﻿596 The late W. Gordon Brown on the 



then the total of all sets passing through the same unit area is 



2Nd m = ND, 



where tubes passing through the area in the direction of N 

 are reckoned positive, and the algebraic total is intended. 

 Thus D represents vectorially the total flux of tubes ; it is to 

 be identified with the D of Heaviside, and, except for the 

 question of units, with the (/, g, li) of Maxwell. 



Let q m be the (vector) velocity of the tubes of the mth set 

 at the point in question, and let 



H = SVq m d m , (2) 



The quantity thus defined will be shown to have the properties 

 of the magnetic force. 



This completes the geometrical and kinematic specification 

 of the properties of the tubes. It is not difficult to see that 

 if we define the charge of an electric particle as the number 

 of tubes leaving it, in the sense that the direction of the 

 tubes at a positive particle is outwards, then the density of 

 electric charge will be given by 



,o = divD . (3) 



If we take the curl of (2) and expand the right member 

 fully, interpreting the terms kinematically, we obtain the 

 equation 



curl H = D 4- 2q m div cU 



= i) + up, (4) 



where D is the time rate of change of D at a fixed point, and 

 u is the mean velocity of translation of the electric particles 

 calculated so as to make up the convection current. 



The second assumption made is dynamical. Let us write 



■=|. (5) 



B=/,H, ....... (6) 



where fx and K are constants, and E and B are new vectors, 

 the electric intensity and magnetic induction. 



Then we assume that the volume densities of kinetic and 

 potential energy are given by 



U = iED, (7) 



T = iHB (8) 



