the following relation between the frequency r and the wave-length À 
c 
Dn 
A 
where c, the “velocity of sound”, has the same value for all the modes 
of vibration. LeNz puts 
ang 
_l 
— 
PT fe 10 
CATE : C= . 
Nm ( 9 
This relation oecurs in the ordinary kinetic theory of a monatomic 
gas and is maintained by Lenz. although the equations he wants 
to derive differ from those of the old theory of gases. 
In cutting off the “sound spectrum” at the wave-length 2, Lunz 
follows the example given by Depyr in his beautiful theory of the 
specifie heat of solid bodies. Just like Drgyre be assumes that the 
energy is distributed over the different modes of motion in the way 
required by the theory of quanta, the quantum proper to each mode 
LC 
having the value 4r = ait By probability considerations upon which 
we need not dwell here the equations for the entropy etc. of the gas 
are then obtained. 
§ 7. In my opinion all this is open to serious objection. In the 
case of a solid body we can imagine an “original” state in which 
all molecules are at rest. The different normal modes of vibration 
which can exist in the bedy are all deviations from this state and 
when they all exist at the same time with sufficiently small ampli- 
tudes, the total energy — if the energy in the original state is taken 
to be 0 — is equal to the sum of the energies belonging to the 
separate modes of motion. The heat motion too may be regarded 
as made up of all the possible normal vibrations. 
The case of a gas is widely different. It is true that here also a 
wave motion may be regarded as an alternating deviation from an 
original state, but the latter is not now a state of rest. On the con- 
trary, it is endowed already with the total energy of the molecular 
motion; in fact it is this latter motion that causes the ‘‘elasticity” 
which serves to maintain the vibrations of sound. It seems rather 
objectionable to aseribe the energy of the internal motions to a 
system of vibrations whose laws are deduced on the assumption of 
a molecular motion that existed already before the vibrations themselves. 
It must further be remarked that the ordinary laws of sound 
motion are true only so long as the wave-length 4 is large compared 
with the mean free path s between two collisions. Only in this case 
