VAPOR-DENSITIES. 375 



These expressions for energy and entropy will undoubtedly apply 

 to mixtures of different gases, whatever their chemical relations may 

 be (with such limitations and with such a degree of approximation 

 as belong to other laws of the gaseous state), when no chemical action 

 can take place under the conditions considered. If we assume that 

 they will apply to such cases as we are now considering, although 

 chemical action is possible, and suppose the equilibrium of the mixture 

 with respect to chemical change to be determined by the condition 

 that its entropy has the greatest value consistent with its energy and 

 its volume, we may easily obtain an equation between ra^ m 2 , etc., 

 t and v.* 



The condition that the energy does not vary, gives 



(m^ + w 2 c 2 + etc.) dt + (cj -f- Ej) dm 1 + (c 2 t + E 2 ) dm 2 + etc. = 0. (1 ) 



The condition that the entropy is a maximum implies that its 

 variation vanishes, when the energy and volume are constant. 

 This gives 



log N t - a 2 log N 2 dm 2 + etc. = 0. (2) 



Eliminating dt, we have 



! - a, - G! - y + c, log N t - ^ log N 



2 a 2 c 2 ^+c 2 log N a 2 log N Jdm 2 +etc. = 0. (3) 



If the case is like that of the peroxide of nitrogen, this equation 

 will have two terms, of which the second may refer to the denser 

 component of the gas-mixture. We shall then have a 1 = 2a 2 , and 

 ^ dm 2 , and the equation will reduce to the form 



1 m Z V A 



log = ~ A - 



where common logarithms have been substituted for Naperian, and 

 A, B and C are constants. If in place of the quantities of the 

 components we introduce the partial pressures, p lt p 2 , due to these 

 components and measured in millimeters of mercury, by means of 



the relations 



P-.V 

 f -^ 



-7, 

 fat 



*For certain a priori considerations which give a degree of probability to these 

 assumptions, the reader is referred to the paper already cited. 



