applied to Magnetic Phenomena. 171 
coming more numerous towards the right. It may be shown 
that if the force increases towards the right, the lines of force 
will be curved towards the right. The effect of the magnetic 
tensions will then be to draw any body towards the right with a 
force depending on the excess of its inductive capacity over that 
of the surrounding medium. 
We may suppose that in this figure the lines of fores are 
those surrounding an electric current perpendicular to the plane 
of the paper and on the right hand of the figure. 
These two illustrations will show the mechanical effect on a 
paramagnetic or diamagnetic body placed in a field of varying 
magnetic force, whether the increase of force takes place along 
the lines or trausverse to them. The form of the second term 
of our equation indicates the general law, which is quite inde- 
pendent of the direction of the lines of force, and depends solely 
on the manner in which the force varies from one part of the 
field to another. 
We come now to the vee term of the value of X, 
Jot 
OY Tanda dy)" 
Here uf is, as before, the quantity of magnetic induction through 
unit of area perpendicular to the axis of y, and Ene Is a 
quantity which would disappear if adx-+ @dy+ydz were a com- 
plete differential, that is, if the force acting on a unit north pole 
were subject to the condition that no work can be done upon 
the pole in passing round any closed curve. The quantity repre- 
sents the work done on a north pole im travelling round unit of 
area in the direction from +z to +y parallel to the plane of zy. 
Now if an electric current whose strength is 7 is traversing the 
axis of z, which, we may suppose, points vertically upwards, then, 
if the axis of w is east and that of y north, a unit north pole will 
be urged round the axis of z in the direction from 2 to y, so 
that in one revolution the work done will be = 47rr. Hence 
7 = — a) represents the strength of an electric current 
parallel to z through unit of area; and if we write 
1 (dy =*)= eet —\-- 1) = ~(% - a) an 
ale - dz) ~ aa\dz~ da) ~? Ga\de dy ae) 
then p, g, r will be the quantity of electric current per unit of 
area perpendicular to the axes of x, y, and z respectively. 
The physical interpretation of the third term of X, —r, is 
that if w8 is the quantity of magnetic induction parallel to y, and 
r the quantity of electricity flowing in the direction of z, the 
