454 Mr. A. Griffiths on Diffusive Convection. 



solution at B and N ; but there is reason to believe that the 

 diminution in strength, under the conditions of the experi- 

 ment, is inappreciable. 



In the diagram A and M are shown at the same level, but 

 AB is longer than MN, and B is at a lower level than N. 



Under these circumstances it will be shown that, when 

 things have attained a steady state, there is a flow T of liquid 

 up the tube AB, and down the tube MN. 



To simplify the mathematical 

 treatment of the problem, it will 

 be assumed that the coefficient of 

 diffusion is a constant, and that 

 the density, d, of the copper 

 sulphate solution is given by the 

 equation d=\ + t, where t is the 

 quantity of copper sulphate per 

 cubic centimetre of solution. 



To show in a simple manner 

 that the flow indicated must take 

 place, imagine that the lower 

 compartment is divided into two 

 parts by a vertical partition, PQ, 

 and that at C on a level with B 

 there is placed a tap which can 

 be opened or closed at will. 

 Let L x = length of AB, 

 „ L 2 = „ MN, 



,, I = distance of a point in AB from the top A, 

 ,, T = quantity of copper sulphate (CuiS0 4 ) per 

 centim. in the lower compartment of the vessel 

 „ g = value of gravity . 



When the tap at C is closed and the diffusion has attained 

 the steady state, the density is given by the equation 



d=l + t, 

 whence in the case of the tube AB, 



d=l+ T -T. 

 Li 



The pressure at C on the left-hand side of the partition, 

 neglecting the initial pressure at the upper ends of the tubes, 

 is given by the equation 



cub. 

 V. 





