The following links are copies of the 1930 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	Forsyth	David Ambrose Smitherman
		North Carolina	Yadkin	Rufus Lee Smitherman
		North Carolina	Yadkin	Nancy E Smitherman Robert Emmett Smitherman James Abner Smitherman John W Smitherman
		North Carolina	Yadkin	Doctor Benbow Smitherman
		North Carolina	Yadkin	Winslow Byron Smitherman