THE DYNAMICAL THEORY OF GASES. 57 



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 second degree. 



Condition of Equilibrium of a Mixture of Gases. 



In a state of equilibrium u^ and M a vanish, p^* becomes p lt and the tan- 

 gential pressures vanish, so that the equation becomes 



<"> 



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, shews 

 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 Dalton considered to exist in a mixed 

 atmosphere in equilibrium, the law of diminution 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 currents arise so as to mix 

 the strata, the composition of the gas will be made more uniform throughout. 



The result at which we have arrived as to the final distribution of gases, 

 when left to themselves, is independent of the law of force between the 

 molecules. 



Diffusion of Gases. 



If the motion of the gases is slow, we may still neglect the tangential 

 pressures. The equation then becomes for the first system of molecules . 



p^ + ^kA^p^-u^ + Xp, ................... (78), 



VOL. II. 8 



