tearpit

from The Century Dictionary.

• noun The so-called lacrymal or suborbital sinus of some animals, as deer; the larmier.

from the GNU version of the Collaborative International Dictionary of English.

• noun (Anat.) A cavity or pouch beneath the lower eyelid of most deer and antelope; the lachrymal sinus; larmier. It is capable of being opened at pleasure and secretes a waxy substance.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun anatomy A cavity or pouch beneath the lower eyelid of most deer and antelope; the lachrymal sinus or larmier.