He was born on 16 January 1743 the son of Alexander Wilson, who preceded him as Regius Professor of Practical Astronomy at Glasgow University. Patrick was appointed his successor in 1784 before his father quit the role. Probably due to the failing health of his father they shared the role until his father's death in 1786. He was Clerk of Senate from 1783 to 1795 and 1796 to 1799, and was awarded an honorary LLD in 1800. He was the second son of Alexander Wilson, the first Regius Professor of Practical Astronomy at the University. In 1782 he was employed as an assistant to his father, to take care of instruments, make observations, and help with teaching. Patrick Wilson continued his father's type-founding business in Glasgow. He was elected Fellow of the Royal Society of Edinburgh on 17 November 1783. Also in 1783, Patrick was elected Clerk to the Senate of the University. 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. Wilson was appointed Regius Professor of Practical Astronomy to succeed his father in 1784, but his father retained the post until his death in 1786. At the end of his period in office, in 1799 Patrick Wilson bequeathed scientific instruments to the University as well as £1,000, the interest on which was to be used to support his successors in the Chair. He appears to have left Glasgow in 1799 and thereafter lived in London. He died in Kensington Square, London on 30 December 1811
...The friendship with Doctor Watson, jun., formed at Bath, was continued till Herschel's death, and brought about a frequent intercourse by letters and many exchanges of visits. This was also the case with Patrick Wilson, the son and successor of Professor Alexander Wilson of Glasgow. He corresponded with Herschel from 1783; in 1795 he expressed some regret that his father's name and his views on the constitution of the sun had not been mentioned in Herschel's paper on the same subject; but Herschel's reply to this letter seems to have satisfied him perfectly. Wilson resigned his professorship at Glasgow at the end of 1798, and settled in London, and he and his sister were on the most cordial terms with Herschel and his wife and sister, and often paid visits to Slough. His letters are always very lengthy ; 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. He died in 1811. With Maskelyne Herschel also corresponded frequently...
Patrick Wilson corresponded with Benjamin Franklin for example;
Monday Augt. 3d 1772 Dear Sir I take my departure for Glasgow in a few Hours, having heard yesterday Evening of an inviting Opportunity of a Ship for the Forth which sails immediately. Im sorry that Im so much hurried as not to be able to see You before I go. I shall take Care and deliver the Vollume of the American Transactions to the Questor of our Library. I beg the favour of being remembered to Mr. Small; I ever am most faithfully and most respectfully Your’s Pat. Wilson Addressed: To / Doctor Franklin / at Mrs. Stevenson’s / Craven Street / Strand
Another document from Patrick Wilson to Benjamin Franklin dated Glasgow University, 27 May 1786 is interesting in that Patrick signs the letter "Patrick Wilson, joint Professor of Astronomy". This being the period when his father Alexander was still in the Regius chair and after he was appointed his successor.
