This is the only John Williams born in Ireland that I have located in Arkansas Census of 1880. The name of the wife is not Agnes and there are only 2 daughters, no sons. Could this possibly be the man you are seeking? Census Place: 3rd Ward, Fort Smith, Sebastian, Arkansas Source: FHL Film 1254056 National Archives Film T9-0056 Page 546C Relation Sex Marr Race Age Birthplace John WILLIAMS Self M M W 45 IRE Occ: Cigar Maker Fa: ENG Mo: ENG Sarah J. WILLIAMS Wife F M W 33 MO Occ: Keeping House Fa: TN Mo: TN Lillie M. WILLIAMS Dau F S W 14 MO Occ: Attending School Fa: IRE Mo: MO Minnie WILLIAMS Dau F S W 11 MO Occ: Attending School Fa: IRE Mo: MO Nellie KENNEDY Other F S W 19 AR Occ: Attending School Fa: IRE Mo: IRE