There is apossibility of being close into the line. My William Smith I have traced backed through the Bermuda Geneology and history web site through their surname project to Samual " Collector' Smith born abt 1660. On your William Henry Smith he possibly could be the grandson of the William noted above. He had a son William John Smith born April 11 1789 in Charelston SC Died August 5 1881 in Charleston. This William was from the first mariage of Wiam Smith to Catherine Spencer in Bermuda in May 12 1795. She died Feb 6 1825 in Charleston and is buried at the Second Presbyterian Church. there were 5 children from that marriage.1 Joseph Spencer Smith died as infant 2 Joseph Spencer Smith born in bermuda and Died 1852 in Charleston 3 William John Smith b April 11 1798 Charelston SC d Aug 5 1881 Charleston SC 4 Deborah Smith B Feb 18 1799 D June 16 1830 5 Edward Smith Smith B Jan 13 1899 Charelston D Dec 7 1869. I descend from Williams second marriage to Eliza Benet and there offspring do not match up to your William. I would look at the sons of William above as possible father to you William. I way be worthwhile to go the the Bermuda Genealogy and History web site for other Smith lines in Bermuda that came over.