5 38 Determination of Diffusion of Solids dissolved in L iq u ids. 



Section VII. — Error due to Diffusive Convection. 



Inequalities in the lengths of the tuhes and inaccuracies 

 in placing them in the diaphragm will, in general, produce 

 convection-currents. There is no intrinsic difficulty in calcu- 

 lating flows of small magnitude, if the tubes are of unequal 

 length ; but, to simplify the algebra, in the following the tubes 

 will be taken of equal length and of equal sectional area. 



Let n = number of tubes. 



By = distance between the top of one tube and the 



average of the tops of all the tubes. 

 B r = corresponding distance for the rth tube. 

 v x = velocity up the first tubo. 

 v r = „ „ rth tube. 



Making the usual assumptions, it can be shown that 



12k =Br - Sl ' 

 Noting that 2*v = 0, 28 r = 0, it can readily be shown that 

 tvL__ —\2B r 



and that the correcting factor equals 



12V+...S; 2 



i + 



jlt n 



With ordinary care in the construction of fhe apparatus, 

 the correcting factor will deviate very little from unity. 



Section VIII. — Some Experimental Results. 



One apparatus has 15 tubes, of average length 4*043 centim., 

 and a total sectional area 0*4102 square centim. It was 

 placed in a cellar the temperature of which fluctuated through 

 a range of about 3° C. per week. The lower compartment 

 contained a solution of copper sulpbate holding 0*0506 of 

 copper to the c.c. At intervals of a week the upper com- 

 partment was renewed with pure water ; similarly the lower 

 compartment was renewed with fresh solution. The tubes 

 were originally full of pure water. The average temperature 

 was about 8° C. By the end of the first week 0*0026 gram 

 of copper had been transmitted ; by the end of the second a 

 total of 0*0077 ; end of third, 0*0144 ; end of fourth, 0*0226 ; 

 end of fifth, 0*0311 ; end of sixth, 0*0403 ; end of eighth, 

 0*0559 ; end of ninth, 0*0662. 



