246 PROF. W. THOMSON ON THE MATHEMATICAL THEORY OF MAGNETISM. 
(4.) Any motion of the body whatever, which is not of either of the kinds just described, nor 
compounded of the two, will bring it into a position in which it will not be in equilibrium. 
(5.) The directing couple experienced by the body in any position depends solely on the angle of 
inclination of the axis described in (1.) to the line along which it lies when the body is in equili- 
brium ; being independent of the position of the plane of this angle, and of the position of the body 
with reference to that axis. 
9. From these observations we draw the conclusion that a magnet always expe- 
riences a directing couple from the earth, unless a certain axis in the body is placed 
in a determinate position. This line in the body is called its magnetic axis*. 
10. The direction towards which the magnetic axis of the body tends in virtue of 
the earth’s action, is called “ the line of dip,” or “ the direction of the total terrestrial 
magnetic force,” at the locality of the observation. 
11. No further explanation regarding phenomena which depend on terrestrial 
magnetism is required in the present chapter ; but, as the facts have been stated in 
part, it may be right to complete the statement, as far as regards the action expe- 
rienced by a magnet of any kind when held in different positions in a given locality, 
by mentioning the following conclusions, deduced in a very obvious manner from 
the general laws of magnetic action stated below, and verified fully by experiment. 
If a m.agnet be held with its magnetic axis inclined at any angle to the line of dip, 
it will experience a couple, the moment of which is proportional to the sine of the 
angle of inclination, acting in a plane containing the magnetic axis and the line of 
dip. The position of equilibrium towards which this couple tends to bring the mag- 
netic axis is stable, and if the direction of the magnetic axis be reversed, the body 
may be left balanced, but it will be in unstable equilibrium. 
12. The directive tendency observed in magnetic bodies, being found to depend on 
their geographical position, and to be related in some degree to the terrestrial poles, 
received the name of polarity ; probably on account of a false hypothesis of forces 
exercised by the pole-star'|' or by the earth’s poles, upon certain points of the load- 
stone or needle, thence called the poles of the magnet.” The terms polarity” and 
‘‘ poles” are still retained, but the use of them which has very generally been made, 
is nearly as vague as the ideas from which they had their origin. Thus when the 
magnet is an elongated mass, its ends are called poles if its magnetic axis be in the 
direction of its length ; no definite points, such as those in which the surface of the 
body is cut by the magnetic axis, being precisely indicated by the term as it is 
* Any line in the body parallel to this might, with as good reason, be called a magnetic axis, but when we 
conceive the magnet to be supported by its centre of gravity, the magnetic axis is naturally taken as a line 
through this point. 
t In the poem of Guiot de Provence (quoted in Whewell’s History of the Inductive Sciences, vol. ii. p. 46), 
a needle is described as being magnetized and placed in or on a straw (floating on water it is to be presumed) — 
“ Puis se tome la pointe toute 
Centre I’estoile sans doute.” 
