David, I agree with you. Ron's note that started this thread associated Gainesborough with Mississippi. Thinking that to be correct, I started looking for a Gainesborough in close proximity to Carthage, Leake County, Mississippi. After some time spent looking and contacting some Leake County experts, it seems your conclusion - that it is Carthage Tennessee - is correct unless Ron has some other information that it is the Leake County Carthage.