1904.] Theory of Amphoteric Electrolytes. 275 



but since r and u are identical in both equations, we obtain by division 



If we are dealing with an electrolyte of markedly acid character, we 

 may, in the expression for a, neglect K in comparison with k a u,* and so 

 obtain 



a - 



a v k a 



Finally, therefore, we have 



Given then the values of 77 and u for one & a , we may easily calculate 

 the value of rj (or of v) for another k a if u and r remain unaltered. 



One is generally confronted, however, with the converse problem of 

 'determining u for a given value of v, but the table may again be utilised 

 in virtue of the following considerations. Neglecting K in comparison 

 with k a u, we may write as before 



77 - u = a 

 or, multiplying both sides by v and re-arrangirig, 



1 Q/C 



Substituting the value of a in terms of u and the constants, we obtain 



+ ru 



or 



v + ruv 



If we now denote the product uv by p, re-arrange, square, and express 

 in powers of p, we obtain as result 



(r - k a r*)p z + (v - 2r - k a rv)p 2 -h (r - 2v - k a v' 2 )p + v = 0. 



v - 2r - k 



* Compare loc. cit., p. 156. 



