360 KENNELLY-NABESHIMA— ESTABLISHING A 



Comparing these values with those taken from the oscillograph 

 Fig. 9, jEr = 796 v iio° max. cyclic volts, and /s = 2.35 vi5° max. 

 cy. amperes. This agreement is satisfactory, and is even closer 

 than the interpretation of the oscillograph record would warrant. 

 The width of the curves in Fig. 9 is greater than in subsequent 

 oscillographs, when the optical technique had been improved ; so 

 that the precision of measurement in Fig. 9 is somewhat below that 

 later attained. 



It is shown in Appendix /, that with a given load of o- vector 

 ohms, applied at 5 to a single smooth line, with a sinewave of unit 

 maximum e.m.f. applied splashlessly at A, the voltage wave at a 

 point P on the feth reflection from the B end, is 



— (i — w)''e~^'*^"^'^ max. cy. volts Z, (29) 



where m is the transmission coefficient to a voltage wave arriving 

 at B, 6 is the angle subtended by the line, and 9' the angle from A 

 to the selected point P. This expresses both the size and slope of 

 the feth return wave at P, with respect to unity size and zero slope, 

 or standard voltage phase, at A. 



The summation of all the e.m.f. waves arriving at the point P, 

 including the ^th reflected wave from B, is also shown to be 



sinh hp , „,.. , sinh 5^ i-r - ■, ■, ^ 1 , / n 



-_^(i_g-2is^) =^-^-— ^.2e-^^'ismh^54 max. cy. volts Z . (30) 

 smh Oa smh Oa 



But the final steady voltage at P is (sinh 8p)/(sinh 8.,) volts Z ; so 

 that the summation to the feth return wave at P, inclusive, is equal 



to the final voltage multiplied by the vector " growth coefficient " 



w = I — e""*^-^ = 26"'^"^^ sinh UIa numeric Z . (31) 



If, then, we denote the final max. cyclic voltage at P by Ep^ vector 

 volts, the corresponding maximum cyclic voltage at an intermediate 

 period, after the arrival of the ^th return wave from B, and before 

 the arrival of the next following incoming wave from A, is 



'Epk = -Epot 'IV max. cy. volts Z . (32) 



