374 VAPOR-DENSITIES. 



determining the proportions of the component gases necessary for 

 the equilibrium of such a mixture under any given conditions, 

 these substances afford an appropriate test for such a law. 



In a former paper* by the present writer, equations were proposed 

 to express the relation between the temperature, the pressure or the 

 volume, and the quantities of the components in such a gas-mixture 

 as we are considering a gas-mixtwe of convertible components in 

 the language of that paper. Applied to the vapor of the peroxide 

 of nitrogen, these equations led to a formula giving the density in 

 terms of the temperature and pressure, which was shown to agree 

 very closely with the experiments of Deville and Troost, and much 

 less closely, but apparently within the limits of possible error, with 

 the experiments of Playfair and Wanklyn. Since the publication 

 of that paper, new determinations of the density have been published 

 in different quarters, which render it possible to compare the equation 

 with the results of experiment throughout a wider range of tem- 

 perature and pressure. In the present paper, all experimental 

 determinations of the density of this vapor which have come to 

 the knowledge of the writer are cited, and compared with the values 

 demanded by the formula, and a similar comparison of theory and 

 experiment is made with respect to each of the other substances 

 which have been mentioned. 



The considerations from which these formulae were deduced may 

 be briefly stated as follows. It will be observed that they are based 

 rather upon an extension of generally acknowledged principles to a 

 new class of cases than upon the introduction of any new principle. 



The energy of a gas-mixture may be represented by an expression 

 of the form 



j + Ej) + m 2 (c 2 t + E 2 ) + etc., 



with as many terms as there are different kinds of gas in the mixture, 

 774, m 2 , etc. denoting the quantities (by weight) of the several com- 

 ponent gases, c lt c 2 , etc., their several specific heats at constant volume, 

 Ej, Ej, etc., other constants, and t the absolute temperature. In like 

 manner the entropy of the gas-mixture is expressed by 



t - C&! log N -^ J + m 2 (^H 2 + c 2 log N t-a 2 logN ) + etc., 



where v denotes the volume, and H^ a 1? H 2 , a 2 , etc. denote constants 

 relating to the component gases, a v a 2 , etc. being inversely pro- 

 portional to their several densities. The logarithms are Naperian. 



"On the Equilibrium of Heterogeneous Substances," this volume, page 55. The 

 equations referred to are (313), (317), (319), and (320), on pages 171 and 172. The 

 applicability of these equations to such cases as we are now considering is discussed 

 under the heading "Gas-mixtures with Convertible Components," page 172. 



