226 ON A DIAGRAM OF FREEZING-POINT 
dilution, not much more trustworthy than their components.* 
It is much safer, therefore, to base conclusions as to depression 
constant on moderate dilution curves, although the conclusions 
they admit of may not be so exact as we might wish. 
Discussion of the Curves. 
Electrolytes such as NaCl, HNO,, KOH, have 1 equivalent 
in the single molecule, and 2 ions. If, therefore, they exist in 
solution in single molecules, their curves should be normal 1—2 
curves. If the molecules are all double or triple, the curves 
should be 2—4 or 3—6 curves, provided the association does 
not involve change in the mode of ionization. If it does, they 
may be 2—2, or 3—4, 3—3, 3—2 curves respectively, according 
to the change that may occur. If the molecules are single at 
extreme dilution, but become double or triple as dilution dimin- 
ishes, the curves should start as 1—2 curves, and undergo 
the appropriate transformation. 
The electrolyte for which we have the most complete and 
trustworthy data, is KCl. The LB—B curve is_ based 
on two series of observations in close agreement and 
by a method exhibiting less divergence than the others. 
Joness runs a little to the right of it; Abegg’s a 
little to the left. Both Raoult’s and Wildermann’s cross it, the 
latter being somewhat steeper, the former less steep. Ponsot’s 
* It follows that it is 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 mean the selection of observations made by methods which have char. 
acteristic errors of the same sign. In fact, a mean curve based on Observations whicn 
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 average of the characteristic errors of the 
observations used, but also neglects the possibility, in some cases the probability. that 
owing to change in association and mode of ionization, the law of the change of cury- 
ature may be very different beyond the limits of observation, from what it is within 
these limits. 
