32 Mr. 0. Heaviside on Maxwell's Electromagnetic 



but the two phenomena are wholly independent. The first of 

 (8) is equivalent to MaxwelFs solution*. The second is its 

 magnetic analogne. 



As, in the first case, there must be initial electrification, so 

 in the second, there should be " magnetification,'" its volume- 

 density to be measured by the divergence of the induction 

 -T-47r. Now the induction can have no divergence. But it 

 might have, if g existed . 



There is no true electric current during the subsidence of 

 Eq, and there would be no true magnetic current during the 

 subsidence of H^. In both cases the energy is frictionally 

 dissipated on the spot, or there is no transfer of energy f. The 

 application of (8) will be extended later. 



4. Purely Solenoidal Fields. — By a purely solenoidal field 

 I mean one which has no divergence anywhere. Any field 

 vanishing at infinity may be uniquely divided into two fields, 

 one of which is polar, the other solenoidal ; the proof thereof 

 resting upon Sir W. Thomson's well-known theorem of De- 

 terminancy. Now we know exactly what happens to the 

 polar fields. Therefore dismiss them, and let Eq and Hq be 

 solenoidal. Then 



q^ = v'^SJ^ + <j^-, (9) 



where V^ is the usual Laplacean operator. Of course cosh qt 

 and q~^ sinh qt are rational functions of q^, so that if the dif- 

 ferentiations are possible we shall obtain the solutions out of 



5. Non-distortional Cases. — Let the subsidence-rates of the 

 polar electric and magnetic fields be equal. We then have 



p = 4:'7rk/c=4:'n-glfjL,J 



in the solutions (7). The fields change in precisely the same 

 manner as if the medium were nonconducting, as regards the 

 relative values at different places ; that is, there is no distor- 

 tion due to the conductivities ; but there is a uniform subsi- 

 dence all over brought in by them|, expressed by the factor 

 g-pi_ ^j-^jg property 1 have explained by showing the opposite 

 nature of the tails left behind by a travelling plane wave 

 according as cr is + or — . 



* Vol. i. chap. X. art. 325, equation (4). 



t This is of course obvious without any reference to Poynting's for- 

 mula. The only other simple case of no transfer of energy which had 

 been noticed before that formula is that of conduction-current, kept up by 

 impressed force so distributed as to require no polar force to supplement it. 



I "Electromagnetic Waves," Part I. § 7, Phil. Mag. February 1888. 



