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Application to optical phenomena.

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"

$t'=t-{\frac {1}{V^{2}}}\left({\mathfrak {p}}_{x}x+{\mathfrak {p}}_{y}y+{\mathfrak {p}}_{z}z\right)$

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

$4\pi V^{2}{\mathfrak {D}}'=4\pi V^{2}{\mathfrak {D}}+[{\mathfrak {p.H}}]$

(IX)

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

$\left({\frac {\partial }{\partial x}}\right)^{'},\ \left({\frac {\partial }{\partial y}}\right)^{'},\ \left({\frac {\partial }{\partial z}}\right)^{'},\ {\frac {\partial }{\partial t'}}$.

Furthermore, according to this notation, we shall understand by

$Div'\ {\mathfrak {A}}$

the expression

$\left({\frac {\partial {\mathfrak {A}}_{x}}{\partial x}}\right)^{'}+\left({\frac {\partial {\mathfrak {A}}_{y}}{\partial y}}\right)^{'}+\left({\frac {\partial {\mathfrak {A}}_{z}}{\partial z}}\right)^{'}$,