and Tivo New Types of Viscosity, 23 



(Vi + v 2 ) 2 ought to be associated with v ± v 2 , and in the three 

 cases just discussed we ought to have coefficients o£ (i^n)* 

 standing to one another as 2 2 2* : 3 2 2(3/2)* : 2 2 4 2 , namely, as 

 1*26 : 5*2 : 16, which are in general agreement with the 

 experimental averages. Thus the new type o£ viscosity 

 helps to account for the remarkable dependence o£ con- 

 ductivity variation with concentration upon the valency 

 o£ the ions. The connexion between the velocity o£ an ion 

 and its dielectric capacity will be considered in Section 8. 



6. Some Exceptional Cases of Ionization, 



The most interesting group of exceptions to the rule of 

 complete ionization is that o£ more than 200 weak organic 

 acids for which Ostwald found the simple mass-action formula 

 to hold, namely, i 2 /(l — i) = k/n, in which k is a parameter 

 characteristic of the acid dissolved in water. The same 

 formula has been found by Godlewski to apply to alcoholic 

 solutions of weak acids (BeibL, Ann, d. Phys. xxix. p. 294). 

 In my previous paper I suggested the following explanation 

 for these exceptional cases. Many of the weak acids are 

 known to polymerize. Probably acetic acid is (CH 3 COOH) 2 . 

 When dissolved in water and alcohol these double molecules 

 are partly dissociated into single molecules, which are ionized 

 completely. The conductivity of an aqueous solution of 

 (CH 3 COOH) 2 is then a measure of the amount of (CH 3 COOH) 2 

 resolved into ions. If at infinite dilution all the double 

 molecules are ionized, then i represents the degree of disso- 

 ciation of (CH 3 COOH) 2 , and Ostwald's formula gives the 

 remarkable result that this dissociation takes place according 

 to the simplest mass-action law. Solutions of these poly- 

 merized weak acids represent a connecting link between 

 electrolytic and non-electrolytic solutions. Out of Ostwald's 

 formula have sprung many variations, from those of Rudolphi, 

 van't Hoff, and Kohlrausch, down to the latest of Bousfield, 

 all designed to express the conductivities of ordinary electro- 

 lytic solutions by an empirical law of mass-action. The 

 reason for their want of success is now plain, because they 

 are seeking to represent by mass-action and incomplete 

 ionization the effects of the two new types of viscosity 

 discussed in the present paper. 



There is another very interesting class of exceptions, 

 namely, that in which a given solute can ionize in two 

 or more different ways. For example, H 2 S0 4 may yield 

 a positive ion H and a negative HS0 4 , or it may yield 

 two positive ions H and a negative S0 4 . Conditions of 



