412 DETERMINATION OF THE FREEZING-POINT DEPRESSION 
If in this equation ea=1 then d=/ which is represented on 
the diagram by DA. Again if a=o then d=h which is repre- 
sented by OE on the diagram. Now suppose that in drawing 
in our straight line we consider some portion as QP or Q’P! as 
straight, and hence get the line as represented by our formula 
to be A’ BE! or AE’, In this case our 7 will be AD or A’D 
instead of the true value AD, and k will be OE’ or OE” instead 
of OE. The error in lis A’A or A’A, while that in k is EE” or 
EE’. It is plain that AA” or AA!’ is less than EE” or EE’, 7. e., 
that the accuracy with which J is determined is greater than 
that with which k is determined. Hence the values of 7 are 
affected with a smaller error than are those of m. 
Since the depressions for dilute solutions are affected with a 
considerable error, the part of the ionization-equivalent depres- 
sion curve near A is very untrustworthy. This is shewn by Dr. 
MacGregor in one of the papers referred to above. He has. 
pointed out that the curves of the different observers for the 
same electrolyte deviate at great dilution, some to the right. 
and others to the left of what their general course is at moderate 
dilution. Not only this, but the different observations of the 
same observer become very irregular as dilution increases. 
As, therefore, the curves of the different observers have this. 
rightward or leftward tendency—and sometimes to a great. 
extent—as dilution increases, it is evident that we get better 
values of k and J, if we obtain them froma part of the ionization- 
equivalent depression curve, which corresponds to a concen- 
tration at which trustworthy determinations of the depressions 
can be made, than if we use the very erratic observations at high 
dilution. I have, therefore, in the determinations of & and lL 
used only the observations on solutions of moderate dilution. 
As, however, some curves begin to curve rapidly as the concen- 
tration increases, even at an early stage, one has to use some 
discretion in choosing a part of the curve, which is least affected 
on the one hand by the natural bend of the curve, and on the 
other by the bend due to the error of method of the observer. 
