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It also follows that the value for the time integral, which is characteristic for the principle of least action, and which is taken from a certain initial state 1 to a certain final state 2, is:

$W=\int _{1}^{2}Hdt$,

which may be described as the (corresponding to the process in question) "influence quantity", having the same value for the primed reference frame as for the unprimed. If we add the theorem that for the influence quantity there exists a certain elementary quantum^[1]: h=6.55 · 10^-27 erg. sec., we can also say: Every change in nature corresponds to a certain number of influence elements which are independent of the reference frame. It is understood that this theorem extends the importance of the principle of least action in a new direction. But at this point, these and related issues will not be further discussed.

Third Section. Applications.

§ 13.

The most important implication of the general relations established in the previous section concerns the dependence of the physical state of a body on its velocity. It can in fact be shown quite generally, that the kinetic potential H and thus all state variables, are directly specify as functions of velocity, volume and temperature, as soon as they are known for the velocity zero as functions of volume and temperature.

We want for this purpose denote by H₀, p₀, S₀, E₀, ... those functions of two variables V and T, in which the functions H, p, S, E, ... of the three variables q, V, T go over, if we set q = 0 within them. We also want denote by H'₀, p'₀, S'₀, E'₀, ... those functions of the three variables q, V, T, in which the functions H₀, p₀, S₀, E₀, ... the two variables V and T go over, if we substitute $V'={\frac {c}{\sqrt {c^{2}-q^{2}}}}V$ instead of V and $T'={\frac {c}{\sqrt {c^{2}-q^{2}}}}T$ instead of T'.

1. M. Planck, Vorlesungen über Wärmestrahlung (Leipzig. J. A. Barth), p. 162, 1906.