32 REPORT OF THE COMMISSIONER OF AGRICULTURE. 



The specific gravity of the liquid remaining in the cane chips in each 

 cell when the liquid from the adjoining cell enters, and also the specific 

 gravity of the liquid entering and leaving each cell, may then be desig- 

 nated as follows: 



cell. 



SPECIFIC! 



GRAVITY OF LIQUID. 











o 



In cino 



Entering 



Leaving 



Q 



chips. 



cell. 



cell. 



1 



S"> 



gt 



gi 



2 





g% 





3 



g* 



9* 



<73 



4 





g* 



g* 



&c. 



<fcc. 



&.O. 



&c. 



n 



g a -\ 



gn+i 



g* 



As the liquid entering any cell soon mixes with that contained in the 

 chips therein, andjpduces the whole volume of fluid to a uniform spe- 

 cific gravity, Ave have- 



* I - a 9» + n\ 



Jl -~~ a + b * * ' ' K) 



Whence 



and in general 





• (2) 



£ (9n-2 ~ 9n-l) 



. (3) 



| (<7n-3 ~ V a-2) • 



• (4) 



J } (9n-4 - 9n-3) 



• (5) 



/r n _! and g n _ 2 from (4) and (5) 



, we get 





• (0) 



9n- 



9n-2 = 9n- 



Substituting in (3) the values of g 



9n — 9n-3 — (9n-i ~ < 



The law governing the formation of the series is now evident, and 

 its complete expression is 



^=, 1 -(,o-, l) {(f>(f) 3 + (f) 3 --GT} • ••<'> 



This formula gives the relations between the specific gravities of the 

 cane juice 3 the diffusion juice taken from the first cell, and the juice re- 

 maining in the chips when they are rejected; and it shows that so long 

 as g — 9i is approximately constant, the smaller b is made with respect to 

 <x, the more efficiently the battery will work. If b is greater than a, the 

 first cell will do most work, and each succeeding cell will do less and less; 

 if b is equal to a, all the cells will work alike; and if b is less than a, the 

 first cell will do least work, and each succeeding cell will do more and 

 more. "When it is remembered that the work of the first cell constantly 



