Page:Elektrische und Optische Erscheinungen (Lorentz) 082.jpg



Reduction to a resting system.
§ 56. The specification of the influence, that the motion of ponderable bodies exerts on the phenomena of light, can be achieved in a very simple manner, if we neglect circular polarization, as it will always take place in this section.

Namely we want, as we did it earlier (§ 31) already, by continuing omission of magnitudes of second order, to introduce (instead of t) the "local time"

as an independent variable; besides we want (instead of $$\mathfrak{D}$$) consider a new vector $$\mathfrak{D}'$$, which we define by the formula

If we consider an arbitrary magnitude as a function of x, y, z and t' , then (as before (§81)) we denote the partial derivative by

Furthermore, according to this notation, we shall understand by

the expression