Sir Marttin of Hollingsborne Hill, Eng, Married Judith, daughter of Sir Martin Calthorpe (Lord Mayor of London). Their grandson was Thomas Barnum (Barnham) b. Eng 1625 d. Danbury, CT Dec. 26, 1695. Thomas married Sarah (Thompson) Hurd (b. about 1642, d. Straford, Conn. June 1718) and they had a son Thomas Barnum (b. Norwalk, July 9, 1663, d. Dec 17, 1730) He maried Sarah, daughter of Samuel Beardsley of Stratfield Society) and had 4 daughters and 4 sons. Son Ephraim was and ancestor of Phineas Taylor Barnum. Unfortunately, I do not know details of that relationship.
My great great grandfather was Noble Sullivan Barnum who had a son Elmer Herbert Barnum who had a daughter Viola Myrtle Barnum (my grandmother). I am told that I am also related to P.T. Barnum but that is all the information I have so far. I hope this helps you. If you know any more about the Barnums, please let me know.