The Collaborative International Dictionary of English v.0.48:

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.
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   2. Entailed; belonging to the eldest son. [Obs.]
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   Bastard eigne, a bastard eldest son whose parents
      afterwards intermarry.
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