400 
Proceedings of the Royal Society 
path is to be found by multiplying the free path for each speed by 
the probability of the particle’s having that speed, and adding the 
results. This gives 
which may be written, after some reductions of an easy kind, in the 
simpler form 
1 4 x^dx 
mrs 2 J , „ r x ' 
•'o *+(2*2+1 )i**fe-*'dx 
It is obvious, from what precedes, that if the particles of the medium 
traversed had been quiescent, the mean path through them (at any 
speeds) would have been simply the first factor of this, viz., 
1 
717TS 2 ° 
Hence the definite integral above, which is, of course, a mere numeri- 
cal quantity, expresses the ratio in which the mean path is shortened 
in consequence of the motion of the particles of the medium tra- 
versed. By a rough process of quadratures (at intervals of 025 
from 0 to 3), I find its value to be about 
0°677 + 
but I hope soon to evaluate it more exactly. To check this result 
I traced by points the curve whose area is expressed by the integral* 
cut it out in stout tinfoil, and compared its weight with that of a 
square unit. The result was 0682, but I had probably allowed too 
much for the infinitely extended part of the area, which it was very 
difficult to represent properly by a process of this nature. 
