SURFACES OF DISCONTINUITY 551 



cannot be formulated correctly until a general formula for 

 potential in terms of concentration has been discovered. 



20. The Empirical Laws of Milner and of Szyszkowski for <x and c. 

 Langmuir's Adsorption Equation. FrenkeVs Equation 



We shall now turn for a moment to one or two empirical 

 relations between surface tension and bulk concentration in 

 solutions. For relatively strong solutions of acetic acid Milner 

 {PhU. Mag., 13, 96 (1907)) found that a formula of the type 



0-0 — a = a + jS log c 



was satisfied, where ctq is the surface tension of water, cr that of a 

 solution of concentration c, and a and ^ are constants. Shortly 

 after, Szyszkowski (Z. physik. Chem., 64, 385, (1908)) sug- 

 gested a somewhat different form, viz., 



^-1^^ . 5 log (l + -^) , 



where a and 6 are constants. He verified this for solutions of 

 the shorter-chain normal fatty acids. It was observed that the 

 constant b had the same value for all the acids, while a was 

 different for each acid. Its values, however, for two acids dif- 

 fering by one carbon atom bore a nearly constant ratio, the three 

 carbon acid having an a 3.4 times larger than the a for the four 

 carbon acid, and so on. This means that 1 + (c/a) is a larger 

 quantity for the same concentration the longer the h3^drocarbon 

 chain in the acid, and so in this homologous series of acids the 

 diminution of surface tension at a given concentration increases 

 rapidly in amount as the hydrocarbon chains are lengthened, 

 which is just an example of a well-known rule due to Traube 

 that the capillary activity of a member of an homologous series 

 increases strongly and regularly as we ascend the series. For 

 by the Gibbs' simple formula 



c da 

 ^ ^ ~Rtdc 

 hao C 

 lit' c + a 



