292 CONCERNING THE EFFECT OF GRAVITY 



i 



In the article referred to above, Vegard proves from con- 

 sideiations of dynamical and thermodynamical equilibrium, 

 that the final distribution of the solute will depend on whether 

 the density of the solution at that particular concentration 

 increases or decreases for an infinitely small increase in con- 

 centration. In the special case in which a small change in 

 concentration makes no corresponding change in density, the 

 concentration of the solution will remain uniform throughout 

 even when exposed to gravity. 



Suppose now the homogeneous solution is exposed to grav- 

 ity, its concentration will begin to change, solute flowing from 

 the top to the bottom or vice versa, according as the density at 

 that particular concentration increases or decreases with the 

 concentration. This flow will be comparatively large at first, 

 but will fall away to zero as an exponential function of the time. 

 When equilibrium is reached, there is the same concentration 

 gradient at every height of the column. If now we consider 

 the force of gravity removed, the solution will begin to diffuse 

 back to its initial condition of uniform concentration, and it 

 seems reasonable to suppose that the flow will be exactly similar 

 to that in the original solution, that is it will be comparatively 

 large at first, and will fall away as an exponential function of 

 the time. 



If this be true, then the original diffusion flow is exactly 

 similar to one in a tube not exposed to any force such as gravity 

 and where the initial concentration gradient 'is equal to that 

 which actually exists in final equilibrium in the solution exposed 

 to gravity. 



Now it is always assumed that the diffusion of a solute is 

 analagous to the flow of heat, and obeys Fourier's linear diffu- 

 sion law, and the conditions in the differential equation: 



r> c ^T 

 da* " = d~t 



