MEMBRANE POTENTIALS 143 



the value 59 (pH inside minus pH outside), i.e., the calculated 

 P.D., is excellent. 



It is of importance that the depressing effect of salts on the P.D. 

 can be derived from the Donnan theory. To show this we must 

 remember that the P.D. is expressed by the following term: 



P.D. == Y log (l + -) millivolts 



When we add NaCl to a gelatin chloride solution we increase the 

 concentration of the chlorine ions not in combination with gela- 

 tin, i.e., y, while the concentration z of the Cl ions in combination 

 with the gelatin remains the same, provided the pH remains the 

 same (neglecting the diminution of ionization of gelatin chloride). 

 Hence, the P.D. must become the smaller the greater y, and with 



steadily increasing y and constant z the value of 1 H must 



approach 1; i.e., the addition of enough salt must depress the 

 P.D. to zero, which is actually the case. 



This is also true when we add another salt, e.g., NaNO 3 , to a 

 gelatin chloride solution. In this case we may assume that 

 gelatin nitrate is formed. 



The depressing effect of the addition of NaCl to gelatin chloride 

 solution on the P.D. can be derived from the values of pH 

 inside minus pH outside. The question arises, Why is it correct 

 to neglect the influence of the Na ion? The writer did not give 

 any reason for this but Dr. J. A. Wilson was kind enough to point 

 out in a letter the mathematical proof justifying the writer's 

 procedure in the following way: 



"The true expression of the P.D. of a gelatin chloride solution 

 the presence of NaCl is 



p RT . [HJ outside + [NaJ outside 



F r +1 r +1 



LH J inside + |_NaJ inside 



Let the system contain the positive ions A, B, C, etc., and the 

 negative ions M, N, 0, etc., whose concentration in the outside 

 solution are, a, b, c, m, n, o, etc., and in the inside solution, 

 a', b r , etc. From the published work of Procter and Wilson it is 

 evident that the product of concentration of any pair of op- 

 positely charged ions is equal in both phases. The following 

 equations are evident, 



