PROF. W. THOMSON ON THE MATHEMATICAL THEORY OF MAGNETISM. 245 
variation in its action on different parts of any ordinary magnet upon which we can 
experiment, and consequently, in the circumstances, no complicacy depending on the 
actual distribution of terrestrial magnetism. We may therefore, with advantage, 
commence by examining the action which the earth produces upon a magnet of any 
kind at its surface. 
6 . At a very early period in the history of magnetic discovery, the remarkable 
property of “ pointing north and south ” was observed to be possessed by fragments 
of loadstone and magnetized steel needles. To form a clear conception of this 
phenomenon, we must consider the total action produced by the earth upon a magnet 
of any kind, and endeavour to distinguish between the effects of gravitation which 
the earth exerts upon the body in virtue of its weight, and those which result from 
the magnetic agency. 
7. In the first place, it is to be remarked that the magnetic agency of the earth 
gives rise to no resultant force of sensible magnitude, upon any magnet with reference 
to which we can perform experiments, as is proved by the following observed facts. 
(1.) A magnet placed in any manner, and allowed to move with perfect freedom in any horizontal 
direction (by being floated, for example, on the surface of a liquid), experiences no action which 
tends to set its centre of gravity in motion, and there is therefore no horizontal force upon the 
body. 
(2.) The magnetism of a body may be altered in any way, without affecting its weight as indicated 
by a balance. Hence there can be no vertical force upon it depending on its magnetism. 
8 . It follows that any magnetic action which the earth can exert upon a magnet 
must be a couple. To ascertain the manner in which this action takes place, let us 
conceive a magnet to be supported by its centre of gravity* and left perfectly free to 
turn round this point, so that without any constraint being exerted which could 
balance the magnetic action, the body may be in circumstances the same as if it were 
without weight. The magnetic action of the earth upon the magnet gives rise to the 
following phenomena : — 
(1.) The body does not remain in equilibrium in every position in which it may be brought to 
rest, as it would do did it experience no action but that of gravitation. 
(2.) If the body be placed in a position of equilibrium, there is a certain axis (which, for the pre- 
sent, we may conceive to be found by trial), such, that if the body be turned round it, through any 
angle, and be brought to rest, it will remain in equilibrium. 
(3.) If the body be turned through 180°, about an axis perpendicular to this, it will again be in 
a position of equilibrium. 
* The ordinary process for finding experimentally the centre of gravity of a body, fails when there is any 
magnetic action to interfere with the effects of gravitation. It is, however, for our present purpose, sufficient 
to know that the centre of gravity exists ; that is, that there is a point such that the vertical line of the resultant 
action of gravity passes through it, in whatever position the body be held. If it were of any consequence, a 
process, somewhat complicated by the magnetic action, for actually determining, by experiment, the centre of 
gravity of a magnet might be indicated, and thus the experimental treatment of the subject in the text would 
be completed. 
