SURFACES OF DISCONTINUITY 693 



brief reference to them in our limited space; so we shall have to 

 be content with giving a few of the most important references 

 and then conclude with some remarks, which, it is hoped, 

 will enable the reader to study these papers more critically 

 than he otherwise might do. 



One line of advance has carried forward a formal development 

 of Gibbs' thermodynamic treatment of the phenomena at 

 charged interfaces. Consult for example: 



Gouy: Ann. phijs., 7, 129 (1917). 



Frumkin: Z. physik. Chem., 103, 55 (1923). 



Frumkin: Z. Physik, 35, 792 (1926). 



Frumkin: Ergeb. der exakt. Naturwiss., 7, 235 (1928). 



O. K. Rice: /. Phys. Chem., 30, 1348 (1926). 



Butler: Proc. Roy. Soc, A, 112, 129 (1926); 113, 594(1927). 



A good summary of this work will be found in Chapter VII 

 of Newman's book and in an article contributed by Frumkin 

 to the Colloid Symposium Annual, Vol. VII, pp. 89-104. 



On the other hand the unsatisfactory nature of the conclu- 

 sions deduced from Helmholtz's condenser-layer theory of the 

 distribution of the charge, and his lack of suggestions as to the 

 manner in which they would be kept apart, has given rise to 

 theories, based on statistical treatment, of "diffuse layers" of 

 double charge. The interested reader can consult the following 

 papers. 



Goiiy: Ann. chim. phys., 29, 145 (1903); 8, 291 (1906); 9, 75 (1906). 



Gouy: Ann. phys., 6, 5 (1916); 7, 129 (1917). 



Chapman: Phil. Mag., 26, 475 (1913). 



Herzfeld: Phijsik. Z., 21, 28, 61 (1920). 



Frumkin: Phil. Mag., 40, 363 (1920). 



Stern: Z. Elektrochem., 30, 508 (1924). 



O. K. Rice: /. Phys. Chem., 30, 1501 (1926). 



This development of theory has been occasioned by the 

 deviation of the ascertained facts from the simple conclusions 

 derived from the combination of Helmholtz's ideas with Lipp- 

 mann's result. We can only mention here one or two of the 

 most important of these deviations. (In the experimental work 

 the solution in contact with the mercury electrodes is generally 

 saturated with an appropriate mercury salt to ensure that the 



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