772 Sir Oliver Lodge on the Transmission 



Hertz oscillator in general. The electric field is there all 

 axial, and is given by 



E = -rv-^3 \ (1 — ?nV) sin (mr— nt) — mr cos (mr — nt) i , 



which may be written with a phase angle (mr — (f>) and a 

 clearly expressed amplitude, thus : — 



el 

 E = ^-3 y/(l — m V + m V) sin { nt — (mr — <f>) } , 



mr 



where tan <b = z ^-2 * 



The magnetic intensity at the same place lies along the 

 equator and is 



-r-r elmn f . , x cos (mr— nt) 1 



±1= < sin (mr—nt) -\ * > ; 



r {. mr ) 



or, rewriting it, 



K=^ </(l + m?r 2 )sm {nt-(mr + <l>')}, 



where tan <b' = — . 



mr 



So at a distance r=\fir\/2, or X/4'4, the amplitude of the 

 electric intensity is 



^^(1-2 + 4) = ^, 



while the magnetic amplitude is 



H - eln /n .ow ^V 3 



Expressing these in terms of current amplitude, whose value 

 may be written alternatively 



~ 2ire 2irev 



we get, at a distance such that mr— */2 or r = \/7r\ / 2, 



•3.Z Cp j/3 . Z . m 2 C Q A/6.7r 2 /^C Q 



