420 DETERMINATION OF THE FREEZING-POINT DEPRESSION 
the value expected from theory. In the case of the undissociated 
molecules, however, the variation of their values is much greater: 
As the depression produced by molecules is supposed on theore- 
tical grounds to be the same as that produced by free ions, the 
difference between the variations of m and 7 is probably due to 
the different degrees of accuracy with which, as seen above, m 
and 2 are capable of determination. 
If we assume, as is customary, that the depression produced 
by the molecules, whether they are undissociated molecules or 
free ions, is the same for all electrolytes in dilute solution, we 
can arrive at better values of both m and 7 by finding the mean 
values. This becomes obvious when we take into consideration 
the sources of error which affect the values of k andl. For the 
straight line, from which & and J are determined, may be either 
too high or too low; or it may be too much or too little inclined 
to the equivalent depression axis. The line may be too high or 
too low because of defective observations of depression, defective 
values of ionization coefficients, or the way in which I have 
drawn it in. So far, at least, as two ot these Sources of error 
are concerned, the resulting errors will in some cases be positive 
and in others negative; and in finding the average these errors 
will in part cancel one another. Defective inclination of the 
line may be due, in addition, to the characteristic error of the 
observers method, which may be such as to make the curve at 
great dilution go off either to the right or the left as dilution 
increases, or to the natural bend of the curve itself which may 
be either to the right or left as concentration increases. The 
errors due to these sources wiil also be, in some cases, positive, 
and in others negative, and hence will practically neutralize one 
another on averaging. 
The determinations of the above table are not all of the same 
order of trustworthiness, Some are based on freezing-point 
observations made by means of old methods; others on those 
of newer and more accurate methods. Some are based on many 
observations, others on few ; some on observations in good agree- 
ment, others on more erratic series. In some eases, also, the 
ionization coefficients employed are more trustworthy than in 
