226 
Proceedings of the Koyal Society of Edinburgh. [Sess. 
electrical quantities are measured in rational units. Let the density of the 
tubes of the mth set and their direction, at any point, be represented by 
the magnitude and direction of the vector ; then the number of tubes 
of that set passing through unit area normal to the unit vector N will 
be Nd^^. 
Let 
( 1 ) 
the summation including all the sets present at the point ; then the total 
of all sets passing through the same unit area is 
SNd^ = 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, h) of Maxwell. 
Let be the (vector) velocity of the tubes of the mth set at the point 
in question, and let 
H = SVq^d^ (2) 
The quantity thus defined will be shown to have the properties of 
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 
p = div D . . . . . • (3) 
If we take the curl of (2) and expand the right member fully, inter- 
preting the terms kinematically, we obtain the equation 
curl H = D + div d^ 
= D + 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. 
3. The second assumption made is dynamical. Let us write 
B = (6) 
where pt and K are constants, and E and B are new vectors, the electric 
intensity and magnetic induction. 
