228 ON A DIAGRAM OF FREEZING-POINT 
If the 1—2 (1.86) intersection, were assumed as the starting 
point of the curve, the mean curve would cut the 2—4 (1.86) 
line. If, therefore, association in molecules with unchanged 
mode of ionization were assumed, some formation of triple mol- 
ecules would be indicated, and if the associated molecules were 
assumed to dissociate into two free ions, a greater extent of such 
association would be indicated. Thus, with this starting point, 
less probable assumptions as to association must be made, to 
account for the observations. 
If the 1—2 (1.84) or even the 1—2 (1.845) intersection were 
taken as the starting point, the curve must bend considerably to 
the left before running out—of which bending none of the 
experimental curves give any indication whatever. 
The most probable conclusion, then, that we can draw from 
the observations, is that the depression constant is 1.85, with a 
limit of error of .01, or perhaps .005, that the electrolyte has 
single molecules at great dilution, and that as dilution diminishes, 
either double molecules with unchanged mode of ionization form 
to a considerable extent, or double molecules dissociating into 
two ions, to a small extent. 
Loomis’s and Barnes’ observations, on which the NaCl 
(L B—B) curve is based, are also in close agreement; but as 
Loomis’s curve for shghtly greater dilution bends slightly to the 
right, the upper part of the L .B—B curve should probably 
have greater curvature. Jones’ curve for moderately dilute 
solutions runs a little to the left of it, and at higher dilutions 
diverges markedly to the right, as separately shown. Abegg’s 
observations are on both sides of it, but at higher dilutions his 
curve also goes to the right. Raoult’s touches it, but goes off to 
the right. Arrhenius’s is considerably to the right, and goes 
widely rightward at greater dilutions. Ponsot’s is a little to the 
left. As the L B—B curve is plotted with Barnes’ coefficients, 
it is probably too low. If it be raised about as much as was 
found necessary in the case of the KCl curve, it will lie along the 
1—2 line, or a little above or below it, with its upper end, as 
drawn, so directed, as to run out probably at a point nearer the 
