178 Mr. A. M c Aulay on a Modification 



Also 



v>H = 47ri>, VyE=-B; .... (11) 



the first being given by equations (36) and (37) of § 50 of 

 ' Electromag.', and the second by equation (20) § 62, and 

 equation (34) § 50. Thus 



d(o—YDB/D)ldt= -v(W + P + P e 4V 2 /2). . (12) 



5. The intensity VDB/D I shall call the Poyn ting intensity. 

 For the present position of matter it is parallel to the Poynting 

 flux VE'H'/^tt. In fact, P being the Poynting flux and Q the 

 Poynting intensity. 



D'Q!=v-*V, (13) 



where v is the velocity l/v(K!fj!) of light in the dielectric. 

 [Note that P here is not quite the same as the P of § 103 of 

 1 Electromag.', as that includes — <f>x'p' = ~-<f> cr -'] 



It will thus be seen that the term V DB/D is in all ordi- 

 nary dielectrics utterly insignificant compared with the term 

 a in equation (12), and probably it would be quite hopeless 

 to detect it by experiment, especially as all fluids are far from 

 perfect. 



Operating on equation (12) by V . v we see that the flux 

 Yy(cr — d) is a constant for every element of the dielectric. 

 Thus Helmholtz' s theorems concerning vortices must be modified, 

 by substituting the velocity — the Poynting intensity for the velo- 

 city. This may be obtained in a different way. Take the 

 line-integral of both sides of eq. (12) between two particles of 

 the fluid. We find that Lord Kelvin's theorem concerning flow 

 must be modified by making the same change and further adding 

 P e to the expression W + P + a 12 /2, which occurs in that theorem . 



6. Though the effect of the Poynting intensity appearing 

 in the equation of motion is insignificant in its influence on 

 the motion of gross matter, it may be quite otherwise in vacuo. 

 It was, in fact, by considering the case of the aether that I was 

 led to eq. (12). 



Turning now to the aether, we will consider three cases: — 



I. The one mentioned in § 2 of ' Electromag.,' viz., where 

 the density D is zero and the ordinary potential energy w is 

 also zero. 



II. Where D is small (compared with the density of gross 

 matter) but not zero, and where w is still zero. 



III. Where D has any value not large and where w (no 

 longer assumed merely a function of D') varies largely with 

 strain except in the neighbourhood of gross matter. 



7. Case I. is an extreme one, but seems to me the most 

 natural to make on the theory developed in ' Electromag.' 



