1136 
plane of a regular tetrahedron. For a volume infinitely little greater 
than the limiting volume the limiting direction of the motion of the 
4th molecule is that which is directed at right angles to the ground 
plane, and in case of collision the three molecules of the ground 
plane are struck at the same time. The sides of the tetrahedron have 
a length equal to 27, and the perpendicular from the top dropped 
2 
on the ground-plane is equal to 2r Ws 
The abbreviation of the length of path in consequence of the 
5) 
. . . « . el . 
dimensions of the molecules is equal to half 2r Vaz if one 
wants to make this comparable with the above found one of a 
because this value referred to the abbreviation at a collision of two 
molecules, whereas the now found abbreviation holds for a collision of 
‘ 
4 3 
4 molecules. The number of times that are greater than 7 Ws ; 
7 by by : 
is the value Ol. = 10E is equal to 
lim bin 
4 3 ie É 
— — = ei 
3 2 3 
8 | p= Fis 
For spherical molecules, therefore, te 1.633 or 7 almost 
8 
equal to 5,9 and s= — 1,633 or about 3,3. And then it would 
G9 | 
follow that these values f=5,9 and s = 3,3 must be considered as 
the smallest possible values. 
But I do not lay claim fo perfect accuracy for these values. 
Doubts and objections may be raised against these results, which I 
cannot entirely remove. Hence the above is only proposed as an 
attempt to caleulate bjimn for spherical molecules. The first objection 
is this — and at first sight this objection seems conclusive. The 
value of bm must be equal to vin. Is the thus calculated value of 
him then the smallest volume in which stationary molecules can be 
contained? This is certainly not the case. The volume of n° stationary 
spheres placed together as closely as possible is equal to 4n*r°V 2 if 
n is very great, and accordingly “2 times smaller than if they should 
be placed so that every molecule would require a cube as volume 
with 2r as side. If this value must be the value represented by dim, 
