1070 
This projection has now to be averaged for all angies 9, taking 
into account, that the chance of a collision for each direction is 
proportional to the relative velocity + and to 4 sin 0dd. The mean 
is therefore given by 
| prsin ddd 
0 
Tt 
Ir sin d dd 
: 0 
As r?>=a’?-+ 6? —2abcos%, it follows, that rdr = ab sin dS. 
After substitution of si 9d9 and of p and integration we obtain 
2m, +m,) a° + m,b? mM, 3 da'4-10a7b?+40* | 
NE : for’ >b 
EE TOR 
2(m,-+-m,) a = 
and 
(2m, Am) a +-m,b° m, 3 a'+10a7b? +564 
EN ze “for a <b; 
m,+m, 10a a’? t- 3b? 
2(m,+m,)a 
these expressions have to replace those given by Jrans (l.c. p. 239). 
With Jrans we may put a= xb. 
ry . mn = . 
The chance per second, that a molecule with velocity a collides 
with a molecule with velocity 5, the relative velocity being 7, is 
aa oe b 
2n, 0 x h® m,* kml? — db r? dr, 
a 
where 7, is the number of molecules im, per unit volume, and as 
2 
the number of molecules per unit volume with velocity a is equal to 
h'm,® . 
An, ehm? qa? da 
nr 
(n, = total number of molecules m, per unit volume), the total 
number of collisions of the kind considered will be 
Sn. n, 62h? Vm? m,? e— hOma?Hmsb?) ab da db r? dr. 
1 8 1 
2 
Integrated with respect to r for a >> b, when the limits of 7 are 
a+ and a—b, this becomes 
16 Ars, 
mt oh Vm'm, ehm atmabì) ab? (Pa? + 5”) da db 
and similarly for a <b 
16 ee STEN 
ie ot h®? Vm? mt eh ma*-+mad?) ab (a° +. 3b?) da db. 
e 
In both expressions we may again put a =x. 
