Determination of Diffusion of Solids dissolved in Liquids. 531 



solution can readily bo transferred to the problem under 

 consideration. 



It will be assumed that the upper extremities of the tubes 

 are kept in contact with pure water, and the lower extremities 

 in contact with a solution of constant strength. 



Let 7 = quantity of dissolved substance which enters the 



upper compartment in unit time, when the 



combined sectional area of the tubes equals 



unity. 



h = coefficient of diffusion (c.G.s. system), assumed 



to be a constant. 

 L = length of tubes in centims. 



T = quantity of substance per c. c. in the lower com- 

 partment. 

 t = time in seconds. 

 Then 



where i is any integer. 



L 2 



[If — 27 log f be taken as the unit of time, the topmost of 



the series of curves given on page 72, vol. ii., of Kelvin's 

 ' Mathematical and Physical Papers/ shows graphically how 

 7 rises to a maximum.] 



Let <? = total quantity of substance transmitted in t seconds. 

 Integrating the preceding expression with respect to t, we 

 obtain 



7.-TI r {-Qo J 2 i = oo T2 —p^M-y 



? =l{ <+2 l ( - i)8 ^- 2 e 1 ( - i) ^^ t ^} (i) 



When t is very large the third term within the brackets 

 may be neglected, and 



or 



_m 2LT7r 2 _m LT _ 



q ~ L " 7T 2 l2~ L ~ 6 ' ' ' * (o) 



The last equation shows that if t is large the quantity 

 transmitted equals kTt/h minus a quantity which is inde- 

 pendent of the coefficient of diffusion. Thus if in the adjoining 

 figure abscissas represent times, and ordinates the quantities 



