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different elements of the 2s-dimensional space involving the coordinates 
p and the momenta q (the micro-elements) are of the same size., 
We consider now, in general, states of the system of molecules 
which are defined by certain conditions — formulated in detail for 
each special problem — in such a way that the number of mole- 
cules or of groups of molecules is determinate for which e.g. certain 
coordinates, mutual distances or orientations of the molecules, their 
momenta or their relative velocities lie between limits previously 
assigned. The formulation of these special conditions and the choice of 
limits must so be made that the supposed numbers of molecules etc, are 
sufficient to determine, in so far as the particular problem under 
discussion is concerned, the state of the system as seen by a macro- 
observer at the particular moment for which those numbers are given. 
In this we are in no case concerned with the individuality of the 
molecules (we assume throughout that we are dealing with a single 
component substance). The limits to which we referred must, moreover, 
be so chosen that the macro-state thus determined can be realised 
from a very large number of different micro-complexions. The assemblage 
of these micro-complexions we shall call a group macro-complexion’). 
As a foundation for further development we shall now assume 
that all micro-complexions represent cases of equal probability *). From 
this it follows immediately that the probability, W, of the occurrence 
of any group macro-complexion is proportional to, or, if we care to 
neglect an arbitrary factor, is equal to the number of micro-com- 
plexions contained in the group macro-complexion *). 
In many cases it will facilitate the calculation of this number to 
first obtain the number of micro-complexions contained in an individual 
1) For constructing a clear molecular kinetic interpretation of a definite macro- 
state, in particular regarding the number of the different micro-states by which it 
can be realised, we regard here as in the GrBBs method at any particular moment 
an assemblage (ensemble) of systems, independent of each other identical as regards 
number, structure and actions of their component particles and as regards their 
exterior coordinates, each of these systems forming a definite micro-complexion 
realising that macro-state. Cf. BorrzMann, Wiss. Abh. 1, p. 259; 3, p. 122; 
MAXWELL, Scient. pap. 2, p. 713. [Note added in the translation.] 
2) In the present paper we shall not justify this assumption, which, in so far 
as it affects the choice of micro-elements, is founded upon LIoUVILLE’s theorem, 
but for it we may refer to the writings of BOLTZMANN, PLANCK (e.g. Acht Vor- 
lesungen, p. 56), and others. (Compare also Art. IV 32 by P. and T. EHRENFEST 
in the Math. Encykl., particularly note 170). 
3) In order to conform to the common definition of probability as a fraction 
between 0 and 1 in value we should have to. divide by the assumed value of the 
constant total number of micro-complexions possible, which would have to include 
all possible values of energy and volume which occur in our considerations. This 
constant is of no importance in any of our considerations, so we shall omit it. 
