252 ON -A DIAGRAM OF FREEZING-POINT 
markedly to the right, although it is farther to the left at its 
lower end. Arrhenius’s is considerably to the right, and diverges 
widely rightwards. The Na,SO, (L A—A) curve is also almost 
coincident with both the Loomis and the Archibald curves. Both 
Raoult’s and Arrhenius’s are considerably to the right, and 
diverge slowly rightwards. Such of these curves as are entered 
on the diagram, being plotted with Archibald’s coefficients, are 
probably somewhat too high or too low, as the case may be. 
Those for great dilutions are too discordant to admit of dis- 
cussion. The mean curves for both salts have the same general 
form, and run down, as drawn, a little below the 2—3 line. 
Their upper ends are so directed as to suggest their running out 
at the 2—3 (1.85) intersection, or thereabout. At their lower 
ends they turn sharply to the left and cross the 2—3 line, going 
towards the region of the double molecule curves, or of the 2—2 
curve. ‘The turns are too sharp, and the 4—6 and 6—9 lines 
too near, to make their transformation into double or triple mol- 
ecule curves, with unchanged ionization, probable. The diagram 
suggests rather their transformation into 4—5, 4, or 2 or 2—2 
curves. If this be accepted, it means that at extreme dilution 
these sulphates exist in solution in single molecules, dissociating 
into three ions, that partial dissociation into two ions or doubling 
of molecules sets in, apparently at an early stage, but increases 
more slowly than in the case of H,SO,, until the dilution has 
been considerably diminished, when it undergoes a rapid increase. 
A close determination of the depression constant cannot be made; 
but even if the curves have to be either raised or lowered a little, 
and if, Loomis’s tendency being leftward, their upper parts have 
to be shifted somewhat to the right, they will be consistent with 
its being about 1.85. 
The Na,CO, curves are too discordant to form a_ basis 
for discussion. But either Loomis’s curve or a mean 
curve, or even Jones’s curve itself, is quite consistent 
with a depression constant of about 1.85; and both curves indi- 
cate the occurrence of rapid association or of rapid change of ioni- 
zation after considerable diminution of dilution. The fact that 
