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I have a Francis Ainsworth married to Julia Ann Donelson (or Larned). I have their son as George Ainsworth born circa 1844. George married Ellen Sarah Brown (born circa 1855) in 1870 in Janesville, WI. George and Ellen's kids are:
Ezra, John, Francis, George, Julia, Charles, Charles, William, Mary Ellen, Edward, Robert, Robert, and Mary (yes I know I repeated some names, but I think they really had kids with the same names). If this looks like the Ainsworths you're looking for, let me know, I have more info.