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Mackay was in charge of the astronomical observatory at Aberdeen from 1781 to 1795. In 1793 he published The theory and practice of finding the longitude at sea or land (London, 2 vols). When the chair of Natural Philosophy at Aberdeen fell vacant in 1800, MacKay was proposed but the election was contested. In 1802, Nevil Maskelyne (1730-1811), the Astronomer Royal, suggested that he should go to Australia to join the expedition led by Matthew Flinders, as their astronomer had returned home early in the voyage. Mackay, however, still hoped that he might win the Aberdeen election and, in addition, felt the pay offered by the Board of Longitude was too small. In 1804, his hopes having failed, he came to London. He was appointed mathematical examiner to Trinity House in 1805 and to similar posts with the East India Company and Christ's Hospital during the year following. As well as teaching and examining, he published further works on astronomy, navigation and mathematics.