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There is a relatively new book JAMES BRINDLEY, CANAL ENGINEER, A New Perspective by Kathleen M. Evans, published by Churnet Valley Books, 43 Bath Street, Leek, Staffordshire, England 011-44-1-538-399033. This book outlines all of James Brindley's brothers and a good genealogy. Printed in Great Britain by the Ipswich Book Company, Suffolk 1997. isbn 1 897949 35 9
James Brindley had brothers Joseph of Alton, Staffs, John of Burslem and Union Hall, Kinver, Staffs, Henry, a miller and farmer, sisters Esther married Samuel Simcock of Leek, Ann married William, and Mary married Abraham Birchenall/Birchinhough of Wildboarclough, Cheshire.
See other sites: www.BrindleyMtn.org and in Family Tree Maker, Home Page, Brindley International Historical Foundation.
Good luck in your search.