214 ON A DIAGRAM OF FREEZING-POINT 
zero, and change sign, the curve thus becoming concave towards 
the ionization coetlicient axis, and possibly crossing the tangent 
line. In such a ease, it will at the start coincide with the normal 
curve of the tangent line determined by the initial conditions as 
to association and mode of ionization, and at the finish, with the 
normal curve of the tangent line, determined by the final con- 
ditions; and between the start and the finish it will gradually 
change from the one to the other. 
If, as dilution diminishes, association of molecules into double 
or other multiple molecules occurs, the mode of ionization 
remaining the same, the equivalent depression will be thereby 
made to diminish more rapidly than it otherwise would, and the 
general effect on the form of the curve, will be of the same kind 
as under the conditions just considered. But the normal curves 
of the tangent lines determined by the final conditions, will be 
quite different in the two cases. 
It follows that by plotting, so far as experiment allows, the 
curves of observed equivalent depression against ionization 
coefficient, and drawing in the tangent lines for different values 
of the depression constant, and on different assumptions as to 
association and mode of ionization, we may be able to determine, 
with a smaller or greater probability, what the state of associa- 
tion and the mode of ionization are, what are the tangent lines 
to whose intersections the curves would run out if observations 
at extreme dilution could be made, and what the values of the 
depression constant are, to which these lines correspond. 
Data for the Diagram. 
To draw the experimental curves, we must have correspond- 
ing values of the depression, and of the ionization coefficient, at 
the freezing point, or, what in most cases would be sufficiently 
near, at 0°C. The former are obtained by direct measure- 
ment; but the latter only indirectly, from conductivity observa- 
tions. It is not, of course, known how closely the ionization 
coefficients, even during the passage of the current, can thus be 
determined, or if the state of ionization during the passage of the 
