He resigned the Chair of Astronomy to become Professor of Natural Philosophy (Physics) in 1803, a position he held until his death in 1846.
He conducted his duties so successfully that he continued to take classes after the incumbent Professor's death and during the tenure of his successor.
In August 1799, King George III issued a commission to William Meikleham to be Professor of Practical Astronomy and Observer at the University of Glasgow, and on 29 October 1799 he was admitted to office.
He proved to be a much more active and dynamic teacher than his colleagues, including his successor in the Chair of Practical Astronomy, James Couper.
William Meikleham appears in the Post Office Glasgow Directories from 1801 to 1803[5] as Professor of Practical Astronomy.