52 
ME. CLEEK MAXWELL ON THE DYNAMICAL THEOEY OF OASES. 
direction over that of those which traverse it in the negative direction, gives a measure 
of the flow of gas through the plane in the positive direction. 
If the plane be made to move with such a velocity that there is no excess of flow of 
molecules in one direction through it, then the velocity of the plane is the mean velocity 
of the gas resolved normal to the plane. 
There will still be molecules moving in both directions through the plane, and carry- 
ing with them a certain amount of momentum into the portion of gas which lies on the 
other side of the plane. 
The quantity of momentum thus communicated to the gas on the other side of the 
plane during a unit of time is a measure of the force exerted on this gas by the rest. 
This force is called the pressure of the gas. 
If the velocities of the molecules moving in different directions were independent of 
one another, then the pressure at any point of the gas need not be the same in all direc- 
tions, and the pressure between two portions of gas separated by a plane need not be 
perpendicular to that plane. Hence, to account for the observed equality of pressure in 
all directions, we must suppose some cause equalizing the motion in all directions. 
This we find in the deflection of the path of one particle by another when they come near 
one another. Since, however, this equalization of motion is not instantaneous, the pres- 
sures in all directions are perfectly equalized only in the case of a gas at rest, but when 
the gas is in a state of motion, the want of perfect equality in the pressures gives rise to 
the phenomena of viscosity or internal friction. The phenomena of viscosity in all 
bodies may be described, independently of hypothesis, as follows : — 
A distortion or strain of some kind, which we may call S, is produced in the body by 
displacement. A state of stress or elastic force which we may call F is thus excited. 
The relation between the stress and the strain may be written F=ES, where E is the 
coefficient of elasticity for that particular kind of strain. In a solid body free from vis- 
cosity, F will remain =ES, and 
^E = E — • 
dt dt 
If, however, the body is viscous, F will not remain constant, but will tend to disappear 
at a rate depending on the value of F, and on the nature of the body. If we suppose 
this rate proportional to F, the equation may be written 
dF dS F 
dt — h dt ~T’ 
which will indicate the actual phenomena in an empirical manner. For if S be constant, 
F=ESe“ f *, 
showing that F gradually disappears, so that if the body is left to itself it gradually 
loses any internal stress, and the pressures are finally distributed as in a fluid at rest. 
If ^ is constant, that is, if there is a steady motion of the body which continually 
