205 



ds = KO {b—a)dt = — vdh =Vda (5) 



From the two last terms of tliis equality follows : 



1 



da = db. 



.T, 



Integration of the two members of this equation over the time 

 ^ = up to t=it' when <^t' <^ Lt and bt~Q ■=^ J)^ and r/,=o = <^i 

 gives the equation 



1 



from which follows 



wherein 



,7,- 4-1 

 b — a = 6 — /:», 



1 



X 



If in the second term of the equality (5) we substitute this value 

 for h — a, we obtain from the second and third term, after rearran- 

 gement, the equation : 



db KO .^•-fl 



dt 



X 



P 



x + l 



KO A'+I 

 in which — . is independent of the time. 



V X 



Integration yields: 



KO .r-(-l 



■V • ' 



If now we remember that /;/— o = h^, it follows that 



KO :(H-1 



* / \ V X 



If now we substitute for t, Lt and for J> the coi'responding value 



1 



b-^ and it also we again replace /> by a^ -\ />„, we obtain after 



X 



rearrangement having regard to (3) 



KO x+\ 



^-«1 = (^-^'o)^' '■ ' " ...... (6) 



Hence, for each element of the lixivialion battery, we have two 

 equations (3 and 6). If the battery contains n elements we maj' put 



l\tr=~ when tn represents the total period of lixiviation of a quantity 



of the mass. 



