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is connected with the temporal variation of the magnetic force. The relation reads

$-4\pi V^{2}Rot\ {\mathfrak {d}}={\dot {\mathfrak {H}}}{,}$

(IV)

if we denote by V the ratio of the electromagnetic and electrostatic units of electricity, or the velocity of light in the aether.

Now we have written down all equations for the aether. If ${\mathfrak {d}}$ and ${\mathfrak {H}}$ for $t=0$ are given everywhere, we know for all subsequent instants the motion of charged bodies, and if we also add the requirement, that ${\mathfrak {d}}$ and ${\mathfrak {H}}$ vanish in infinite distance, then these vectors are definitely specified.

Where $\rho =0$, the equations go over into the formulas for pure aether, from which it is knowingly given, that the variations represented by ${\mathfrak {d}}$ and ${\mathfrak {H}}$ propagate with the velocity of light.

Since the equations are linear, various solutions can be composed to a more general one by addition. For example, the motion of n ions shall be given, and n value systems of ${\mathfrak {d}}$ and ${\mathfrak {H}}$ shall be found that determine the state of the aether for the case in which only one ion exists, and the others were neglected. Then we obtain by superposition the state of the aether, being in agreement with the motions of all n ions. In this sense we may say, that any ion influences the state of aether in exactly such way, as if the others wouldn't exist.

§ 8. If the ponderable matter is at rest and ${\mathfrak {d}}$ is independent of time, then ${\mathfrak {S}}$ and ${\mathfrak {H}}$ vanish, while ${\mathfrak {d}}$ will be determined by

$Div\ {\mathfrak {d}}=\rho$

(I)

and

$Rot\ {\mathfrak {d}}=0.$

This last equation says, that ${\mathfrak {d}}_{x},\ {\mathfrak {d}}_{y},\ {\mathfrak {d}}_{z}$ can be considered as partial derivatives of a single function, which we want to call $-{\tfrac {\omega }{4\pi }}$. We thus put