Drink Deep.
Drink a deep draught. The allusion is to the peg tankards. Those who drank deep, drank to the lower pegs. (See Peg.)
Weʹll teach you to drink deep ere you depart.”—Shakespeare: Hamlet, i. 2.
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Entry taken from Dictionary of Phrase and Fable, edited by the Rev. E. Cobham Brewer, LL.D. and revised in 1895.