Proofing using Gauging Manual Table 6

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Hello,

I'd like to interpolate Table 6 in order to figure out the component parts of alcohol and water in spirits at fractions of whole proofs. I've imported the table into MS Excel but can't seem to get an equation that works for this data set (water content vs. proof)... Are we supposed to interpolate the data points similarly to how the Gauging Manual goes about handling fractional proofs in Table 1?

Has anyone successfully developed an equation for this relationship? Or, alternatively, am I over thinking the problem of "How do you reduce 166.2 proof spirit to 80 proof?"

Thanks,

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Not sure if this helps, but according to the gauging manual:

Quote

§ 186.66 Table 6, showing respective volumes of alcohol and water and the specific gravity in both air and vacuum of· spirituous liquor.

This table provides an alternate method for use in ascertaining the quantity of water needed to reduce the strength of distilled spirits by a definite amount. To do this, divide the alcohol in the given strength by the alcohol in the required strength, multiply the quotient by the water in the required strength, and subtract the water in t~1e given strength from the product. The remainder is the number of gallons of water to be added to 100 gallons of spirits of the given strength to produce a spirit of a required strength.

Example:  It is desired to reduce spirits to 191 proof to 188 proof.
We find that 191 proof spirits contains 95.5 parts alcohol and 5.59 parts water, and 188 proof spirits contains 94.0 parts alcohol and 7.36 parts water.
95.5 (the strength of 100 wine gallons of spirits at 191 proof) divided by 94.0 (the strength of 100 wine gallons of spirits at 188 proof) = 1.01.

7.36 (the water in 188 proof) multiplied by 1.01 = 7.43.
7.43 less 5.59 (the water in 191 proof spirits) = 1.84 gallons of water to be added to each 100 wine gallons of 191 proof spirits to be reduced.

This rule is applicable for reducing to any proof; but when it is desired to reduce· to 100 proof, it is sufficient to point off two decimals in the given proof, multiply by 53.73, and deduct the water in the given strength.. Thus, to reduce 112 proof spirits to 100 proof:
1.12x53.73-47.75 =  12.42 gallons of water to be added to each 100 wine gallons of spirits to be reduced.
This table may also be used to obtain ·the proof gallonage of spirituous liquor according to weight and percent of proof.
Example
It is desired to determine the number of gallons in 400 pounds of spirits of 141 percent of proof. Multiply the weight of one gallon of water in air by the specific gravity in air of the spirits-8.32823 by 0.88862-the product (7.40063) divided into 400 gives 54.049 wine gallons, which rounded to the nearest hundredth is 54.05 and multiplied by 1.41 gives 76.2 proof gallons. In rounding off where the decimal is less than five, it will be dropped; if it is five or over a unit will be added.
(72 Stat. 1358; 26 U.S.C. 5204)

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Classik, that's exactly the process I'm trying to use, but what if the spirit to be reduced is 191.X proof, instead of a whole proof value? Table 6 only gives water percents for whole proofs. What is the appropriate method to perform the interpolation with a starting spirit proof that isn't a whole value?

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Sending you a PM now.

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There is no simple equation, it's why the tables are published.

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Yes, the interpolation in Table 6 is very similar to that for Table 1.  In fact it is a bit easier because you only have two parameters to deal with (proof vs parts of water) while in Table 1 you have three parameters (apparent proof, true proof and temperature).

I have not seen the TTB data in the form of an equation - only as the Tables.  There must be an equation because the Tables could not have been generated from experiments at every published point, and must have been generated from an equation.  I just have not seen it.

The data that is openly available as a formula is the European OIML alcohol-water density data.  This is the data that forms the basis of my AlcoDens program.  The OIML and TTB data are based on much of the same original experimental data but they are presented in different terms.  The TTB data is (mostly) presented as densities and masses measured in air but the OIML data is presented as absolute or "in vacuum" values.  Fortunately it is possible to convert between "in air" and "in vacuum" data so it is possible to select in AlcoDens whether you want to match the TTB or OIML tables.

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Given the rounding artifacts in the TTB tables, my guess is that key data points were collected and the rest were derived by linear interpolation without an over-arching formula.

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