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The fundamental equations for a system of ions located in the aether.

The equations for the aether.

§ 5. When forming the equations of motion we will express all magnitudes in electromagnetic measure, and preliminarily use a coordinate system that is at rest in the aether. Now according to Maxwell, two kinds of deviations from the equilibrium state can exist in this medium. The deviation of first kind, which (among others) can be found in the vicinity of any charged body, we call the dielectric displacement; it is a vector quantity and may get the designation ${\mathfrak {d}}$^[1]. It is solenoidally distributed in "pure" aether, i.e. in the spaces between the ions, and we have

$Div\ {\mathfrak {d}}=0.$

(3)

We now want to assume, that aether exists in the space where an ion is located, and that a dielectric displacement can happen at this place, i.e. that the dielectric displacement caused by a single ion is extended over the interior of the other ions.

The charge of an ion we see as distributed over a certain space; the spatial density may be called $\rho$, and we want to assume, that this function steadily goes over to 0 when passing from the interior of the particle into the pure aether.

1. A prove of the designations employed can be found at the end of the treatise.