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on that matter, except a small example in (2), but we will only 
mention how we have formulated the problem because that is 
important for another reason. First the problem was limited to 
one dimension for the sake of simplicity. Where DeBije already 
introduced the great simplification of considering longitudinal waves 
only, it is easy to understand that for a more strict calculation 
it is necessary to go as far as to consider provisionally only such 
waves as run in a special direction. Let us e.g. consider the 
longitudinal waves of a thin bar. The equation of motion for this 
case is strictly linear if the law of Hooke is accepted. Generally 
this has been accepted, also in the case of the for the rest quite 
analogous discrete problem of a series of molecules with elastic forces 
between them. Therefore we may always represent the movement 
of the bar by a superposition of normal-vibrations. This is done in 
the case of the well-known calculations of the specific heat. It is 
necessary to suppose hereby a special statistical distribution of the 
energy over the different vibrations. At a high temperature e.g. one 
is inclined to take equipartition for it without troubling about how 
it occurs. But it is remarkable that in this case there can be no 
question of equipartition establishing itself as it occurs in 
a gas by the collisions. For during thé movement the energy of each 
normal-vibration remains constant so that any method of division 
continues to exist permanently. We may put it statistically like this: 
time-ensemble and microcanonical ensemble are very different from 
each other and consequently are not practically equivalent. 
This difficulty, which is essentially connected with the existence of 
normal-vibrations of the system, disappears as soon as non-linear 
terms of higher order are introduced into the equation of motion. 
When these terms are very small, and this is sufficient, then we can 
speak of the guasi-normal vibrations of the system. During a short time 
the quasi-normal-vibrations behave at first approximation like normal- 
vibrations. The non-linear terms however bring about a slow exchange 
of energy between the quasi-normal-vibrations. We intend to revert 
later on to the calculations regarding this subject which we have 
performed. As we mentioned already they did not produce a valuable 
result for the theory of heat conduction. It remains still to be examined 
which other phenomenon corresponds with the molecular action 
mentioned. Probably it will also be possible to prove later that by 
the terms mentioned the system will slowly approach the condition 
of equi-partition. 
2. In contrast to the calculations mentioned above, we shall record 
