1135 
but also the double tangent ones will not take place, and the factor 
4 wiil not diminish so rapidly as might have been expected without 
taking this in consideration. 
To make clear what I mean, imagine a molecule in motion to 
strike against another. On the supposition of spherical molecules 
draw a sphere which has its centre in the second molecule with a 
radius = 27 (if 7 is the radius of a molecule). Then at the moment 
of the impact the centre of the colliding molecule must lie on that 
sphere with a radius twice as long as its own. Now imagine also 
through the second molecule a central plane at right angles to the 
direction of the relative motion, in which ease the second molecule 
may be taken as stationary, then the mean abbreviation of the free 
length of path is the length of the mean distance at which the 
centre of the moving molecule lies from the said central plane. In 
very large volume the chance that the centre of the moving molecule 
strikes against a certain area of the sphere with 27 as radius is 
proportional to the extension of the projection of this area on the 
said central plane. It follows from this that the mean abbreviation 
of the free length of path is the mean ordinate of a haif sphere 
; 4r . vie 
with 4xr’ as basis, and so equal to a It is true that this is the 
abbreviation of the length of path for 2 molecules, but this is com- 
pensated by the fact that an abbreviation of the same value exists 
also at the beginning of the free length of path for the moving 
molecule. 
If also in a small volume the chance to a collision with the 
sphere with 2r as radius could be determined, the way had been 
found to determine the value of 6 in every volume. For v <45 the 
double central impacts must be eliminated, but also the double 
tangent ones. And strictly speaking in every volume, however great, 
if not infinitely great, the chance to double central and double 
tangent impacts must have lessened. Here a course seems indicated 
to me which might possibly lead to the determination of the value 
of 6 for arbitrary volume. I do not know yet whether this will 
sueceed, but at any rate it has appeared to me that this may serve 
to calculate by, and not only for spherical molecules. The latter 
is certainly not devoid of importance, as the case of really spherical 
molecules will only seldom occur. 
Let me first demonstrate this for spherical molecules. In the extreme 
case when they are stationary, they lie piled up, as is the case with 
heaps of cannon balls, each resting on three others. Let us think 
the centres of these three molecules as forming the tops of the ground 
74 
Proceedings Royal Acad. Amsterdam. Vol. XV, 
