and by
![{\displaystyle Rot'{\mathfrak {A}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0eb5af08aacbee361e7fb2342a723584795c4641)
a vector with the components
![{\displaystyle \left({\frac {\partial {\mathfrak {A}}_{z}}{\partial y}}\right)^{'}-\left({\frac {\partial {\mathfrak {A}}_{y}}{\partial z}}\right)^{'}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/59a03a7e40af6059d9c1d0c039f124f044e08190)
etc.
The introduction of t' and
gives the advantage, that (as I will show now) the equations (
) — (
) assume the same form as the formulas that apply to
.
§ 57. At first we obtain, by consideration of formulas (35),
![{\displaystyle 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)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cdc6d8a833365af7da22c7db96f86aac5856e404)
,
or by (
), if we replace (in the terms multiplied by
)
by
and Div by
.
|
|
Hence the equation (
) becomes
|
|
In a similar way
![{\displaystyle 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)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9d6bb06d684476aa16f50943c88cdee0ae8cca1c)
i.e., by (
),
,
|
|
so that it can be written for (
)
|
( )
|
Now let us turn to formula (
). In this one,