected to lie between the values given in the first and third 

 columns of Table XI. 



63. In comparing the experimental values with the theory, 

 the following points may be noted : — 



(1) In one case (in Table XI.) experiment and theory give 

 identical values (last line). 



(2) In two cases the theory seems over-corrected (lines 

 1 & 5) . 



(3) In three cases the correction to the theory fails to bring 

 the values down to those experimentally determined. 



(4) Hence the outstanding discrepancy is on the side of 

 slightly less reflected and les> transmitted than theory 

 predicts, though further experiments under a greater 

 variety of conditions would be needed to establish this 

 view of the case. 



(5) Turning now from the question of the amplitudes of 

 the reflected and transmitted waves to that of the phase- 

 change, a, introduced on reflexion, we see from rigs. 9, 

 10, & 11 that the theoretical and experimental results 

 aie in fair agreement. 



2 E 2 



