220 Dr. Meyer Wilderman : Connexion hetween the 

 Putting E + ~E 1 +j>'v / = x / , we get 



y'dt' +j/dv' '^m/dfi/ + m l 'd\Y„:+m n / dfj n ' + WdX»'=0. (v.) 

 Putting E + Et — «V- J jP , « / =? r , w e get 



— t'dv' -tp'dv' + m^dpi +?n l / d\/ . . . -f ???„W/x/+/»,/rZX,/ = (vi.) 



Equations iii., iv., v., vi. are Gibbs' modified fundamental 



equations o£ condition, when each of the conponents contains 

 two potentials. 



From equation (i.) we further get 



. , , /</E+dEA f , , , ,. . 



A4l ' + \ 1 ' = f_^_ r -Mi7 / , v, m 2 '...m n ', . . (i.) 



i. e., it' we assume that to a given homogeneous mass an 

 infinitely small quantity of m/ is added, while the mass remains 

 homogeneous, and its entropy in light, volume, and the rest 

 of the substances remain constant ; then the sum of the 

 chemical and of the light-kinetic potentials of the introduced 

 substance is equal to the ratio of the increase in the energy 

 E and in the energy E x (stored by light in the system), 

 caused by this introduction of the substance ???/, to the intro- 

 duced quantity of dm^ *. 



It is further evident that if an equation of chemical 

 reaction exists between the units of the substance of the 

 system 



n 1 A l + n 2 A 2 .. . = ?ra 1 A l + ??/ 2 B 2 ... 7 . . . (i r .) 



where A l3 A 2 ,...Bi, B 2 ... are the units of the different sub- 

 stances, and raj, n 2 ...m 1} m 2 . . . numbers, then if the reasoning- 

 given by Gibbs in the case of one potential be further 

 applied to our case with tv\o potentials, we have also 



i^aZ + Xa/) + "2 (/*a/ + Xa/). • • = '>*i(/"b/ + Xb/) + m 2 {fi B ^ + X, B /) • • ■ (i"0 

 Let us now return to the consideration of the equation (iii ), 

 first when the system consists of one gaseous substance 

 only. It assumes in the first instance the torm 



rfdt'—xfdp' + in/*//*/ + m x V/X./ = 0. 

 Here r/dt\ v'dp', m/d/ii, jh/c/X./, are the variations in the 



* In the same manner we have 





