412 DETERMINATION OF THE FREEZING-POINT DEPRESSION 



If in this equation n = l then 6=1 which is represented OD 

 the diagram by DA. Again if a=o then 6-h which is repre- 

 sented by OE on the diagram. Now suppose that in drawing 

 in our straight line we consider somfe portion as QP or Q'P' a& 

 straight, and hence get the line as represented by our formula, 

 to be A"E" or A'E'. In this case our I will be A"D or A'D- 

 instead of the true value AD, and k will be OE' or OE" instead 

 of OE. The error in I is A"A or A'A, while that in k is EE" or 

 EE'. It is plain that A A" or A A' is less than EE" or EE', i. e., 

 that the accuracy with which I is determined is greater than 

 that with which k is determined. Hence the values of i 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 wo get better 

 values of k and I, if we obtain them from a 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. 1 have, therefore, in the determinations of k and I 

 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. 



