ILLUSTRATIONS OF THE DYNAMICAL THEORY OF GASES. 389 



The number of particles which after collision reach a distance between nl and 

 (n + dn) I is 



Nje~ n dzdn (19). 



The proportion of these which strike on unit of area at distance z is 



""' (*):"* 



the mean velocity of these in the direction of z is 



^ <*'> 



Multiplying together (19), (20), and (21), and M, we find the momentum at 

 impact 



MN ~ t (nV - z 2 ) e- dz dn. 

 4n"l* v 



Integrating with respect to z from to nl, we get 



X /V/ f\l / 11 lf>~ /"I'M 

 "Jr.iJ-t.iT c/ /frC \Julvt 



Integrating with respect to n from to oo , we get 



for the momentum in the direction of z of the striking particles ; for the 

 momentum of the particles after impact is the same, but in the opposite 

 direction ; so that the whole pressure on unit of area is twice this quantity, or 



This value of p is independent of I the length of path. In applying this 

 result to the theory of gases, we put MN=p, and v' = 3k, and then 



which is Boyle and Mariotte's law. By (4) we have 



'y > = fa 2 , .'. a 2 = 2& (23). 



We have seen that, on the hypothesis of elastic particles moving in straight 

 lines, the pressure of a gas can be explained by the assumption that the square 

 of the velocity is proportional directly to the absolute temperature, and inversely 

 to the specific gravity of the gas at constant temperature, so that at the same 



