of the Rate of Diffusion of Solids dissolved in Liquids. 533 



For simplicity, two tubes only will be considered whose 

 lengths and sectional areas are the same. The expansion cf the 

 material of the tubes will be neglected. To make the problem 

 amenable to mathematical treatment, it will he assumed that 

 the density of water equals (1 — aQ), where is the tempera- 

 ture, and a is approximately equal to an ideal coefficient of 

 expansion. It will also be assumed that 



d=(l-cc6 + t), 



where (/ — the density of the solution, 



£ = the concentration. 



Let l = i\ie temperature of one tube. 



■i^ssthe velocity of the liquid up the tube. 

 6 2 = the temperature of the second tube. 

 r 2 = the velocity of the liquid up the tube. 

 L = the length of each tube, assumed constant. 

 k = the coefficent of diffusion, assumed constant. 

 T = the concentration of the solution at the bottom of 

 each tube. 



From considerations similar to those adopted in " Diffusive 

 Convection "*, Sect. II. and III., it can be shown that, neglect- 

 ing viscosity, 



9V- 









=<Kl- a fl 2 )L+ • 9T ^ aL - 



1 — e k 



kgT 



V 2 



Dividing throughout by g, and expanding, 

 (l-^L+TL^+j+jLj+Ao.)-- 



= (1-«0 2 )L + TL f-L + I + i ^ +&c.) -^; 

 v ' \v 9 L 2 12 12A: J v« 



and 



(v 2 -v 1 )= ^j— , approx. 



* Phil. Mag. Nov. 1898, pp. 453-465. 

 Phil. May. S. 5. Vol. 47. No. 289. June 1899. 2 



