366 KENNELLY-NABESHIMA— ESTABLISHING A 



the dielectric at the end A of the line. The quantity v is the ap- 

 parent velocity of transmission. 



Similarly, if / is the linear inductance in henrys per km., the 

 sinusoidal outgoing current at A has an instantaneous value i and a 

 maximum cyclic value /q amperes, the magnetic energy in an element 

 dx of the line is r{l/2)dx joules. The total magnetic energy in a 

 complete outgoing wave as it passes A is (/0V2) • (//2) -A joules. 

 But 



-^0 = — ^ = -,f=- = £4 • a/t ; so that I^r = EJ • y , 

 or 



lo' I EJ C • , , N 



— • - = • - joules, (47) 



2222 '^' 



The magnetic energy in the wave is therefore (E ^/2)-{c/2)-\ 

 joules, which is the same amount as the electric energy. The mag- 

 netic energy is distributed in the dielectric as volume energy of 

 magnetic flux of the type zvm = Bm~/{87rix) ergs per c.c, where Bm 

 is the magnetic flux density in gausses, and /* the permeability of the 

 air. Be^Bni numerically, and We = Wm ergs/c.c. The energy of 

 any initial outgoing wave is thus half electric flux energy, and half 

 magnetic energy. The rate of delivering this magnetic energy at 

 A is 



77 2 ^ 77 2 . ^ 



P„, = -^ • - • fX = -^^— • V watts. (48) 



2 2 "^ 4 ^ 



Thus Pm'^Pc. The total power 



P = • V = — V watts. (40) 



2 2 



The mechanism of electric power transmission, as contemplated 

 in the initial transient state, is the energization of the dielectric with 

 electric and magnetic fluxes, which at each point have equal numer- 

 ical values and volume energies, and, in shipping off these slabs of 

 flux at the transmission speed v. Continual reflections of these 

 waves, from both ends of the line, subsequently build up a standing- 



