The Collaborative International Dictionary of English v.0.48:

Besaiel \Be*saiel"\, Besaile \Be*saile"\, Besayle \Be*sayle"\,
   n. [OF. beseel, F. bisa["i]eul, fr. L. bis twice + LL.
   avolus, dim. of L. avus grandfather.]
   1. A great-grandfather. [Obs.]
      [1913 Webster]

   2. (Law) A kind of writ which formerly lay where a
      great-grandfather died seized of lands in fee simple, and
      on the day of his death a stranger abated or entered and
      kept the heir out. This is now abolished. --Blackstone.
      [1913 Webster]

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

BESAILE or BESAYLE, domestic relations. The great-grandfather, proavus. 1 Bl.
Com. 186. Vide dile.