DHTFLT I 



Hence, when the process of diffusion is complete, the density of each gas at 

 any point of the vessel is the same as if no other gas were present. 



If I" is the potential of the force which acts on the gas, and if in tin- 

 equation !,-,/>,, i\ is constant, as it is when the temperature is uniform, 

 then the equation of equilibrium becomes 



the solation of which is 



Hence if, as in the case of gravity, V is the same for all gases, but / is 

 different for different gases, the composition of the mixture will be different 

 in different parts of the vessel, the proportion of the heavier gases, for which 

 k is smaller, being greater at the bottom of the vessel than at the top. It 

 \\.nild be difficult, however, to obtain experimental evidence of this difference 

 of composition except in a vessel more than 100 metres high, and it would 

 be necessary to keep the vessel free from inequalities of temperature for more 

 than a year, in order to allow the process of diffusion to advance to a state 

 even half-way towards that of ultimate equilibrium. The experiment might, 

 however, be made in a few minutes by placing a tube, say 10 centimetres 

 long, on a whirling apparatus, so that one end shall be close to the axis, 

 while the other is moving at the rate, say, of 50 metres per second. Thus 

 if equal volumes of hydrogen and carbonic acid were used, the proportion of 

 hydrogen to carbonic acid would be about xl^ greater at the end of the tube 

 nearest the axis. The experimental verification of the result is important, as 

 it establishes a method of effecting the partial separation of gases without the 

 selective action of chemical agents. 



Let us next consider the case of diffusion in a vertical cylinder. Let TO, 

 U- the mass of the first gas in a column of unit area extending from the 

 bottom of the vessel to the height x, and let v, be the volume which this 

 mass would occupy at unit pressure, then 



,, 



dm. 



-~ar' 



dv, 



' 



