[ 30 ] 



V. On Liquid Diffusion. 

 By Dr. Adolph Fick, Demonstrator of Anatomy, Zurich^. 



A FEW years ago Graham published an extensive investiga- 

 tion on the diffusion of salts in water, in which he more 

 ■ especially compared the diffusibility of different salts. It appears 

 to me a matter of regret, however, that in such an exceedingly 

 valuable and extensive investigation, the development of a fun- 

 damental law, for the operation of diffusion in a single clement 

 of space, was neglected, and I have therefore endeavoured to sup- 

 ply this omission. 



It was quite natural to suppose, that this law for the diffusion 

 of a salt in its solvent must be identical vrith that, according to 

 which the diffusion of heat in a conducting body takes place ; 

 upon this law Fourier founded his celebrated theory of heat, 

 and it is the same which Ohm applied with such extraordinary 

 success, to the diffusion of electricity in a conductor. Accord- 

 ing to this law, the transfer of salt and water occurring in a unit 

 of time, between two elements of space filled with differently 

 concentrated solutions of the same salt, must be, ceteris jjaribus, 

 directly proportional to the difference of concentration, and in- 

 versely proportional to the distance of the elements from one 

 another. 



In mathematical language this may be thus expressed : — In a 

 volume of salt solution, let the concentration in each horizontal 

 elementary stratum be constant and —y,& function of the height 

 X of this stratum above any other stratum which may be assumed 

 as the primary horizontal plane ; the limitation being made, that 

 the function y must diminish as x increases, that is, each higher 

 stratum nnast be less concentrated, and therefore lighter, than 

 all the subjacent ones, because it is only under this condition, 

 that the diffusion will not be interfered with by gravity ; then 

 from the stratum between the horizontal planes at x and 

 x + dx (in which the concentration is y) there will pass, during 

 an element of time dt, into the immediate superjacent stra- 

 tum, bounded by the horizontal planes x + dx and x-\-2dx (in 



which the concentration y-\-j-dx prevails), a quantity of salt 



■=—(^,k.-~-dt, in which Q signifies the surface of the stratum, 



and k a constant dependent upon the nature of the substances. 

 It is evident that a volume of water equal to that of the salt 

 passes simultaneously out of the upper stratinn into the lower. 

 Exactly according to the model of Fourier's mathematical 



* From PoggendoviF's Annalen, vol. xciv. p. 59 ; abstracted and com- 

 municated by the Author. 



