364 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



Gas-mixtures with convertible components. The theory of the 

 phases of dissipated energy of an ideal gas-mixture derives an especial 

 interest from its possible application to the case of those gas-mixtures 

 in which the chemical composition and resolution of the components 

 can take place in the gas-mixture itself, and actually does take place, 

 so that the quantities of the proximate components are entirely deter- 

 mined by the quantities of a smaller number of ultimate components, 

 with the temperature and pressure. These may be called gas-mixtures 

 with convertible components. If the general laws of ideal gas- 

 mixtures apply in any such case, it may easily be shown that the 

 phases of dissipated energy are the only phases which can exist. 

 We can form a fundamental equation which shall relate solely to 

 these phases. For this end, we first form the equation in p, t, JJL V 

 fj. 2 , etc. for the gas-mixture, regarding its proximate components as 

 not convertible. This equation will contain a potential for every 

 proximate component of the gas-mixture. We then eliminate one (or 

 more) of these potentials by means of the relations which exist between 

 them in virtue of the convertibility of the components to which they 

 relate, leaving the potentials which relate to those substances which 

 naturally express the ultimate composition of the gas-mixture. 



The validity of the results thus obtained depends upon the applica- 

 bility of the laws of ideal gas-mixtures to cases in which chemical 

 action takes place. Some of these laws are generally regarded as 

 capable of such application, others are not so regarded. But it may 

 be shown that in the very important case in which the components of 

 a gas are convertible at certain temperatures, and not at others, the 

 theory proposed may be established without other assumptions than 

 such as are generally admitted. 



It is, however, only by experiments upon gas-mixtures with con- 

 vertible components, that the validity of any theory concerning them 

 can be satisfactorily established. 



The vapor of the peroxide of nitrogen appears to be a mixture of 

 two different vapors, of one of which the molecular formula is double 

 that of the other. If we suppose that the vapor conforms to the laws 

 of an ideal gas-mixture in a state of dissipated energy, we may obtain 

 an equation between the temperature, pressure, and density of the 

 vapor, which exhibits a somewhat striking agreement with the results 

 of experiment. 



Equilibrium of stressed solids. The second part of the paper* 

 commences with a discussion of the conditions of internal and external 

 equilibrium for solids in contact with fluids with regard to all possible 

 states of strain of the solids. These conditions are deduced by 



* [See footnote, p. 184.] 



