348 KENNELLY-NABESHIMA— ESTABLISHING A 



ported by other cases, so far as they have been examined ; namely, 

 that at the impressed frequency of 60'~', nearly sinusoidal, if the 

 voltage is impressed without splash at an instant of zero e.m.f., 

 the artificial line behaves substantially like its conjugate smooth line, 

 the greatest discrepancy being in the current-wave transient at the 

 sending end. Consequently, any similar artificial line of. a like 

 degree of lumpiness, should be available, in the laboratory, for the 

 study of initiating and casual a.-c. wave transients. 



Arrival Times. — The apparent velocity of transmission of an 

 a.-c. wave over an artificial line subtending an angle of ^ = ^i + JO2 

 hyps radians Z , at a given impressed frequency / — ■ is^° 



Leo km. 



' = -K sec:' ^4) 



where L is the length of the line in kilometers. This velocity is the 

 " group velocity " of the waves at this frequency. For the artificial 

 line considered, at 60.6 '—', z'=: 292,300 km./sec. It tends to reach 

 the limit 300,000 km./sec. at very high frequencies, in air. 



The number of single passages, or single transits, of the wave 

 over the line per second, is 



V 0) numeric 



In the case of this line at 60.6'—', n = 232.9 transits per second. 

 The transit time T, or time interval of a single passage over the 

 line, from one end to the other, is* 



T = - = — seconds. (6) 



n CO 



In the case to which Fig. 9 refers, ^0 = 1.041 quadrants, and 

 (0 = 60.6X4 = 242.4 quadrants per second. Hence, 7 = 0.004295 

 second, or nearly 4.3 milliseconds. At a point P, whose angular 

 distance from the ends A and B are 0' = 0^' + jd.' and 9" = Q^' 



10 Bibliography 30, p. 283. 

 * Bibliography 30, p. 283. 



