William (Lewis) is the middle child out of 13. For census records, his name is given as William. His grave stone has his name as Lewis William Smith. Spouse and children names & ages agree with the census records.
Coopers Plains Cemetery (Coopers Plains, Steuben County, New York, USA). Lewis William Smith. www.findagrave.com Memorial #51792476. Created by Karma, 29 Apr 2010.
"United States Census, 1900," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MSG6-RPX : accessed 17 September 2017), William Smith, Erwin Township (west part), Steuben, New York, United States; citing enumeration district (ED) 83, sheet 8B, family 200, NARA microfilm publication T623 (Washington, D.C.: National Archives and Records Administration, 1972.); FHL microfilm 1,241,163.