Page:AbrahamMinkowski1.djvu/20

 From that it follows

while (49a) gives

Since one now has according to (48c)

$\begin{array}{c} \mathfrak{E}'_{x}\mathfrak{P}_{y}-\mathfrak{E}'_{y}\mathfrak{P}_{x}=

thus it is given

The insertion of this expression and the corresponding magnetic term into (31), gives (instead of value (32) of momentum density) the corrected value

That relation (18) is satisfied, can easily be verified.

If the value (50) of $$c\mathfrak{g}$$ is inserted in the general formula (19) for the energy density, then it follows instead of (33)

One also obtains, because of (20), the corrected formula for the energy current

From (50) and (52) one can see, that also in 's theory (when modified in the given way) the relation between the energy current and momentum density exists:

which we already encountered in 's theory.

This result was to be expected; after the equations connecting $$\mathfrak{D}$$ and $$\mathfrak{B}$$ with $$\mathfrak{E'}$$ and $$\mathfrak{H'}$$, are brought into agreement, no essential difference exists any more between both theories from the standpoint of our system.