applied to Electric Currents. 285 
ld 
7 3 ou (m,(e—2) re ms(2—2,) ) 
ld ld i 
+592 (miymm) +melv—v) +592 (mlemai) mle 29) 
ar i eta) t na(a—2) ) ic = (n,(y—y,) +ns(y—ys) ) 
—3 oF (m(e—2,) +m (2—2,)). = oie gg Md es dice s+ 
In effecting the summation of SupdS, we must remember that 
round any closed surface =/dS and all similar terms vanish ; also 
that terms of the form S/ydS, where / and y are measured in 
different directions, also vanish; but that terms of the form 
SledS8, where / and z refer to the same axis of coordinates, do 
not vanish, but are equal to the volume enclosed by the surface. 
The result is 
—- 1 (/{dy 
eee a, 
d 
=) (V,+V,+&.); » . (82) 
or dividing by V=V,+ V.+ &c., 
1 (dy d8 
P =e Pp (3 — re Py . . . ° e . e e (33) 
If we make 
1 
p= a7’ ° : e > ° e e e ) e * (34) 
then equation (33) will be identical with the first of equations (9), 
which give the relation between the quantity of an electric cur- 
rent and the intensity of the lines of force surrounding it. 
It appears therefore that, according to our hypothesis, an 
electric current is represented by the transference of the move- 
able particles interposed between the neighbouring vortices. We 
may conceive that these particles are very small compared with 
the size of a vortex, and that the mass of all the particles 
together is inappreciable compared with that of the vortices, and 
that a great many vortices, with their surrounding particles, are 
contained in a single complete molecule of the medium. The 
particles must be conceived to roll without sliding between the 
vortices which they separate, and not to touch each other, so 
that, as long as they remain within the same complete molecule, 
there is no loss of energy by resistance. When, however, there 
is a general transference of>particles in one direction, they must 
pass from one molecule to another, and in doimg so, may ex- 
