Supposed by poets to shed tears. The drops, however, which fall from their eyes are not tears, but an oily secretion from the so-called tear-pits.
A poor sequestered stag ... Did come to languish ... and the big round tears Coursed one another down his innocent nose In piteous chase.
Shakespeare: As You Like It, ii. 2.
But mice and rats, and such small deer, Have been Tom's food for seven long year.
Shakespeare: Lear, iii.4.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894