The Collaborative International Dictionary of English v.0.48:

Branchial \Bran"chi*al\, a. (Anat.)
   Of or pertaining to branchi[ae] or gills.
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   Branchial arches, the bony or cartilaginous arches which
      support the gills on each side of the throat of fishes and
      amphibians. See Illustration in Appendix.

   Branchial clefts, the openings between the branchial arches
      through which water passes.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Cleft \Cleft\, n. [OE. clift; cf. Sw. klyft cave, den, Icel.
   kluft cleft, Dan. kl["o]ft, G. kluft. See Cleave to split
   and cf. 2d Clift, 1st Clough.]
   1. A space or opening made by splitting; a crack; a crevice;
      as, the cleft of a rock. --Is. ii. 21.
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   2. A piece made by splitting; as, a cleft of wood.
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   3. (Far.) A disease in horses; a crack on the band of the
      pastern.
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   Branchial clefts. See under Branchial.

   Syn: Crack; crevice; fissure; chink; cranny.
        [1913 Webster]