330 Mr. 0. Heaviside on the Electromagnetic Efects due 



trie/' and is given by 



„ 1 ^W 

 F= — - — 



^)2 dt' 



where W = VEH/47r is the transfer-of-energy vector. 



It must, however, be confessed that the real distribution of 

 the stresses, and therefore of the forces, is open to question. 

 And when gether is the medium, the mechanical force in it, 

 as for instance in a light-wave, or in a wave sent along a 

 telegraph-circuit, is not easily to be interpreted.] 



The companion to (11) in a nonconducting dielectric is now 



curl H = cj9E + 47rpu (13) 



Eliminate E between (11) and (13), remembering that H 

 has no divergence, because yu-o is constant, and we get 



(p2/y2_y2^H = CUrl 47r/3U, .... (14) 



the characteristic of H. Here \/'^ = d'^/da;^+ . . ., as usual. 



Comparing (14) with the characteristic of H when there is 

 impressed force e instead of electrification p, which is 



{p^/v^ — V^)H = curl cpe, 

 we see that pu becomes cpe/4:7r. We may therefore regard 

 convection-current as im2Dressed electric current. From this 

 comparison also, we may see that an infinite plane sheet of 

 electrification of uniform density cannot produce magnetic 

 force by motion perpendicular to its plane. Also we see that 

 the sources of disturbances when p is moved are the places 

 where pn has curl ; for example, a dielectric sphere uniformly 

 filled with electrification (which is imaginable), when moved, 

 starts the magnetic force solely upon its boundary. 



The presence of " curl " on the right side tells us, as a 

 matter of mathematical simplicity, to make H/curl the variable. 



^^* H = curlA, (15) 



and calculate A, which may be any vector satisfying (15). 

 Its characteristic is 



(j9>2-v2)A=47rpii (16) 



The divergence of A is of no moment, and it is only vexatious 

 complication to introduce ^. The time-rate of decrease of A 

 is not the real distribution of electric force, which has to be 

 found by the additional datum 



div cE = 47r/3, (17) 



where E is the real force. 



9. " Symbolically " expressed, the solution of (16) is 



47rpu _ -47rpu/V^ 



^-p2y^2_y2- l_^2y„2y2 K^^ ) 



