STEADILY ALTERNATING CURRENT ON A LONG LINE. 363 



the load a, as developed at P, will be the same, after the passage of 

 the ^th reflected wave of voltage and current, as in the final steady 

 state or 



Zpj. = Y^ = Zo tanh 8p = Zp^ = constant ohms Z . (37) 



It is here assumed that the ^th reflection of voltage from B has 

 passed P, and also the ^th reflection of current, as the two are, in 

 general, dephased by a definite amount. 



It may be noted that when, as in Fig. 9, the current is observed 

 at the A end of the line, the oscillogram includes, with the ^th re- 

 flection from B, the (fe + i)th outgoing wave from A. The point 

 P of observation would have to be shifted to a suitable distance from 

 A, in order to separate these two impulses. Consequently, when 

 summing up the growth of current at A, the (fe-l-i)th outgoing 

 wave must be added to Ip . This increment is 



I'aic = h{n - i)^e-''"^ = /oe-'*^^ max. cy. amperes Z . (38) 



The accompanying Table V. shows the successive values of the 

 growth coefficient w for the artificial line under test from ^=1 to 

 k=i2, inclusive, both for voltage at B and current at A. 



The vector diagram of Fig. 15, shows the planevector increase 

 of voltage at B and current at A for the case represented by the 

 oscillogram. Fig. 9. The voltage Oa = 239.7 V93°.33' and is the 

 first wave at B, including immediate reflection there. The angle 

 A''Oa = 93°.33', or OX, represents the standard phase of impressed 

 e.m.f. at A.. If the Hne had been of exactly a quarter wave-length, 

 this angle XOa would have been reduced to just one quadrant. 

 This wave Oa commences to arrive at B, 4.3 milliseconds (93° -55 

 electrical degrees on a 60.6 ^ circuit) after closing the switch at A. 

 The second wave reflection at B will commence to develop after 

 the outgoing wave has run three times over the line {AB, BA, AB), 

 or a total lapse of 12.9 milliseconds after switch closing. Its vector 

 value in the Table is 172.0 V 100°. 37' and it is represented by ab 

 in Fig. 15. 



