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Robert, you said that you are a descendant of William Coram, brother of Capt. Thomas Coram (1668 - 1751). The recent book, "Thomas Coram, Gent." by Gillian Wagner, Boydell Press, Woodbridge, 2004, states that William Coram was baptised 18 Apr 1671 and buried 29 Apr 1671, eleven days afterwards. The burial record is from the Dorset Records Office, Lyme Regis Register of Burials 1653 - 1958. What information do you have to help resolve this inconsistency?
Another ambuguity is that the Corams who are entitled to the Coram Coat of Arms, are William Coram (b. 1581) and his heirs. William's pedigree is listed in the "Visitation of the County of Devon" by J. L. Vivian, containing the Herald's Visitations of 1620. There is nothing in that pedigree that would suggest that Capt. Thomas Coram is related.