390 ILLUSTRATIONS OF THE DYNAMICAL THEORY OF OASES. 



pressure and temperature the value of NMtf is the same for all gases. But 

 we found in Prop. VI. that when two sets of particles communicate agitation 

 to one another, the value of Mif 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 I, the mean length of the path 

 of a particle between consecutive collisions. The most direct method of doing 

 this depends upon the feet, that when different strata of a gas slide upon 

 one another with different velocities, they act upon one another with a tan- 

 gential force tending to prevent this sliding, and similar in its results to the 

 friction 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 into another layer having a different velocity of translation ; and 

 by striking against the particles of the second layer, exert upon it a tangential 

 force which constitutes the internal friction of the gas. The whole friction 

 between two portions of gas separated by a plane surface, depends upon the 

 total action between all the layers on the one side of that surface upon all the 

 layers on the other side. 



PROP. XIII. To find the internal friction in a system of moving particles. 



Let the system be divided into layers parallel to the plane of xy, and 

 let the motion of translation of each layer be u in the direction of x, and 

 let u = A + Bz. We have to consider the mutual action between the layers on 

 the positive and negative sides of the plane xy. Let us first determine the 

 action between two layers dz and dz', at distances z and z' on opposite sides 

 of this plane, each unit of area. The number of particles which, starting from 

 dz in unit of time, reach a distance between nl and (n + dn)l is by (19), 



m 



N j e~* dz dn. 



The number of these which have the ends of their paths in the layer dz' is 



N -e~ 



The mean velocity in the direction of x which each of these has before impact 

 is A + Bz, and after impact A+Bz'; and its mass is M t so that a mean 



