3o6 
CHEMISTRY: F. E. BARTELL 
Proc. N. a. S. 
and combining the two, 
(13) 
T c)(^, T) 
which is the generaHzed Clapeyron-Clausius equation. Making use of 
this in (11) we obtain the "well-known equation" mentioned by Professor 
Lewis, and given by van der Waals, p. 52: 
Applying this to the case mentioned by Professor Lewis, 
p = (piiv) + T(p2{v) 
which is the case under which van der Waals' familiar equation comes, 
we find, to be sure, that Cj, is independent of the volume, but on solving 
for T, and writing 
T = pV,{v) + V2{v) 
and applying equations (1) and (2), we do not find anything particularly 
simple for Cp. 
All this is very simple, but what I wish to call attention to is that in 
any case, the specific heats being defined by a partial differential equation 
of the first order, there is one perfectly arbitrary function, by no means 
necessarily of the temperature. In any case I believe that the teaching 
of thermodynamics by means of the equation of the so-called ideal gas 
or by means of van der Waals' equation is by no means conducive to 
clearness. 
ANOMALOUS OSMOSE 
By F. E. Bartei.1. 
ChemicaIv Laboratory, University of Michigan* 
It has repeatedly been noted that solutions of electrolytes with differ- 
ent types of "semi-permeable" membranes give osmotic pressure values 
quite different in magnitude from the calculated maximum values derived 
from the gas law formulations. We may define normal osmotic pressure 
values as those which conform to the gas law formulations. We have an 
example of this type when a solution of cane sugar is used with a semi- 
permeable membrane such as copper ferrocyanide. Anomalous osmotic 
pressure values are those which do not conform to the gas law formulations ; 
they may be greater or less than the normal values. The abnormality 
of the effects may be of considerable magnitude and may even result in 
so-called negative osmose, in which case the direction of flow of liquid is 
from the concentrated to the more dilute solution. 
* Communicated by M. Gomberg, April 20, 1920 
