I saw your query regarding your grandmother, Rachel Brearley. It's such an unusual name, I thought I'd write.
My husband's great-grandmother was Sophia Brearley, daughter
of William Brearley and Alice Booth of Bury St. Mary's,
Lancashire, England. They moved to Hopkinton, RI about 1877. Sophia married George Jackson in 1881.
Could you be a relation?