MR. CLERK MAXWELL OK THE DYNAMICAL THEORY OE GASES. 
73 
pendently 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 
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 consider- 
able time perfectly undisturbed. If currents arise so as to mix the strata, the composi- 
tion 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 
^+%= IcA ^U u -2-u 1 )+Xp 1 , ( 78 ) 
and for the second, 
&! ( 79 ) 
In all cases of quiet diffusion we may neglect the first term of each equation. If we 
then put -\-jp 2 =.p, and we find by adding, 
I = x e ( 80 ) 
If we also put p x ii x -\-p 2 u 2 =pu, then the volumes transferred in opposite directions across- 
a plane moving with velocity u will be equal, so that 
p(u,-u)=piu-u 2 )=-^^- ( 81 ) 
Herep^Mj— u) is the volume of the first gas transferred in unit of time across unit 
of area of the plane reduced ‘to pressure unity, and at the actual temperature; and 
p 2 (u — u 2 ) is the equal volume of the second gas transferred across the same area in the 
opposite direction. 
The external force X has very little effect on the quiet diffusion of gases in vessels of 
moderate size. We may therefore leave it out in our definition of the coefficient of 
diffusion of two gases. 
When two gases not acted on by gravity are placed in different parts of a vessel at equal 
pressures and temperatures, there will be mechanical equilibrium from the first, and u 
will always be zero. This will also be approximately true of heavy gases, provided the 
denser gas is placed below the lighter. Mr. Graham has described in his paper on the 
Mobility of Gases experiments which were made under these conditions. A vertical 
* Philosophical Transactions, 1863. 
VDCCCLXVII. 
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