nical distribution is the most probable one, provided the only condi- 
tion, to whieh the ensemble is subjected, be that the mean value of 
the energy of the systems is a preseribed quantity; but the main 
difficulty happens to be to answer the question whether this is indeed 
the only condition. Systems e.g., consisting of spherical, mutually 
equal molecules, will not be distributed canonically, for they are still 
subjected to another condition, namely the distance of two centres of 
molecules can never be less than the diameter. To assume the cano- 
nical distribution comes therefore to the same as to neglect the volume 
of the molecules, but it is not easy to decide whether nothing else 
is neglected. In fact choosing the distribution of the systems of an 
ensemble is equivalent to choosing the cases, which we are to consider 
as “eases of equal probability” in a more direct application of the 
‘alculus of probabilities. Both are subject to the chance, that the proba- 
bility a posteriori will prove to be another than we had assumed a priori. 
Yet such like considerations can be useful, in the known region 
of thermodynamics, because they bring its laws very simply and 
elegantly together under one point of view ; in the yet wnknown region, 
because they may perhaps suggest formulae, for which comparison 
with the experiments may decide, whether they are in accordance 
with the phenomena of nature or not. 
Law of conservation of density-in-phase. 
In an investigation, whether the considerations of GiBBs are also 
applicable for electro-magnetic systems, we have in the first place to 
examine, whether the “law of conservation of density-in-phase” holds 
also for them. In the beginning we will confine ourselves to systems 
devoid of material, electrical or magnetical masses. 
Now we imagine an ensemble of systems. The different systems 
are congruent spaces, enclosed by perfectly reflecting walls. We divide 
each system into m equal eubie elements of space de dy dz. These 
elements are so small that the eleetrie and magnetic forces in them 
may be considered to be constant.. The state of each system will be 
perfectly defined, if in each element of space the components 
?, g and h of the electric displacement, and the components a, Band y 
of the magnetic induction are given. So the state is determined by 
means of 67 data; according to the assumption, that electric energy 
is potential, magnetic energy kinetic, the 3 7 components of the electric 
displacement would represent coordinates, the 8 7 components of mag- 
netic conduction generalized momenta, or at least they wouid be 
proportional to them. 
