[MACGREGOR] DEPRESSION OF THE FREEZING-POINT 5 
APPLICABILITY OF THE EXPRESSION TO SIMPLE SOLUTIONS. 
To find whether or not the above expression fits the observations on 
the solutions of any electrolyte, we may either apply the method of least 
squares or proceed graphically. I have used the latter method. 
If we call the quotient of the depression of the freezing-point by the 
concentration in gramme-equivalents per litre, the equivalent depression, 
indicating it by 6, the expression referred to above takes the form 
6=k (l—a) + la=k-+ (IX) a. 
If therefore this expression is applicable, the curve obtained by plot- 
ting equivalent depression against ionization coefficient should at sufi- 
cient dilution become practically a straight line, 7.e., should be capable 
of being represented by a straight line within the limit of error of the 
observations. Having plotted this curve in the case of each series of 
solutions and found by inspection the portion of it which was practically 
rectilinear, I drew in the straight line which best represented the observa- 
tions, so far as I could judge, and determined the values of the constants, 
k and l, by reading off the values of 6 and « for two points on the line so 
drawn and solving the two simultaneous equations obtained by substitut- 
ing these values in the expression for 0. 
Before plotting such curves, however, in order to get rid of the 
accidental errors of the single observations as far as possible, I plotted 
curves both of ionization coefficients and of equivalent depressions against 
concentration, using in the case of the latter not only Archibald’s and 
Barnes’s observations but also those of Loomis, with which they were in 
closer agreement than with those of other experimenters. The ionization 
coefficients of the various series agreed very closely with one another and 
only in a very few cases did the values obtained direct from experiment 
seem to need some slight correction to make them consistent with the other 
values of the same series. In the case of the freezing-point observations, 
which have been found even by the most experienced observers to be 
subject to accidental errors of considerable magnitude, it was in some 
cases difficult to draw in the most probable smooth curve with confidence, 
In some of these cases Loomis’s observations enabled me to do so, and in 
such cases I used the interpolated values instead of the actual observa- 
tions in testing the applicability of the above expression. In the tables 
given below, the values obtained directly from the observations are given 
as well as the corrected values, the latter being inclosed in brackets; but 
all the observations on which the corrections were based are not given, 
only those made on the more dilute solutions. 
