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 i is probably due to 

 the different degrees of accuracy with which, as seen above, m 

 and i 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 i by finding the mean 

 values. This becomes obvious when we take into consideration 

 the sources of error which affect the values of k and I. For the 

 straight line, from which k and I 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 of 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 

 observer's 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 will 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 

 oider 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 cases, also, the 

 ionization coefficients employed are more trustworthy than in 



