512 Prof. J. G. MacGregor on a Diagram of 



less tendency to diverge than those of any other observers. 

 And although this may be partially, it is not wholly, due 

 to their having worked at moderate dilution only ; for in 

 several cases, pointed out below, the curves of other observers 

 start on a divergent course within their limit of dilution. 

 But the fact that their curves usually agree with LoorcnVs 

 would lead one to suspect them of a leftward tendeucy also. 



The divergence, as shown on the diagram, is most marked 

 in the case of highly dissociated electrolytes (NaCl, HC1, &c.),. 

 in which at great dilution the rate of increase of ionization 

 with dilution is small, the curves being crushed up, therefore, 

 into a small space. But it is obvious also in the K 2 S0 4 

 curves (especially Abegg's) and the BaCl 2 curves (including 

 Ponsot's, not shown). And although for MgS0 4 and H 3 PO i5 

 whose ionization increases rapidly with dilution, the single 

 curves do not reveal it, the relative positions of the two 

 curves in each case are what they might be expected to be, if 

 they were tending unduly, Jones's to the right and Loomis's 

 to the left. 



This tendency is explicable at once when we reflect that as 

 it is equivalent depression that is plotted, the errors of the 

 observations are brought into greater and greater prominence 

 as dilution increases. According, therefore, as the character- 

 istic error of an observer's method of measuring total de- 

 pression is positive or negative, will his curves of equivalent 

 depression diverge at great dilution to the right or left of 

 their true course ; and they must diverge even if the error 

 is very small. 



The equivalent- depression curves of individual observers 

 are therefore open to grave suspicion at high dilutions ; and 

 since one can never be sure that the errors of different 

 methods will even approximately neutralise one another,, 

 mean high-dilution curves are not much more trustworthy 

 than their components *. It is much safer, therefore, to base 



* It is consequently inadmissible to proceed as Raoult has done, in 

 determining depression-constants (loc. cit. p. 658), viz., by selecting high- 

 dilution curves which are in agreement and applying extrapolation to a 

 mean curve derived from them ; for such procedure may involve the 

 selection of observations made by methods which have characteristic 

 errors of the same sign. In fact a mean curve based on observations 

 which agree well at low dilution, but disagree markedly at high dilution, 

 would be likely to give a better result, as more probably combining 

 observations with small characteristic errors of opposite sign. Raoult's 

 procedure is open to other objections. For (1) his curves of equivalent 

 depression against total depression make series of observations appear to 

 be in greater disagreement than they really are, and are thus not helpful 

 in making a judicious selection of observations to be used; and (2) 

 extrapolation of such curves not only gives a result affected by the 



