165 
6. Internal motions of the atoms in the molecule *). 
Note. In accordance with Pranck’s first quantum-theory we have 
provisionally assumed the lowest quantum-grade to be that of no 
quanta. N. Bonr’s investigations (On the Quantum Theory of line- 
spectra (Part ID, D. Kgl. Danske Vidensk. Selsk. Skrifter, Natur- 
vidensk. og mathem. Afd., 8. Raekke N. 1, Kgbenhavn, 1918) show, 
that probably in many cases the stage with the quantum-number 1 
must be taken as the lowest possible. The corresponding modifications 
might easily be introduced in the theory (and also specially the 
contribution of the kinetic side by side with the potential energy). 
§ 2. The phase-space of a molecule (u-space). 
The u-weight {u}. 
If a molecule consists of §, , § atoms of say three different 
chemical elements, its ‘‘phase” may be determined by means of 
6(S Hu 45) cartesian co-ordinates and momenta, i.e. by a point 
in a 6(§-+ 4-+ 5)-dimensional ‘“u-space”’ (phase-space of the mole- 
cule). In consequence of the assumptions IIa and 115 of the previous 
section, however, as long as the molecule is not dissociated, its 
phase-point (“u-point’) is confined to a portion of the u-space, namely 
to a 2X6, 2 <5 or 2 X 3-dimensional region according as the 
molecule is poly-atomic, di-atomie or monatomic. 
Considering for a moment the case of a poly-atomic molecule 
(EH + < atoms), this sub-space may be described af follows: 
owing to the rigidity of the molecule the 3(§ + 1 +5) cartesian 
co-ordinates of the atoms may be expressed by 6 co-ordinates 
Gi» Ya ++ Go, Which fix the position and orientation of the molecule. 
Similarly the cartesian momenta are determined by the six momenta 
Py» Ps -+-Pe Corresponding to the q,...g,. If in accordance with 
assumption I of the previous section we imagine the quantities 
g,---pP, to vary continuously within any arbitrary limits, the 
“u-point’ describes inside the 6 (& + n +5) dimensional u-space a 
1) This assumption underlies so far all derivations of the chemical constants 
for di-or monatomic molecules; for the theories never go beyond ,,rigid’’ molecules. 
This assumption seems more extra-ordinary in the present theory, in which the dis- 
sociation of the molecules is directly considered. Indeed, the molecules must first be 
gradually loosened, before they can dissociate. Still our method of calculating agrees 
with the following assumption: either every internal degree of freedom of the 
molecule is on its lowest quantum-grade, or the molecule is completely dissociated. 
This is of course only meant as an approximation in the calculation, similar to 
what is done in the thermodynamic derivations, where the variable contribution to 
the specific heat is neglected which would be due to a loosening of the molecules. 
