In technical operations of reducing spirits from a higher to a lower strength it is common to disregard the effect of contraction when no great accuracy is required. The calculations are then much simplified. From the principle that the volume is inversely as the strength, the volume which the reduced spirit will have is calculated. The difference between this and the original volume is taken as the volume of water to be added. A few examples will make the method clear.

Example (1). Given 54.5 gallons of spirit at strength 8.5 over proof; how much water is required to reduce it to 3.5 over proof ?

Here the given strength = 108.5 per cent. of proof spirit, and the required strength = 103.5. Since the volumes are inversely as the strengths, the volume of the reduced spirit will be

54.5 X 108.5/103.5 = 57.1 gallons.

The volume of water to be added is therefore taken as 57.1 - 54.5 = 2.6 2 6 gallons. The exact quantity should be 2.76 gallons, if contraction were allowed for, but the result is sufficiently accurate for technical purposes.

Example (2). A much greater discrepancy, however, may occur when the two strengths differ more widely. Take, for instance, the example already worked out (p. 279), viz., how much water is required to reduce 100 gallons of spirit at 60 o.p. to a strength of 20 o.p.?

Here the volume of the spirit after reduction to the lower strength will be: -

100 x 160/120 = 133.3 gallons, and the quantity of water to be added would be taken as 133.3 - 1000 = 333 gallons.

The accurate quantity would be 36.2 gallons, as already shown.

Example (3). Given volume 80 gallons, at strength 10 over proof; how much water must be added to reduce the spirit to 25 under proof ?

Here the percentage strengths are respectively 100 + 10 and 100 - 25, or 110 and 75; and the resulting volume of the reduced spirit is

80 X10/75 = 117.3 gallons.

The quantity of water to be added is therefore taken as 117.3 - 80.0 = 37.3 gallons. The correct quantity would be 386.

Example (4). It is sometimes convenient to calculate the equivalent proof gallons before proceeding to find the final volume of the reduced spirit, as in the following instance: -

Given 50 gallons of spirit at 12 over proof, and 20 gallons at 10 under proof; how much water must be added to the mixture of these in order to reduce the strength of the whole to 25 under proof ?

First calculate each quantity to proof gallons: -

50 gallons at 12 o.p. =50 X 112/100 = 56.0 gallons at proof strength.

20/70 „ 10 u.p. = 20 x 90/100 = 18.0

Total . . == 740

Then 74.0 at proof = 74.0 x 100 / 75 = 98.7 „ 25 under proof.

Hence the water to be added is taken as 98.7 - 70.0 = 28.7 gallons.

Dilution of alcohol from given strength to required lower strength.