.ILLUSTRATIONS OF THE DYNAMICAL THEORY OF GASES. 395 



in equilibrium, and the dynamical measure of the force exerted on the stratum 

 will be the resultant momentum of all the particles which lodge in it during 

 unit of time. We shall first take the case in which there is no mean motion 

 of translation, and then consider the eifect of such motion separately. 



Let a stratum whose thickness is a (a small quantity 

 compared with I), and area unity, be taken at the origin, 

 perpendicular to the axis of x ; and let another stratum, of 

 thickness dx, and area unity, be taken at a distance x from 

 the first. 



If MI be the mass of a particle, N the number in unit of volume, v the 

 velocity of agitation, I the mean length of path, then the number of collisions 

 which take place in the stratum dx is 



N j dx. , ', 



The proportion of these which reach a distance between nZ and (n + dn)l is 



e~ n dn. 



The proportion of these which have the extremities of their paths in the 

 stratum a is 



a 



Znl' 



The velocity of these particles, resolved in the direction of x, is 



vx 

 ~nl' 



and the mass is M ; so that multiplying all these terms together, we get 



NMtfax . ., , , . 



2nV . e "dxdn (30) 



for the momentum of the particles fulfilling the above conditions. 



To get the whole momentum, we must first integrate with respect to x 

 from x= nl to x = +nl, remembering that I may be a function of x, and is a 

 very small quantity. The result is 



d /NMv*\ , , 

 di(-3-) ane dn - 



50-2 



