508 Prof. J. Gr. MacGregor on a Diagram of 



on the average into a smaller number of ions, the equivalent 

 depression will diminish more rapidly than it otherwise would. 

 The curvature of the curve will therefore diminish and may 

 possibly become zero and change sign, the curve thus becoming 

 concave towards the ionization-coefficient axis and possibly 

 crossing the tangent line. In such a case the curve 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 conditions ; 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 association 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 corre- 

 sponding- values of the depression and of the ionization- 

 coefficient at the freezing-point, or what in most cases will 

 be sufficiently near, at 0° C. The former are obtained by 

 direct measurement ; but the latter only indirectly from con- 

 ductivity observations. 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 current is to be regarded as being 

 the same as when the current is not flowing. But as it has 

 been shown that electrically determined coefficients enable^ 

 us to predict, within the limit of error of observation, not only 



