742 
§ 6. The hypothesis of quanta has been used in a wholly different 
way in an other paper by Terropr’) and also by Lenz and after- 
wards by Kersom®), the method followed in these cases being the 
same that has been used with much success in the theory of the 
specific heat of solid bodies. We shall confine ourselves to the 
considerations of lenz, which have been communicated by SOMMERFELD’). 
Let the gas be contained in a vessel having the form of a cube 
with the edge /. In this system stationary waves of sound of many 
different kinds can exist. If v is the volume of the cube the number 
of modes of motion for which the wave-length lies between 4 and 
4+ dà is given by 
Aanv … 
di, 
34 
4 
the largest value of 2 being 2/. 
Now Lenz assumes that the ordinary theory of stationary waves 
of sound may be applied down to very small values of 4 and that 
we may regard the state of motion of the gas as composed of a 
great number of such waves with wave-lengths between 2/ and a 
certain minimum value, which he calls 4,. The latter is chosen in 
such a manner that the whole number of modes of motion is equal 
to the number of degrees of [reedom of the system of molecules, 
Le. to 3. This is expressed by the equation 
al 
‘4arv ; 
| hee SIN 
gs 
a 
40 
or 
1 | Sok 
pt Br re 
0 
* ge u . . . . 
if we ‘put d° = which means that d is the distance at which, 
i N’ 
4 
in the case of a cubical arrangement, the particles would le from 
each other in the principal directions. If now the vessel contains a 
very large number of particles so that / is very much greater than 
1 
d, the term ar ERY be neglected and we find 
It is further assumed that, for every mode of vibration, we have 
1) Phys. Zeitschr., 14 (1913), p. 212. 
2) Proc. Acad. Amsterdam, 16 (1913), p. 227; 17 (1914), p. 20. 
3) Vorträge Wolfskehl-Kongress, p. 125. 
