Prof. W. OstwalcPs Electrochemical Researches. 113 

 whence 



tan 771 : 



K' 



This final equation seems to be sufficiently simple. It 

 includes one constant, v 0j dependent on the nature of the acid ; 

 the other constant, *4124, depends on the units chosen. But 

 there seem to be two objections to the expression. There is 

 a general agreement between the observed and calculated 

 results, but individual acids show greater divergences than 

 can be accounted for by experimental errors. If one attempts 

 to explain these discrepancies, one is forced to admit that the 

 formula has no rational foundation. An angle-function is 

 never used in mathematical physics, so far as the author is 

 aware, for a quantity which has no evident connection with 

 angles. 



The author has attempted to develop other, rationally 

 grounded, expressions for the nature of the action of the 

 water on the acid molecules ; but none has yet been found to 

 agree so closely with the observed results as that given above. 

 The mathematical treatment of the problem must be reserved 

 for future consideration. 



The author then proceeds to discuss the results obtained 

 with the polybasic acids. The behaviour of polybasic acids as 

 regards dilution differs from that of monobasic acids. In one 

 of his earlier papers the author suggested that when a solu- 

 tion of a polybasic acid is electrolyzed, only one of the hy- 

 drogen atoms of the acid goes to the cathode ; the electrolysis 

 takes place according to the scheme H | HE/' and H | H 2 R /// . 

 Sulphuric acid appeared as an exception. Further investi- 

 gation has, however, shown that when the maximum conduc- 

 tivity is nearly reached by dilution, the second, and eventually 

 the third, hydrogen atom takes part in the transfer of elec- 

 tricity, and electrolysis proceeds in accordance with the scheme 

 H 2 1 R" and H 3 1 R ;// . The participation of the second and 

 third atom of hydrogen depends upon the nature of the acids ; 

 those which have but feeble acid properties, e. g. selenious, 

 phosphorous, or phosphoric acid (shown by the impossibility 

 of titrating these acids by the use of litmus) exhibit molecular 

 conductivities which follow much the same course as the con- 

 ductivities of the monobasic acids. The results for some of 

 the polybasic acids are given in the following tables ; the 

 molecular conductivities are referred to the same units as 

 before, The values of log tan m and the differences are also 

 given, so that comparisons may be made between the poly- 

 basic and monobasic acids. 



Phil Mag. S. 5. Vol. 22. No. 135. August 1886. I 



