236 CHAPTER XI 



But eo=r{i + e^) {i -\- r) + r e.,. 



wherefore, substituting for e-^, 



g ::=: ' ■■' I 



and e^ = r {i + e^ 



whence e, = ^j^^z_^r^_2r ^ r + (i - r)^ 



and, generally, the recovery in a system of compound imbibition is given by 



the expression -. ^ where r is the constant factor of recovery and 



• r + (I — ry 



n is the number of mills in series. 



As a numerical example, again let/ ~ o-i, w = o-i and m = 0-5 when 



r = ^,—, r and 



wm -{- f [1 — m) 



Single compound: r- = 0*500 = recovery. 



Double compound : — — -, r-„ = o • 667 = recoverv. 



r + (i — r)2 



Treble compound: -, r5-= o-8oo = recovery. 



r + (i — y)3 



Quadruple compound : — --—- ^ = o • 889 = recovery. 



Comparison of these results with those already obtained for the simple 

 scheme indicates the superiority of the compound process, especially when 

 the number of units increases, as in this case the simple scheme does not 

 give much benefit as due to the subdivision of the water. 



It wiU be readily seen from inspection of the above analysis that the 

 dry crushing has a very great effect in determining the total recovery, and 

 that it is onl}^ hy the use of excessive quantities of water that compensation 

 for an inferior dry crushing can be obtained. Attention to this point has 

 been a dominant factor in determining very high extractions, such as are 

 those which are obtained in the Hawaiian Islands. 



A second important factor to be considered is the fibre in the cane, and 



as this increcises so decreases the extraction due to the dry crushing. A 



greater quantity of sugar remains in the bagasse, but if this is operated upon 



efficiently very high extractions with a high fibre content in the cane can 



be economically obtained. For example, with / = o • i and m = o • 5 the 



dry crushing will recover 0-8889 of the sugar in cane, as compared with 



0-8235 when /rises to 0*15. With treble compound imbibition, and with 



li) =■ j (i.e., added water 10 per cent, in the one case and 15 per cent, in the 



y 

 other) the value of ^ is 0*5 and of -—. r3 is o-8. The total recoveries 



are then o - 8889 +0-5 X o-iii =0-9777, and 0-8235 + 0-5 X 0-1765 = 

 0-9647. 



These results are of the same order of magnitude ; but if single simple 

 imbibition be used the total extractions are reduced to 0-9444 and 0-9117. 

 This example indicates the greater importance of long trains and systematic 

 hnbibition when the fibre is high, and in this case also it is fortunate that the 

 fuel is plentiful. 



Experimental results comparing trains of different nimibers of units are 



