Dr. A. Tick on Liquid Diffusion. 31 



development for a current of heat, we can obtain from this fun- 

 damental law for the diffusion-current, the differential equation 



when the section Q of the vessel in which the current takes 

 place is a function of its height above the bottom. If the sec- 

 tion be constant {i. e. the vessel cylindrical or prismatic), the 

 differential equation becomes simplified to 



h--k^^ . (2) 



Several methods for the experimental confirmation of this dif- 

 ferential equation, and consequently of the fundamental law 

 above advanced, presented themselves. In the first place, by 

 integration of equation (2) the expression y=f{x, t) could be 

 obtained, and the calculated value of y compared with its observed 

 value. I have, however, entirely omitted this method, because 

 even in those cases in which the integral has a finite form, 

 the numerical calculation of a sufficient number of values would 

 have been extremely troublesome, whilst other unequivocal proofs 

 were possible. For the same reason I also here omit to develope 

 the particular integrals of equation (2) for special cases of diffu- 

 sion-currents. 



The experimental proofs just alluded to, consist in the investi- 

 gation of cases in which the diffusion- current has become sta- 

 tionary, in which a so-called dynamic equilibrium has been pro- 

 duced, i. e. when the diffusion-current no longer alters the con- 

 centration in the spaces through which it passes, or in other 

 words, in each moment expels from each space-unit as much 

 salt as enters that unit in the same time. In this case the ana- 

 lytical condition is therefore ;it = 0. Such cases can be always 



produced, if by any means the concentration in two strata be 

 maintained constant. This is most easily attained by cementing 

 the lower end of the vessel filled with solution, and in which the 

 diffusion-current takes place, into a reservoir of salt, so that the 

 section at the lower end is always maintained in a state of perfect 

 saturation Ijy immediate contact with solid salt; the whole being 

 then sunk in a relatively infinitely large reservoir of pure water, 

 the section at the upper end, which passes into pure water, 

 always maintains a concentration =0. Now, for a cylindrical 



vessel, the condition -|^=0 becomes by virtue of equation (2), 



' at 



«=g (^) 



