Page:Zur Dynamik bewegter Systeme.djvu/24

mass of the body, while on the other hand, the derivative ${\frac {dG}{dq}}$ is the "longitudinal" mass. In the longitudinal mass is, however, the "isothermal-isochoric" mass to be distinguished from the "adiabatic-isobaric" mass, etc.; because the derivative has only one definite value when the path of differentiation is given. For the special speed q = 0, transverse and longitudinal masses of all forms become the same, i.e. they become (48).

The mass of a stationary cavity radiation is, therefore, given by (5):

${\frac {4aT^{4}V}{3c^{2}}}$

the transverse mass of a moving cavity radiation:

${\frac {G}{q}}={\frac {4ac^{4}T^{4}V}{3(c^{2}-q^{2})^{3}}}$,

the longitudinal isothermal isochoric mass of that^[1]

${\frac {\partial G}{\partial q}}={\frac {4ac^{4}(c^{2}+5q^{2})}{3(c^{2}-q^{2})^{4}}}T^{4}V$,

the longitudinal adiabatic isochoric mass:^[1]

$\left({\frac {\partial G}{\partial q}}\right)_{S,V}={\frac {4ac^{4}(3c^{2}-q^{2})}{9(c^{2}-q^{2})^{4}}}T^{4}V$,

the longitudinal adiabatic-isobaric mass, on the contrary:

$\left({\frac {\partial G}{\partial q}}\right)_{S,p}={\frac {4ac^{6}T^{4}V}{3(c^{2}-q^{2})^{4}}}$. $\left({\frac {\partial G}{\partial q}}\right)_{S,p}={\frac {4ac^{6}T^{4}V}{3(c^{2}-q^{2})^{4}}}$.

§ 17.

Especially notable in relation (48) is the close connection of the mass of a body with the thermal function R₀. Since mass M can easily be measured in grams, then the quantity of R₀ immediately can be given by the absolute CGS system. But this value can not be tested directly by thermodynamic means; because an additive constant of the thermal function, as well as of energy, remains unspecified by pure thermodynamics. In this respect, relation (48) is essentially a complement to the thermodynamic definition of energy.

In contrast, there arises a possibility of an experimental test of the theory by taking into account the variability of the

1. See K. von Mosengeil, l.c. § 9. There, the mass is not, as here, defined by the momentum, but by the energy.