Page:Elektrische und Optische Erscheinungen (Lorentz) 083.jpg

 and by

$$Rot'\mathfrak{A}$$

a vector with the components

$$\left(\frac{\partial\mathfrak{A}_{z}}{\partial y}\right)^{'}-\left(\frac{\partial\mathfrak{A}_{y}}{\partial z}\right)^{'}$$ etc.

The introduction of t'  and $$\mathfrak{D}'$$ gives the advantage, that (as I will show now) the equations ($$I_c$$) — ($$V_c$$) assume the same form as the formulas that apply to $$\mathfrak{p}=0$$.

§ 57. At first we obtain, by consideration of formulas (35),

$$Div\ \mathfrak{D}=Div'\ \mathfrak{D}-\frac{1}{V^{2}}\left(\mathfrak{p}_{x}\dot{\mathfrak{D}}_{x}+\mathfrak{p}_{y}\dot{\mathfrak{D}}_{y}+\mathfrak{p}_{z}\dot{\mathfrak{D}}_{z}\right)$$,

or by ($$III_c$$), if we replace (in the terms multiplied by $$\mathfrak{p}_{x},\mathfrak{p}_{y},\mathfrak{p}_{z}$$) $$\mathfrak{H}'$$ by $$\mathfrak{H}$$ and Div by $$Div'$$

Hence the equation ($$I_c$$) becomes

In a similar way

$$Div\ \mathfrak{H}=Div'\ \mathfrak{H}-\frac{1}{V^{2}}\left(\mathfrak{p}_{x}\dot{\mathfrak{H}}_{x}+\mathfrak{p}_{y}\dot{\mathfrak{H}}_{y}+\mathfrak{p}_{z}\dot{\mathfrak{H}}_{z}\right)$$

i.e., by ($$IV_c$$),

so that it can be written for ($$II_c$$)

Now let us turn to formula ($$III_c$$). In this one,