( 864 ) 
after their union a system of the same temperature. He supposes 
the connection performed in such a way that the two systems form 
together a new system, of which the reciprocal energy is small in 
comparison with ¢, + ¢,. The connection enables the systems to inter- 
change energy. The quantity + of Hertz is related to the average 
kinetical energy in the ensemble and is interpreted by : 
en nV on 
oe 
ce oe Ebina 
n being the number of degrees of freedom, V the volume of the 
o 5 
extension in phase where the energy of the represented systems is 
yr 
less than ¢, w is put instead of 
de 
Hertz determines in a very elegant manner the conditions 
necessary for two microcanonical ensembles of the energies e, and &, 
and having 1,(e,) equal to r‚(e,) to form after their connection an 
ensemble of the energy «, + ¢, and the temperature t1,,(&, + €) 
so that 
Tis (e, Ei 5) — tT, (€,) — T; (€,). 
His considerations teach us only something about the equilibrium of 
temperature for stationary systems if we have shown that the average 
kinetical energy of a degree of freedom is equal to that in the 
most frequently occurring system, while the conditions of Hertz 
are complied with. We shall suppose this as proved and if we then 
consider that two ensembles of energy ¢, and ¢, and of equal 
t-value produce an ensemble of the same t-value, and that the mean 
kinetical energy in the original ensembles is also equal and with it 
the kinetical- energy of the most frequently occurring systems, we 
shall find that also the temperature of the stationary systems are 
equal before and after the union. 
Even if we unite systems in non-stationary state, we can deduce 
something. If the temperature of the considered systems would be 
equal after they had come to a stationary state, they would belong 
to ensembles of equal tr. The system formed by their union belongs 
to an ensemble with the same value of t, the temperature therefore 
adopted by the system formed if we unite two non-stationary systems 
is, if this system has become stationary the same as that which would 
have been adopted by the separate systems in their stationary state. 
Also for the canonical ensemble we find the same results. GrBBs 
1) Conf. P. Hertz loc. cit. p. 243. 
1) For gases and fluids | have proved this in my dissertation. 
