If one inserts Minkowski's connecting equations between the electromagnetic vectors into our system, then the momentum density in the moving body becomes equal to the energy current divided by .
From (40) and (21) it follows, with respect to (37)
where the vector
is determined from
Let us direct the -axis into the direction of , and let us set
then the components of become
and it follows from (40a)
The previous derivation has a gap; the proof is missing that equations (39) (assumed as being valid) are really satisfied. In order to prove this, we calculate the vector
Since one has
then it becomes with respect to (40a)
One can – because according to the things said, the component of coinciding with the direction of vector , is equal to zero – also write
By that, condition (18a) is shown to be valid, and at the same time the gap in the previous derivation of the value of is closed.
From (19) the value of the energy density follows: