NOTES ON THE CALCULATION OF THE OSMOTIC PRES- 
SURE OF EXPRESSED VEGETABLE SAPS FROM THE 
DEPRESSION OF THE FREEZING POINT, WITH A TABLE 
FOR THE VALUES OF P FOR A = o.ooi° TO A = 2.999°^ 
J. Arthur Harris and Ross Aiken Gortner 
By far the simplest method of determining the osmotic pressure of 
expressed vegetable saps is that of the depression of the freezing 
point by use of the Beckmann^ apparatus or some substitute procedure.^ 
Particular emphasis has been laid upon the practicability and accuracy 
of the freezing point method by Lewis. ^ Renner^ has done a good 
service to biologists by pointing out that inconsistencies between the 
plasmolytic and the cryoscopic method are, in considerable part at 
least, due to the difference between weight normal and volume normal 
solutions. Thus one objection to the cryoscopic method is removed. 
In this note we desire merely to call attention to an important factor 
which has been very generally neglected by biologists in the calcula- 
tions of the osmotic pressure from the experimentally determined data, 
and to lighten somewhat the routine of those working in this field by 
the publication of a little table from which P for A = 0.001° to 
A = 2.999° C. may be at once determined. 
The freezing point of a solution is the temperature at which ice and 
solution exist in equilibrium. Pure water separates upon freezing, 
hence the liquid which remains, and whose temperature in equilibrium 
with the mass of ice crystals is read from the thermometer, is not the 
1 From the Station for Experimental Evolution, The Carnegie Institution of 
Washington. 
2 See any textbook of physical chemistry for the general methods. For some 
special points of technique in dealing with vegetable saps see Gortner and Harris, 
Notes on the Technique of the Determination of the Depression of the Freezing 
Point of Vegetable Saps, Plant World, 17: 49-53. 19 14. 
3 Dixon, H. H. and Atkins, W. R. G. Sci. Proc. Roy. Dublin Soc, n. s. 12: 
275-311, loc. cit. 13: 49-62. 191 1. 
* Lewis, G. N. The Osmotic Pressure of Concentrated Solutions, and the Laws 
of the Perfect Solution. Journ. Amer. Chem. Soc. 30: 668-683. 1908. 
^ Renner, G. Uber die Berechnung des osmotischen Druckes. Biolog. Centralbl. 
32: 486-504. 1912. See also review of C. A. Shull, Bot. Gaz. 56: 444. 1913. 
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