By the first action of water in 1, 1/2 of the sugar was left in cell 1; by the second 1/4 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. INVERSION OF SUGAR IN THE DIFFUSION CELLS. In the experiments at Fort Scott in 1886, much difficulty was experienced on account of inversion of the sugar in the diffusion battery. The report shows that this resulted from the use of soured cane and from delays in the operation of the battery on account of the imperfect working of the cutting and elevating machinery, much of which was there experimental. Under the circumstances, however, it became a matter of the gravest importance to find a method of preventing this inversion without in any manner interfering with the other processes. On the suggestion of Prof. Swenson, a portion of freshly precipitated carbonate of lime was placed with the chips in each cell.[1] In the case of soured cane, this took up the acid which otherwise produced inversion. In case no harmful acids were present, this chalk was entirely inactive. Soured canes are not desirable to work under any circumstances, and should be rejected by the chemist, and not allowed to enter the factory. So, also, delays on account of imperfect machinery are disastrous to profitable manufacturing, and must be avoided. But for those who desired to experiment with deteriorated canes and untried cutting machines, the addition of the calcium carbonate provides against disastrous results which would otherwise be inevitable. [Footnote 1: For this improvement Prof. Swenson obtained a patent Oct. 11, 1887, the grant of which was recently made the subject of congressional inquiry.]