Right, alcohol and numbers, two of my favourite topics (and probably an apt description of my average Friday night).
The original term Alcoholic Proof comes from the 1500s in England and refers to a particular test that was performed for tax reasons. Spirits were soaked onto a pellet of gunpowder before a tester would try to ignite them. Those above 57.15% ABV (alcohol by volume, the current system) would catch alight and would be subject to a higher tax rate. We call these spirits 100 degree proof, as in everything below that limit was too wet for its alcohol content and so was fire proof. There was a myth that it was pirates and sailors that were carrying out this test so that their quartermasters couldn't water down their rum. However I think the connection must come from the gunpowder used since I can't find any primary sources that this was the case; it seems it was just the government.
In 1816 this test was replaced with another that defined 100 degrees proof as any alcohol which had a gravity (read density) of 12/13s that of water, which again works out as 57.15%. Since alcohol is lighter than water the higher the ABV the lower the gravity. I find it pleasing that such a neat fraction of 12/13s gives the same alcoholic content as the original limit.
During the 1980s England joined the rest of the EU in switching from their various regional systems into ABV. Since 4/7 as a fraction is equal to around 57.14% the conversion rate from ABV into the old system of degrees proof is legally defined as just multiplying by 7/4 to make calculations easier.. So pure ethanol which is 100% was 100*7/4 = 175 degree proof. Typically hard spirits are around 40% nowadays which = 40*7/4 = 70 degree proof.
The US uses a different historical definition, where instead of multiplying ABV by 7/4, they multiply by 2 instead. So 50% ABV would by 100 proof instead, but it doesn't seem to refer to any natural phenomena; it is a mostly arbitrary scale. If it feels like I'm having a go at America for their various bad choices of units (see A4 paper from yesterday), then yes I am. They should have picked units rationally.
In the UK ABV has to be written plus minus 0.5%. While this doesn't matter with your gin, as a proportion of the alcohol this makes a huge variation in the low alcohol beers. Your 3.8% ale is somewhere between 3.3% and 4.3% which is a massive swing. Craziness.
Right, now go and read the blog of my friend Toby (who I met during teacher training). His article on understanding the maths of getting the most alcohol for your money is essential reading for students. Have a nice weekend.