115 
the particles of magnetic bodies , &c. 
over them, and on which I suppose the whole action to take 
place ; s the arc of the latter circle between the point which is 
vertical to the pole of one of the magnets and the portion d s , 
whose force is to be determined. Referring the induced 
magnetism developed in every magnetic particle in d s, to two 
poles, the force with which these poles act upon the pole of 
the magnet, and consequently with which this pole acts upon 
them, will vary directly as the intensity of the magnetism de- 
veloped, and inversely as the square of the distance : the south 
pole of the magnet, that which in the experiments was nearest 
to the ring, will attract the induced north pole, and repel the 
induced south pole according to this law ; and the axis of 
polarisation will be in the direction of the line joining the 
centre of the particle and the pole of the magnet. If we call 
the intensity of the magnetism developed in each induced 
pole, i ; the distance of each pole from the centre of the par- 
ticle, k ; the distance of the centre of the particle from the 
pole of the magnet, p ; then the action of the magnet on the 
particle in the direction of the line drawn from its centre to 
that of the magnet, being the difference of the attractive and 
repulsive forces on the two poles, will be represented by 
h 1 1 (p - W (p + W 1 ; 
{f-wy * 
„ i 4p£ . 
^ • / a 7o\ ^ • 
or by 
or, since k is exceedingly small compared with p, by 
4 //. k '• 
f* being a constant multiplier. 
As this will represent the force on each magnetic particle 
in ds , the whole force on ds, taking m for the constant mul- 
tiplier, may be represented by 
\m ids 
