(33) 



more kinds of Moving Particles among one another. 25 

 may write the equation 



* -!= x <» • < 32 ) 



the ordinary hydrodynamical equation. 



Prop. XVII. To find the resultant effect of the collisions upon 

 each of several different systems of particles mixed together. 



Let M„ M 2 , &c. be the masses of the different kinds of par- 

 ticles, N u N 2 , &c. the number of each kind in unit of volume, 

 »i, u 2 , &c. their velocities of agitation, /„ / 9 their mean paths, 

 PuPv &c. the pressures due to each system of particles; then 



- r =A/3 1 -f B/> 2 + &c. 



-j-=fy 1 +Dft+ &c. 



The number of collisions of the first kind of particles with each 

 other in unit of time will be 



H l v 1 Ap v 



The number of collisions between particles of the first and second 

 kinds will be 



N^jB/Dg, or ffg&gCpi, because v 1 3 B=v 2 3 C. 



The number of collisions between particles of the second kind 

 will be N 2 %Djo 2 , 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 



* dx' ' 



The proportion of these which strike particles of the first kind is 



A Pl l v 



The whole momentum of these remains among the particles of 

 the first kind. The proportion which strike particles of the 

 second kind is 



The momentum of these is divided between the striking particles 



M 



in the ratio of their masses ; so that g — K-=- of the whole goes 



1VX| -j" 1VJ. 2 



M 



to particles of the first kind, and M 2 M to particles of the 



second kind. 



