300 BOTANICAL GAZETTE [OCTOBER 
osmotic pressures developed therein has been carried out during 
the past summer. 
Owing to the as yet insurmountable difficulties in determin- 
ing directly the osmotic pressure of a solution, the indirect 
method by freezing points was resorted to. It has been well 
established+ that for dilute solutions a uniform relation obtains 
between the osmotic pressure, the depression of the freezing 
point, and the elevation of the boiling point. Thus if A, 
denotes the depression of the freezing point, the osmotic pres- 
sure is given by the formula P-= 12.07 A,, wherein P, is the 
osmotic pressure at the freezing point of the solution. Similarly, 
P;=574;, wherein P, is the osmotic pressure at the boiling 
point and A, the elevation of the boiling point. The depression 
of the freezing point was determined by means of Beckmann’s 
apparatus,’ for the mineral solutions described in the previous 
paper, as far as these were at hand when the tests were made. 
From these data the osmotic pressure at the freezing point 
(practically 0° C.) was derived by the formula given above, and 
from this the pressure at 25°C. was obtained by the formula 
P,= P; (1 + 0.00367 2),° wherein P, is the pressure at any given 
temperature (¢). 
Since ionization is usually more complete at high tempera- 
tures than at low ones, it was thought advisable to make some 
sample tests of osmotic pressure by determining the elevation of 
the boiling point. This was done for a limited number of solu- 
tions only. For this purpose the improved apparatus of Beck- 
mann? was used. After the determination of P, and P; (supra), 
P,, was obtained by interpolation between them thus: P,,=/% 
+ 25 X 0.00367 (P; — P-). The results show that the difference 
: 4 NERNST, W.: Theoretical chemistry, translated by C. S. Palmer, p. 123 ef seg. 
1895. 
5 BECKMANN : Zeitschr. Physik. Chem. 2: 638. 1888. 
| ° Simply the law of Gay-Lussac, which holds for osmotic pressures of weak solu- 
tions. NERNST cit., p. 134 ef seg. Also Ostwa.p, W., Outlines of general 
chemistry, translated by J. Walker, p. 128 ef seg. 1895. 
7 BECKMANN: Zeitschr. physik. Chem, 8: 223. 1891. 
