396 ILLUSTRATIONS OF THE DYNAMICAL THEORY OF GASES. 



Integrating with respect to n from n = to n = oo , the result is 



d 



as the whole resultant force on the stratum a arising from these collisions. 



Now - - =p by Prop. XII., and therefore we may write the equation 

 3 



(32), 



WWf 



the ordinary hydrodynamical equation. 



PROP. XVII. To jind the resultant effect of the collisions upon each of 

 several different systems of particles mixed togetJier. 



Let MI, M t , &c. be the masses of the different kinds of particles, N lt 

 N t , &c. the number of each kind in unit of volume, v lt v t , &c. their velocities 

 of agitation, ?,, I, their mean paths, p lt p t , &c. the pressures due to each 

 system of particles ; then 



1 



,(33). 



The number of collisions of the first kind of particles with each other in unit 

 of time will be 



The number of collisions between particles of the first and second kinds will be 



Nj.\Bp tt or NjojCp lt because v'B = v*C. 



The number of collisions between particles of the second kind will be 

 N t v t Dpn and so on, if there are more kinds of particles. 



Let us now consider a thin stratum of the mixture whose volume is unity. 



The resultant momentum of the particles of the first kind which lodge in 

 it during unit of time is 



_dp 1 



dx ' 





