Page:Zur Elektrodynamik bewegter Systeme II.djvu/13

 In the case of variable states, an amount of terms are added to $$f_0$$, which are all represented as complete derivatives with respect to time. This circumstance excludes the possibility, that momentary actions of periodic processes are arbitrarily summed up. On the other hand, every single term in the {}-brace is a very small quantity: $$\Sigma$$ as well as the quantities in the are of order $$w$$; however, $$\Sigma$$ is connected with a factor that is very small for all easily movable bodies (gases), and the  have as factors the components of $$p=10^{-4}$$, if we assume that the reference system of our equations is fixed with respect to the fixed stars. What is added to $$f_0$$, is thus imperceptible; however, $$f_0$$ itself is independent of $$p$$, as soon as one chooses the terrestrial local time as fourth variable.

Thus, also the consideration of mechanical forces verifies our earlier result: no experience hinders us, to arbitrarily relate our fundamental equations to a spatial reference system that is at rest in Earth, or to such a system that has an arbitrary uniform velocity, whose order is the relative velocity of Earth - fixed stars. We only have to adapt the temporal reference system to the freely chosen spatial system.