The state legislature's canvass gives the following figures in Butte County: 1,409 for Bigler and 1,207 for Reading. This results in statewide totals of 23,174 for Bigler and 22,733 for Reading.
Candidates' party affiliations obtained from 9/24/1851 Sacramento Daily Union. https://www.cdnc.ucr.edu/?a=d&d=SDU18510924.2.9.1&e=-------en--20--1--txt-txIN--------
Source for Popular Vote data: California State Archives, "Governor," Abstract of Returns of an Election held for Governor and Lieut. Governor on the third day of September A.D. 1851 in the Several Counties of this State (Vallejo, 1851)