STEADILY ALTERNATING CURRENT ON A LONG LINE. 361 



The growth coefficient w is not a continuous function of time. It 

 increases by a sudden jump at each moment when a new reflected 

 wave arrives. The size of iv is zero up to the time when k^i, 

 and attains unity when k= cc, but it may exceed unity during the 

 process of increase. That is, the max. cychc voltage Ej^h may 

 happen to be greater at some stage of the regular transient state, 

 than in the final steady state. The slope of w may also vary over 

 a considerable range during the period of regular transient growth. 



Similarly, referring to Appendix I., Table IV. shows that the 

 attenuation coefficient of the current wave at a point P on the feth 

 reflection from the B end of the line is 



(n - i)^e-(-'"^-''^ = e-'^-"^^-^'' numeric Z , (33) 



where n is the transmission coefficient of a current wave arriving 

 at B. The summation of all the current waves arriving at the point 

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



cosh^ 

 ^« ^^ cosh 5^^' ' ^ 



cosh 5p _, . 

 = Ia — jT^ * 2e "^ smh k8A max. cy. amperes Z , (34) 



where / , is the max. cy. current at A in the steady state, ordinarily 

 taken to E^^ as standard phase. 



But the max. cyclic current at P in the steady state is known 

 to be 



cosh 8p Ea cosh bp 



Ipx = I A v-T- = — • . , ; , max. cy. amperes Z , (35) 



cosh bA Zo smh Ba 



so that 



Ipk = Ipxii - e-'"'^) = /poc •2e-"'^ sinh k8A 



= IpxW max. cy. amperes Z . (36) 



This means that the growth coefficient Wk, after the passage of the 

 feth reflection back from B, is the same for both the voltage and 

 current at P. It also means that the impedance of the line PB and 



