The hair of the dog
A small measure of drink, intended to cure a hangover.
The fuller version of this phrase, i.e. 'the hair of the dog that bit me', gives a clue to the source of the name of this supposed hangover cure. That derivation is from the mediaeval belief that, when someone was bitten by a rabid dog, a cure could be made by applying the same dog's hair to the infected wound. How many people managed to get bitten again when trying to approach the aforesaid dog to acquire the hair to achieve this completely useless remedy isn't known. The knowledge of the derivation should at least put paid to the frequent 'hare of the dog' misspelling.
With most metaphorical phrases that have a literal origin, for example toe the line and on the warpath, the later figurative use doesn't become popular until the literal use has fallen out of use. 'The hair of the dog' is unusual in that the figurative version is recorded before any known examples of the literal meaning.
John Heywood, in his invaluable early text, A dialogue conteinyng the nomber in effect of all the prouerbes in the Englishe tongue, 1546, uses the phrase with a clear reference to drinking:
I pray thee let me and my fellow have
A hair of the dog that bit us last night -
And bitten were we both to the brain aright.
We saw each other drunk in the good ale glass.
Another useful text, Randle Cotgrave's A dictionarie of the French and English tongues, 1611, also records the 'drinking' version of the expression:
Our Ale-knights [habitual drinkers] often use this phrase, and say, Give us a haire of the dog that last bit us.
It isn't until the 18th century that the literal use of dogs' hair to cure bite wounds is recorded in print. Robert James alludes to the method in A Treatise on Canine Madness, 1760:
The hair of the dog that gave the wound is advised as an application to the part injured.
In fact, James is rather skeptical about the treatment, preferring another commonly believed but equally unpromising remedy - the application of the ashes of river crabs.
Whilst the hair of the dog that bit us is now dismissed as an effective rabies treatment, the taking of additional alcohol to cure a hangover has some scientific basis. The symptoms of hangover are partly induced by a withdrawal from alcohol poisoning. A small measure of alcohol may be some temporary relief, even if in the longer term it makes the hangover worse.