Re: Frank Smith, father of Vesta Smith
The only NH Governor "Smith" is:
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Jeremiah Smith who served 8 Jun 1809 - 5 Jun 1810
b 29 Nov 1759 Peterborough, NH
d 21 Sep 1812 Dover, NH
Buried Winter St. Cemetery, Exeter, NH
Search "NH Governors"; you will see a Wikapedia site with "list of governors"; click on Jeremiah Smith and see a biography.