402 
Proceedings of the Royal Society 
It gives for the reducing factor the approximate value 0*647 ; 
which falls short of 0*677 nearly as much as that, in its turn, falls 
short of 0*707. 
From the point of view here taken, the process usually adopted 
virtually amounts to assuming that the mean value of a number of 
fractions is to be found by dividing the mean of the numerators by 
the mean of the denominators. The reason for the close approxi- 
mation of the results obtained by these different methods is to be 
sought in the fact that the great majority of the particles have 
speeds differing but little from the mean square. 
It is usual to express the result of this_ investigation in the form 
of the ratio of two fractions ; 
A = 
Mean Path 
Diameter of Particle ’ 
and 
Volume occupied by the particles 
Sum of the volumes of the particles * 
The values of B/A are 
According to Clausius 8 
„ „ Clerk-Maxwell ^72 = 8*48 nearly 
6 
„ „ above reasoning ^^ = 8*86 „ 
6 
„ „ alternative 777 ^ = 9*27 . 
U*o47 
It may be worth while to remark, in this connection, that the 
somewhat elaborate process, by which Meyer* obtains the mean 
number of collisions undergone by a particle in unit of time, can be 
very much simplified. For, by what is said above, it is easy to see 
that ev represents the average number of collisions which will be 
undergone, per second, by a particle whose speed is, and remains , v. 
Hence, taking account of the distribution of speed among the im- 
pinging particles, we have for the average number of collisions per 
particle, per second, Meyer’s expression 
OO 
1 6 ns 2 r g 
^ J o 
2 
* Dissertcitio dc gasorum theorid, 1866. Quoted in his work Die Kinetische- 
Theorie der Gase, 1877, p. 294. 
