Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/232

and this gives on averaging

$\mathrm {div} \ \mathbf {E} =\rho _{1}+{\overline {\rho }}$,

where ρ₁ denotes the volume-density of free electric charge, i.e. excluding that in the doublets; or

$\mathrm {div} \ (\mathbf {E} +\mathbf {P} )=\rho _{1}$,

or $\mathrm {div} \ (\epsilon \mathbf {E} )=\rho _{1}$. This is the fundamental equation of electrostatics, as modified in order to take into account the effect of the specific inductive capacity ε.

The conception of action propagated step by step through a medium by the influence of contiguous particles had a firm hold on Faraday's mind, and was applied by him in almost every part of physics. "It appears to me possible," he wrote in 1838,^[1] "and even probable, that magnetic action may be communicated to a distance by the action of the intervening particles, in a manner having a relation to the way in which the inductive forces of static electricity are transferred to a distance, the intervening particles assuming for the time more or less of a peculiar condition, which (though with a very imperfect idea) I have several times expressed by the term electro-tonic state."^[2]

The same set of ideas sufficed to explain electric currents. Conduction, Faraday suggested,^[3] might be "an action of contiguous particles, dependent on the forces developed in electrical excitement; these forces bring the particles into a state of tension or polarity;^[4] and being in this state the contiguous particles have a power or capability of communicating these forces, one to the other, by which they are lowered and discharge occurs."

1. Exp. Res., § 1729.
2. This name had been devised in 1831 to express the state of mutter subject to magneto-electrio induction; ef. Exp. Res., § 60.
3. Exp. Res. iii, p. 513.
4. As in electrostatic induction in dielectrics.