You will not find a birth certificate from that era! State mandated vital records began after 1900 but compliance lagged for several decades thereafter. I was born 1946 but my birth was filed as "delayed recording" in 1948. Too, the accuracy of info on vital records depends on the knowledge/truthfulness of the informant. Per death certificates, James Harvy Rich was born 27 Dec 1862 and his sister Ophelia Nall was born 20 Aug 1862? That didn't happen! Then, we need to confirm Elizabeth's parents. What was her complete lifespan and where did she die?