By the first action of water in 1, ½ of the sugar was left in cell 1; by
the second ¼ was left, by the third 1/8 was left, by the fourth 1/16 was
left, by the fifth 1/32 was left, by the sixth 1/64 was left, by the
seventh 1/128 was left, by the eighth 1/256 was left, by the ninth 1/512
was left. The fractions representing the strength of the juice on the
one hand and the sugar left in each cell on the other hand, after the
battery is fully in operation, are not so readily deduced. The theory is
easily understood, however, although the computation is somewhat
intricate. Those who desire to follow the process by mathematical
formula are referred to pages 9 and 10, Bulletin No. 2, Chemical
Division U.S. Department of Agriculture, where will be found the formula
furnished by Professor Harkness, of the U.S. Naval Observatory.
For the sake of simplifying the explanation, it was assumed that the
water added is equal in volume to the juice in a cellful of cane chips.
In practice more water is added, to secure more perfect exhaustion of
the chips, and with the result of yielding about thirteen volumes of
juice for every nine volumes as it exists in the cane, and of extracting
92.04 per cent. of all the sugars from the cane, as shown by the report
of Dr. C.A. Crampton, Assistant Chemist of the U.S. Department of
Agriculture.