28 REPORTS ON THE STATE OF SCIENCE.—1918. 
resulted and arrived at the following generalization, which may be 
regarded as the converse of Wiedamann’s third law : 
“When water is forced at a certain rate through a porous 
diaphragm, the difference of potential produced is independent of the 
dimensions of the diaphragm but is proportional directly to the 
hydrostatic pressure.” 
The problem was subsequently taken up by Helmholtz,7 who 
developed quantitatively and mathematically an hypothesis which 
Quincke has previously put forward in a qualitative way. It was 
suggested that, under most circumstances, solids and liquids become 
electrically charged when brought into contact. The distribution of 
charges is such that the surface of the solid is charged oppositely to 
the more or less mobile layer of liquid next it and with which it is 
in contact. This orientation of charges gives rise to a so-called 
electrical double layer. A potential gradient applied externally 
tends to produce a displacement of the electrically charged layer of 
liquid (in case the solid is fixed in the form of a capillary tube or 
diaphragm) and if the liquid is not a perfect insulator, the displace- 
ment results in a continuous flow’ of liquid along the surface of the 
solid. 
Freundlich,’ following a treatment used by Perrin! has developed 
the following expression for the amount of liquid (V,) transported in 
unit time through a porous diaphragm : 
Ve GED se. Diy 0 aaa aia 
di nl 
In this equation E is the total fall in potential through the 
diaphragm, D and » are respectively the dielectric constant and the 
viscosity coefficient of the liquid and e is the potential of the 
Quincke-Helmholtz double layer at the solid-liquid interface. Since 
K=RI and R=1/ yq where R is the total resistance, I is the 
current strength, 1 and q refer respectively to the length and cross 
section of the diaphragm, while y is the specific resistance of the 
liquid, equation (1) may be written 
fete Ei (2). 
Ar nY 
Since for a given liquid and diaphragm at constant temperature, 
«,n, Dand y are constant, V, is proportional only to the current, 
which flows through the diaphragm and the equation stands in 
agreement with the first of Wiedemann’s empirical laws. If one 
calculates the difference of hydrostatic pressure P, produced by 
electrical endosmose equation (3) is the result : 
Pa= 6 22ED : : ’ Maik (3 
where ( is inversely proportional to the size of the pores in the 
diaphragm. OD, «, and f being constant for a given diaphragm and 
liquid at constant temperature, equation (3) is a mathematical state- 
ment of Wiedemann’s third law.!! 
7 Wied. Ann., '7, 337 (1879) et. seq. 
5 Of. Lamb, Phil. Mag., (5) 25, 52 (1888). 
° Kapillarchemie, 225 (1909) ; Cf. Briggs: Jour. Phys. Chem. 2] (1917). 
10 Jour. Chim. Phys., 1904. 
1 Cf. Quincke, Pogg Ann., 118, 513 (1861). 
