328 
16 
to the left: 
‘Ror tim (© ailaly OX eee Ca. sg 
(27) 
with a given wo OF 
For t > O the wall stops the molecule @=O aty:9: 
(28) Fer allt S50) ee oly 
Clearly (27) should only apply to the right half, i.e. to a=/,2,. 
Now (25) conserves the energy (26), i.e. the total kinetic plus 
potential energy, while (11) i.e. (20), excludes such a conservation. And 
the laws of Rankine and Hugoniot, on which (11) is based, are merely applica- 
tions of the basic conservation principles, which hold for (25) too. How 
then can (25) still conserve the energy (26)? 
The plausible answer is that (25) will produce something like a 
shock under the conditions specified, but that the motion of the sc beyond 
the shock will not be the smooth hydrodynamical one, but rather one with a 
superposed oscillation. This oscillation should contain, as a kinetic ener- 
gy, that degraded energy which can only be accounted for in the hydrodynamical 
case ((15) with (10), (14)) by introducing a separate thermic energy Wee" 
Indeed, (25) describes a quasi-molecular model, and in such a model the 
thermic energy appears necessarily as a part of the kinetic energy. 
§12. These considerations suggest the surmise that (25) is always 
a valid approximation of the hydrodynamical motion, i.e. of (15) with (10), 
(14), but with this qualification: It is not the a= Mere of (£5) 
which approximates the X = x(a t) of (15), but the average of the ee 
over an interval (of sufficient length) of contiguous a's. The xX, them- 
selves perform oscillations around these averages, and these oscillations do 
not tend to zero, but they make finite contributions to the total energy (26). 
