110 
te. that the ratio of the concentration of the second component in 
the vapour and in the liquid is very small, this rule can be perfectly 
rigorously derived for the limiting value purely thermodynamically 
in the wellknown way. Purely thermodynamically, because we have — 
then only to do with the logarithmic part of the thermodynamic 
functions, and need not know anything more about the system. But 
this definition of “difference in volatility” is not the only possible 
one, and not the only one that naturally suggests itself. We might 
as well, perhaps better, understand by this idea, that one pure 
component has a very much lower vapour-pressure than the other 
at a definite temperature. And these two detinitions by no means 
always coincide. Let us e.g. take a system for which the equations 
1—4 hold. On the supposition 7—=7 and 7);,=477;, it follows that 
the quantity p,/p, is of the order 10~'§ at a temperature of */,7%,. 
So there seems, indeed, to be every reason to say that the second 
component is much less volatile than the first. Yet by no means 
ge ei rk 
lim. =O. On the contrary, if we put /=1, it follows from the 
Hij 
1 
above that the p,z,-line begins ascending, so z, > ,; in the begin- 
ning the second component is present in the vapour in greater 
quantity than in the liquid, and van ’r Horr’s law by no means holds 
any longer even for the extremest dilutions. Exactly the same thing 
b ze 
applies for other values of —. So we must supplement the condition 
) 
1 
for the validity of van ’r Horr’s law also for the extremest dilutions 
as follows, that the components differ greatly in vapour-pressure, 
and that there be no region of unmixing in the neighbourhood. 
For if this were not the case we should already soon get a vapour 
in which the partial pressure of the second component would be 
greater than the total pressure of the component at the chosen 
temperature, and this is not possible for absolutely stable states *). 
So where the rule of van ’t Horr does not hold with great difference 
in vapour pressure, this will be in the closest connection with this 
pressure lines on the side of their component it always holds that they point to 
the opposite angle with their initial direction, as immediately follows by differentia- 
tion of the equation on p. 103. 
1) We used this thesis already above to conclude to the existence of unmixing. It 
may be proved as follows. It follows from the differential equations of the two 
partial vapour-pressure lines (Cont. II, p. 163) that they will possess a maximum 
or a minimum only on the borders of the stable and unstable region. So :f there 
is no unmixing, the partial vapour-pressure line of the first component is always 
descending, that of the second always ascending. If there is a region of unmixing, 
