E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Take a Hair of the Dog that Bit You.
After a debauch, take a little wine the next day. Take a cool draught of ale in the morning, after a nights excess. The advice was given literally in ancient times, If a dog bites you, put a hair of the dog into the wound, on the homopathic principle of Similia similibus curantur (like cures like).