"Kentucky Births and Christenings, 1839-1960," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:FWVZ-8X8 : 11 February 2018), John S. Smelser in entry for Jane Smelser, 15 Aug 1852; citing Hart County, Kentucky, reference item 5; FHL microfilm 216,826.
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DNA Connections
It may be possible to confirm family relationships with Jane by comparing test results with other carriers of her ancestors' mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Jane: