PROF. W. THOMSON ON THE MATHEMATICAL THEORY OF MAGNETISM. 249 
inents which he made, it appears that the intensity of the magnetization must have 
been very nearly constant from the middle of each of the bars, to within a short 
distance from either end, where a gradual decrease of intensity is sensible*. 
22. These circumstances having been attended to. Coulomb was able to deduce 
from his experiments the true laws of the phenomena, and arrived at the following 
conclusions : — 
(1.) If two thin uniformly and longitudinally magnetized bars be held near one 
another, an action is exerted between them which consists of four distinct forces, 
along the four lines joining their extremities. 
(2.) The forces between like ends of the two bars are repulsive-f-. 
(3.) The forces between unlike ends are attractive. 
(4.) If the bars be held so that the four distances betw’een their extremities, two 
and two, are equal, the four forces between them will be equal. 
(5.) If the relative positions of the bars be altered, each force will vary inversely 
as the square of the mutual distance of the poles between which it acts. 
23. To establish a standard for estimating the strength of a magnet, let us con- 
ceive two infinitely thin bars to be placed so that either end of one may be a unit of 
distance from an end of the other. Then, if the bars be equally magnetized, each 
uniformly and longitudinally, to such a degree that the force between those ends 
shall be unity, the strength of each bar- magnet is unity 
24. If any number, m, of such unit bars, of equal length, be put with like ends to- 
gether, so as to constitute a single complex bar, the strength of the magnet so formed 
is denoted by m. 
If there be any number of thin bar-magnets of equal length, and each of them of 
such a strength that q of them, with like ends together, would constitute a unit-bar; 
and if p of those bars be put with like ends together, the strength of the complex 
magnet so formed will be -• 
25. If a single infinitely thin bar be magnetized to such a degree that in the same 
positions it would produce the same effects as a complex bar of any strength m (ati 
integer or fraction), the strength of this magnet is denoted by m. 
26. If two complex bar-magnets, of the kind described above, be put near one an- 
* See note on § 38, below. 
t Hence we see the propriety of the terms north and south applied to the opposite polarities of a magnet, as 
explained above. Thus we designate the polarity, or the imaginary magnetic matter, of the northern and 
southern magnetic hemispheres of the earth, as northern and southern respectively ; and since the poles of ordi- 
nary magnets which are repelled by the earth’s northern or southern polarity must be similar, these also are 
called northern or southern, as the case may be. 
+ The Royal Society in its Instructions for making observations on Terrestrial Magnetism adopts one foot 
as the unit of length ; and, that force which, if acting on a grain of matter, would in one second of time gene- 
rate one foot per second of velocity, as the unit of force ; which is consequently very nearly of the weight, 
in any part of Great Britain or Ireland, of one grain. 
2 K 
MDCCCLI. 
