270 CHAPTER XIV 



through an angle of 180 and join the downward stream. These particles 

 have also a gyratory motion, and particles may leave the upward stream 

 and join the downward one and vice versa. As the particles in the down- 

 ward stream approach the top of zone 5 many particles are seen to detach 

 themselves from the current, and, falling vertically a short distance, join 

 zone 5 ; these particles then become settled particles, and thenceforth 

 gravitate slowly downwards, so that, while it is being built up, zone 5 is sim- 

 ultaneously shrinking. During this stage of settling, there is, however, 

 a net increase in the height of the column. Zone 4 during the process of 

 settling is continually decreasing in depth both from above and below, and 

 eventually there comes a time when the system is reduced to zones 1, 3 and 5, 

 as by this time nearly all the stragglers will have caught up with zone 3. 

 Zone 3 now very rapidly passes into zone 5, and at this moment, which can be 

 recognised with great exactness, the suspension may be said to have settled. 

 This position was termed by Coe and Clevenger 2 the critical position, and this 

 term will be adopted here. At this moment there is a rapid decrease in the 

 rate of settling, which now becomes progressively slower and slower. 



The following principles were found to hold in a study of the settling of 

 suspensions of alumina hydroxide. 



Let c concentration of the suspension, h= height of the column at the 

 commencement of settling, ^=height of the column of settled material at the 

 critical position taking place at time t. 



1. When c is constant, -=- = constant, and - = constant. 



n t 



2. For values of c up to 0-08 grams per 100 c.c. the value of (h d) /t 

 remains constant, i.e., the particles fall independently of each other, and 

 consequently the value of c (h d) jt is proportional to c. 



3. For values of c o 08 to o 50 grams per 100 c.c. the value of (h d) /t de- 

 creases, but at the same time the value of c (h d) jt increases until c reaches 

 a value of about o 2 gram per 100 c.c. From this value up to one of o 5 

 grams per 100 c.c., the value of c (h d) ft remains constant, that is to say, in 

 unit time the same quantity of material is settled. 



4. If d be the height of the settled column at the critical position, 

 and d n be the height when settling has become very slow, then 



log f -~ =constant where d t is the height of the settled column at 



t a t d n 



time t. 



5. If di and d 2 be the heights of columns of settled material at the 

 critical position obtained from columns of original height h-^ and h 2 , then if in 

 time t the column d^ has settled to height d\ and d 2 has settled to d' z> then 

 d 1 /d' 1 approximates in value to d z /d' 2 . 



The Settling of Cane Juice. The mechanism of the settling of cane juice 

 under the influence of heat and lime is essentially similar to that which has 

 been described in detail as found for alumina hydroxide. It may be best 

 examined in a tube of length about one metre, completely enveloped in a 

 steam jacket. The apparatus used by the writer was developed out of a 

 Liebig condenser, one end of which was blinded off. The results described 

 below were obtained in such an apparatus, and before making an experiment, 

 the juices were boiled gently for one minute in a flask fitted with a reflux 

 condenser, so as to expel any air, the presence of which would have vitiated 

 the experiment. 



