STEADILY ALTERNATING CURRENT ON A LONG LINE. 353 



namely, (i) the phase angle oit, which increases uniformly with t, 

 the time elapsed from switch closure; (2) the angle 9^, 3^,) 5^2> etc., 

 which is a multiple of the circular angle 9^ subtended by the line, 

 and is the phase delay due to i, 3, 5, etc., wave passages over the 

 line; (3) the slope of the vector coefficient m, m(i — m), etc., which 

 takes into account the change of phase in the voltage wave due to 

 reflections. The scalar sum of the terms in (i8a) agrees at any 

 instant with the projection on OX in Fig. 17. 



Summary. 



1. Oscillographic measurements over a lumpy artificial power- 

 transmission line in the laboratory, are reported for certain initiating 

 wave transients. The technique is described. One of these oscil- 

 lographs is analyzed, and compared with the elementary theory of 

 steady-state attainment. The discrepancies between the observed 

 and computed values are negligible for the voltage waves at the 

 receiving end of the line. They are distinct, but not very serious, 

 for the outgoing current waves at the sending end. 



2. A lumpy artificial line can be used for the measurement of 

 initiating a.-c. wave transients, if an automatic circuit-closing switch 

 is set to connect the generator to the line at a moment of zero e.m.f . 



3. A provisional classification of transients is ofifered. Particu- 

 lar cases of splash transients, lumpiness transients, casual transients, 

 and regular initiating transients are offered, from experimental 

 observations. 



4. The growth factor of a regular series of transients is analyzed 

 for any point P in a single line loaded at the receiving end. This 

 growth is a discontinuous function of time, its increase occurring by 

 little vector jumps. The envelope of the growth-factor vector is 

 an equiangular spiral. The growth factors for current and voltage 

 are the same. 



5. The transitory impedance at and beyond any one point on a 

 line such as is described, is constant at successive B reflections, after 

 the first reflection from B, and is equal to the impedance at that 

 point in the final steady state. 



6. The position angle of the B end of a loaded line in the steady 



