Dr. A. Fick on Liquid Diffusion. 35 



centric cylindrical film of radius r, of the porous partition will 

 evidently be constant^ and =/(p — r). Respecting the nature of 

 this function, it can only be said that its value for ?' = p, which 

 is equal to 0, and that from this point it must increase (probably 

 very rapidly) with the decrease of r ; but if necessarily under all 

 circumstances for r = 0, it must be increased up to the density 

 of the circumambient solution, is left undetermined, and appears 

 to me, in fact, for very narrow pores very improbable. In a 

 word, the density in the pore will increase from the wall towards 

 the centre, and in the cylindrical film of the radius r there can 

 certainly occur no higher concentration than f{p — r) (but pos- 

 sibly a lower one). The radius p of the pores must be imagined 

 so small, that a filtration of liquid, by virtue of their cohesion, 

 together with the attraction of the membrane itself, is prevented, 

 even under high pressure ; and that also equalization of the dif- 

 ferences of pressure when liquid is present on both sides of the 

 porous membrane, if possible at all, is only so in a relatively 

 long space of time ; further, that currents of mixture, by virtue 

 of the variations of specific gravity within the pore, cannot 

 occur. 



Let us now suppose that a membrane of this description sepa- 

 rates a saturated solution of salt from pure water, and further, 

 that the former is above, and the latter under this horizontal 

 membrane. In any cylindrical pore of the said membrane, whose 

 radius may be again =p, let us suppose a concentric elementary 

 stratum, bounded by two cylindrical films infinitely near to each 

 other, the radii of which are respectively r and r + dr. At the 

 upper extremity, the highest possible concentration, /(p—r-), of 

 the layer will immediately be produced. On the other hand, the 

 lower extremity, by immediate contact with a relatively infinite 

 quantity of pure water, will be constantly maintained at a con- 

 centration = 0; and when a stationary condition is brought about, 

 the degrees of concentration, within the assumed elementary stra- 

 tum, must increase from to f[p — r), in proportion to the height 

 above the lower boundary surface of the membrane. This arrange- 

 ment would have the effect of producing a diffusion-current in the 

 elementary stratum, which, according to our laws, would deliver 



a quantity of salt 'Ztt . k . -^^ — - dr downwards, and an equal 



volume of water upwards, if we understand by k, as above, the 

 diffusion-constant fur the combination of salt and water in 

 question, and by h the thickness of the membrane, consequently 

 the length of the pore. No regard has been ])aid, however, to 

 the retardation which the flowing molecules suffer from the 

 attraction of the substance of the membrane along the sides of 

 the pores ; it is certain, however, that the total quantity of salt, 



D2 



