247 
determined from the same elements of the proper space as the macro- 
complexion. With regard to the distribution of the molecules throughout 
the space we must distinguish between various elements of volume, - 
which are supposed small in comparison with the dimensions of a 
molecule, for, in ascertaining if a certain micro-complexion occurs in 
the macro-complexion determined by (4), it is of importance to know 
if the centre of any particular molecule lies within or without 
the distance sphere of any other molecule. Hence we divide 
the volume-elements of the macro-complexion into smaller volume- 
elements, thus 
dv, into x equal volume-elements dw... dwi, 
dv, ”? EE) ” 2 do, Pd ds, 
eit. 
A micro-complexion is now determined by specifying for each mole- 
cule in which of the elements dw and dw it is present at the par- 
ticular moment under consideration (understanding that a molecule 
is present in the micro-volume-element dw, when its centre of mass 
is there). 
W is now the number of micro-complexions thus determined present 
in the macro-complexion given by (4); in this we must remember that 
all micro-complexions are excluded in which the distance separating 
the centres of any two molecules is smaller than the diameter of a 
molecule. 
For the permutability index of the macro-complexion we obtain 
nl! 
IT NAE (7D 
Nn 
As we shall have to deal only with such macro-complexions as 
correspond to states of equilibrium or to states differing but little 
therefrom, it follows from the conditions laid down regarding the 
magnitude of dv and dw, that for each element dvidw; of the 6- 
dimensional space in which, for any specified state, molecules may 
be present, the number Nij will be large. We shall, in the mean- 
time, be obliged to compare macro-complexions whose total volumes v 
are not the same *), for instance in the development of the thermal 
equation of state. This can be done if, in the determination of the 
macro-complexion, we also take account of volume-elements lying 
in this ¢ase use equal elements in the velocity diagram for determining micro- 
complexions of equal probability. 
1) When, as in the present instance, we consider states in which the substance 
is not split up into different phases, we shall indicate the volume etc. by small 
letters v.w,8, which, when referred to 1 gram of the substance, cau then be 
regarded as spec'fic quantities. 
