458 Mr. A. Griffiths on Diffusive Convection. 



-j- and -— are small, 



siderable labour, but if —A an d —r^ are small, it can be 



shown that 



v = vtv ' (7) 



or, if L x — L 2 = SL, and either length = L approximately, 



3ASL ,„ 



As a practical example take 



k =2*47 x 10~ 6 , the value of the coefficient of diffusion 



for copper sulphate, 

 L =4 centim., 



SL = O05 centim., i.e. half a millimetre. 

 Substituting in (8) we obtain 



v=2 , 306xl0~ 8 centim. per second 

 = 5*09 centim. per year. 

 The author has tested the accuracy of this approximation 

 in the original equation (6), and with seven figure logarithms 

 has found the value of v to be exactly correct. He finds that 

 (8) gives a value correct to a fraction of a per cent. 



Section IV. 



Effect of Diffusive Convection on the quantity of dissolved 

 substance transmitted when the tubes are of equal bore. 



The quantity transmitted, per second, of the tube L t equals 

 from Section II. 



rAT 



1-e T 



expanding by the exponential theorem and dividing out we 

 obtain 



Tr( 1+ 2^ + i2^ + &c -> 



It is obvious that the expression within brackets is the 

 correcting factor for the velocity of the liquid up the tube. 



Taking the case considered in the previous section, with 

 Li = 4 centim., and # = 2'306 x 10 ~ 8 centim. per second, the 

 value of this correcting factor works out as 1*019 approxi- 

 mately ; which shows that a velocity of about 5 centim. per 

 year up a tube 4 centim. long produces an increase in the 

 quantity of copper sulphate transmitted of about 2 per cent. 



