applied to Magnetic Phenomena. 165 
those near two magnetic poles of the same name; but we know 
that the mechanical effect is that of attraction instead of re- 
pulsion. The lines of force in this case do not run between the 
bodies, but avoid each other, and are dispersed over space. In 
order to produce the effect of attraction, the stress along the 
lines of gravitating force must be a pressure. 
Let us now suppose that the phenomena of magnetism depend 
on the existence of a tension in the direction of the lines of force, 
combined with a hydrostatic pressure; or in other words, a pres- 
sure greater in the equatorial than in the axial direction: the 
next question is, what mechanical explanation can we give of 
this inequality of pressures in a fluid or mobile medium? The 
explanation which most readily occurs to the mind is that the 
excess of pressure in the equatorial direction arises from the 
centrifugal force of vortices or eddies in the medium having their 
axes in directions parallel to the lines of force. 
This explanation of the cause of the inequality of pressures 
at once suggests the means of representing the dipolar character 
of the line of force. Hvery vortex is essentially dipolar, the two 
extremities of its axis being distinguished by the direction of its 
revolution as observed from those points. 
We alsc know that when electricity circulates in a conductor, 
it produces lines of magnetic force passing through the circuit, 
the direction of the lines depending on the direction of the cir- 
culation. Let us suppose that the direction of revolution of our 
vortices is that in which vitreous electricity must revolve in order 
to produce lines of force whose direction within the circuit is the 
same as that of the given lines of force. 
We shall suppose at present that all the vortices in any one 
part of the field are revolving in the same direction about axes 
nearly parallel, but that in passing from one part of the field to 
another, the direction of the axes, the velocity of rotation, and 
the density of the substance of the vortices are subject to change. 
We ‘shall investigate the resultant mechanical effect upon an 
element of the medium, and from the mathematical expression 
of this resultant we shall deduce the physical character of its 
different component parts. 
Prop. I.—If in two fluid systems geometrically similar the 
velocities and densities at corresponding points are proportional, 
then the differences of pressure at corresponding points due to 
the motion will vary in the duplicate ratio of the velocities and 
the simple ratio of the densities. 
Let / be the ratio of the linear dimensions, m that of the velo- 
cities, n that of the densities, and p that of the pressures due to 
the motion. Then the ratio of the masses of corresponding por- 
tions will be /°n, and the ratio of the velocities acquired in 
