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The Collaborative International Dictionary
Bastard eigne

Eigne \Eigne\, a. [OF. aisn['e], ainsn['e], F. a[^i]n['e], fr. L. ante natus born before. Cf. Esnecy.]

  1. (Law) Eldest; firstborn.
    --Blackstone.

  2. Entailed; belonging to the eldest son. [Obs.]

    Bastard eigne, a bastard eldest son whose parents afterwards intermarry.

Wiktionary
bastard eigne

n. A bastard eldest son whose parents afterwards intermarry.