PROPERTIES OF MATTER IN THE GASEOUS STATE. 777 
is the condition of the molecules which cross a plane supposed to be drawn through 
the point, which plane may or may not be in motion along its normal. 
The molecules which cross this plane are considered as consisting of two groups, one 
crossing from the positive to the negative side of the plane, and the other crossing 
from the negative to the positive side. Considered in opposite directions, the mean 
characteristics (the number, mass, velocity, momentum, energy, &c.) of these two 
groups are not necessarily equal : they may differ in consequence of the motion of 
the gas, the motion of the plane through the gas, or a varying condition of the 
gas. And the determination of the effects of these causes on the mass, momentum, and 
energy that may be carried across by either group is the more general result of the 
investigation. 
61. As a preliminary step, it is shown that whatever may be the nature of the 
encounters between the molecules within a small element, the encounters can produce 
no change on the mean component velocities of the molecules which in a definite time 
pass through the element; and hence, whatever may be the state towards which the 
encounters tend to reduce the gas, this state must be such that the mean component 
velocities of the molecules which pass through the element in a unit of time remain 
unaltered. These mean component velocities, it is to be noticed, are not the mean 
component velocities of the molecules within an element at any instant. 
Certain assumptions are then made. These do not involve any law of action 
between the molecules. They are equivalent to assuming that the tendency of the 
encounters within an element is to reduce the gas to a uniform state. 
From these assumptions two theorems (I. and II.) are deduced. From theorem I. 
it follows that the rate of approximation to a uniform gas is inversely proportional to 
a certain distance s, which distance is inversely proportional to the density and is 
some unknown function of the mean velocity of the molecules. From theorem II. it 
follows that the molecules which enter a small element from any particular direction 
arrive as if from the uniform gas to which the actual gas tends at a point distant s in 
the direction from which the molecules come. 
When the gas is continuous about the element for distances large compared with 
s, then s is independent of the direction from which the molecules come ; but near a 
solid surface s is a function of this direction and of the position of the element with 
respect to the solid surface. 
These theorems are fundamental to all the reasoning which follows ; and the dis¬ 
tance s enters as a quantity of primary importance into all the results obtained. 
It is proposed to call this distance the mean range of the characteristics of the 
molecules. Thus we have the mean range of the mass, the mean range of momentum, 
and the mean range of energy. By qualifying the term “ mean range ” by the name of 
the quantity carried, instead of considering it as a general characteristic of the condition 
of the gas, two things are avoided— 
5 G 2 
