By reversing the above operation, the measure of alcohol corresponding to any given weight of spirit, at any strength, may also be easily found. The weight of 1 gal. of absolute alcohol being 7·938 lbs.; that of 1 gal. of proof spirit, 9·2 lbs,; and that of the ‘alcohol’ in 1 gal. of proof spirit, 4·53 lbs.; the weight of any number of gallons or volumes of either, and their equivalents, may be easily found. Thus:—— gallons of alc. × 7·938 = lbs. weight of alc. ” pf. sp. × 9·2 = lbs. w. of pf. spt. and—— gallons of alc. × 16·121 = lbs. weight of pf. spt. ” pf. spt. × 4·53 = content in lbs. weight of alc. In these cases a knowledge of the first four rules of decimal fractions is necessary, or, at least, advantageous; as the Excise officers carry their calculations to two figures of decimals, or 1/100ths. Their plan is to reject the third decimal figure when less than 5; but to carry 1 to the next figure on the left hand, when it exceeds 5. Thus, 5·432 is set down as only 5·43; but 5·437 is written 5·44. In the delicate chemical processes of the laboratory, even greater accuracy is observed. Formerly, spirit was said to be 1 to 3, 1 to 4, &c., over-proof, by which it was meant that 1 gal. of water added to 3 or 4 gals. of such spirit would reduce it to ‘proof.’ On the other hand, 1 in 5, or 1 in 8, under-proof, meant that the 5 or 8 gals., as the case might be, contained 1 gal. of water, and the remainder represented the quantity of ‘proof spirit.’ This method of calculation has now long given way to the ‘centigrade system,’ which not only admits of greater accuracy, but is quite as simple. It should be adopted by every spirit-dealer in England, from being that which is employed by the Revenue officers, whose ‘surveys’ it is absolutely necessary that the trader should understand, in order that his own estimation of his stock and his business calculations should correspond with theirs.