( 736 ) 
$ 5. For this proof I must refer to a formula of Cravsmvs used 
by me already before’). Imagine a point which can freely move 
in a space W. Crausmus®) shows — which is already plausible 
beforehand — that the number of collisions of this point per second 
against a wall of area S is proportional to S/W (the factor of 
proportion depends only on the velocity of the point). 
Let us now consider a wall as defined under 2, and draw a 
plane parallel to that wall at a distance */, 6 (6 is the diameter of 
the molecules, which we think spherical); this plane we call plane 
of impact, because the centre of a molecule, which strikes against 
the wall, lies in this plane. Now we apply Cravstus’ formula to 
this wall. In this we must allow for the fact that the centre of a 
molecule cannot move freely throughout the volume of the fluid; 
for within the distance spheres (spheres drawn round the centre of 
every molecule with a radius 6) it cannot come; instead of 7 we 
have therefore to put v—2b, when 2/*) is the volume of the distance 
spheres. Now the whole plane of impact, however, is not accessible 
to collisions either, part of it also falls 
within the distance spheres. In order to 
fix this part we draw two planes at 
distances A and / + dh parallel to the 
plane of impact. We determine how 
many centres of molecules are found 
between them and what part of the 
plane of impact is within their distance 
sphere. In order to find what part of 
the plane of impact falis at all within 
distance spheres, we must integrate with respect to A between O 
and */, 5. It appears then, that instead of S we must put S(1—6/r) 
in the formula for the number of collisions against the wall, so 
Fig. 1. 
that the pressure becomes proportional to 
or in first approximation 
) These Proc. VI. 791. 
2) Kinetische Theorie der Gase, 60. 
5) For simplicity L confine myself to the first term, even if we have to deal with 
liquids; this is permissible here, because the cther terms have no more influence 
on our question (the derivation of the law of Van ‘r Horr) than the first. 
