( 8t% ) 
Applying the known elementary theory of mean free path we have 
to put this number proportional to (» + 7,)?. If we admit that all 
possible configurations still occur in a large number, we can put 
for the contribution of the xtb element to the velocity 
9 
ee (» + 1,)? 
The coefficient « depends on the nature of the forces in the colli- 
7 a 
A Pa (Va 
sions. We therefore find for = (; ) in the system in question: 
qs | 
l 
k . 
a = (yp + 1,)° 
| 
and for the velocity 
mis al 2 
ve = — +e (v-+t,) 
™, 1 
For the system with equal but opposite deviations we find: 
9 k 
AE oss ‘ 
(ee le aes (pt sae)” 
m 1 
ke 
Taking into account that 2 71, — 0, we find 
l 
De, I I I 
Omer OS eet = 6, + ee fee, 
ule l 1 l 
v, being the mean velocity for the homogeneous system. 
The mean value of velocity for the deviating system is therefore 
always greater than the one for the homogeneous system. The colli- 
sions with the walls are neglected, this is permitted, as their number 
is much smaller than that of the mutual collisions; moreover their 
contribution is for long periods of time the same for the three 
systems. The path through which the homogeneous system passes on 
k 
in a long time 7’isv, 7’, for the deviating systems («, +a 2e) T, the 
l 
deviations of these values being small compared with the values 
themselves. So the path is smallest for the most frequently occurring 
system and equal for deviating but equally probable systems. 
