32 Dr. A. Fick un Liquid Diffusion. 



The integral of this equation y=.ax + h contains the following 

 proposition : — " If, in a cylindrical vessel, dynamic equilibrium 

 shall be produced, the differences of concentration of any two 

 pau's of strata must be proportional to the distances of the strata 

 in the two pairs," or in other words, the decrease of concentra- 

 tion must diminish from below upwards as the ordinates of a 

 straight line. Expei-iment fully confirms this proposition. 



For the determination of the decrease of concentration in 

 the cylindrical vessel conducting the diffusion-current, I sunk 

 into the stratum to be estimated a glass bulb suspended from 

 the beam of a balance, and calculated the specific gravity from 

 the weight which required to be placed in the other scale-pan to 

 balance the glass bulb. This method creates little confidence 

 at first sight, nevertheless preliminary experiments showed it to 

 be sufficiently accurate. The quotation of the numerical results 

 of one experiment may suffice here. 



Depth of Stratum below the Surface. 

 lOmillims. 32-2 54-4 76-6 98-8 121-0 143-2 165-4 187-C 209-8 220-9. 



Specific Gravity* of Stratum. 

 1-009 1-032 1-053 1073 1093 1115 M35 1152 1170 M87 M9C. 



That the degrees of concentration in the lower layers decrease 

 a little more slowly than in the upper ones, is easily explained 

 by the consideration, that the stationary condition had not been 

 perfectly attained. 



A second case of dynamic equilibrium was also observed, by 

 replacing the cylindrical vessel in the above-described arrange- 

 ment, by a funnel-shaped one with the apex downwards. As the 

 section was now no longer constant, the condition for the dynamic 

 equilibrium was deduced from the more general equation (1) in 

 the form 



0=^ + 1.^.^ (4) 



hx^ Q dx Sx 



For a perfect cone with circular base (the funnel-shaped vessel), 

 we have Q = 7r . arx'^, if the origin be placed in the a])ex of the 

 cone, and we call a the tangent of half the angle of aperture. 

 By the substitution of this value, equation (4) becomes 



dx"^ X dx' 



the integral of which y-\-c'= ^. The two constants c and c' 



are to be so determined, that for a certain x (where the cone is 

 cut off and rests upon the salt reservoir), y is equal to perfect 



* The excess of which over unity is proportional to the concentration. 



