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objections of more or less value, but that they are outweighed by 
the practical advantage that calculations with the osmotie pressure 
are so much simpler than with the thermodynamic potential, but 
this objection lacks all foundation. For kinetic calculation cannot be 
meant in this, and for the thermodynamic calculation it holds on 
the contrary, that when making use of the thermodynamic potential 
we need not take one step, which we are not obliged to take in exactly 
the same way when making use of the osmotic pressure. In order to 
prove this, L should like to reprint and follow step by step the 
proof given by Van ’r Horr in his Vorlesungen, but as this proof — 
carefully selected by Van ’r Horr from considerations partly from 
himself, partly from Lord Ray.eien, partly from Dr. Donnan, so 
undoubtedly the finest and simplest to be found — covers two pages 
in print, I shall only indicate the principal operations and put in 
juxtaposition the operations, which are required for the thermody- 
namic potential with the same neglections. 
1. Remove from a solution of 1. The thermodynamic poten- 
osmotic pressure P a quantity of | tial is: 
solvent, occupying a volume wv. 7 
The substance yields an amount Mu=pe+ | piv MRT ee 
of work — Pv. 
ee 
Day i il (2) de 
Òr/or 
pe becomes here pr, 
2. Negleet the change in vapour 2. Neglect the variability of p 
tension and the eontraction of the | with « and the compressibility of 
solution. (This is not expressly | the liquid, then 
stated, but is evidently necessary |, ve, 
for the proof). Op \ ; f 
proot) | —]dv=0 en pdv = 0. 
Oa: 
. . %o ro 
3. Let the quantity of dissolved 3. 
substance, dissolved in v, evaporate Vey 
diosmotically ; let its volume be es 
: ‘ | pdo = pe (ve, — ve) 
V, the work done is: 
Ur 
p V cy 
(when we neglect v by the side 
of WA): 
