262 
ete, in which c and 4 are constants. If we retain only the terms’ 
of the rank of principal or first order terms in log, W, we get, since 
4 
n, Penis is small compared with dv, : 
| — nr? 
3 —huy) 
Nila — © | a é 
dv, 27 A ABO 
( Zee) huwe) 
11,1 — C{ 101 ENE é 
1 
The constant c is determined by the condition that the total 
number of molecules must be equal to n. Let us write c = c’dw, = 
=c'd3, dy, dö,, and then summation (integration) of (30) with 
respect to dw, gives 
2n\* 4ar,?dr 
ny) = c? ( z= ee 
hm dv, 
Summation with respect to 7, and addition of the value of 7, 
yields an expression for 7”, which leads to the conclusion that the 
distribution of the molecules in space in the state of equilibrium is - 
uniform in the macroscopic sense. c’ is next determined by summation 
with respect to dv,. We then obtain 
2 
n : 
Nin == Aarf dr, bk) do ts orn OS (GH 
De 
If we divide this by 2 it gives us, to a first approximation, the 
number of pairs of molecules whose distance apart lies between 7, 
and 7, + dr, in the state of equilibrium. This expression is in 
agreement with that given by BOLTZMANN (p. 257 note 1) which was 
also used by REINGANUM (p. 257 note 2). 
We find, moreover, that 
2 3 
n? (hm 'lz ies ef Nu 
Ana == = (=) Aar dre GS ee do: dos or EN 
v \2ar 5 
so that the velocity distribution is the same for molecules in each 
other’s neighbourhood as for single molecules. 
For the number of single molecules we get 
n (hm *!2 n 
Nu = — | 5 Wee AE 
Vv aw Vv 
P= OQ are dn oe. Boe Pe eee eee) 
0 
ea died A S83 
in which 
