506 , Prof. J. G. MacGregor on a Diagram of 



Construction and Properties of the Diagram. 



If an extremely dilute solution contain an electrolyte whose 

 molecule as it exists in solution contains p equivalents and 

 dissociates into q free ions, and if a is its ionization-coefficient, 

 and k its depression-constant, the equivalent depression will 

 be : 



8=|(l + «(?-l)). 



If, therefore, we plot a diagram of curves with ionization- 

 coefficients as ordinates, say, and equivalent depressions as 

 abscissa?, the resulting curves must at extreme dilution (a = l) 

 be tangential to the straight lines represented by the above 

 equation, provided the proper values of &, jo,and q be employed. 

 These straight lines, which for shortness we may call the 

 tangent lines of the curves, can readily be drawn in the 

 diagram with any assumed value of k, and on any admissible 

 assumptions as to the values of p and q. In the diagram 

 (PI. IV.) the broken lines are the tangent lines for the electro- 

 lytes examined, on various assumptions as to constitution in 

 solution and mode of ionization, and for &=1'85. They are 

 indicated by the inscriptions 1-2, 2-3, &c, the first figure in 

 each giving the number of equivalents in the molecule as it is 

 assumed to exist in solution, and the second the number of 

 free ions into which the molecule is assumed to dissociate. 

 Thus 1-2 is tbe tangent line for an electrolyte such as NaCl, 

 on the assumption that it exists in solution in single molecules, 

 each of which has therefore 1 equivalent and dissociates into 

 2 ions. If assumed to associate in double molecules with 

 unchanged mode of ionization, its tangent line would be 

 indicated by 2-4 ; and if tbe double molecules were assumed to 

 dissociate into Na and NaCl 2 , by 2-2. The line for H 2 S0 4 on 

 the assumption that its molecules undergo no association and 

 have thus 2 equivalents, and tbat they dissociate each into 3 

 ions, would be indicated by 2-3. 



In a few cases dotted lines have been introduced to show 

 what the tangent lines would be with other values of k, 1*83, 

 Ac, the constant used in such cases being indicated. 



Tbe curve for any given electrolyte must start at tbe inter- 

 section of its tangent line with the line «=1, to which point 

 we may refer for shortness as the intersection of its tangent 

 line. What its form will be may be anticipated from the 

 following theoretical considerations : — The equivalent depres- 

 sion in dilute solutions of non-electrolytes is proportional to 

 the product of the osmotic pressure, P, and the dilution, V, 

 which corresponds to the product of the pressure p and specific 



