From the momentum equations (8), we find the expression for the performance of work of the ponderomotive force

${\begin{array}{ll}{\mathfrak {mK}}={\mathfrak {w}}{\frac {\delta {\mathfrak {g}}}{\delta t}}&+{\frac {\partial }{\partial x}}\left({\mathfrak {w}}_{x}X'_{x}+{\mathfrak {w}}_{y}Y'_{x}+{\mathfrak {w}}_{z}Z'_{x}\right)\\\\&+{\frac {\partial }{\partial y}}\left({\mathfrak {w}}_{x}X'_{y}+{\mathfrak {w}}_{y}Y'_{y}+{\mathfrak {w}}_{z}Z'_{y}\right)\\\\&+{\frac {\partial }{\partial z}}\left({\mathfrak {w}}_{x}X'_{z}+{\mathfrak {w}}_{y}Y'_{z}+{\mathfrak {w}}_{z}Z'_{z}\right)\end{array}}$
${\begin{array}{r}\left\{X'_{x}{\frac {\partial {\mathfrak {w}}_{x}}{\partial x}}+Y'_{x}{\frac {\partial {\mathfrak {w}}_{y}}{\partial x}}+Z'_{x}{\frac {\partial {\mathfrak {w}}_{z}}{\partial x}}+X'_{y}{\frac {\partial {\mathfrak {w}}_{x}}{\partial y}}+Y'_{y}{\frac {\partial {\mathfrak {w}}_{y}}{\partial y}}+Z'_{y}{\frac {\partial {\mathfrak {w}}_{z}}{\partial y}}\right.\\\\\left.+X'_{z}{\frac {\partial {\mathfrak {w}}_{x}}{\partial z}}+Y'_{z}{\frac {\partial {\mathfrak {w}}_{y}}{\partial z}}+Z'_{z}{\frac {\partial {\mathfrak {w}}_{z}}{\partial z}}\right\}\end{array}}$

If we set here for abbreviation
(13) 
${\begin{cases}P'&=X'_{x}{\frac {\partial {\mathfrak {w}}_{x}}{\partial x}}+X'_{y}{\frac {\partial {\mathfrak {w}}_{x}}{\partial y}}+X'_{z}{\frac {\partial {\mathfrak {w}}_{x}}{\partial z}}\\\\&+Y'_{x}{\frac {\partial {\mathfrak {w}}_{y}}{\partial x}}+Y'_{y}{\frac {\partial {\mathfrak {w}}_{y}}{\partial y}}+Y'_{y}{\frac {\partial {\mathfrak {w}}_{y}}{\partial z}}\\\\&+Z'_{x}{\frac {\partial {\mathfrak {w}}_{z}}{\partial x}}+Z'_{y}{\frac {\partial {\mathfrak {w}}_{z}}{\partial y}}+Z'_{z}{\frac {\partial {\mathfrak {w}}_{z}}{\partial z}}\end{cases}}$ 
then the energy equation (9) gives with respect to (12)
(14) 
$Q+\mathrm {div} {\mathfrak {S}}'={\frac {\delta \psi }{\delta t}}+{\mathfrak {w}}{\frac {\delta {\mathfrak {g}}}{\delta t}}+P'$ 
This relation gained from the momentum and energy theorem, will prove itself to be still important.
Common to all theories of electrodynamics of moving bodies, is the form of the two first mainequations
(I) 
$c\ \mathrm {curl{\mathfrak {H}}'={\frac {\partial '{\mathfrak {D}}}{\partial t}}+{\mathfrak {J}},}$ 
(II) 
$c\ \mathrm {curl{\mathfrak {E}}'={\frac {\partial '{\mathfrak {B}}}{\partial t}}.}$ 
They are nothing else than a general scheme, which obtains a physical sense only by addition of two relations between the four arising vectors; and two such relations are necessary, to reduce the number of unknown vectors to two; the temporal change of the field of these two vectors, is then described by the two first mainequations.