4 
248 
outside the volume v. A similar remark holds regarding the energy 
u. The conditions represented by (4) must then beso understood that 
the number of molecules in each of these outlying elements of the 
6-dimensional space is zero, and for each of these elements the 
figure 1 must be put in the denominator of the permutability index. 
We have still to calculate the number of micro-complexions contained 
in the individual macro-complexion; this is determined by specifying that 
n,, Specified molecules are present in dv,dw, 
| (5) 
Nel ‘3 3 45 fs … dordw.. 
These micro-complexions differ only in the different dispositions of the 
n, =n,, + … “17 molecules in the volume-element dv, etc. The diffe- 
rent volume-elements are here to be regarded as independent of each 
other. We then obtain the total number of micro-complexions by cal- 
culating the number of different ways in which the n, molecules 
can be placed in the volume dv,, the same then for dv, ete, and 
by then multiplying these numbers together. 
Let us first put the first of the », molecules in dv,. For this there 
are x places available. For the second molecule there are then left 
4 \ 
—wo'l 
x 1 — [places available. Of these there is a comparatively small 
v, 
number for which the distance between the centres of molecules 
is such that the distance spheres of the two molecules partially 
overlap. In placing the third and succeeding molecules we shall omit 
these cases, for bringing them into the calculation would introduce 
terms of the second order of small quantities compared with the 
principal terms of W, and would have no effect upon the value of 
the virial-coefficient B. The influence of these terms would have to 
be more closely investigated only in the determination of C and 
succeeding coefficients. The number of places available for the third 
a, 
' ee | 
molecule can then be written x {1—2. = \. Proceeding in this 
Er 
fashion we obtain 
8 
5 n,—1 Sine 
05) TE 1—t 
(== dv, 
different dispositions of the 7, molecules in dv,. Doing the same for 
dv, ete., we obtain the number of micro-complexions in the individual 
macro-complexion. 
