( 166 ) 
In my opinion the minimum would indicate the point, where the 
influence of the deviation from the diluted state in this special case 
becomes so great, that the direction in which 7 varies is thereby 
reversed. 
A difficulty remains in the difference between what has been 
observed by means of the method of decrease of the vapour-tension 
and that of the lowering of the freezing-point. Not only is there 
e.g. for NaCl solutions a difference in absolute value of # at every 
concentration, but above the concentration 0,5 gr. mol. there had 
up to now not been found an increase of # with the concentration 
by means of the freezing-point method, whereas this singular course 
has been so clearly observed by means of the method of vapour- 
tension at 0° and that of the boiling-point at 100°. 
Though it was formerly found that below the concentration 1 gr. 
mol. the molecular lowering of the freezing-point and with it 7 
pretty quickly decreased with increase of the concentration, this is 
no longer so. RAouLr!) found a very slow decrease with increase 
of the concentration; afterwards CHROUSTCHOFF*®) found constant 
values and a few months ago KAHLENBERG®) published the following 
results, which confirm my suspicion, that possibly also at the deter- 
mination of the freezing-point soon a minimum may be found. 
Concentration Lowering Molecular lowering 
in of the of the i 
gr. mol. per 1000 gr. HO. freezing-point. freezing-point. 
0.2043 0.693 | 3.393 1.82 
0.4359 1.512 3.469 1.86 
0.5077 1.750 3.447 1.85 
0.6713 2.300 3.426 1.84 
0.8400 2.866 3.412 1.83 
0.9814. 3,395 3.459 1.86 
1) Zeitschr. f. Phys. chem. 27. S. 617 (1898). 
2) Comt. Rend. 181. p. 883 (1900). 
3) Journal of Phys. chem. 5, 339 (1901). 
