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Just for the record, the Bradbury Memorial which is quite a good genealogical record of the Bradbury family, does Not have this couple included. There is no Joshua EARLE or Heirl or any other variation of that spelling in the Index, but what they do have is Hannah Bradbury, baptized 1746 who married April 1766 to Joshua HEAD of Berwick, ME. Hannah was a daughter of Jacob Bradbury (Jacob, William, Thomas 1) who married Abigail EATON. Jacob moved from Biddeford to Buxton, Maine where he died in 1797.
I don't know if the author of this old genealogy (1890), misread the last name as HEAD from Heirl or Hearl, but it is quite likely. I am still searching for the answer to this big mystery.
Thank you for any help.