of Perfectly Elastic Spheres. 29 
and if 7, be the mean distance for a particle of the first kind, 
b= VPmaNy tra) 14 2 es SINGS Wests ED) 
Similarly, if 7, be the mean distance for a seetitle of the second 
kind, 
ie V 2ms2N.+7 \/ Le YPN, os fateh Levy 
2 oP) 
The mean density of the particles of the first kind is N,M,=p,, 
and that of the second N,M,=p,. If we put 
Dot vom, Bara/1+% oa? C=1A Vike ae 
ee ee 
1 1 
Ali ad a That De, - + (15) 
and 
AE ei ae eR IRF 
C7 Mo, o> 
Prop. XII. To find the pressure on unit of area of the side of 
the vessel due to the impact of the particles upon it. 
Let N = number of particles in unit of volume ; 
M = mass of each particle; 
v = velocity of each particle ; 
7 = mean path of each particle ; 
then the number of particles in unit of area of a stratum dz 
poe IGEEO 0, nagieiry, ssastracqenge me) 
The number of collisions of these particles in unit of time is 
Nias Oma hie. rama 
The number of particles, which after collision reach a distance be- 
tween n/ and (n+ dn)l, is 
Noe" dz dn. Se te cats, Sal TOs 
The proportion of these which strike on unit of area at distance 
sal nl—z 
onl 3 (20) 
the mean velocity of these in the direction of z is 
n+z (21) 
yan 
