STEADILY ALTERNATING CURRENT ON A LONG LINE. 359 



so that in terms of m, 



n = 2 — m numeric Z (27) 



and 



n — 1 = 1 — m numeric Z (28) 



These rules are of general application, and may be thus ex- 

 pressed. The sum of the voltage and current transmission coeffi- 

 cients at a junction point in a line is equal to 2. The two reflection 

 coefficients have the same size, but have mutually opposite signs. 



Appendix II. 



On the Case of Line AB Connected as in Fig. i, and Oscillographed 



as in Fig. p (Film No. 40), zvith 100 Volts R.m.s. Sinusoidal, 



Impressed at A, zvith Negligible Splash and Negligible 



Luynpiness Transient. 



Taking the tabulated constants of the artificial line from Table 

 II., the impedance of the oscillograph load at B was (7 = 9900 Z o" 

 ohms. The angle 8^ subtended by this load 



, . 9900 Z 0° I • O U 



= tanh-^ o / = 0.03451 +J O.9983 hyp. 



This is the position angle 8^ of the end B of the line in the steady 

 state. The position angle of the A end is Z^=^6 -{-hj. =^ 0.1660- 

 + y 2.o393 hyps. 



The e.m.f. at B in the final steady state with 141. 4 Z 0° max. 

 cyclic volts at A will be 



sinh (0.03451+ 70-9983 ) „ , , 



Eb= 141. 4 Z 0° X . , , — 77 — r~- r = 795-8^ iio°36'volts.- 



^ ^ smh (0.1660 -|-j 2. 0393 ) 



Similarly, the sending-end final current at A in the steady 

 state is 



Ea i4i.4Zo° 



7- = '::l^ = 



^ 2o tanh 5^ 342.5 \ 4° 24' X 0.17571 Z 20° o' 45" 



141. 4 Z o*^ 



60.180 Z 15° 36' 45 



7, = 2.350 \ 15° 36 '45" amperes. 



