plays the role of the inner energy in a system moving with constant velocity.

Let the entropy of the resting system be , that of the moving one can be expressed by . The relations hold

but also

since it is indeed (at constant )

.

Since the system was adiabatically brought from the state of rest to that of motion, the entropy has the same value in both cases, thus:

therefore also

From that, also equations (6) and (8) are immediately given.

5. Momentum.

Thus far we have presupposed the existence of momentum, without making a special assumption concerning its value. Now we want to assume in agreement with the theory of Lorentz and Abraham, that momentum is equal to the space integral of the (absolute)