The following links are copies of the 1850 census, in which I have found Smitherman families that are descendants of Samuel Smytheman, the emigrant.

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Link	Page2	State	County	Head of Household
		North Carolina	Surry	Lucinda Smitherman
		North Carolina	Moore	Jesse Cox Smitherman
		North Carolina	Randolph	Noah Smitherman
		Alabama	Bibb	Thomas Smitherman, Jr.
		Alabama	Bibb	John M Smitherman