250 PROF. W. THOMSON ON THE MATHEMATICAL THEORY OF MAGNETISM. 
Other, each bar of one will act on each bar of the other with the same forces as if all 
the other bars were removed. Hence, if the distance between the two poles be unity, 
and if the strengths of the bars be respectively rn and m', (whether these numbers be 
integral or fractional,) the force between those poles will be mm!. If, now, the rela- 
tive position of the magnets be altered, so that the distance between two poles may 
be f, the force between them will, according to Coulomb’s law, be 
mrrl 
-jr. 
According to the definition given above of the strength of a simple bar-magnet, it 
follows that the same expression gives the force between two poles of any thin, uni- 
formly and longitudinally magnetized bars, of strengths m and m!. 
27 . The magnetic moment of an infinitely thin, uniformly and longitudinally mag- 
netized bar, is the product of its length into its strength. 
28. If any number of equally strong, uniformly and longitudinally magnetized 
rectangular bars of equal infinitely small sections, be put together, with like ends 
towards the same parts, a complex uniformly magnetized solid of any form may be 
produced. The magnetic moment of such a magnet is equal to the sum of the mag- 
netic moments of the bars of which it is composed. 
29. The magnetic moment of any continuous solid, uniformly magnetized in 
parallel lines, is equal to the sum of the magnetic moments of all the thin, uniformly 
and longitudinally magnetized bars into which it may be divided. 
It follows that the magnetic moment of any part of a uniformly magnetized mass 
is proportional to its volume. 
30. The intensity of magnetization of a uniformly magnetized solid is the magnetic 
moment of a unit of its volume. 
It follows that the magnetic moment of a uniformly magnetized solid, of any form 
and dimensions, is equal to the product of its volume into the intensity of its mag- 
netization. 
31. If a body be magnetized in any arbitrary, regular or irregular manner, a por- 
tion may be taken in any position, so small in all its dimensions that the distribution 
of magnetism through it will be sensibly uniform. The quotient obtained by dividing 
the magnetic moment of such a portion, in any position P, by its volume, is the in- 
tensity of magnetization of the substance at the point P ; and a line through P parallel 
to its lines of magnetization, is the direction of magnetization, at P. 
Chapter III. On the Imaginary Magnetic Matter hy means of which the Polarity 
of a Magnetized Body may he represented. 
32. It will very often be convenient to refer the phenomena of magnetic force to 
attractions or repulsions mutually exerted between portions of an imaginary mag- 
netic matter, which, as we shall see, may be conceived to represent the polarity of a 
magnet of any kind. This imaginary substance possesses none of the primary qualities 
