401 
of Edinburgh, Session 1885 - 86 . 
Clausius gave, from his point of view (equal speeds, equally dis- 
tributed in all directions), the factor 
0 * 75 . 
This can he readily obtained from the above formulae before the in- 
troduction of the distribution of speed. It is accurate from the 
point of view taken by Clausius, hut it is inapplicable to the kinetic 
theory. 
1 
Clerk-Maxwell gave the value —= or, nearly, 
v ^ 
0 - 707 . 
But his process is, I think, based on a questionable definition, 
which has since been adopted by Meyer, Watson, and others, who 
have written on the Kinetic Theory. It involves the assumption 
that the mean free path is expressed by 
Average speed of a particle 
Average number of collisions per particle per second. 
But, in order to find either the numerator or the denominator of 
this fraction, recourse is had to the ordinary definition of a mean, 
that which we have used above. 
Those who adopt this deviation, from the ordinary method of 
finding a mean, must face the question : — Why not adopt another 
equally plausible deviation, and define the mean free path as 
(Average time of describing a free path) x (average speed) 1 
If n v be the fraction of the whole particles which have speed v, 
p v their mean free path ; the definition of the mean free path, which 
we have adopted as the natural one, gives for its value 
2(n v p v ) . 
The definition usually adopted gives 
^(n v v) 
(n v -) 
\ Pv / 
That which is suggested above, as an alternative to this last, gives 
Pv 
- i . /• 
9 
SU^). S («,«)■ 
VOL. XIII. 
