PART II. ELECTRO-MAGNETIC PHENOMENA.
§ 7. Fundamental Equations for bodies at Rest.
After these preparatory works, which have been first
developed on account of the small amount of mathematics
involved in the limitting case ε = 1, μ = 1, σ = 0, let
us turn to the electro-magnatic phenomena in matter.
We look for those relations which make it possible for
us—when proper fundamental data are given—to
obtain the following quantities at every place and time,
and therefore at every space-time point as functions of
(x, y, z, t):—the vector of the electric force E, the
magnetic induction M, the electrical induction e, the
magnetic force m, the electrical space-density ρ, the
electric current s (whose relation hereafter to the conduction
current is known by the manner in which conductivity
occurs in the process), and lastly the vector u, the
velocity of matter.
The relations in question can be divided into two classes.
Firstly—those equations, which,—when v, the velocity of matter is given as a function of (x, y, z, t),—lead us to a knowledge of other magnitude as functions of x, y, z, t—I shall call this first class of equations the fundamental equations—
Secondly, the expressions for the ponderomotive force, which, by the application of the Laws of Mechanics, gives us further information about the vector u as functions of x, y, z, t).
For the case of bodies at rest, i.e. when u (x, y, z, t) = 0 the theories of Maxwell (Heaviside, Hertz) and
