﻿604 The late W. Gordon Brown on the 



total activity flux will be 



-SjqmE.cL-id^E + VqJB)}, • • • (39) 

 and the whole flux, adding (38) and (39), 

 W = i2d*(E - Vq m B) . q w - 2q m E . d m + $4.(1! + Vq m B)q m 

 = 2(d ni E.q m — qJE.d m ) 



= VEXVq w d m 



=VEH. (40) 



8. Since we have shown that this theory leads to the 

 ordinary equations of the electromagnetic field, it is un- 

 necessary to give a separate proof of the uniform propagation 

 of disturbances with velocity 1/ V/^K. It is perhaps as well, 

 however, to examine shortly the mechanism of propagation, 

 particularly since the mental picture of electromagnetic 

 radiation afforded by the theory is in many respects very 

 satisfactory. 



N. Campbell gives a short discussion of the question, and 

 shows that a tube at rest may be compared to a flexible cord 

 of linear density fiD under a tension D/K ; the square of 

 the velocity of propagation of transverse disturbances being- 

 then l//iK by the elementary dynamics of cords. To extend 

 this result to the case of a tube having a general velocity v 

 perpendicular to its own direction, we have only to remember 

 that, by equation (35) above, the stress to which the restoring 

 force is due will now be the quasi-tension E + VqB, where q 

 is the velocity of the tubes, of which we shall suppose that 

 only one set need be taken into account ; and with this last 

 assumption we may drop the suffix m and so write 



B = /*VqD, E=g. 



The d component of E + VqD is the only effective part of the 

 stress, and its magnitude is given by 



(E + VqB)d 1 = (| + A »VqVqd)d 1 , 



where d : is the unit vector parallel to d, or d = <id 1 . This 

 equals 



J(l + / ,Kd 1 VqVqd) 

 = |{l- /t K(Vd 1 q)^ 



, ; VK = 1. 



-ii 1 -?}- • ™ 



