He was re-elected each year until 1799 with the exception of 1795, when the Senate minutes record that Patrick Cumin was elected in his absence.

At the end of his period in office in 1799, Wilson bequeathed scientific instruments to the University and £1,000, the interest on which was to be used to support his successors in the Chair.

[5] Extract from The Scientific Papers of Sir William Herschel, Volume 1:[6] ...The friendship with Doctor (afterwards Sir William) Watson, jun., formed at Bath, was continued till Herschel's death, and brought about a frequent intercourse by letters and many exchanges of visits.

His letters are always very lengthy (there are more than eighty of them extant); in the years 1807-1810 there is a good deal in them on coloured rings, on which subject he sided with Herschel against the Royal Society.

With Maskelyne Herschel also corresponded frequently... Patrick Wilson corresponded with Benjamin Franklin for example:[1] (Presumably, Wilson was carrying out the request in William Smith’s letter of 16 May, to present the University of Glasgow with a copy of the first volume of the American Philosophical Society Transactions.)