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t, without changing it by collisions. It is casy to show, that the 
entropy would then remain constant. 
Let us first think the gas enclosed in a small cube with a centre 
O, the axes being taken parallel to the sides. We get 
H =f EL "log (IF) de dy de dE dn de 
— n ¢ representing the components of the velocities of the mole- 
cules. The first three integrals for « y and z must be taken between 
the limits — }aand + 34, where a represents the edge of the cube, 
and the other three for § 7 and ¢ between — oo and + om. If the 
volume of the cube was 0, the velocity of the molecules which had 
reached after one second the point P(2’y'z') at a distance r from 
O would also be r and their density a? 2’(2'y! 2’). 
By assuming this density as being the real one, we shall make 
a slight error. For the velocity we must however take into account 
that the velocity of molecules, which reach P after one second, 
starting from different points of the cube, is different. 
The probability that the components of the velocity of a molecule 
which has reached point P, are enclosed between the limits: 
a tev and He ddr §' + dé 
gyn and y+y+qy=y +a) 
2étze=0 ander Hede! dh 
#, y and z representing the coordinates of the point of the cube, 
from which the molecule has started, is: 
dedydz _ dE dy! dg 
na as 
we find for MZ after one second: 
4 1 1 
Mf = Hilfe I" — log G F =) dx’ dy dz' d&' dy' at’ 
t ay A a? az 
=f PLP fe 0) ae dy ae as an a 
F is obtained, as we have seen, by substituting r in F for the velo- 
city; 7 represents the distance from an arbitrary point to the origin. 
