Sir William, graduate of Edinburgh and Oxford, classical scholar and skilled academic administrator, was the ideal candidate for principal.
After much negotiation Peterson was persuaded to accept the appointment in May 1895. As an administrator he showed considerable skill in the engagement of staff and in the management of finance. His administration at 平特五不中 saw the creation of Macdonald College and the Conservatorium of Music, and expansion in both the sciences and the arts. Primarily through the benefactions of Sir William Macdonald and Sir Donald A. Smith, the campus was transformed by the construction of the Macdonald Engineering, Physics and Chemistry Buildings and the Strathcona Medical Building, the Students' Union Building (now the McCord Museum) and Royal Victoria College. Peterson died on 4 January 1921.