( 749 ) 
+. Let the vapour expand to 4. 
infinite volume, the work done is: 5 
7 7 | pee = ee 
{pac = MRT I= = e Vey 
a J Veg ir 
ze 2 
5. Now press the vapour again 5. The thermodynamic poten- 
into the solution, then a work is | tial of pure water is: 
done by the substance : / 
ce) y Mu = pv + | pdv -+ VAHL) 
— {pte a # 
J g 
V uy 
fow — MRTI— ; pv = Pe Ves 
Vey —_—— 
Vg 
6. The total quantity of work 6. The two potentials are the 
must be zero, so: | same, so: 
Bor | (pope) %, = — MREU(I—e) 
which in spite of the different notation is the same, when log (1 — x) 
is replaced by — z. 
So it is seen that to every integration on the right corresponds 
an operation on the left of exactly the same nature, though it does 
not always refer to the same substance. The only difference is that 
on the right the integration is carried out directly and that on the 
left pistons and membranes are worked with. Now I do not think 
that any one can easily set greater store by a clear physical meaning 
of operations than I do, but that we should not be able to carry 
out an integration along an isotherm without bringing in two pistons 
and three membranes, seems rather too much of a good thing. 
§ 8. And now we have considered the most favourable case : 
dilute solutions; how is it with more concentrated ones ? It will 
certainly be possible to devise also for them cycles so that the 
calculations introduced in my first paper may be carried out without 
mentioning the name: “thermodynamic potential’, but it will not be 
found possible by a thermodynamic method to draw up a formula for the 
osmotic pressure without determining the integrals occurring in it. 
In this way it would seem as if the two methods were essentially 
the same; it is not so, the osmotic pressure method has drawbacks, 
of which the other is free. For what is it that we really wish to 
learn by the cwo different methods ? Not the osmotie pressure itself, 
and the properties of the solutions under that pressure, that is 
for concentrated solutions; in sensibly compressed state. What we 
SL 
