J. W. Gibhs — Equilihi'mDi of Heterogeneous Substances. 215 



variable (m). We may obtain correspoiulincj fundamental equations 

 for a mixture of gases, in which the proportion of the components 

 shall be variable, from the following considerations. 



It is a rule which admits of a very general and in many cases very 

 exact experimental verification, that if several liquid or solid sub- 

 stances which yield difi^erent gases or vapors are simultaneously in 

 equilibrium with a mixture of these gases (cases of chemical action 

 between the gases being excluded,) the pressure in the gas-mixture 

 is equal to the sum of the pressures of the gases yielded at the same 

 temperature by the various liquid or solid substances taken separately. 

 Now the potential in any of the liquids or solids for the substance 

 which it yields in the form of gas has very nearly the same value 

 when the liquid or solid is in equilibrum with the gas-mixture as 

 when it is in equilibrium with its own gas alone. The difference of 

 the pressure in the two cases will cause a certain difference in the 

 values of the potential, but that this difference will be small, we may 

 infer from the equation 



C^) =(,*) , (272) 



\ dp ft, m \dm^lt,p,m ^ 



which may be derived from equation (92). In most cases, there will 

 be a certain absorption by each liquid of the gases yielded by the 

 others, but as it is well known that the above rule does not apply to 

 cases in which such absorption takes place to any great extent, we 

 may conclude that the effect of this circumstance in the cases with 

 which we have to do is of secondary importance. If we neglect the 

 slight differences in the values of the potentials due to these cii-cum- 

 stances, the rule may be expressed as follows : 



The pressure in a mixture of different gases is equal to the sum of 

 the pressures of the different gases as existing each by itself at the 

 same temperature avid with the same value of its potential. 



To form a precise idea of the practical significance of the law as 

 thus stated with reference to the equilibrium of two liquids with a 

 mixture of the gases which they emit, when neither liquid absorbs the 

 gas emitted by the other, we may imagine a long tube closed at each 

 end and bent in the form of a W to contain in each of the descending 



C= - (^-y-l ^=- ^ • 



a \ dm I / a am , 



With respect to some of the equations which have here been deduced, the reader 

 may compare Professor Kirchhoff " Ueber die Spannung des Dampfes von Mischungen 

 aus Wasser und Schwefelsaure," Pogg. Ann., vol. civ. (18.58), p. 612 ; and Dr. Raukine 

 "On Saturated Vapors,'' Phil. Mag., vol. xxxi. (1866), p. 199. 



