30 Prof. Maxwell on the Motions and Collisions 
Multiplying together (19), (20), and (21), and M, we find the 
momentum at impact 
MN 
v? 
4n?/3 
Integrating with respect to z from 0 to ni, we get 
4MNv? ne~ dn. 
Integrating with respect to x from 0 to 0, we get 
4MNv? 
for the momentum in the direction of z of the striking particles ; 
the momentum of the particles after impact is the same, but in 
the opposite direction; so that the whole pressure on unit of area 
is twice this quantity, or 
potMNe*, — 0) foe) Se es 
This value of p is independent of / the length of path. In 
applying this result to the theory of gases, we put MN=p, and 
v?= 3h, and then 
(n21? —z®)e-" dz dn. 
p=hp, 
which is Boyle and Mariotte’s law. By (4) we have 
fe Ay t-PA gee RATA!) 
We have seen that, on the hypothesis of elastic particles 
moving in straight lines, the pressure of a gas can be explained 
by the assumption that the square of the velocity is proportional 
directly to the absolute temperature, and inversely to the specific 
gravity of the gas at constant temperature, so that at the same 
pressure and temperature the value of NMv? is the same for all 
gases. But we found in Prop. VI. that when two sets of par- 
ticles communicate agitation to one another, the value of Mz® is 
the same in each. From this it appears that N, the number of 
particles in unit of volume, is the same for all gases at the same 
pressure and temperature. This result agrees with the chemical 
law, that equal volumes of gases are chemically equivalent. 
We have next to determine the value of 7, the mean length of 
the path of a particle between consecutive collisions. The most 
direct method of doing this depends upon the fact, that when 
different strata of a gas slide upon one another with different ve- 
locities, they act upon one another with a tangential force tend- 
ing to prevent this sliding, and similar in its results to the fric- 
tion between two solid surfaces sliding over each other in the 
same way. The explanation of gaseous friction, according to 
our hypothesis, is, that particles having the mean velocity of 
translation belonging to one layer of the gas, pass out of it ito 
another layer having a different velocity of translation ; and by 
striking against the particles of the second layer, exert upon it 
