244 PROF. W. THOMSON ON THE MATHEMATICAL THEORY OF MAGNETISM. 
FIRST PART.— ON MAGNETS, AND THE MUTUAL FORCES BETWEEN MAGNETS. 
Chapter I. Preliminary Definitions and Explanations. 
3. A magnet is a substance which intrinsically possesses magnetic properties. 
A piece of loadstone, a piece of magnetized steel, a galvanic circuit, are examples of the varieties 
of natural and artificial magnets at present known ; but a piece of soft iron, or a piece of bismuth 
temporarily magnetized by induction, cannot, in unqualified terms, be called a magnet. 
A galvanic circuit is frequently, for the sake of distinction, called an “ electro-magnet but, 
according to the preceding definition of a magnet, the simple term, without qualification, may be 
applied to such an arrangement. On the other hand, a piece of apparatus consisting of a galvanic coil, 
with a soft iron core, although often called simply “ an electro-magnet,” is in reality a complex 
arrangement involving an electro-magnet (which is intrinsically magnetic as long as the electric cur- 
rent is sustained) and a body transiently magnetized by induction. 
4. In the following analysis of magnets, the magnetism of every magnetic sub- 
stance considered, will be regarded as absolutely permanent under all circumstances. 
This condition is not rigorously fulfilled either for magnetized steel or for loadstone, 
as the magnetism of any such substance is always liable to modification by induction, 
and may therefore be affected either by bringing another magnet into its neighbour- 
hood, or by breaking the mass itself and separating the fragments. When, however, 
we consider the magnetism of any fragment taken from a steel or loadstone magnet, 
the hypothesis will be that it retains without any alteration the magnetic state 
which it actually had in its position in the body. The general theory of the distribu- 
tion of magnetism founded upon conceptions of this kind, will be independent of the 
truth or falseness of any such hypothesis which may be made for the sake of con- 
venience in studying the subject ; but of course any actual experiments in illustration 
of the analysis or synthesis of a magnet would be affected by a want of rigidity in 
the magnetism of the matter operated on. For such illustrations, electro-magnets 
are extremely appropriate, as in them, except during the motion by which any 
alteration in their form or arrangement is effected, no appreciable inductive action 
can exist. 
5. In selecting from the known phenomena of magnetism those elementary facts 
which are to serve for the foundation of the theory, all complex actions, depending 
on the irregularities of the bodies made use of, should be excluded. Thus if we were 
to attempt an experimental investigation of the action between two amorphous frag- 
ments of loadstone, or between two pieces of steel magnetized by ordinary processes, 
we should probably fail to recognize the simple laws on which the actions, resulting 
from such complicated circumstances, depend ; and we must look for a simpler case 
of magnetic action before we can make an analysis which may lead to the establish- 
ment of the fundamental prineiples of the theory. Much complication will be 
avoided if we take a case in which the irregularities of one at least of the bodies do 
not affect the phenomena to be considered. Now the earth, as was first shown by 
Gilbert, is a magnet ; and its dimensions are so great that there is no sensible 
