He set up an observatory in Cookstown, County Tyrone, which included an achromatic telescope, a transit instrument and clocks for solar and sidereal time.
[6][9][10] The observatory building bears a plaque stating that Hamilton commenced the post in 1793; his first recorded observation - with a transit instrument - was on 18 July 1793.
His scientific patron, Archbishop Robinson, with whom he appeared to spend much time in Bath, died in 1794, so the stream of funds for commissioning equipment for the observatory was blocked by the board of trustees.
Nonetheless, a 42-inch (107 cm) focal length refractor by Dollond was acquired, a 10-foot Newtonian reflector by Herschel, outstanding clocks by Thomas Earnshaw in particular and Dublin-based John Crosthwaite, and a comparatively inferior transit instrument by local horologist James Waugh.
Hamilton provided references for Earnshaw's fine work which led to the latter being awarded a share of the 'longitude prize', the principal recipient being the great John Harrison.
[6][10][11][12] He made a number of entries in The Transactions of the Royal Irish Academy concerning his astronomical observations at Armagh and Greenwich and the usage of associated equipment.