102 THE ROYAL SOCIETY OF CANADA 
be used and may be made to yield consistent numerical results even in 
cases where the symbols separately have no physical meaning as in 
the osmotic theory of electromotive force. The frequent references 
in the current literature to the molecular pressures in liquids and solids 
involving pressures running up to hundreds of thousands of atmos- 
pheres, and even in one case, to millions,’ cannot represent any real 
physical quantity because the assumed force function is erroneous. 
The *Present Theory Supported by Recent Osmotic Theory 
If there still remains any doubt as to the validity of applying the 
equation of a perfect gas to the work done by the forces concerned during 
an isothermal change in volume from a vapour to a liquid, the atten- 
tion should be directed to what is known as the van’t Hoff equation 
for osmotic pressure and to the equation for the work done by osmotic 
pressure. Here the work is due to the molecular pressure of a liquid 
and is given by an equation identical in form with that required to ex- 
press the work done by a perfect gas. The present writer has given a 
rigid thermodynamic proof ? (the only one, so far as his knowledge 
goes) of that which the labors of Professor Morse and Dr. Frazer * had 
already conclusively establihed experimentally, that the volume in the 
equation 
W = pv loge #2 
Vy 
where p is the osmotic pressure, really refers to the volume of the liquid 
solvent and not to the volume of the solute; and as thus interpreted is 
not confined to dilute solutions. In a later paper (Le. p. 651) it was 
shown that “the volume concerned in osmotic pressure is the volume 
of the solvent increased in the ratio — while the pressure is diminished 
n 
PA he oes ; a 
in the ratio— ‘This is equivalent to ascribing to the one-n th part of 
the solvent a volume n times as large as it actually occupies with a cor- 
responding diminution in pressure.” 
The present proposal is then merely extending to the whole liquid 
what has been experimentally and theoretically established for years 
and has given satisfactory and consistent results when applied to the 
one-n th part of the liquid solvent. This evidence taken in connection 

* For a résumé see W. C. Lewis, Transactions of the Faraday Soc. Vol. 7, 94 
(1911). 
? Jour. Phys. Chem. 14, 260 (1910). 
* Am. Chem. Jour. 36, 39 (1906). 
