J. W' . Glbbs — Kqa 11 lb I'll (III of Jleteroi/aneoiis Sabst<incef<. 2;{7 



mate, are supposed constant). If we vise the same metliod of geome- 

 trical representation as before, the point representing- the vohime, 

 entropy, and energy of the mass will describe a line in the n-ij-f: sur- 

 face of an ideal gas-mixture of inconvertible components, the form 

 and position of this surface being determined by the proximate comi)0- 

 sition of 31. Let us now suppose the same mass to be carried beyond 

 the limit of inconvertibility, the variations of state after passino- the 

 limit being such as not to alter its proxinuxte composition. It is 

 evident that this will in general be possible. Exceptions can only 

 occur when the limit is formed liy phases in which the proximate 

 composition is uniform. The line traced in the region of convertibility 

 must belong to the same »-?/-£ surface of an ideal gas-mixture of in- 

 convertible components as before, continued beyond the limit of 

 inconvertibility for the components of 31, since the variations of 

 volume, entropy and energy are the same as would be possible if the 

 components were not convertible. But it must also belong to the 

 v-7]-8 surface of the body J/, which is here a gas-mixture of conver- 

 tible 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 y-;/-£ 

 surface of the body 31 in the region of convertibility must thus be 

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

 possible proximate composition consistent with the ultimate composi- 

 tion of 31, 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 sui-faces, 

 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 prob- 

 ability 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 equa- 

 tions 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 



