[Keep in mind how old this is. I leave these around to show where I have been and when.]
For a while I’ve been trying to learn more about what I drink through quantitative beverage analysis (it also might come in handy as a wine maker or distiller some day). Curiosity really built up over so many occasions of tasting wines and getting into arguments if there was residual sugar or not. I wanted to prove that the wine in question had negligible unfermented sugar and therefore the “sweet” sensation was due to other variables. Answering specific questions like how dry are dry wines led to wanting to measure the structural variables of any mystery liquid. How would I model a fruit wine I was making myself or understand a liqueur I was trying to replicate.
With sugar content, when a solution contains both alcohol and water, tools like hydrometers and refractometers need adjustments to have meaning (brix refractometers over estimate sugar in the presence of alcohol and brix hydrometers under estimate sugar), but what are the correlations? and who has already constructed all the necessary empirical charts that are needed to make corrections?
One way to find the sugar content of an alcohol containing mystery solution is to distill off the alcohol and dilute it back to its normal volume with distilled water. I’ve done this before in previous posts and though it works, its a bitch. It also over engineers the problem if you already know the alcohol content confidently which in the case of commercial liqueurs is by law printed on the label. Distillation also destroys the sample. (I will point out that there is also a crazy way for dessert wine makers to analyze their wines by using a formula that uses the over and under estimates of both a refractometer and a hydrometer).
When you know the alcohol variable you can easily use a short range hydrometer to find the sugar content of any liqueur bottling you posses (and maybe without even having them) without destroying product. This is simple because sugar increases specific gravity and we know by how much because there are lots of charts and the opposite is true of alcohol of which there are charts as well. If you find the effect the alcohol has on obscuring the specific gravity from revealing the true sugar content, the effect can be added to the obscured measure to reveal the true brix.
If it isn’t clear, the benefit of all this measuring is to either produce intuitively used products based on favorite models or to create relationships between products for the fun of intuitive substitution (you cannot easily substitute liqueur 43 for lillet because the sugar model is so different but you probably can substitute pineau de charentes or even st. germain for lillet). The other benefit is to reduce drink prices (or increase drink profits) by creating successful house made recipes with ingredients where you have a comparative advantage. If you have a walnut tree in your back yard you can probably make nocino cheaper than buying it. Modeling the sugar and alcohol content of great commercial nocino can help make yours great (intensity of aroma will be your only tough to crack variable). You will be able to celebrate walnut cocktails cheaper than anyone else and your celebration will be awesome because the intuitive modeling helps reveal the trees terroir relative to another.
One way to start measuring things if you are lazy or lack the requisite hydrometer is to look at specific gravity tables of commercial products that exist all over the web. These tables were all created for the sake of layering liqueurs in pousse cafes. Gary regan’s (the link breaks periodically but is from books.google.com) is by far the best though it should be considered that many brands (d)evolve over time. Regans’ chart expresses sugar relative to alcohol so because its not yet a useful number you simply add the specific gravity influence of the alcohol listed on the label which can be converted with this chart (which also periodically breaks). Once you find the specific gravity of an alcohol water solution that has the same proof as the liqueur, you add 1.0 minus the specific gravity of the particular ratioed alcohol-water solution to the obscured gravity to get the true sugar content un-obscured by alcohol.
Unfortunately your not out of the woods yet. You are still dealing with specific gravities which do not mean much to a pastry scale. To convert specific gravity to g/L or brix you can use the “circular of the national bureau of standards C440″ (easily googled to find the indispensible PDF) for easy conversion.
So now with the alcohol printed on the label and one narrow range precision hydrometer you can figure out a sugar content in under three minutes! No refractometer, no distilling.
(Another way to find the density without using a hydrometer is to simply use a kitchen scale) because density = mass / volume. This method can be useful for dealing with volumes too small for a hydrometer though accuracy is sacrificed.