Endosmose and other Allied Phenomena. 57 



-^ +u,V 2 iv = 0. 

 dz 



are satisfied b y p = const. To form the boundary condition 

 corresponding to (1), let ds be a linear element drawn on the 

 surface in the direction of the flow of liquid, and therefore 

 also of electricity. We obtain 



where /is the rate of shear in a plane through ds normal to 

 the surface. If I be small in comparison with the linear 

 dimensions of the channels, the first term of this equation 

 may, in the cases at present under consideration, be neglected 

 in comparison with the rest*, so that (13) is satisfied provided 



X=~l<i> (14) 



everywhere. Hence the flow of liquid is everywhere in the 

 same direction as that of electricity, and stands to it in the 

 ratio of % to — <p/a, that is in the ratio ap/ft. The formula (11) 

 embraces all the laws discovered experimentally by Wiedemann 

 for the electric transport of liquids through porous vessels. 



2. If a difference of pressure obtains between the two sides 

 of a porous wall, or between the two ends of a capillary tube, 

 the flux above calculated must be superposed on that which 

 would be maintained (as in Poiseuille's experiments) by this 



* To see this, take the origin at any point of the boundary, and the 

 axis of z along the normal, and let the equation to the boundary then be 



z=i(Ax 2 +2Bxy+Cf)+&c. 



If the axis of x be in the direction of the flow at 0, we have to prove that 

 ld~xldxdz may be neglected in comparison with d-^Jdx, It is proved in 

 the appendix to this paper that at we must have 



*? =Ku+Bv, 

 dx 



and therefore 



dxdz dx 



which proves the statement made above, when I is small in comparison 

 with the radii of curvature of the wall. 



