76 
J. ARTHUR HARRIS AND ROSS AIKEN GORTNER 
same but is more -concentrated than the original solution. In conse- 
quence the observed depression is lower than the true freezing point 
of the solution under investigation. That this factor may become of 
considerable importance in physiological work is shown at once by a 
comparison of corrected and uncorrected values taken from unpub- 
lished observations: 
A' 
Depression of the freez- 
ing pcjint as read from 
the thermometer 
A 
Depression corrected for 
weight of ice separated 
Difference between cor- 
rected and uncorrected 
depressions. 
Apple 
Apple 
Pear 
Passiflora: 
1.209° 
1.131° 
1-332° 
1.461° 
0-738° 
0.630° 
1.166° 
1.093° 
1.289° 
1.412° 
0.710° 
0.607° 
0.043° 
0.038° 
0-043° 
0.049° 
0.028° 
0.023° 
Such differences cannot be neglected. They may be minimized by 
"salting" with a few crystals of frost after the solution has been cooled 
to below its freezing point, or an absolute correction may be made 
where the volume of the solvent, not the volume of the solution, and 
the amount of under^cooling {i. e., the difference between the point to 
which the mercury fell before the separation of ice began, and the 
maximum temperature reached in the system, solution + ice) are 
known. For i cc. of solution,^ volume v, having a density of d, freezing 
at A' after an under-cooling of u, and yielding total solids s, the 
weight of water is, of course d — s. Since for each degree of under- 
cooling 12.5 g. of water separates as ice in each liter, i/8oth of the 
weight of the solvent is removed and the concentration of the solu- 
tion is proportionally increased. Hence the correction 
/ A/ 
V 
or in terms of freezing point lowering and undercooling only 
A = A' — 0.0125 ul^' 
must be applied. 
Some slight differences are to be noted in the literature in the 
method of computing the osmotic pressure in atmospheres (P) from 
6 For simplicity of calculation merely unit-volume is adopted. In practice 
several cubic centimeters must be used to secure accurate figures for A' and s. 
