Prof. W. Ostwald's Electrochemical Researches. Ill 



This result is identical with that already stated ; for, if 

 equal conductivities of the various acids are exhibited at 

 equally proportional dilutions, then the dilution-exponents, 

 which can be represented as logarithms of the dilutions (with 

 the base 2), must show constant differences. The form of the 

 curve is indicated by the results obtained ; it runs asymptotic 

 between the axis of p and a parallel placed at a distance 

 equal to 90 units, and appears to be symmetric to right and 

 left and also above and below. The maximum of increase, 

 as already observed, lies at 45, where the curve shows an 

 inflexion-point. 



As we have here undoubtedly to do with a natural law, no 

 exception to which is shown by any of the results obtained 

 for 90 to 100 monobasic acids, it is reasonable to suppose 

 that the curve must be capable of representation by a fairly 

 simple analytical expression. At first sight a tangent-function 

 is suggested. The results were therefore reduced so that the 

 maximum fell at the value 90 ; they were then regarded as 

 angles, and the corresponding tangents were found. The 

 tangents, however, formed not an arithmetical but a geome- 

 trical series ; the logarithms of the tangents gave approxi- 

 mately constant differences, they increased proportionately 

 with the dilution-exponents. A few examples are given. 



Acetic Acid. 



jp. 



mol. c. 



log tan mol. c. 



Difference. 



1 



1 



2 

 3 

 4 

 5 

 6 

 7 



I 



10 



0-5196 

 0-7550 

 1-078 

 1-514 

 2-123 

 2-943 

 4-084 

 5-642 

 7-753 

 10-47 



7-9576 

 8-1199 

 8-2745 

 8-4220 

 8-5690 

 8-7110 

 8-8537 

 8-9947 

 9-1340 

 9-2667 



1 

 0-1620 

 0-1546 

 0-1475 

 01470 

 0-1420 

 0-1427 

 0-1410 

 0-1393 

 0-1327 



