30 THE DYNAMICAL THEORY OF OASES. 



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 

 w the mean velocity of the gas resolved normal to the plane. 



There will still be molecules moving in both directions through the plane, 

 and carrying with them a certain amount of momentum into the portion of 

 gaa 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 inde- 

 pendent of one another, then the pressure at any point of the gas need not 

 be the same in all directions, 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 pressures 

 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 hypo- 

 thesis, 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 viscosity, F will remain = ES, and 



_ 



dt~ J 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 

 eft dt ~ T' 



