134 Mr. 0. Heaviside on Electromagnetic Waves, and the 

 de/dz through distance dz instantly produces 



=-£** ( 10 > 



at the place. If, therefore, e=f(z,t), the H solution at any 

 point consists of the positive waves coming from planes of 

 de/dz on the left, producing, say, H], and of H 2 due to tlie 

 negative waves from the planes of de/dz on the right side, 

 making the complete solution 



E= f .v(K 1 -H 2 ) J W 



where 



*-££&*(*-'-=£><)*>> ■ ■ (21) 



This is the most rational form of solution, and includes the 

 case of e=f(t) only. The former ma} r be derived from it by 

 effecting the integrations in (21) and (22) ; remembering in 

 doing so that the differential coefficient under the sign of 

 integration is not the complete one with respect to :', as it 

 occurs twice, but only to the second z' } and further assuming 

 that £=0 at infinity. 



4. Waves in a Conducting Dielectric. How to remove the 

 Distortion cine to the Conchictivity . — Let us introduce a new 

 physical property into the conducting medium, namely that 

 it cannot support magnetic force without dissipation of energy 

 at a rate proportional to the square of the force, a property 

 which is the magnetic analogue of electric conductivity. We 

 make the equations (2) and (3) become, i£p=d/dt s 



curlH = (47r£ + cp)E, (23) 



-curl E=(4tt# + ^)H; .... (24) 



if there be no impressed force at the spot, where g is the 

 new coefficient of magnetic conductivity, analogous to k. 

 Let 



4ark/2c = q 1} 4tt#/2^ = q S) ^ 



<2i + q2=q, qi-q 2 =s, > . . . (25) 



Substitution in (23), (24) lead to 



curlH^c^+^Ei, (26) 



-curl E^ni-s+p)^ (27) 



