1175 
an extensive temperature region, so that the molecule has tive degrees 
of freedom. It is then still necessary to assume that at a definite 
point of the solid body which is to be thought as a crystal, the molecule 
axis passing through the centres of gravity of the atoms can only have 
one definite direction, from which it will of course deviate periodi- 
cally by small angles on account of the heat motion. If the two 
atoms are then still supposed to be different, so that the opposite 
direction does not mean the same thing, and is therefore not possible, 
we find for the entropy of the gas’): 
S=kN log (kT) — logp + $log(2am) + log(2aJ/)— dloyh+ log(4ar)+ ¥} ‚ (17) 
and for the constant a 
a 2am 
5 2rJ 
ine 5 + log —— : 
Tr + log(4m),. . . (18) 
in which J is the principal moment of inertia of a molecule, of 
course for an axis which is normal to that passing through the 
centres of gravity of the atoms. 
If on the other hand we assume the two atoms in the molecule 
as perfectly equal and indistinguishable, so that at any point in the 
crystal the axis of the molecule might as well be rotated by 180°, 
we find for S, resp. a a kNlog2 smaller value. In the formula 
analogous with (8) we get then namely 2” 7’! instead of 7'/. 
In reality we shall have to assume at Jeast in most cases, that 
also 2 similar atoms in a molecule perform a different function, e.g. 
that one is positive, the other electrically negative, or else that the 
molecule possesses a magnetic moment, that they are therefore indeed 
to be distinguished and the molecule can only have one direction at 
any place in the erystal. Then the formulae (17) and (18) will be 
universally valid. 
§ 5. On the dissociation of di-atomic gas molecules. 
We can come to the same conclusion when we investigate the 
dissociation of a di-atomie gas statistically-mechanically, and assume 
the formula (16) for the entropy of the mon-atomie components to 
be correct. 
We must then assume that the atoms in the molecule vibrate 
against each other with a frequency rv, so that the energy of the 
render the distance variable by only a practically insignificant amount for mole- 
cules consisting of heavier atoms; for hydrogen this would, however, be consi- 
derable. (The value of » may be calculated from the specilic heat at high tempe- 
ralures, the moment of inertia from EUCKEN’s experiments and formulae (16) and (17)). 
4) For the calculation cf. SS 6 and 7. 
