38 Dr. A. Fick on Liquid Diffusion. 



with solution of the there highest possible concentration, and 

 cannot therefore give origin to a usual double diffusion-current. 

 Water will, however, pass over from the lighter to the denser 

 solution, because a force of suction comes into play on each side 

 of the membrane, proportional to the difference of concentration, 

 consequently a stronger force at the upper side corresponding to 

 the saturated solution. On the other hand, all those strata lying 

 nearer to the axis, behave exactly in the above manner, with the 

 single diff'erence, that in them the concentration, instead of in- 

 creasing from 0, now increases from below upwards from c to 

 the respective maxima, and consequently an absolutely weaker 

 diff"usion -current is produced. It therefore follows in this case, 

 that in places where, in the first instance, salt passed to the one 

 side and water to the other, only a single diffusion of water takes 

 place, consequently the proportion between water and salt (the 

 endosmotic equivalent) must be greater here than there. If, for 

 instance, c> (p — ?') (which is possible in the case of very fine 

 pores), no salt whatever could pass through; the endosmotic 

 equivalent would be = oo, or the current one-sided. 



This conclusion is also confirmed by experiment. Even the 

 above-cited experiments of Ludwig and Cloetta intimate this to 

 be the case. I have myself obtained stdl more decided results. 

 A membrane which gave an equivalent between 5 and 6, when it 

 separated a saturated solution from pure water, yielded an equi- 

 valent = 11 "05, in another case even =17'05, when the pure 

 water was replaced by a solution of common salt of 22 per cent. 

 Lastly, if we analyse the case in which, instead of a saturated 

 solution, a dilute one be placed above, and again pure water 

 below. Let us again express the concentration of the upper 

 solution by c. Evidently in an axial cylinder whose radius )• is 

 so great, as exactly to make/(p— r)=c, the concentration from 

 the lower to the ujjper end, will now regularly increase from 

 to c, and a usual diffusion-current take place, which will jiass a 

 volume of salt downwards, exactly equal to the volume of water 

 propelled upwards. Only in those layers situated nearer to the 

 wall, can the concentration at the upper end never rise to c, and 

 there will therefore pass through these layers alone, according to 

 the previous considerations, more water than salt. The radius r, 

 of the above-mentioned axial cylinder, is evidently as much greater 

 as c is smaller, therefore the endosmotic equivalent must also 

 decrease very rapidly with c ; and we might expect that, for 

 moderately small values of c, the endosmotic equivalent would be 

 found smaller than unity (because a volume of salt weighs more 

 than an equal volume of water). Ludwig's experiments with 

 common salt are perfectly in accordance with this conclusion ; in 

 some cases in his experiments, the equivalent sunk from 4 to 1 



