EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 155 



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 circum- 

 stances, the rule may be expressed as follows : 



The presswe in a mixture of different gases is equal to ike sum of 

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

 same temperature and 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 

 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 144-150 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 pressures in the separate gases, all these pressures 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 regarded 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 2 X the sum of all similar terms obtained by 

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



(gj-gj-ai ci+i Mi~-gi\ /0>7Q\ 



. <v "' 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 



