Page:Zur Dynamik bewegter Systeme.djvu/18

 This is by (26), (14) and (13):

This is given by substitution with respect to (8) and (7):

$$\mathfrak{G}'_{x'}=\frac{1}{c\sqrt{c^{2}-v^{2}}}\{(c^{2}-v\dot{x})\mathfrak{G}_{x}+vH-v\dot{y}\mathfrak{G}_{y}-v\dot{z}\mathfrak{G}_{z}-vpV-vTS\}$$

or from the introduction of the energy E (10):

If we introduce instead of the energy E the "thermal function at constant pressure" R by Gibbs:

whose variation in isobaric processes describes the supplied heat, then the last relation is simply given by:

§ 11. By differentiating the equation (29) by time t:

$$\frac{d\mathfrak{G}'_{x'}}{dt}=\frac{d\mathfrak{G}'_{x'}}{dt'}\cdot\frac{dt}{dt}=\frac{c}{\sqrt{c^{2}-v^{2}}}\left\{ \frac{d\mathfrak{G}{}_{x}}{dt}-\frac{v}{c^{2}}\left(\frac{dE}{dt}+p\frac{pV}{dt}+V\frac{dp}{dt}\right)\right\}$$,

the relation between the x-components of the force $$\mathfrak{F}$$ follows with consideration of (27), (20), (14) and (11), namely:

Comparing this relation with the one found above (21), it follows that those have no general meaning, but only apply if $$\dot{p} = 0$$ and $$\dot{S} = 0$$, that is, when the process runs isobaric and adiabatic. In fact, this property is