Evidence from census and church records proves that the Williamson family arrived in Utah between 1851 and 1853.  Their names appear on the 1850 Iowa census, and the first documentation to place them in Utah is the rebaptism of Samuel on 11 June 1854, which is prior to the arrival of that season's emigration.  Further research is needed to determine the year of their arrival and the name of the pioneer company they traveled to Utah with.

Family Tree shows his name as "William Samuel Williamson," but the death certificates of Joseph and Sarah Ann both show their father's name as "Samuel Williamson."