They give to empty space (where and , and become identical) the known values of the Maxwell pressure, the current, and the energy density. To ponderable bodies in a resting state, the values (21a) and (21c) of the pressure and energy density are acceptable, yet not the value (21b), because it is
,
then the energy current would be
which differs from the current given by the Poynting vector
by
.
So we must subtract from the invariant (given by equation (20)), another , which contains as a factor, and which is equal to zero for empty space.
To obtain such a , we consider two ; first the -"velocity"
then the "rest ray", given by equations (12):
We introduce the
(22)
with being a ,
which forms a .
Now we compose, according to scheme (2), two :
which are both linear in , and we multiply them. Thus a is given, being a homogeneous second-order function of :
(23)
By adding , and , which are given by (20) and (23), we form the new
(24)
and we are using this instead of as a characteristic invariant, which determines the pressures, the current, and the electromagnetic energy density, by setting: