Your Arthur Hamilton appears in the 1861 Canada Census along with the William Hamilton / Isabella L.(Lennox) Blackburn family. His is 21 years old, single, and a "surveyor". His place of birth appears as New Brunswick in this census record.

While none of the information in this census record clarifies Arthur's relationship to William Hamilton (who is 36 years of age at this point), it does connect him with this family in some manner.