Energy of Light and Chemical Energy. 219 



and subtracting from this equation (i.) we get 

 rj'dt' — v'dp -T-mi'dfix + w 1 'd\ 1 \. . +m n 'dfi a ' + iw»'rfX»'==0. (iii.) 



Here we have a connexion between 2n + 2 variables 

 £', jt/ 5 ft'. . ,/in', X/. . .X*t'. If this connexion is known, the equa- 

 tion concerning rj', t/, ???/...???/, which are functions of the 

 same variables, will be known as well, and we shall have in 

 the total 7i + 2 such independent equations. Here, however, 

 dfjb is not independent of d\. General considerations of the 

 conditions of equilibrium of a chemical system in light lead 

 to the conclusion that for this the temperature, the pressure, 

 and the sum of the chemical and of the light-kinetic potentials 

 of each of the components must be constant through the 

 whole system. Therefore 



/V + Al' = (V, /*n' + \n=Gn- ... (7) 



Thus we have in the total 2n+2 equations for the 2n + 2 

 variables t' ,p\fju^ X,'. . .p n ', >,/, and these with (ii.) give in total 

 2n + 3 known equations, while the total number of variables 

 E', 7/, t\ p',v', /&/, X,', mj...fxj, X,/, m n is 3/2 + 5. If the 

 system consists of one substance only, then equation (iii.) 

 becomes 



rfdl 1 — v'dp' + mjdpj + nix'dX/ = 0. 



Equations (iii.) and (7) give the variation of temperature, 

 or of pressure, or of chemical, or of the light-kinetic potential, 

 or of several of them with the variation of one or some of 

 the variables when all the rest of the variables remain 

 constant. 



In case of a gas-mixture there is every reason to assume 



that the energy, pressure, density (ue.,W 9 f/y.and—h 



temperature, entropy, potentials of each of the gases separ- 

 ately are the same when they are together as they would be 

 if they were alone, provided that the gases do not act one 

 upon another chemically. This is an extension of Dalton's 

 law applied not only to pressures but to all other thermo- 

 dynamic factors of the same. Thus the variation of tem- 

 perature or of the chemical potentials and of the light-kinetic 

 potentials of each of the gases in dependence upon the 

 variation of all the rest will be the same as if the system 

 consisted of the given gas alone. 



Making use of functions $', ^', £", introduced by Gibbs 

 in his treatment of heterogeneous systems when no light- 

 energy is stored in the same, we ultimately get, putting 

 E + Ei-fW^'j 

 —t'dri'—v'dp' + m l 'dfi l ' + m l 'dhi'...-\ »w,/<fyt,/ + M*»'</Xi/=0. (iv.) 



