27r- 



36 Dr. A, Fick on Liquid Diffusion. 



passed through the entire pore, could not be greater than 



But the passage of the water to the other side requires a sepa- 

 rate consideration. We have seen, namely, that at the upper 

 extremity of the cylindrical stratum-unit, with the internal 

 radius r, no higher concentration could take place than/(p — ;•), 

 which is certainly less than perfect saturation, and, in fact, 

 becomes proportionally smaller the greater r is assumed to be. 

 If, as we sujjpose, a relatively inexhaustible volume of saturated 

 solution (obtained by the addition of crystals) be present on the 

 upper side of the membrane, then, at the upper extremity of our 

 elementary stratum, there must take place a sudden increase in the 

 concentration, from /(p — ?•) to perfect saturation. If we assumethat 

 this is the case for the first moment, there will now be, according to 

 the general principles of diffusion, from the elementary stratum a 

 relatively (in comparison with the amount which a continual trans- 

 ition of density requires) infinite quantity of water required, and 

 an equally infinite amount of salt forced in. The latter will be 

 inevitably hindered by the nature of the membrane, and the 

 excess of salt forced against the pore must in some way glide off 

 laterally ; on the other hand, more water, than the arrangement 

 of the densities in our elementary stratum requires, can easily, to 

 a certain extent, be drawn through towards the denser solution, 

 so that in the pore, the particles of water move upwards with a 

 greater velocity than the particles of salt move downwards. The 

 excess of water now spreads out on all sides, into the saturated 

 solution (as the mouths of the pores must lie at a certain distance 

 from each other), partly by diffusion, partly by mixing streams 

 proceeding from difference of specific gravity ; until a stationary 

 condition has been in such a way produced, that a conical space 

 increasing upwards is supported upon the up])er annular section 

 of the elementary stratum, in which spacj the concentration 

 f{p — r) increases to perfect saturation, and which determines 

 a diffusion-current of such a strength, that thereby exactly 

 as much water is passed upwards, as in the same time can dif- 

 fuse itself into the reservoir of saturated solution from the 

 upper end of the space, without changing the concentration. 

 Then the above-mentioned space would evidently be immedi- 

 ately lengthened upwards, (and thereby the intensity of the dif- 

 fusion-current be diminished) so soon as more water passed 

 through, and therefore the concentration at the upper end of the 

 space continues to vary ; and if, on the contrary, less water 

 passed upwards, sudden transition of concentration must imme- 

 diately occur in certain places, which sudden changes determine^ 



