316 EEPOET — 1886. 



the conductivity of the mixture 1"972. Many such experiments were arranged, 

 and all showed the superiority of the second view. All the experiments discussed 

 in this paper also prove the soundness of this view. We shall consequently adopt 

 this second view in what follows. 



3. Fundamental fonnula. — If two electrolytes (in dilute aqueous solution) are 

 mixed in the proportion of m : n, and if the conductivity of the one solution be a, 



and that of the other h, then the conductivity of the mixture will be '"" "*" " if the 



m + n 



solutions suffer no change in the mixing. This formula is the mathematical ex- 

 pression of the idea that the conductivity depends solely upon the number of 

 electrolytic (active) molecules per unit volume, and ou the friction of the ions 

 in the solvent. This friction undergoes no appreciable change iu very dilute 

 solutions. 



4. Consequences of the interchange of xoater in the mixture of solutions. — When 

 hydrochloric acid solution is diluted, the number of electrolytic molecules increases 

 but very little :' for the sake of simplicity we may assume that the number does 

 not increase at all. When, however, a solution of «cef^■c acid is diluted, the number 

 of electrolytic molecules is considerably increased {e.tj., by dilution to twice the 

 volume, from a standard solution, the increase is in tlie ratio of 1-51 : 1). When 

 therefore solutions of hydrochloric acid and acetic acid are mixed, the conductivity 

 will be greater than the above formula shows, if water is transferred from the 

 hydrochloric acid to the acetic acid solution, and vice versa. In general when 

 solutions of a stronger and a weaker acid are mixed, and the weaker acid takes 

 water from the stronger, the conductivity will be greater than that given by the 

 formula ; and conversely if the stronger acid takes the water of solution from the 

 weaker. A formula for this phenomenon is easily deduced; it shows that if the 

 above consideration is valid the conductivities of the original solutions must not be 

 very widely different; it likewise shows that the greatest deviations from the 

 formula occur when the solutions are mixed iu equal quantities. 



5. Isohydric solutions. — If a given solution of an acid be mixed in equal volumes 

 with solutions of another (stronger) acid of different degrees of concentration it is 

 found that the above formula is applicable for a certain degree of concentration. 

 For greater concentration negative deviations will be found, and on the other hand 

 for less concentration positive deviations ; according to the explanation given 

 above, that solution of the second stronger acid, which possesses the particular 

 degree of concentration, is of such a nature that it neither takes away water from 

 the first solution nor gives any up to it when the two are mixed. On this ground 

 I call two such solutions of diiierent acids relatively isohydric. I have defined the 

 concentrations of the solutions by their conductivities. 



The experimental method for the determination of the conductivity of isohydric 

 solutions will be most easily explained by means of an example. 



To find the hydrochloric acid solution which is isohydric with tartaric acid 

 (75-51).^ Under ' observed ' is placed the conductivity found, under 'calculated,' 

 the conductivity calculated by the formula given. 



Obs. Cal. Diff. 



5 cc. tartaric acid solution (75-51) + 5 cc. 



hydrochloric acid solution (94-62) . 84 49 85-07 -0-58 



5 cc. tartaric acid solution + 5 cc. hydro- 

 chloric acid solution (85-68) . . 81-34 8060 +-78 



By interpolation (and allowing for error of observation =0-5 p.c), we get as 

 isohydric with the tartaric acid solution (75-51) the hydrocliloric acid solution 

 (89-2x2-9). In a similar manner the numerical values contained in what follows 

 have been obtained. 



6. Examination of the vieto adopted in § 2. — This examination was conducted 



' I.e., the molecular conductivity increases very little — I refer always here to dilute 

 solutions. 



- By this is luiderstood tartaric acid of conductivity 75-51. The units here em- 

 ployed may be reduced to Kohlrausch's by multiplication by 10-*. 



