He then studied theology; but, after two sessions at St Andrews and one at Edinburgh University, he abandoned all idea of the church, and in 1786 he became an assistant-teacher of mathematics and natural philosophy in the newly established Dundee Academy.
[3] He published a memoir with an analytical expression for the rectification of the ellipse in the Transactions of the Royal Society of Edinburgh (1796), and two others on cubic equations (1799) and the Kepler problem (1802).
In 1804 the flax-spinning company he managed was dissolved, and he obtained one of the mathematical chairs in the Royal Military College, Great Marlow (later moved to Sandhurst), at which he remained until 1816, when failing health obliged him to resign.
[3] During this period he published several important memoirs in the Philosophical Transactions, which earned for him the Copley Medal in 1814 and ensured his election as a Fellow of the Royal Society in 1815.
[3] In 1831, on the recommendation of Lord Brougham, King William IV granted him a yearly pension of £300 and appointed him Knight of the Royal Guelphic Order.