144 THEORY OF COLLOIDAL BEHAVIOR 



a X m = a' X in' 

 b x m = b' X m' 



(a + b + c + . . . )m = (a' + 6' + c' + . . . X 

 (a + 6 + c + . . )(w + n + o + . . . ) = 



(a' + 6' + c' + ... )(ro' + n' + o' + . . . ) 

 whence 



a b _c a + 6 + c + . . . " 

 a 7 == 6' ~? == a' + 6' + c' + . . . 



It is, therefore, immaterial which ion is singled out for the 

 calculation of the P.D. on the basis of the Donnan effect. For 

 the sake of the accuracy of measurement the hydrogen ion was 

 selected. 



It is perhaps worth while to point out that the agreement 

 between calculated and observed P.D. is better in the experi- 

 ments with salts than in the experiments without salts, especially 

 near the isoelectric point. It seems almost as if the presence of 

 too low a concentration of electrolyte increased the error of the 

 measurements . 



THE INFLUENCE OF THE SIGN OF CHARGE 



The fact that the P.D. of a protein-acid salt solution is a 



function of the term log (1 + -), where z is the concentration of 



y 



the anion in combination with the protein ions and y the con- 

 centration of the anion of the free acid, explains a phenomenon 

 which is fundamental in colloidal behavior, namely, that when- 

 ever a salt depresses any physical property of a protein (or a 

 colloidal solution in general) this action is due to that ion of the 

 salt which has the opposite sign of charge to that of the protein 

 ion. That this is true for the influence of salts on viscosity, 

 osmotic pressure, and swelling has been discussed in Chap. VI, 

 and we shall see that it is true also for the precipitation of certain 

 protein solutions. In the latter case it is known as Hardy's rule 

 of the precipitating action of salt. In all these cases the effi- 

 ciency of the salt increases with the valency of the efficient 

 ion of the salt. These rules are a consequence of the Donnan 



