406 PROCEEDINGS OP THE AMERICAN ACADEMY. 



maximum ordinate of AB. If we therefore increase its value by this 

 amount and increase the observed value of A of every other point as B' 

 by this amount multiplied by the inverse ratio of the concentrations 

 corresponding to B' and A respectively, a new series of values corre- 

 sponding to the curve CD is obtained. The value C is still seen to be 

 in error by an amount as great as CF (F being equal again to the max- 

 imum ordinate of the new curve CD); the other values on this curve 

 are in error by an amount less in proportion to the greater concentration 

 to Avhich they correspond : Ave therefore increase all the values in the 

 same way as before, producing a third curve, and this process is repeated 

 till the maximum point on the resulting curve lies on the ordinate 

 through ACF and the curve has the form of GH, This method may 

 also be described algebraically as follows. The true specific conductivity 

 Kc, of the acid (that which it would exhibit in pure water at any con- 

 centration c), is equal to the observed conductivity of the sohition k„ 

 diminished by that of the water k^, and increased by a quantity 8, 

 constant at all concentrations and equal to the reduction in conduc- 

 tivity produced by mutual influence of the acid and impurities; that is, 

 i<c=^ i^s — Kw + S> 01" expressed in terms of equivalent conductivities, 



Ac 3= Aobs + - where A^ is the true equivalent conductivity of the acid and 



Aoi, is the " observed " equivalent conductivity as above defined. The 

 value of 8 is then determined from this equation by a series of approxima- 



tions as described above ixntil finally - = and A,, coincides with Ao(„. 



It should be imderstood, however, that this method gives only a 

 minimum value for the equivalent conductivity at the highest dilution, 

 for it is only in case the Mass- Action Law equation holds that the con- 

 ductivity curve approaches asymptotically to a maximum with increas- 

 ing dilution. If the empirical formula of Kohlrausch Aq — A^ = KG 

 is applicable, the upward slope of the curve must continually in- 

 crease with decreasing concentration. In fact, Kohlrausch found that 

 the behavior of neutral salts at very low concentrations (0.001 — 

 0.0001 normal) was intermediate between that required by these two 

 formulae. The values extrapolated with the help of the cube-root 

 formula will therefore give in all probability a maximum limit for the 

 conductivity at the greatest dilution, and the true value will lie be- 

 tween it and that derived by the method just described. 



In applying these methods to our results, from O.OG to 0.1 inilli- 

 equivalents per liter was taken as the standard initial concentration, 



