260 
question in one of these places there are, since the second of the 
pair must come within a distance between 7, and 7, + dr, of the 
first, 
Anr,*dr, 
47 
dv 
1 
places available. This is so at least for all those cases in which the 
first molecule is placed within a distance not less than r+ 7, of 
any of the 7, molecules already in position. When that distance is 
not exceeded complications are introduced by the fact that a portion 
of the shell 4zr,*dr, lies within the sphere of influence of that other 
molecule. If we wished to confine ourselves strictly to cases in 
which one molecule is acted upon at any time by no more than 
one other molecule, then these portions of the shell which are over- 
lapped by other spheres of influence ought not to be included in the 
summation. 
But cases in which these complications occur form but a small 
fraction of the whole, both for this and for subsequent pairs of 
4 
n,.—ar* 
molecules, the order of magnitude being Tae which is very 
v 
ae 
4ar,*dr ; 
—— give rise to terms in log, W which are of the 
small. The terms x : 
1 
first order of small quantities, and which we shall have to take into 
account. Subsequent terms, however, may be omitted, and in that 
case we may also neglect the effects of the complication referred 
to above. Likewise we shall for the same reason neglect corresponding 
complications for subsequent pairs, of which the placing of the first 
molecule already gives rise to a factor which we change ina corre- 
sponding manner. 
As the method here described gives all the positions possible, after 
the 2, single molecules have been disposed of, for the first pair of 
molecules whose distance apart lies between r, and 7, + dr, the 
placing of this pair gives rise to 
4 
—_ nT? 
3 Anr dr, 
x 1 — nj, 
dv, dv, 
possibilities. In this expression we shall introduce a factor 1—(m, + 1) 
— nt 
Pia: these factors, too, of which there is one for each pair of mo- 
Pa 
