William Davison was ten years old when his father moved from Pennsylvania to Butler County, Ohio. He worked as a cooper in Butler county and in several places in Indiana. For two years he farmed in Arkansas. Later he lived in Madison, Indiana, and returned to Butler County, Ohio, before the census of 1850. In November, 1852, he located on a farm in Clinton County, Indiana. In 1817 he moved to the town of Jefferson in Clinton County and resumed the trade of cooper. A few years later he went into the hotel business at which he was fairly successful. In about 1871 he retired from active life. According to Arthur Henry Davison he died June 4, 1893, while Joseph Claibaugh says he died on July 22 of that year.
Davison, Arthur Henry. History and Genealogy of Davison, Davisson, Dividson Families. Cedar Rapids, IA: The Torch Press, 1935)
US Census 1850 Oxford, Butler, OH
US Census 1880 Jefferson, Clinton, IN
"Butler, Ohio" or "Butler County, Ohio"?
"Ohio, County Marriages, 1789-2013," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:XZDH-P3Y : accessed 30 November 2015), William D. Davidson and Clariss Sithian, 02 Feb 1830; citing Butler, Ohio, United States, reference v l p 277; county courthouses, Ohio; FHL microfilm 355,779.