Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/452

 420 ELECTE1C THEORY OF MAGNETISM. [8 35.

continuous substance, the magnetization of which varies from point to point according to some easily conceived law,, but as a multitude of molecules, within each of which circulates a system of electric currents, giving rise to a distribution of magnetic force of extreme complexity, the direction of the force in the interior *pf a molecule being generally the reverse of that of the average force in its neigh bourhood, and the magnetic potential, where it exists at all, being a function of as many degrees of multiplicity as there are molecules in the magnet.

835.J But we shall find, that, in spite of this apparent complexity, which, however, arises merely from the coexistence of a multitude of simpler parts, the mathematical theory of magnetism is greatly simplified by the adoption of Ampere s theory, and by extending our mathematical vision into the interior of the molecules.

In the first place, the two definitions of magnetic force are re duced to one, both becoming the same as that for the space outside the magnet. In the next place, the components of the magnetic force everywhere satisfy the condition to which those of induction are subject, namely, j a JQ j

��In other words, the distribution of magnetic force is of the same nature as that of the velocity of an incompressible fluid, or, as we have expressed it in Art. 25, the magnetic force has no convergence.

Finally, the three vector functions the electromagnetic momen tum, the magnetic force, and the electric current become more simply related to each other. They are all vector functions of no convergence, and they are derived one from the other in order, by the same process of taking the space-variation, which is denoted by Hamilton by the symbol V.

836.] But we are now considering magnetism from a physical point of view, and we must enquire into the physical properties of the molecular currents. We assume that a current is circulating in a molecule, and that it meets with no resistance. If L is the coefficient of self-induction of the molecular circuit, and M the co efficient of mutual induction between this circuit and some other circuit, then if y is the current in the molecule, and y that in the other circuit, the equation of the current y is

-Ry, (2)

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