I found a couple family trees for Harden Black on ancestry.com and according to them, the "S" stands for Sanford. I found him listed as Sanford Black in the 1900 census. The ages are off a bit; I don't know why, but this is the family.

Source Citation: Year: 1900; Census Place: Hannan Dist, Mason Co., West Virginia
Roll: T623_1765; Page: 154A; Enumeration District: 58

Sanford Black, 42, b.Jan 1858, married 27 yrs.
Joanna Black, 36, b. Nov. 1863, mother of 5 living children
Kiah Black, 19, b. Feb. 1881
Emerson Black, 16, b. March 1884