1152 
substance in the vapour (viz. 2) is larger (smaller) than in the liquid 
(viz. w,) then the boiling-point under constant pressure is lowered 
(raised) and the vapour-tension at constant 7’ is raised (lowered) ; 
when the new substance is not volatile (consequently 2 = 0) then 
the boiling-point under constant P is raised and the vaponr-tension 
at constant 7’ is lowered. 
We consider the invariant (P or 7’) equilibrium 
BNG WD PTA AEN A VERA) 
viz. a complex of liquids in equilibrium with their vapour G. We 
write the reaction which may occur in £: 
deiner Aad Phe A A tea een ANE ee ee 
When all reaction-coefficients 4,4, ... are positive, then all liquids 
take part in the formation of vapour in the ratio 4,:A,:a,..., 
then we shall say that the vapour has a “average” composition. 
When, however, in (6) one or more of the reaction-coefficients are 
negative, then also one or more liquids arise at a time with the 
vapour; the vapour has then a ‘‘non-average’ composition. 
When we represent by AW the heat, wanted to form one quantity 
of vapour, and the corresponding increase of volume by AV, then 
AW and AV are positive, unless in very special cases. 
Now we may write for (12) and (15) (XX): 
he (ae) RT > (42) 
———_———————— a —— en 
(dT)p = — AW nd (dP)r = AV (7) 
Herein is: 
= (Ar) =a —(Aa, + Aye, + aa, He.) 2. « . (8) 
Now we take a mixture of the liquids Z, Z,... in such a ratio 
that it has the same composition as the vapour G. We call this 
mixture or complex of phases the “reduced mixture’. As appears 
from (6) this mixture has the composition: 
An Ba Aa oR uae BY DNA oale sink ener (AN 
in which one or more of the coefficients may also be negative. 
When the vapour has an average composition, then all coefficients 
in (9) are positive; when the vapour, however, has a non-average 
composition, then one or more of the coefficients in (9) are negative. 
When we put now: 
AyHilot Acts dydgtenckiot VERN =) sibs 
consequently c is the concentration of the new substance X in the 
reduced mixture. Instead of (7) we may write now: 
