[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)

eigne, persons. this is a corruption of the french word aine, eldest or 
first born. 
     2. it is frequently used in our old law books, bastard eigne. signifies 
an elder bastard when spoken of two children, one of whom was; born before 
the marriage of his parents, and the other after; the latter is called 
mulier puisne. litt. sect. 399. 

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