214 ON A DIAGRAM OF FREEZING-POINT 



zero, and change sign, the curve thus becoming concave towards 

 the ionization coefficient axis, and possibly crossing the tangent 

 line. In such a case, 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 0C. 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 



