'2J0 



The latter equation yields by integration of the two terms 



1 



rt = — l> -]- const., 



X 



from wliirh follows, heoanse when a = 0, A = A„ 



1 



(/'-/'.) (15) 



or 



x-\ 1 



h — a=z h \ hy,. 



,r X 



Substitution of this value for A — a in (13) and rearrangenieul gives 



dh _ 1 KO x — l 



1 .<?/, r X 



h + h„ 



X — 1 



in wl» it'll 



_ dl 



' '' "~ dtu 



Integration yields : 



. KO x-\ i_ 



/> -\ />,, z= e'-'^»-"! X^ >■ ■ J • Sf^ 



X — 1 



from wliioli follows, because when / = 0, // = b„ : 



M -K = (h„-\- — -K)^'"^'^'^. • • . (10) 



X — 1 \^ X — 1 J 



This equation is that of the line which i-epresents llie progressive 

 change of the coucenlration h as a function of /. If we want to 



represent /> as a function of ihe time, we can substitute =/. 



By performance of this last substitution and substitution for A 

 and / of the corres|wnding values h„ and /,, and some rearrangement, 

 we now find fi-oni (1(^) the expression-) for ( ' : 



1) The expression found aLso ap|)lies to the case when the vohunes of the tn-o 



spaces in which move llic combired liquid and the lixivialing- liquid do not stand 



r dl . dï 



in llie pioporlion of -.^ . In tlial case —-- is not equal to — — - and /„ not equal to 

 ' ' V dfi, ' dt„ a ' 



d! 

 1)~ 

 dt„ V 



tn • The deduction is made in ihe same manner, when 



dl V 



= X. 



E 



• dti, 



We obtain for U the expression (III) hut must I herein replace t^^ by tn . 

 Hence (with eq lal x) it is a ma'der of indilTerence for the leaching whether Ihe 



