—
b. (When the number of the ingredients or prices is odd.) Required the proportions of teas at 3s., 5s., and 6s., the pound, to sell at 4s. Here the odd number must be taken a second time:—
c. (When the number of the ingredients is not merely odd, but the prices are unequally distributed either above or below the required price.) A dealer having wines of the same name at 7s., 9s., 11s., 12s., and 14s., per gallon, wishes to produce a mixture of them worth 10s. per gallon:—
It will be seen that by varying the manner of linking the numbers, different answers may often be obtained to the same question. It also often happens that the dealer or operator desires to use a given quantity of one particular article, or to produce a certain quantity only of the mixture instead of those indicated by the above calculations. In these instances he has simply to apply the common rule of ‘practice’ or the ‘rule of three,’ as the particular case may demand.
In the above manner the proportions of the constituents of a compound may be determined from their specific gravity, when no change of volume has arisen from their admixture; but when this is the case, as in alloys, alcoholic mixtures, &c., it is either quite inapplicable or the results obtained are mere approximations to the truth. It may, however, be conveniently employed for calculations connected with the ‘mixing’ and ‘reduction’ of spirits and other liquids, by substituting their per-centage value in ‘proof gallons’ or other corresponding denomination, for the prices in the above examples; water, when introduced be reckoned, = 0. Thus:—A spirit merchant having two puncheons of rum of the strengths of 17 and 21 o. p., wishes to know what proportions of each and of water he must take to form a spirit 10 u. up. The proof value of 100 gallons of these spirits are respectively equal to 121, 117, 90, and 0 (water). Therefore—
Suppose the dealer required to use different proportions of the spirits referred to, instead of equal measures, he has only to take such aliquot parts of the quantities thus found referring to the smaller proportion; or such