208 PROCEEDINGS OP THE AMERICAN ACADEMY. 



any concentration C and the limiting conductivity A at zero concentra- 

 tion : 



A -A 



C 3 



Ap-A 



A 3 6' 3 



K (Kohlrausch), 

 K (Barmwater), 



A ° 3 A = K (van't Hoff), 



A 5 <7 2 



A -A 



A 2 C* 



= K (Rudolphi). 



It seemed therefore to be of especial interest to test the applicability of 

 these formulas at the widely different temperatures employed in our ex- 

 periments. In making such a test, it must be borne in mind that the 

 results will be in a high degree dependent on the values of A employed, 

 since in dilute solutions A — A is a relatively small quantity; yet in 

 several instances authors have not given sufficient consideration to this 

 matter. The most satisfactory method of procedure seems to us to be 

 the elimination of the A value, which cannot be determined with sufficient 

 accuracy by extrapolation, by writing the functions in the following 

 form : 



A = A — K C l (Kohlrausch), 



A = A — KA l <7 3 (Barmwater), 



A = A - Kh? C* (van't Hoff), 



A = A -KA 2 C l (Ostwald), 



and then plotting the values of A along one co-ordinate axis and those 

 of the C-A function constituting the last term (that is, C», A^C*, etc.) 

 along the other axis, as is illustrated by Figure 9. If the function in 

 question holds, the points will of course lie upon a straight line ; 

 and by comparing, in the case of the different functions, the deviations 

 of the separate points from the best representative straight line that 

 can be drawn, a measure of the degree of applicability of each function 

 is obtained. All our complete series of measurements and those of 

 Kohlrausch and Maltby on the same salts at 18° have been studied in 

 this way, a plot on a very large scale being employed. The straight 

 lines were drawn in every case so as to make the percentage deviations of 

 the two conductivity values for the two more concentrated solutions and 



