The Collaborative International Dictionary of English v.0.48:

Secundine \Sec"un*dine\, n. [Cf. F. secondine.]
   1. (Bot.) The second coat, or integument, of an ovule, lying
      within the primine.
      [1913 Webster]

   Note: In the ripened seed the primine and secundine are
         usually united to form the testa, or outer seed coat.
         When they remain distinct the secundine becomes the
         mesosperm, as in the castor bean.
         [1913 Webster]

   2. [Cf. F. secondines.] The afterbirth, or placenta and
      membranes; -- generally used in the plural.
      [1913 Webster]