The Collaborative International Dictionary of English v.0.48:

Tres-tyne \Tres"-tyne`\, n. [L. tris, tres, three + E. tyne.]
   (Zool.)
   In the antler of a stag, the third tyne above the base. This
   tyne appears in the third year. In those deer in which the
   brow tyne does not divide, the tres-tyne is the second tyne
   above the base. See Illust. under Rucervine, and under
   Rusine.
   [1913 Webster]