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X. A Mathematical Theory of Magnetism. By William Thomson, Esq., M.A., 
F.R.S.E., Fellow of St. Peter s College, Cambridge, and Professor of Natural 
Philosophy in the University of Glasgow. Communicated by Lieut. -Colonel Sabine, 
R.A., For. Sec. R.S. 
Received June 21, — Read June 21, 1849. 
Introduction. 
1. The existence of magnetism is recognized by certain phenomena of force which 
are attributed to it as their cause. Other physical effects are found to be produced 
by the same agency ; as in the operation of magnetism with reference to polarized 
light, recently discovered by Mr. Faraday; but we must still regard magnetic force 
as the characteristic of magnetism, and, however interesting such other phenomena 
may be in themselves, however essential a knowledge of them may be for enabling 
us to arrive at any satisfactory ideas regarding the physical nature of magnetism, 
and its connection with the general properties of matter, we must still consider the 
investigation of the laws, according to which the development and the action of 
magnetic force are regulated, to be the primary object of a Mathematical Theory in 
this branch of Natural Philosophy. 
2. Magnetic bodies, when put near one another, in general exert very sensible 
mutual forces ; but a body which is not magnetic, can experience no force in virtue 
of the magnetism of bodies in its neighbourhood. It may indeed be observed that a 
body, M, will exert a force upon another body A ; and again, on a third body B ; 
although when A and B are both removed to a considerable distance from M, no 
mutual action can be discovered between themselves : but in all such cases A and B 
are, when in the neighbourhood of M, temporarily magnetic ; and when both are 
under the influence of M at the same time, they are found to act upon one another 
with a mutual force. All these phenomena are investigated in the mathematical 
theory of magnetism, which therefore comprehends two distinct kinds of magnetic 
action : — the mutual forces exercised between bodies possessing magnetism, and the 
magnetization induced in other bodies through the influence of magnets. The First 
Part of this paper is confined to the more descriptive and positive details of the sub- 
ject, with reference to the former class of phenomena. After a sufficient foundation 
has been laid in it, by the mathematical exposition of the distribution of magnetism 
in bodies, and by the determination and expression of the general laws of magnetic 
force, a Second Part will be devoted to the theory of magnetization by influence, or 
magnetic induction. 
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