Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/85

 430.] in the same direction, so that opposite poles are in contact. The north pole of the weak magnet points in the same direction as those of the strong ones, but since it is in contact with the south pole of a stronger magnet, there is an excess of south magnetism in the neighbourhood of its north pole, which causes the small magnet to appear oppositely magnetized.

In some substances, however, the apparent magnetization is negative even when they are suspended in what is called a vacuum.

If we assume κ = 0 for a vacuum, it will be negative for these substances. No substance, however, has been discovered for which κ has a negative value numerically greater than $$\frac {1}{4 \pi}$$, and therefore for all known substances μ. is positive.

Substances for which κ is negative, and therefore μ less than unity, are called Diamagnetic substances. Those for which is κ positive, and μ greater than unity, are called Paramagnetic, Ferromagnetic, or simply magnetic, substances.

We shall consider the physical theory of the diamagnetic and paramagnetic properties when we come to electromagnetism, Arts. 831-845.

430.] The mathematical theory of magnetic induction was first given by Poisson. The physical hypothesis on which he founded his theory was that of two magnetic fluids, an hypothesis which has the same mathematical advantages and physical difficulties as the theory of two electric fluids. In order, however, to explain the fact that, though a piece of soft iron can be magnetized by induction, it cannot be charged with unequal quantities of the two kinds of magnetism, he supposes that the substance in general is a non-conductor of these fluids, and that only certain small portions of the substance contain the fluids under circumstances in which they are free to obey the forces which act on them. These small magnetic elements of the substance contain each precisely equal quantities of the two fluids, and within each element the fluids move with perfect freedom, but the fluids can never pass from one magnetic element to another.

The problem therefore is of the same kind as that relating to a number of small conductors of electricity disseminated through a dielectric insulating medium. The conductors may be of any form provided they are small and do not touch each other.

If they are elongated bodies all turned in the same general