[1] : The Collaborative International Dictionary of English v.0.48

eigne \eigne\, a. of. aisn'e, ainsn'e, f. a^in'e, fr.
   l. ante natus born before. cf. esnecy.
   1. law eldest; firstborn. --blackstone.
      1913 webster

   2. entailed; belonging to the eldest son. obs.
      1913 webster

   bastard eigne, a bastard eldest son whose parents
      afterwards intermarry.
      1913 webster
see also:
esnecy bastard eigne 

[2] : Bouvier's Law Dictionary, Revised 6th Ed (1856)

bastard eigne', eng. law. elder bastard. by the old english law, when, a man 
had a bastard son, and he afterwards married the mother, and by her had a 
legitimate son, the first was called a bastard eigne, or, as it is now 
spelled, aine, and the second son was called puisne, or since born, or 
sometimes he was called mulier puisne. see mulier; eigne, 2 bl. com. 248. 

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