[141 
on this diminution of 6 has not yet been decided. In case of greater 
velocity there are indeed, more collisions, but we may also assume 
that they are of shorter duration. At the moment, however, I shall 
leave this point undecided. What I have said here about the cause 
of the diminution of 6 with smaller v is practically what I had 
assumed as cause already before when I assumed the so-called 
overlapping of the distance spheres as cause. 
- by by 
The formula then derived for b = 6, — a a + 2 @ etc. was not 
satisfactory, and gave a far too rapid decrease with the calculated 
coefficients a and 8. And the cause of this at least I think I shali 
have to attribute to the quasi association. If fora moment I disregard 
the motion, and think all the molecules to be distributed in pairs, 
every pair being in contact, the dimination in the value of 6 is 
} N-times the overlapping of the space at the collision between these 
molecules. But if in the motion I again admit the arbitrary pretty 
regular distribution and if I assume the original space, the diminution 
in 6 would of course be much less, and would only hold for those 
that collide. So for every kind of collision either of 2 or 3 or 4 
or perhaps of a greater number the chance that such a collision 
occurs in the given volnme must be calculated, and this fraction — 
must be multiplied by the parts of the spaces which overlap at 
every kind of collision. 
b,—b by 8 by 3 by 
In the formula — =a—+ gl etc. — represents the chance 
b Uv v v B 
g ) 
that 2 molecules come near enough to each other to bring about 
ie 
8 5 : ] 
overlapping of the distance spheres; in the same way a) the 
7] 
chance that 3 distance spheres overlap ete. And multiplied by a 
certain coefficient this would also be the case in complete absence 
of any cause of association, so if there are no special reasons for 
the molecules to aggregate. The quantities «, 8, are the pieces of 
the distance spheres that overlap. For 6, all the molecules without 
exception are counted, whether they are separate or whether they 
are part of an aggregation — and for the factor of @ all the groups 
of 2 molecules, whether or no they appertain to a larger aggregation. 
But I have not yet calculated all this. 
That with diminution of the volume the decrease of 5 will take 
place more and more rapidly may already be inferred from this 
that the number of every kind of collision or rather sufficient 
approach to each other, increases in a heightened degree, and at 
last if only the volume has become small enough, it may be assumed 
