During a long series of experiments on the preparation of ethers, it appeared a desideratum to find a ready method of ascertaining how much spirit of any density would be equal to one chemical equivalent of absolute alcohol.  By a modification of a rule employed by the Excise, this question may be easily solved.  The Excise rule is as follows:—­

To reduce from any given strength to any required strength, add the overproof per centage to 100, or subtract the underproof per centage from 100.  Multiply the result by the quantity of spirit, and divide the product by the number obtained by adding the required per centage overproof, or subtracting the required per centage underproof, to or from 100, as the case may be.  The result will give the measure of the spirit at the strength required.

Thus, suppose you wished to reduce 10 gallons of spirit, at 54 overproof, down to proof, add 54 to 100 = 154; multiply by the quantity, 10 gallons (154 x 10) = 1540.  The required strength being proof, of course there is nothing either to add to or take from 100; therefore, 1540 divided by 100 = 15.4 gallons at proof; showing that 10 gallons must be made to measure 15 gallons, 3 pints, 4 fl. oz., by the addition of water.

To ascertain what quantity of spirit of any given strength will contain one equivalent of absolute alcohol.  Add the overproof per centage of the given spirit to 100, as before; and with the number thus obtained divide 4062.183.  The result gives in gallons the quantity equal to four equivalents (46 x 4).

Example.—­How much spirit at 54 per cent. overproof is equal to 1 equivalent of absolute alcohol?

Here,

54 + 100 = 154 and 4062.183 = 26.3778 galls., or 26 galls. 3 pts.
--------
154

which, divided by 4, gives 6 gallons, 4 pints, 15 oz.

Suppose the spirit to be 60 overproof,—­

4062.183                    {one-fourth of which is equal
then ---------- = 25.388 gallons, {to 6 gallons, 2 pints,
(100 + 60)                   {15-1/2 oz.

This rule is founded on the following data.  As a gallon of water weighs 10 lbs., it is obvious that the specific gravity of any liquid multiplied by 10 will give the weight of one gallon.  The specific gravity of absolute alcohol is 0.793811; hence, the weight of one gallon will be 7.93811 lbs., and its strength is estimated at 75.25 overproof.

4 equivalents of alcohol = 46 x 4 = 184,

and

23.17936 gallons x 7.93811 lbs. per gallon, also = 184.0003094.

Hence it appears that 23.17936 gallons of absolute alcohol are equal to 4 equivalents.  By adding the overproof per centage (75.25) to 100, and multiplying by the quantity (23.17936 gallons) we get the constant number 4062.183.

The rule might have been calculated so as to show at once the equivalent, without dividing by 4; but it would have required several more places of decimals; it will give the required quantity to a fraction of a fluid drachm.