Page:Elektrische und Optische Erscheinungen (Lorentz) 063.jpg

 Eventually in formula (49) we obtain

where the sum is extended over all ions of sphere I, and

or by (48)

§ 42. Equations ($$I_b$$) — ($$VII_b$$) (§ 20) may form the initial point for the subsequent considerations. At first we notice, that the first of them is equivalent to

for an arbitrary closed surface (n is to be drawn into the outside), when E is the electric charge enclosed by it. If now in one element $$d\mathfrak{r}$$ of the inner space in equilibrium state, a density $$\rho_0$$ exists, and if (for an element of the surface) $$\epsilon$$ has the meaning given above, then

where the sum is related to all elements $$d\sigma$$.

By that

From the definition of the average we easily find now

Since now

and

it is eventually given