216 J. W. Gibbs — Equilibrium of Heterogeneous Substances. 



loops one of the liquids, and above these liquids the gases which they 

 emit, viz., the separate gases at the ends of the tube, and the mixed 

 gases in the middle. We may suppose the whole to be in equilibrium, 

 the difference of the pressures of the gases being balanced by the 

 proper heights of the liquid columns. Now it is evident from the 

 principles established on pages 203-210 that the potential for either 

 gas will have the same value in the mixed and in the separate gas 

 at the same level, and therefore according to the rule in the form 

 which we have given, the pressure in the gas-mixture is equal to the 

 sum of the pi'essures in the separate gases, a/^ (^Aese joressiwes being 

 measured at the same level. Now the experiments by which the rule 

 has been established relate rather to the gases in the vicinity of the 

 surfaces of the liquids. Yet, although the differences of level in these 

 surfaces may be considerable, the corresponding differences of pres- 

 sure in the columns of gas will certainly be very small in all cases 

 which can be I'egarded as falling under the laws of ideal gases, for 

 which very great pressures are not admitted. 



If we apply the above law to a mixture of ideal gases and distin- 

 guish by subscript numerals the quantities relating to the different 

 gases, and denote by ^'^ the sum of all similar terms obtained by 

 changing the subscript numerals, we shall have by (270) 



-ff, — Cj— a, Ci+a, fi^—E, 



(a, a, ttit \ 



, a^ e t e /, (273) 



It will be legitimate to assume this equation provisionally as the 

 fundamental equation defining an ideal gas-mixture, and afterwards 

 to justify the suitableness of such a definition by the properties which 

 may be deduced from it. In particular, it will be necessary to show 

 that an ideal gas-mixture as thus defined, when the proportion of its 

 components remains constant, has all the properties which have 

 already been assumed for an ideal gas of invariable composition ; it 

 will also be desirable to consider more rigorously and more in detail 

 the equilibrium of such a gas-mixture with solids and liquids, with 

 respect to the above rule. 



By differentiation and comparison with (98) we obtain 



= ^^\ («,+«,- ^-7—^) e t e ;, (274) 



V t 



