﻿602 The late W. Gordon Brown on the 



To see that this is true we have only to apply the theorem 

 of divergence; in the first place we note that since 



|T-=Vd,„B, (18) 



summing for all values of m we have VDB equal to the 

 momentum per unit volume. But 



t„V=|,VDB ) (32) 



a result easily deduced (Heaviside, loc. cit.) from the circuital 

 laws, and usually expressed in words by stating that Maxwell's 

 stress gives rise to a translational force per unit volume 

 equal to the rate of change at a fixed point of the momentum 

 per unit volume (the absence of electrification being assumed). 

 We are thus entitled to say that -^ N is the flux of momentum 

 per unit area of a fixed surface. Now it is clear that 

 VDB . qN is the flux per unit area due to the motion of the 

 surface with velocity q. Hence t/t is the general operator 

 giving the flux of momentum. The equation of rate of 

 change of momentum per unit volume at a point whose 

 velocity is q is 



fv=|rVDB+ Vq.VDB 



ot 



= |^VDB + qv.DB + VDB.divq, . . (33) 



the first two terms giving the rate of change of density of 

 momentum at the moving point, and the last term the rate of 

 change due to expansion at the rate div q. 



This flux of momentum yjr is partly due to convection, and 

 partly to be ascribed to a stress. It is interesting to note 

 that if all the tubes were of one set, we could determine the 

 stress by simply putting q equal to this velocity. We should 

 then have H = VqD, and the stress would be 



<£ = (E + VqB).D-i(E + VqB)D 



= F.D+^(HB-ED) (34) 



In general the stress operator will be obtained by sub- 

 tracting from ty the operator — 2(Vd m B . q TO ) which gives the 

 convective flux of momentum relative to a fixed point ; thus 



