PROF. W. THOMSON ON THE MATHEMATICAL THEORY OF MAGNETISM. 247 
generally used. If, however, the body be symmetrical about its magnetic axis, and 
symmetrically magnetized, whether elongated in that direction or not, the poles 
might be definitely the ends of the magnetic axis (or the points in which the surface 
is cut by it), unless the magnet be annular and not cut by its magnetic axis (a ring 
electro-magnet, for instance), in which case the ordinary conception of poles fails. 
Notwithstanding this vagueness, however, the terms poles and polarity are extremely 
convenient, and, with the following explanations, they will frequently be made use 
of in this paper. 
13. Let O be any point in a magnet, and let N O S be a straight line parallel to 
the line defined above as the magnetic axis through the centre of gravity. If the 
point O, however it has been chosen, be called the centre of the magnet, the line 
N S, terminated either at the surface, on each side, or in any arbitrary manner, is 
called the magnetic axis, and the ends, N, S, of the magnetic axis are called the poles 
of the magnet*. 
14. That pole (marked N) which points, on the whole, from the north, and in 
northern latitudes upwards, is called the north pole, and the other (S), which points 
from the south, is called the south pole. 
15. The sides of the body towards its north pole and south pole, are said to possess 
“ northern polarity ” and southern polarity ” respectively, an expression obviously 
founded on the idea that the surface of a magnet may in general be contemplated as 
a locus of poles. 
16. If a magnetic body be broken up into any number of fragments, each morsel 
is found to be a complete magnet, presenting in itself all the phenomena of poles 
and polarity. This property is generally contemplated when, in modern writings 
on physical subjects, polarity is mentioned as a property belonging to a solid body ; 
and a corresponding idea is involved in the term when it is applied with reference to 
the electric state which Mr. Faraday discovered to be induced in non-conductors of 
electricity (“ dielectric ”), when subjected to the influence of electrified bodies-j-. 
However different are the physical circumstances of magnetic and electric polarity, 
it appears that the positive laws of the phenomena are the same:}:, and therefore the 
mathematical theories are identical. Either subject might be taken as an example of 
a very important branch of physical mathematics, which might be called “ A Mathe- 
matical Theory of Polar Forces.” 
17 . Although we have seen that any magnet, in general, experiences from the earth 
an action subject to certain very simple laws, yet the actual distribution of the mag- 
netism which it possesses may be extremely irregular. We may certainly conceive 
* A definition of poles at variance with this is adopted in some special cases, especially in that of the earth 
considered as a great magnet, but the manner in which the term will be used in this paper will be such as to 
produce no confusion on this account. 
t Faraday’s Experimental Researches in Electricity, Eleventh Series. 
J See a paper “ On the Elementary Laws of Statical Electricity,” published in the Cambridge and Dublin 
Mathematical Journal (vol. i.) in December 1845. 
