Lieber and Rintel 



respect to salinity, in a laboratory. Therefore the presence of vertical 

 boundaries produced currents resembling the ones first observed in vertical 

 tubes and incisively interpreted in the literature (Taylor, 1954). 



In the 38th Guthrie Lecture delivered in 1954, Sir G. I. Taylor examined 

 conditions for convection of a fluid contained in a vertical column (tube) and 

 subjected to a gradient in the concentration of a diffusive substance. His pur- 

 pose was to determine the effect of gravity on dispersion in a vertical tube as 

 an adjunct of his comprehensive study on "Diffusion and Mass Transport in 

 Tubes," inspired by a physiological problem. In so doing, Taylor established 

 on theoretical grounds that equilibrium becomes stable and that vertical cur- 

 rents stop when the vertical gradient in concentration, dc/dz, becomes less 

 than 67.94. D/x/gpa a"*, where 2a is the diameter of the tube, D is the coeffi- 

 cient of diffusion, g the acceleration of gravity, and ij. the viscosity. 



When we set /3' = in the present work, we obtain a result that corre- 

 sponds to the results obtained in 1954 by Taylor for diffusion in a vertical tube 

 of radius a. For if we define x = a/h and identify our K" with Taylor's sym- 

 bol D for the coefficient of diffusion, the result of Eq. (12) reduces, when use 

 is made of the relation in Eqs. (3), to 



dc D/Li 



(Ra^) 7 ' (14) 



dz 



which corresponds to Taylor's result 



dcg D/x 



= 67.94 

 dz 



g/oaa" 



(15) 



Thus the fact of the proportionality of dc^/dz to D/j./gpaa'* is found to be the 

 same in both works. We may rewrite Eq. (14) as 



dc 



D/x 



= e . 



dz ^ gpaa* (16) 



and Eq. (15) as 



dcp D/x 



dz gpaa'^ 



(17) 



where Cj = Rg x'' in the present work and e^ is given numerical value 67.94 in 

 Taylor's work. If we regard the upper and lower boundaries to be free, then 

 we may take Rg = 658, which makes e^ = 658 x''. 



If now we require that e^ = e^, then this would mean that 



62 = 658 x'* . (18) 



700 



