Page:On Faraday's Lines of Force.pdf/38

192 If we make


 * $$\frac{da}{dx}+\frac{db}{dy}+\frac{dc}{dy}=4\pi \rho................(C)$$,

$\int edS=4\pi\iiint \rho dx dy dz $,

where the integration on the right side of the equation is effected over every part of space within the surface. In a large class of phenomena, including all cases of uniform currents, the quantity $$\rho$$ disappears.

Magnetic Quantity and Intensity.

From his study of the lines of magnetic force, Faraday has been led to the conclusion that in the tubular surface formed by a system of such lines, the quantity of magnetic induction across any section of the tube is constant, and that the alteration of the character of these lines in passing from one substance to another, is to be explained by a difference of inductive capacity in the two substances, which is analogous to conductive power in the theory of electric currents.

In the following investigation we shall have occasion to treat of magnetic quantity and intensity in connection with electric. In such cases the magnetic symbols will be distinguished by the suffix 1, and the electric by the sufﬁx 2. The equations connecting $$a, b, c, k, \alpha, \beta, \gamma, p,$$ and $$p$$, are the same in form as those which we have just given. $$a, b, c$$ are the symbols of magnetic induction with respect to quantity; $$k$$ denotes the resistance to magnetic induction, and may be different in different directions; $$\alpha, \beta, \gamma$$, are the effective magnetizing forces, connected with $$a, b, c,$$ by equations $$(B)$$; $$p$$ is the magnetic tension or potential which will be afterwards explained; $$\rho$$ denotes the density of real magnetic matter and is connected with $$a, b, c$$ by equations $$(C)$$. As all the details of magnetic calculations will be more intelligible after the exposition of the connexion of magnetism with electricity, it will be sufﬁcient here to say that all the deﬁnitions of total quantity, with respect to a surface, the total intensity to a curve, apply to the case of magnetism as Well as to that of electricity.