applied to Hlectric Currents. 339 
it is broken, there will be a current through C in the same direc- 
tion as the primary current. 
We may now perceive that induced currents are produced 
when the electricity yields to the electromotive force,—this force, 
however, still existing when the formation of a sensible current 
is prevented by the resistance of the circuit. 
The electromotive force, of which the components are P, Q, R, 
arises from the action between the vortices and the interposed 
particles, when the velocity of rotation is altered in any part of 
the field. It corresponds to the pressure on the axle of a 
wheel in a machine when the velocity of the driving wheel 1s in- 
creased or diminished. 
The electrotonic state, whose components are F, G, H, is 
what the electromotive force would be if the currents, &c. to 
which the lines of force are due, instead of arriving at their actual 
state by degrees, had started instantaneously from rest with their 
actual values. It corresponds to the impulse which would act on 
the axle of a wheel in a machine if the actual velocity were sud- 
denly given to the driving wheel, the machine being previously 
at rest. 
If the machine were suddenly stopped by stopping the driving 
wheel, each wheel would receive an impulse equal and opposite 
to that which it received when the machine was set in motion. 
This impulse. may be calculated for any part of a system of 
mechanism, and may be called the reduced momentum of the 
machine for that point. In the varied motion of the machine, 
the actual force on any part arising from the variation of motion 
may be found by differentiating the reduced momentum with 
respect to the time, just as we have found that the electromotive 
force may be deduced from the electrotonic state by the same 
process. 
Having found the relation between the velocities of the vor- 
tices and the electromotive forces when the centres of the vortices 
are at rest, we must extend our theory to the case of a fluid 
medium containing vortices, and subject to all the varieties of 
fluid motion. If we fix our attention on any one elementary 
portion of a fluid, we shall find that it not only travels from one 
place to another, but also changes its form and position, so as to 
be elongated in certain directions and compressed in others, and 
at the same time (in the most general case) turned round by a 
displacement of rotation. 
These changes of form and position produce changes in the 
velocity of the molecular vortices, which we must now examine. 
The alteration of form and position may always be reduced to 
three simple extensions or compressions in the direction of three 
rectangular axes, together with three angular rotations about 
Z 2 
