373 



a suitable assumption about the manner in which En, Hn and k 

 depend on n. The simplest supposition no doubt which we can 

 make regarding En is, that in a union of M grms of simple 

 molecules in the ideal gaseous state with jiM grms of n fold 

 molecules to form {n-\-l) fold molecules a quantit}' of potential 

 energ}' E is lost which is independent of n^); on this assumption 

 we have : 



En = E,-'^--E, (10) 



n 



dEn dHn 



and thus also, seeing that— — = 7'— — - *) 



dl dJ 



Hn=H,-'^H, . ..... (10') 



n 



where El and ^i now refer to simple molecules "). These equations 

 are of the same form as that which was assumed above between 

 k and n and which we shall again introduce here. 

 Equation (8) now leads to : 



M.. A—X—71 Y _ 



(11) 



where 



'la f «-1 

 1 8 



RTv 



2a f . a— I 



RTv ^ ^ V a 





■e— 



so that 



and hence 



1) This assumption which is tantamount to assuming an equal binding of all 

 molecules in the complex, was made by me before (vid. Acad. Roy. de Belgique, 

 Mém. cour., 1896, p. 54). 



dE, dH, ^ ^ , dE „öf^,., .,, „ ., ,i, » r. j 



3) — \ = T — -\ = Cj and also —=, = T -y= (it will appear further on that E9ina 

 dl' dT dT dl 



H must be assumed to be also functions of the temperature). It follows that 



n— 1 dE ^ fa—\\dE 



Cn = (\ TTT, and also Col=C^—\ h^. 



n dl \ a yClJ 



3) Provided e—Y < 1, which is confirmed by the result, at least unless 



e—Xr=0, or X = oo, which is only the case at 7=0 or at v = biim- 



