PROF. W. THOMSON ON THE MATHEMATICAL THEORY OF Mi\GNETISM. 251 
of ordinary matter, and it would be wrong to call it either a solid, or the magnetic 
fluid,” or ‘‘fluids”; but, without making any hypothesis whatever, we may call it 
“ magnetic matter,” on the understanding that it possesses only the property of 
attracting or repelling magnets, or other portions of “matter” of its own kind, ac- 
cording to certain determinate laws, which may be stated as follows : — 
(1.) There are two kinds of imaginary magnetic matter, northern and southern, to 
represent respectively the northern and southern magnetic polarities of the earth, or 
the similar polarities of any magnet whatever. 
(2.) Like portions of magnetic matter repel and unlike portions attract, mutually, 
(3.) Any two small portions of magnetic matter exert a mutual force which varies 
inversely as the square of the distance between them. 
(4.) Two units of magnetic matter, at a unit of distance from one another, exert a 
unit of force, mutually. 
33. If quantities of magnetic matter be measured numerically in such units, and 
if the positive or negative sign be prefixed to denote the species of matter, whether 
northern (which, by convention, we may call positive) or southern, all the preceding 
laws are expressed in the following proposition : — 
If quantities, m and m', of magnetic matter he concentrated respectively at points at 
a distance, {,from one another, they will repel with a force algebraically equal to 
m rri 
1 ^' 
34. It appears from the explanations given above, that the circumstances of a 
uniformly magnetized needle may be represented if we imagine equal quantities of 
northern and southern magnetic matter to be concentrated at its two poles, the 
numerical measure of these equal quantities being the same as that of the “strength” 
of the magnet. 
The mutual action between two needles would thus be reduced to forces of attrac- 
tion and repulsion between the portions of magnetic matter by which their poles are 
represented. 
35. Any magnetic mass whatever may, as we have seen, be regarded as composed 
of infinitely small bar-magnets put together in such a way as to produce the distribu- 
tion of magnetism which it actually possesses ; and hence, by replacing the poles of 
these magnets by imaginary magnetic matter, we obtain a distribution of equal 
quantities of northern and southern magnetic matter through the magnetized sub- 
stance, by which its actual magnetic condition may be represented. The distribution 
of this matter becomes very much simplified from the circumstance that we haVe in 
general unlike poles of the elementary magnets in contact, by which the opposite 
kinds of magnetic matter are partially (or in a class of cases wholly^) destroyed 
through the interior of the body. The determination of the resulting distribution of 
* In all cases when the distribution is “ solenoidal.” See below. Chap. V. § 68. Communicated to the 
Royal Society, June 20, 1850. 
2 K 2 
