EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 175 



vertible components. Moreover, as the inclination of each of these 

 surfaces must indicate the temperature and pressure of the phases 

 through which the body passes, these two surfaces must be tangent 

 to each other along the line which has been traced. As the v-q-e 

 surface of the body M in the region of convertibility must thus be 

 tangent to all the surfaces representing ideal gas-mixtures of every 

 possible proximate composition consistent with the ultimate composi- 

 tion of M, continued beyond the region of inconvertibility, in which 

 alone their form and position may be capable of experimental demon- 

 stration, the former surface must be an envelop of the latter surfaces, 

 and therefore a continuation of the surface of the phases of dissipated 

 energy in the region of inconvertibility. 



The foregoing considerations may give a measure of a priori 

 probability to the results which are obtained by applying the ordinary 

 laws of ideal gas-mixtures to cases in which the components are con- 

 vertible. It is only by experiments upon gases in phases in which 

 their components are convertible that the validity of any of these 

 results can be established. 



The very accurate determinations of density which have been made 

 for the peroxide of nitrogen enable us to subject some of our equations 

 to a very critical test. That this substance in the gaseous state is 

 properly regarded as a mixture of different gases can hardly be 

 doubted, as the proportion of the components derived from its density 

 on the supposition that one component has the molecular formula NO 2 

 and the other the formula N 2 O 4 is the same as that derived from the 

 depth of the color on the supposition that the absorption of light is 

 due to one of the components alone, and is proportioned to the separate 

 density of that component.* 



MM. Sainte-Claire Deville and Troost^ have given a series of 

 determinations of what we shall call the relative densities of peroxide 

 of nitrogen at various temperatures under atmospheric pressure. We 

 use the term relative density to denote what it is usual in treatises on 

 chemistry to denote by the term density, viz., the actual density of a 

 gas divided by the density of a standard perfect gas at the same 

 pressure and temperature, the standard gas being air, or more strictly, 

 an ideal gas which has the same density as air at the zero of the 

 centigrade scale and the pressure of one atmosphere. In order to test 

 our equations by these determinations, it will be convenient to trans- 

 form equation (320), so as to give directly the relation between the 

 relative density, the pressure, and the temperature. 



As the density of the standard gas at any given temperature and 



*Salet, "Sur la coloration du peroxyde d'azote," Comptes Rendus, vol. Ixvii. p. 488. 

 t Gomptes Rendus, vol. Ixiv. p. 237. 



