nected in a simple way with the osmotic pressure in dilute solutions, 
but we have not a single reason to assume this also for concentrated 
solutions, or rather we may state with almost perfect certainty that 
this will not be the case. How on the other hand those quantities 
may be determined with the aid of the thermodynamic potential, 
Van per Waars taught us already fifteen years ago. 
§ 9. And let us finally not forget that though solutions of non- 
volatile substances at low temperatures do play an important part 
in nature, yet they are not the only substances which exist, nor the 
only ones which deserve scientific consideration. And yet, the theory 
of the osmotic pressure must necessarily be confined to them. One 
is so customed to derive the laws of the rise of the boiling point and 
the decrease of the vapour tension from the osmotic pressure, but 
it is generally forgotten, that many mixtures have on the contrary lowe- 
ring of the boiling point and rise of the vapour tension *), and that at 
any rate if the dissolved subsiance is but in the least volatile, the 
changes in boiling point and vapour tension cannot be derived 
any more from the osmotic pressure. And it is obvious why. It is 
inherent in every definition of the osmotic pressure, that it can only 
be applied to those cases, in which one component may be separated 
from the mixture in pure condition, as Nernst has clearly stated 
for the first time. Hence this does not only exclude the whole region 
of higher temperatures, at which all substances become more or less 
volatile, but also all cases of not perfect separation in the liquid 
or solid state. Also the lowering of the freezing point is touched by 
this objection. It is true that the lowering of the freezing point may 
be computed from the osmotic pressure, but only when, as in water 
and sugar, the solid substance, which deposits, is not of variable 
composition. Solid solutions and mixed crystals, which attract at 
present so much attention in chemistry, cannot be treated in this way. 
Physical chemistry in its present state reminds us strongly with 
regard to its quantitative part, of the navigation of a people, which 
does not yet know the compass. The coasting-trade is carried on 
with great vigour, the same limited region is traversed again and 
again; but they do not dare to venture on the main sea far from 
the coast, and with reason, for great is the danger of ruin in the 
towering waves of random hypotheses. This can only be remedied 
by a trustworthy compass. Physical chemistry may obtain it if it 
will abandon the method of the osmotic pressure and adopt that of 
the thermodynamic potential in connection with a well-grounded 
equation of state. 
1) Cf. Théorie Moléculaire § 17. 
