I have a partially photocopied genealogy entitled, GARDINER/GARDNER GENEALOGY INCLUDING THE ENGLISH ANCESTRY OF GEORGE GARDINER IMMIGRANT ANCESTOR OF NEWPORT, R.I. & MANY OF HIS DESCENDENTS ESPECIALLY HIS GRANDSON STEPHEN GARDINER OF GARDNER LAKE,CT., compiled by Clara Gardner Miller and John Milton Stanton...I'm afraid I only have certain pages, and I didnt notice your Willam Gardiner--but he may be in there if you can find the book---i found it on microfiche--also a couple of other Gardiner genealogies you can try to find...GARDNER HISTORY AND GENEALOGY, by C. M. and L. M. GARDNER---also TheGARDINERS OF NARRAGANSETT by Caroline Robinson----good luck---my particular line is through the Stephen Gardiner mentioned in 1st book above so I have info regarding that line...also doing research on the LESTER's of New LONDON---Dave Lester