Energy of Light and Chemical Energy. 221 



thermal, mechanical, chemical, and light-kinetic energy of 

 the total mass of the system. We can naturally express the 

 mass in any unit we may desire to adopt. Let this unit he 

 the gram-molecule of the gas, because this will allow a simple 

 use of the gaseous laws and will also be in conformity with 

 the form and content of the equations for chemical reaction 

 which for many reasons were finally adopted by the chemist. 

 Let the total mass of the gas be m/ gram-molecules. Then 

 we have : the total chemical energy is /a/m/, and the above 

 variation in the same 7n l 'd/ub 1 ' ; the total light-kinetic energy is 

 m/A,/, and the variation in the same mi'd\\ ; the total 

 mechanical energy of the mass is p , v' = m l , Rt\ or nearly 

 = m 1 '. 2 cal., since (/W) of 1 gr.-mol.— B/, and the above 



Variation in the same is v'dd^v'dl -^7— ), where v is the 



volume of the gas ; the total 9/ of the mass =m/ 1 -7- +K/J, 



/ , in n , ■, dW (of 1 gr -mol ) , , A e 



when (drf) of 1 gr.-mol. = v -F ; , and (1/) of 



1 gr.-mol. = — +K/, where K/ is an integration-constant. 



Thus we get instead of (iii.) 



and ^/ + x/=B^-+B« , lg^-H / lg^+K l V + K 1 // , 



where K/ ; is another integration-constant. 



Now we are entitled to assume that in the case of a gaseous 

 mixture Dalton's law will hold good in the wider sense, 

 namely, not only for E = 2(E), p = 2Qy), 97=2(17), i|r = 2(^), 

 ^ = S(y),as indicated by Gibbs, but also for the chemical 

 and the light-kinetic potentials of each gas in the gas- 

 mixture. 



Having now a chemical equation of reaction expressed in 

 gram-molecules, 



n x gr.-m. of <Ti + n 2 gr.-m. of o-. 2 = )) 3 gr.-m. of cr«, 

 and n 1 (/x 1 / -fX/)+r? 2 (yLt 2 / + X 3 / ) = w 3 (/x 3 / + A 3 / ) ) 



we thus get 



n x rUrlg^M (U + K/K-H/lgr + kY'] 

 + »,[B/]g^?- / +(R + K 8 y-'H 1 / Ig< / +K 1 _ 

 = nSm f ]g''" a - + (K + K/) / - H 3 ' Ig / 4- K, ] , 



