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that has a steady position with respect to the new axis; in the same way, by rest or motion of a physical particle we shall mean the relative rest or the relative motion in relation to ponderable matter. With ions, which move in this sense of the word, we will have to do as soon as the displaced matter is the seat of electric motions.

By ${\mathfrak {v}}$ we shall not represent the real velocity, but the velocity of the previously mentioned relative motion. The real velocity is thus

${\mathfrak {p}}+{\mathfrak {v}}{,}$

and hereby ${\mathfrak {v}}$ is to be replaced in equations (4) and (V).

In addition, we have, instead of the derivatives with respect to x, y, z and t, to establish such with respect to (x), (y), (z) and t.

The first mentioned derivative I denote by

${\frac {\partial }{\partial x}},\ {\frac {\partial }{\partial y}},\ {\frac {\partial }{\partial z}},\ \left({\frac {\partial }{\partial t}}\right)_{1}{,}$

however, the latter by

${\frac {\partial }{\partial (x)}},\ {\frac {\partial }{\partial (y)}},\ {\frac {\partial }{\partial (z)}},\ \left({\frac {\partial }{\partial t}}\right)_{2}.$

Now we have, by application to an arbitrary function,

${\frac {\partial }{\partial x}}={\frac {\partial }{\partial (x)}},\ {\frac {\partial }{\partial y}}={\frac {\partial }{\partial (y)}},\ {\frac {\partial }{\partial z}}={\frac {\partial }{\partial (z)}}{,}$

$\left({\frac {\partial }{\partial t}}\right)_{1}=\left({\frac {\partial }{\partial t}}\right)_{2}-{\mathfrak {p}}_{x}{\frac {\partial }{\partial (x)}}-{\mathfrak {p}}_{y}{\frac {\partial }{\partial (y)}}-{\mathfrak {p}}_{z}{\frac {\partial }{\partial (z)}}.$

By that it follows, that we can write for $Div\ {\mathfrak {A}}$ the expression

${\frac {\partial {\mathfrak {A}}_{x}}{\partial (x)}}+{\frac {\partial {\mathfrak {A}}_{y}}{\partial (y)}}+{\frac {\partial {\mathfrak {A}}_{z}}{\partial (z)}}{,}$

and for the components of $Rot\ {\mathfrak {A}}$

${\frac {\partial {\mathfrak {A}}_{z}}{\partial (y)}}-{\frac {\partial {\mathfrak {A}}_{y}}{\partial (z)}}{\text{, etc.}}$

The expressions $Div\ {\mathfrak {A}}$ and $Rot\ {\mathfrak {A}}$ have still the meaning given in § 4, g and h, if, after having abandoned the old coordinates one and for all, for simplification we don't indicate the new ones with (x), (y), (z), but with x, y, z.