404 PROCEEDINGS OP THE AMERICAN ACADEMY. 



Thus, the underlying idea is tlie preparation, by the addition of a little 

 acid, of a sample of solvent the impurities in which shall have no ap- 

 preciable influence on the conductivity of subsequently added portions 

 of acid. Theoretically, it seems highly probable that this must be prac- 

 ticable; for any basic constituents of the water like ammonium or other 

 alkaline hydroxides or carbonates would be completely neutralized, and 

 any weakly acid constituent like carbonic acid which Kohlrausch * has 

 shown to be undoubtedly the chief source of impurity, would have its 

 dissociation reduced nearly to zero, as soon as the concentration of 

 the strong acid added reached a value as great as, or a few times 

 greater than, the concentration of the impurity. It is true that even 

 though the impurities may have been thus rendered harmless, the in- 

 crease in conductivity produced by the added portion of acid will not 

 be strictly identical with the conductivity which it would have if it were 

 added to pure water; for the acid originally present will be somewhat 

 reduced in dissociation, and will itself reduce the dissociation of the 

 added acid : but this effect is known to be very small at high dilutions, 

 and the last-mentioned part of it is eliminated by regarding the calcu- 

 lated equivalent conductivity as corresponding to the final concentra- 

 tion rather than to the difference in concentration, t 



In regard to the choice of the initial concentration, it may be pointed 

 out that this must be taken so large that the maximum effect of the 

 impurities in the water and of the acid on the conductivity of each other 

 shall be attained, and that this condition is shown to be fulfilled when 

 the equivalent conductivities calculated from two successive values of 

 the initial concentration are in substantial agreement. The fact that 



volume of the solution is somewhat increased, whereby the observed conductance 

 and concentration would be decreased in the same proportion. Thus if mw, »ij 

 and m^ are the weights of water, of the first portion of added acid of a concen- 

 tration Cq, and of the second portion respectively, then, placing volumes propor- 

 tional to weights, whicli at the dilutions in question produces no error, we have : 



/fi = k\ ; — . Also C„- C. = 0-^^ 



viw + nil + mg i i ,„^ _j_ ^^ ^ j,,^ 



* Wissensch. Abhandlungen d. phys.-tech. Reichsanstalt, 3, 193 (1900). 



t For example, it is readily calculated from Kohlrausch's mean values (Wicd. 

 Ann., 66, 794, 1898) of the change of the conductivity at 18° of tlie ions of neu- 

 tral salts with tiie dilution that the mean error in their equivalent conductivity 

 would be 0.42 per cent at 0.0002 normal and 0.25 per cent at 0.0005 normal if 

 computed by the metiiod here described, taking 0.0001 as tiie initial concentration. 

 In the case of the strong acids, whose conductivity changes much less rapidly 

 with dilution, the error from this source would be about one-half as great. 



