Sorry guys, I was a little brief. Here is how I do it. All this assumes that you know how much alcohol you started with, preferably by weight, and you determined the proof by distilling a known volume of the liqueur, collecting all the alcohol, replacing the missing volume with water, keeping temp constant, etc and then measuring the proof. The key is to take the sugar content out of the equation. It’s irrelevant when you calculate the proof, so just assume that you’re working with alcohol and water. If you have significant alcohol loss from the maceration then it isnt this straight forward, but I always make a syrup by weight and measure its density so I can make weight corrections easily. Also, by weighing the pre-proofed sample and the proofed result gives you a relative density of the two so you can take out the dissolved solid component of weight. It also helps to have a laboratory still, a precision bench scale and a water bath.
Lets assume that the proof you got was 74. And you started with 100 lbs of 190 proof.
Then 100lbs *.14718 lbs/gal (table 4) = 14.718gal @ 190pf => 13.98gal @100% => 37.78 gal @ 74 pf
=> 37.78 gal / .12557lbs/gal = 300.87 lbs = W1 (this is what it would have weighed if you just were using water and alcohol.)
Now, 13.98 gal @ 100% => 34.95 gal @ 40% abv (80pf)
=> 34.95 gal / .12616 lbs/gal = 277.03 lbs = W2
W1 – W2 = 23.84 lbs excess water
So, how much 190pf to add (lbs) to get to 80pf when you have 23.84lbs of water?
Total Weight (T) = Weight(190) + Weight(H2O) = W(190) + 23.84
Total weight is also equal to: T = 190/80 * (.14718/.12616) * W(190) (here is where the magic happens)
W(190) + 23.84 = 2.375 * 1.1666 * W(190) = 2.77 * W(190)
=> 23.84 = 2.77 * W(190) – W(190) => 23.84/1.77 = W(190)
=> W(190) = 13.47 lbs
(Sorry for those of you who didn’t want an algebra lesson.)