His father died from the privations of the voyage almost immediately after his return to Rhode Island from Ireland, whither has had repaired in order to enter his son at Trinity College Dublin.
(1784), and in 1784 became an advocate in the courts of delegates, prerogative, admiralty, and consistory, and for a long time held the vicar-generalship of the Diocese of Kildare.
In 1783 he was returned to the Irish House of Commons as member for Dublin University, which he continued to represent in three parliaments until 1800.
The defection of such a respected figure from the anti-Union side was a major blow to the cause, and some of his former friends never forgave him.
In addition to his chair of law, Browne thrice held the Regius Professorship of Greek at Dublin (from 1792 to 1795, from 1797 to 1799, and from 1801 to 1805).
When a college corps of yeomanry was formed on the appearance of the French in Bantry Bay in December 1796, Browne was unanimously elected to the command.
Browne published, in imitation of Montaigne, two volumes of ‘Miscellaneous Sketches, or Hints for Essays,' 8vo, London, 1798, the first of which was inscribed ‘to his daughter, M. T. B.,’ the second ‘to the memory of Marianne,’ his first wife.
Beauty and the Heart, an Allegory; translated from the Persian Language,’ &c., 4to, Dublin, 1801, and he was also the author of ‘A Brief Review of the Question, Whether the Articles of Limerick have been violated?'