The FamilySearch transcription for the 1871 census has incorrectly transcribed another line for David's occupation. He was actually in Iron Works.
Sources
"England and Wales Census, 1851," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QKV6-LQ3P : accessed 14 January 2016), David Matthews in household of William Matthews, Merthyr Tydfil, Glamorganshire, Wales; citing Merthyr Tydfil, Glamorganshire, Wales, p. 19, from "1851 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing PRO HO 107, The National Archives of the UK, Kew, Surrey.
"England and Wales Census, 1861," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M7HR-KKC : accessed 14 January 2016), David Matthews, Middlesbrough, Durham, England; from "1861 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing PRO RG 9, The National Archives, Kew, Surrey.
"United States Census, 1880," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MCC4-7LS : accessed 28 January 2016), David Matthews, Newport, Campbell, Kentucky, United States; citing enumeration district ED 42, sheet 205A, NARA microfilm publication T9 (Washington D.C.: National Archives and Records Administration, n.d.), roll 0407; FHL microfilm 1,254,407.
"Pennsylvania, Pittsburgh City Deaths, 1870-1905," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:XZ79-2BY : accessed 28 January 2016), David Mathews, 01 Sep 1899; citing v 96 p 51, Allegheny County Courthouse, Pittsburgh; FHL microfilm 505,865.