STEADILY ALTERNATING CURRENT ON A LONG LINE. 345 



age at A, owing to the fact that the hne AB is nearly of quarter- 

 wave length.'' 



In a similar manner, the successive currents and reflections at A 

 are indicated by the vectors OA, AB, BC, etc., together with the 

 successive vector sums OA, OB, OC, etc., as far as the thirteenth 

 wave inclusive, when the final steady state is nearly reached. 



We should therefore expect that the voltage at B would, in 

 the first wave, attain the crest value Oa, in the next reflection the 

 crest value Oh, in the next following reflection Oc, and so on. A 

 comparison between the observed and computed waves is given 

 graphically in Fig. i6. Here the upper line of waves deals with the 

 sending-end current, the middle series with the impressed voltage, 

 and the lowest series with the voltage at B. Referring to the latter 

 series, the successive reflected voltage waves Oa, ah, he, etc., of Fig. 

 15, are marked with the numerals I., II., III., etc., in Fig. 16, and 

 these are superposed, by point to point addition, in the heavy wavy 

 line No. i. No. 2, No. 3, etc. This heavy wave is the computed 

 resultant regular transient of c,-. If there were no errors in the 

 assumptions or mode of computation, the oscillogram of er should 

 coincide with this line. The oscillogram of e,- in Fig. 9 actually 

 does coincide very nearly with this theoretical line, the small deriva- 

 tions therefrom being indicated at the crests of the first few waves. 

 Thus, at the crest of wave No. 3, the computed maximum value is 

 531.9 volts; whereas the oscillograph shows 539 volts, a deviation of 

 1.3 per cent. This is the largest discrepancy detected between the 

 observed and computed values of er. We are, therefore, entitled to 

 conclude that in the case of this artificial line, with the switch closed 

 splashlessly, the lumpiness of the line had very little effect upon 

 the voltage at the distant free end. 



Referring to the upper line of waves is in Fig, 16, the same 

 procedure has been followed. The heavy line is the sum of the 

 reflected waves, according to the vector sums OA, OB, OC, of Fig. 

 15. This heavy wavy line is, therefore, the theoretical summation 



9 If the line had been freed at B, instead of being grounded through the 

 oscillograph of 9900 ohms, the final voltage £ at 5 would have been in- 

 creased from E X 5-63Viio° 36' to E X 6.82^7116° 20', and the transient 

 e.m.f. waves would also have been materially modified. 



