applied to Electric Currents. 283 
We know that the lines of force are affected by electric cur- 
rents, and we know the distribution of those lines about a cur- 
rent; so that from the force we can determine the amount of the 
current. Assuming that our explanation of the lines of force 
by molecular vortices is correct, why does a particular distribu- 
tion of vortices indicate an electric current? A satisfactory 
answer to this question would lead us a long way towards that 
of a very important one, ‘‘ What is an electric current ?” 
I have found great difficulty in conceiving of the existence of 
vortices in a medium, side by side, revolving in the same direc- 
tion about parallel axes. The contiguous portions of consecu- 
tive vortices must be moving in opposite directions; and it is 
difficult to understand how the motion of one part of the medium 
can coexist with, and even produce, an opposite motion of a part 
in contact with it. 
The only conception which has at all aided me in conceiving 
of this kind of motion is that of the vortices being separated by 
a layer of particles, revolving each on its own axis in the oppo- 
site direction to that of the vortices, so that the contiguous sur- 
faces of the particles and of the vortices have the same motion. 
In mechanism, when two wheels are intended to revolve in 
the same direction, a wheel is placed between them so as to be 
in gear with both, and this wheel is called an “idle wheel.” 
The hypothesis about the vortices which I have to suggest is 
that a layer of particles, acting as idle wheels, is interposed be- 
tween each vortex and the next, so that each vortex has a ten- 
dency to make the neighbouring vortices revolve in the same 
direction with itself. 
In mechanism, the idle wheel is generally made to rotate 
about a fixed axle; but in epicyclic trains and other contrivances, 
as, for instance, in Siemens’s governor for steam-engines*, we 
find idle wheels whose centres are capable of motion. In all 
these cases the motion of the centre is the half sum of the motions 
of the circumferences of the wheels between which it is placed. 
Let us examine the relations which must subsist between the 
motions of our vortices and those of the layer of particles inter- 
posed as idle wheels between them. 
Prop. 1V.—To determine the motion of a layer of particles 
separating two vortices. 
Let the circumferential velocity of a vortex, multiplied by the 
three direction-cosines of its axis respectively, be a, 6, y, as in 
Prop. II. Let J, m, n be the direction-cosines of the normal to 
any part of the surface of this vortex, the outside of the surface 
being regarded positive. Then the components of the velocity 
of the particles of the vortex at this part of its surface will be 
* See Goodeve’s ‘ Elements of Mechanism,’ p. 118. 
