STEADILY ALTERNATING CURRENT ON A LONG LINE. 365 



The Energy Content of an Outgoing Wave. — Fig. i8 presents 

 a diagrammatic view of a single pair of outgoing waves from the 

 generator A on to the uniform line AB, E being the voltage wave 



Fig. i8. Diagram of Single Wave Current and E.M.F., launched on a Uni- 

 form Distortionless Line. 



and / the current wave. If the line is taken as distortionless, in the 

 simplest case, the two waves will be emitted in cophase. The 

 maximum cyclic value of the sinusoidal impressed e.m.f. being Ea 

 volts, and the linear capacitance c farads per km., the electric energy- 

 given to the wave in an element of length dx km. will be e-{c/2)dx 

 joules, where e is the instantaneous value of the e.m.f. The total 



. . . E\ c 



electric energv in the wave will be — • - • X joules, where A is 



2 2 



the length of the wave in km. ; because Ej^/2 is the average square 

 of <? integrated over the wave-length. This electric energy is dis- 

 tributed in the dielectric in the form zve^=Be^/S7rK ergs per c.c, 

 where Be is the electric flux density in " statgausses," and k the in- 

 ductivity of air. The frequency of the impressed e.m.f. being / '—', 

 the rate of delivering electric flux energy to the line is 



Ea" c E ^-c 

 Pe = • - • A = -^ • V watts. (46) 



The wave attenuates as it advances along the line, but the last 

 equation expresses the initial power of supplying electric flux into 



