Page:Lorentz Simplified1899.djvu/13

 being the electric force. By both signs I shall now denote, not the whole vector, but the part that is due to the vibrations.

The equations may again be written in a form in which the velocity of translation does not explicitly appear. For this purpose, it is necessary to replace the variables x', y', z', t', $$\mathfrak{F}',\mathfrak{H}',\mathfrak{a}$$ and $$\varrho_{0}$$ by new ones, differing from the original quantities by certain constant factors.

For the sake of uniformity of notation all these new variables will be distinguished by double accents. Let $$\varepsilon$$ be an indeterminate coefficient, differing from unity by a quantity of the order $$\mathfrak{p}_{x}^{2}/V^{2}$$ and let us put

so that t" is a modified local time; then we find