206 



Hence, we find together the following 2 Xn equations: 



/ (3) , (6) 



/>„-_! —bn -{-xan^\ I ^i— 1 =('^« —an-])K' 



KO x-\-\ in 



in wliich K' = ^ '" ^ " . 



If from this we eliminate a^, a^, a., .... (7„^i there remain n equations, 

 which may be written in this manner 



pbo—'P 1 #1 + 7^^2 - ^ 



' (7) 



pbn-2 ' {p r qVh, - 1 + q^'n = o \ 



-p/., .,4- (^ f /("-!)/>, = 

 ill which 



KO x-\-\ ^l 

 q z=z K'x -]- \ =z .ve V ' X H J. 1 



KO x-\-\ 'n 

 p z=z K' -f ,(■ r=: e " ' ••*•■ « f- W 



Elimination of the n — 1 valnes h, . . . . b„-\ gives, after rearran- 

 gement, the relation 



'9 y 



'-^^.uJ^^^ - (/) 



bn X — 1 



If we add together the equations (3) then 



^0 - bn = xa^ (8) 



Hence, if />„ i^^ known and />„ obtained from (/) a^ may be calcu- 

 lated from (8) also. 



If KO (or tn) is very large we get — = .i' so that we find for U 



P 

 the expression that we have deduced previously for very great 

 diffusion velocity (or a prolonged period of leaching). 



The discussion of the expression found will be found below in 

 connexion with the results of the other working processes. 



A lixiviation process which is being conducted in a continuous 

 manner may be brought in the following manner in a form, which 

 renders possible a mathematical formulation ^). 



^) See note 1 p. 209. 



