FREEZING POINTS OF NUTRIENT SOLUTIONS 347 



freezing point of the solution. When such an undercooled so- 

 lution freezes, a sufficient amount of pure solvent crystallizes 

 out to raise the temperature of the remaining solution to its freez- 

 ing point. Thus the solution actually frozen is more concen- 

 trated than the original one, and it becomes necessary to apply a 

 correction for this increase in concentration due to the separation 

 of ice from the solution. Such a correction was applied in these 

 determinations, the method used being well stated by Harris and 

 Gortner.^ If v denotes the volume of the solvent and u the un- 



uv 

 dercooling of the solution in degrees Centigrade, ^ (or 0.0125 uv) 



represents the total volume of the solvent removed, since for 

 each degree of undercooling one-eightieth of the total weight of 

 the solvent is removed from the solution as ice. It then follows 

 that V — 0.0125i*?^ represents the volume of the solvent remain- 

 mg in the solution after the formation of ice due to undercooling. 

 Hence A = A' (1 — 0.0125^), where A' is the apparent lowering 

 of the freezing point and A is the corrected lowering. For facility 

 m computation the value of u was taken as 2.5°C.; since the un- 

 dercooling was never much more than 3°C. and never much 

 less than 2°C., the error thus introduced is not greater than that 

 attributable to slight inconsistencies in experimentation. 



The structure of the Beckmann thermometer is such that a 

 considerable column of mercury is exposed to temperature con- 

 ditions external to the freezing apparatus, and the mercury 

 column so exposed is of course, subject to contraction and ex- 

 pansion with fluctuations in the temperature conditions under 

 which the determinations are made. This renders it necessary 

 either to apply a correction for variation in length of the mercury 

 column with fluctuations in room temperature, or to redetermine 

 the apparent freezing point of the solvent whenever such fluc- 

 tuations may occur. The latter is by far the simpler procedure. 

 There is no definite point in the mercury column where the in- 



^ Harris, J. A., and Gortner, R. A., Notes on the calculations of the osmotic 

 pressure of expressed vegetable saps from the depression of the freezing point, 

 with a table for the values of P for a = 0.001° to A = 2.999°. Amer. Jour. 

 Bot. 1:75-78, 1914. 



