198 Mr. J. C. Maxwell on the Dynamical Theory of Gases. 



fluid. Combining this equation with that from which it was 

 obtained; we find 



a more convenient form of the general equation. 



Equations of Motion (a). 

 To obtain the equation of motion in the direction of oc, put 

 Q=M 1 (M 1 -|-f 1 ), the momentum of a molecule in the direction 

 of x. 



We obtain the value of -~r from equation (51) ; and the equa- 

 tion may be written 



P^ + a^ {p ^ 2)+ ^ {p ^ ) + ^ ipl ^ ) X • (76) 

 =^A 1 p 1 p 2 (w 2 ~w 1 )+Xp 1 J 



In this equation the first term denotes the efficient force per 

 unit of volume,, the second the variation of normal pressure, the 

 third and fourth the variations of tangential pressure, the fifth 

 the resistance due to the molecules of a different system, and 

 the sixth the external force acting on the system. 



The investigation of the values of the second, third, and fourth 

 terms must be deferred till we consider the variations of the se- 

 cond degree. 



Condition of Equilibrium of a Mixture of Gases. 

 In a state of equilibrium u x and u 2 vanish, p^ * becomes p v 

 and the tangential pressures vanish, so that the equation becomes 



!=% w 



which is the equation of equilibrium in ordinary hydrostatics. 



This equation, being true of the system of molecules forming 

 the first medium independently of the presence of the molecules 

 of the second system, shows that if several kinds of molecules 

 are mixed together, placed in a vessel and acted on by gravity, 

 the final distribution of the molecules of each kind will be the 

 same as if none of the other kinds had been present. This is 

 the same mode of distribution as that which Balton considered 

 to exist in a mixed atmosphere in equilibrium, the law of dimi- 

 nution of density of each constituent gas being the same as if 

 no other gases were present. 



This result, however, can only take place after the gases have 

 been left for a considerable time perfectly undisturbed. If cur- 



