The James Moses in the 1870 census is not to be found in any census after that. So far there are no birth records available on-line, but that could change in the future. The only other option I can think of is Family History Centers, which you can find locations for on FamilySearch.org. They should be able to order microfilm of birth records for a small fee. There were a grat many people from Wales in Pennsylvania in that era. I suspect that the Hyde Park in PA is a likely birthplace for your relative.