As "to fell," is "to make to fall," and "to lay," to make to lie." so "to drench," is "to make to drink."
Trench.
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Give my roan horse a drench.
William Shakespeare. The First Part of Henry the Fourth
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Men. A letter for me! it gives me an estate of seven years’ health, in which time I will make a lip at the physician. The most sovereign prescription in Galen is but empiricutic, and, to this preservative, of no better report than a horse-drench. Is he not wounded? he was wont to come home wounded.
William Shakespeare. The Tragedy of Coriolanus
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So Joe starts telling the citizen about the foot and mouth disease and the cattle traders and taking action in the matter and the citizen sending them all to the rightabout and Bloom coming out with his sheepdip for the scab and a hoose drench for coughing calves and the guaranteed remedy for timber tongue.
James Joyce. Ulysses
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my nerves were already weak, that drenching me like a horse and restricting my diet would make me worse.