the particles of magnetic bodies, &c. 95 
In order to obtain from these experiments the law accord- 
ing to which the force urging the ring at different distances 
varied, I assume that the whole action of the magnets may be 
referred to a single point, near the extremity in each, as a 
pole ; and I consider that, within certain limits of the distances 
of the point acted on, no sensible error will arise from this 
supposition. My first trials were to ascertain whether this 
force varied inversely as any exact power of the distance, and 
I found that the supposition that it varied inversely as the 
4 th power of the distance, would give results approximating 
very closely to those obtained by observation. As however, 
on the principle that time is requisite both for the develope- 
ment, and for the dissipation of magnetism, the induced poles 
in the ring would always be in the rear of the magnets, it 
appeared probable, that the supposition of the force varying 
inversely as some power of the distance between the pole of 
each magnet, and a point in the ring at a certain distance in 
the rear of it, would give results approximating even more 
closely to the observations ; and on trial I found that this 
was decidedly the case. 
Calling c the vertical distance of the upper surface of the 
magnets from the middle horizontal section of the ring, p the 
distance of the poles of the magnets from their upper sur- 
faces, and s a constant horizontal distance from the pole of 
either magnet to a point behind it in the ring, I found that 
the formula, 
M T2 
(p + cf + « 1 j 
where M and p are constants which, with e, are to be deter- 
mined from the observations, gave results approximating 
much more closely to the observations than the formula, 
(O. 
