492 Prof. H. F. Weber's Researches on 



First Method of Investigation. 



Description. — A plane circular amalgamated zinc plate was 

 fitted to the bottom of a glass cylinder of about 11 centims. 

 width. Upon the zinc plate a considerably concentrated solu- 

 tion of sulphate of zinc, freed from air, was poured, up to the 

 height of l 2 centims. The concentration varied in each series 

 of experiments between 0*25 and O3o. A thin disk of cork 

 was then hud upon the free surface of the solution, upon which 

 a much less concentrated solution (the concentration chosen 

 between 0*15 and 0*20) was let trickle slowly from a*finely 

 drawn-out glass tubule. This latter solution slowly spread over 

 the lower more concentrated one; and a dividing surface formed 

 between the two solutions, which was perfectly plane (except 

 only along the margin, where a capillary action was visible in 

 a zone of about 1*5 millim. breadth) and reflecting. When 

 the second solution had attained the thickness l x centims. the 

 supply was interrupted, and a plane circular amalgamated 

 zinc plate, exactly fitting into the glass cylinder, was cautiously 

 let down by means of a guide until complete contact took place 

 between the upper bounding surface of the upper layer of salt 

 and the lower surface of the zinc plate. Herewith the expe- 

 riment was ready for the measurings, which consisted in mea- 

 suring, at certain, usually equidistant moments of time, the 

 electromotive force present between the two zinc plates of the 

 diffusion-vessel. By determining the time-rate of this electro- 

 motive force, we gain, as the following theoretic treatment will 

 show, a means for a very delicate testing of the accuracy of 

 Fick's elementary law of hydrodiffusion. 



Theory. — We have first, from Fick's elementary law and 

 the realized conditions of the experiment, to ascertain that 

 function which represents the value of the concentration z, of 

 any layer at the depth x below the upper electrode, at any 

 time t. 



The concentration z has at all times, and at every place be- 

 tween ^ = and =/ 1 + / 2 , to fulfil Fick's elementary law — that 

 is, to satisfy the partial dfferential equation 



it =k ^ (1) 



The limiting conditions of the experiment are — 

 For a* = 0, for all values of t, 



fe=°> <*> 



