applied to Electric Currents. 343 
The physical meaning of the terms in the expression for the 
electromotive force depending on the motion of the body, may 
be made simpler by supposing the field of magnetic force uni- 
formly magnetized with intensity « in the direction of the axis 
of z. Then if /, m, n be the direction-cosines of any portion of 
a linear hidaathe, and § its length, the electromotive force 
resolved in the direction of the conductor will be 
=S(P/+Qm+Rn), 5 2... (78) 
dz _ nit), 
e=Sya(m Foti) bs ales Vicars @ 
that is, the product of we, the quantity of magnetic induction 
or 
== ; nl ; ), the area swept 
out by the conductor 8 in unit of time, resolved perpendicular 
to the direction of the magnetic force. 
The electromotive force in any part of a conductor due to its 
motion is therefore measured by the number of lines of magnetic 
force which it crosses in unit of time; and the total electromo- 
tive force in a closed conductor is measured by the change of the 
number of lines of force which pass through it ; and this is true 
whether the change be produced by the motion of the conductor 
or by any external cause. 
In order to understand the mechanism by which the motion 
of a conductor across lines of magnetic force generates an elec- 
tromotive force in that conductor, we must remember that in 
Prop. X. we have proved that the change of form of a portion of 
the medium containing vortices produces a change of the velocity 
of those vortices; and in particular that an extension of the 
medium in the direction of the axes of the vortices, combined 
with a contraction in all directions perpendicular to this, pro- 
duces an increase of velocity of the vortices ; while a shortening 
of the axis and bulging of the sides produces a diminution of the 
velocity of the vortices. 
This change of the velocity of the vortices arises from the in- 
ternal effects of change of form, and is independent of that pro- 
duced by external electromotive forces. If, therefore, the change 
of velocity be prevented or checked, electromotive forces will 
arise, because each vortex will press on the surrounding particles 
in the direction in which it tends to alter its motion. 
Let A, fig. 4, represent the section of a vertical wire moving 
in the direction of the arrow from west to east, across a system 
of lines of magnetic force running north and south, The curved 
lines in fig. 4: represent the lines of fluid motion about the wire, 
the wire being regarded as stationary, and the fluid as having a 
over unit of area multiplied by (m 
