Page:Elektrische und Optische Erscheinungen (Lorentz) 084.jpg

 three equations are summarized, namely in the first of them on the left side, the expression

is stated. For that, we can write with respect to (35)

and thus for the equation itself

The two other equations admit of a similar transformation, and therefore we have

Furthermore, as regards the first of equations $$IV_c$$), this one goes over, since

into

so that ($$IV_c$$) is equivalent with

Eventually it follows from

§ 58. To introduce the new variables also into the limiting conditions, we consider the perpendicular n for the considered point, and also two directions h and k that are perpendicular to one another and to n. There, the direction n shall correspond to a rotation by a right angle from h to k. Consequently it follows from (IX) (§ 56)

Now, since $$\mathfrak{D}_{n,}\ \mathfrak{H}'_{k}$$ and $$\mathfrak{H}'_{h}$$ are steady, then this must also be so for $$\mathfrak{D}'_{n}$$.