Sorry, I can't help you with Jane Thompson, but I'm sure your Achesons are from the same family as mine. I have several Matthew Achesons, but none born later than 1788. They are descended from John Acheson and Catherine Clark who settled in Little Britain, Lancaster Co., PA (from Northern Ireland) around 1735. They later moved to Mt. Pleasant Twp., Washington Co., PA, then to Muskingum Co., OH. Can you connect with this family?