146 
The layer will however not be able to resist a strong normal 
impulse. When the radial relative component a is great enough, the 
two internally colliding particles may leave each other’s sphere of 
attraction. Here also the tangential velocity component will not 
change. The normal component on the contrary will. 
The quantity }ma?-+2y will therefore have the same value 
before and after the impulse. 
We thus must take for 2 and y the integration limits — oo and 
+ oo and for aa positive value that satisfies } ma* + 2y = 0, and + op. 
With these limits the integration with respect to «,@ and y gives 
in (2) a factor 
TE ARNE 
Abr 
Let us write S for the surface of the layer. The surface in (21) 
gives a factor S. 
The integration with respect to §, 4, ¢ a factor 
x \% 
2 hm 
Thus we finally find for the number of molecules dissociating 
per unit of time and per unit of volume ' 
aa NE mw \% S 
a 2 \ hm 2 hm x 
Dividing this by the number of molecules (1) per unit of volume, 
we find the following value for the velocity constant 
p —- = 
S 1 Ss — kT 
hk, eth - — e kI ze Gan (ZI) 
V2nhm ©@ am 
while from (/) and (J/) we find for &, 
kT 
4 =15|% = a ap 
JEM 
Of course the £, can be found in the same way as &,. 
Thus far we have supposed, that every impulse is followed by 
a combination. The meaning of k,v,* is therefore the number of 
collisions per unit of time and volume. We find for it’) 
kT 
kv = oes —- 
m 
in agreement with (///). 
k 
This gives therefore a verification of the equation K = = 
1 
» Eg. BOLTZMANN, Vorl. über Gastheorie I, pag. 69. 
