128 REPORT—1885. 
current, then Maxwell in his paper on a ‘Dynamical Theory of the 
Electromagnetic Field,’ ‘ Phil. Trans., 1885,’ puts 
2h grip ett dg ay 4th 
u=pt-—, =q+—, wart oe 
é pee Nag ae or et: Dig, 
Since PRE a 
Bg: dg dh 
d cy gs NB ata 
ne He dy Gas? 
where p is the volume density of the free electricity, we see that 
du dv dw 
ase aati) 
de dy in dz 
If the values of the quantities in a medium A be denoting by putting 
the suffix 1 to the symbols representing them, and those in another 
dielectric B by putting the suffix 2, then if /, m, m are the direction 
cosines of the normal from A to B, we have at the boundary of the two 
media 
d 
L(pi-p2) + ™ (41-4) + (m1 —1) = = 
L(fi—fo) + m (g1—g2) + 2 (hi —hg) = — 9, 
where o is the surface density of the electricity ; thus 
1 (uy —Ug) + m (¥;—vq) + 2 (W1;— Wg) =0; 
so that wu, v, w satisfy the same equations as the components of the velocity 
of an incompressible fluid. 
This assumption about the magnitude of the effects produced by the 
alteration in the dielectric polarisation makes the mathematics of the 
theory as simple as possible. If Maxwell had merely assumed that the 
alteration of the dielectric polarisation produces effects analogous to those 
produced by ordinary conduction currents, and that the equivalent con- — 
duction current was proportional to the rate of alteration of the dielectric 
polarisation, then these equations would have been 
dX 
at’ 
a 
a 
aid, 
dt ” 
u=p+a 
=qt 
w=r+ 
so that in a homogeneous dielectric 
du , dv, dw =—#f1.48t} 
ee aera ger Fy 
d dN aN 
U(u,— Uy) + m (vj — %) + 2 (W1— 2) = =o qj =i 
where N is the component of the electromotive force normal to the 
surface. 
