( 858 ) 
Physics. — “Some remarks on the mechanical foundation of thermo- 
dynamics.” 5 II. By Dr. L. S. Ornstrin. (Communicated by 
Prof. H. A. LORENTz. 
(Communicated in the meeting of Januari 28, 1911). 
§ 4. In § 2 I have discussed some ensembles and [ have shown 
that they can be used to deduce the properties of a real system 
because they are connected with the time ensemble and because the 
majority of their systems is equivalent. I shall give in this paragraph 
another deduction which for this purpose may show the importance 
of the energy-space ensemble (and of the microcanonical one). 
If in reality we want to obtain a system with a given energy 
we take a system of the same kind and supply energy to it or 
abduce energy from it, giving at the same time the appropriate 
values to the external coordinates. Let us suppose that it is possible 
for us to construct a system that contains exactly the required 
energy. If we do not take special care to get a system of a definite 
internal state, we shall obtain by our operations one of the systems 
possible with the given energy, but it will be impossible to indicate 
what kind of system will be produced. We can by no means 
practically regulate the internal state arbitrarily, as it is impossible 
for us to influence directly a single degree of freedom (e.g. the 
phase of the molecules). But we can only give the values we desire 
to the energy, density, or concentration in rather large parts, and 
even this with a moderate precision. If in a great number of cases 
we give the energy & to a system we shall obtain it over and over 
again in other states, and the same will be the case if we bring 
the energy of a great number of systems together to the value €”) 
The ensemble obtained in this way may be called a “real” energy 
space-ensemble. 
Instead of giving the energy « to N systems we can also select 
them in nature. I shall term the ensemble thus obtained a nature 
energy-space ensemble. The real and the nature energy-space ensemble 
i) See These Proceedings page 817., Putting for the probability of the homo- 
eencous system Wp we find for that of a system specified by the numbers +, 
Ww — We 
B is a function of the volume, the diameter of the molecules and the temperature. 
2) The circumstance must be taken into account that the original system will 
differ also in phase. 
