Barrington's other writings are chiefly to be found in the publications of the Royal Society and the Society of Antiquaries: he was elected to both bodies in 1767, and afterwards became a vice-president of the latter. Many of these papers were collected by him in a quarto volume entitled "Miscellanies on various Subjects" (1781). He contributed to the Royal Society's "Philosophical Transactions" for 1770, an account of Mozart's visit at nine years of age to London. In his "Miscellanies" on varied subjects he included this with accounts of four other prodigies, namely, William Crotch, Charles and Samuel Wesley, and Garret Wesley, 1st Earl of Mornington. Among his works are studies on "Experiments and Observations on the Singing of Birds" and an essay on the language of birds. Barrington attempted cross-fostering experiments on birds and noted that young linnets raised with foster parents could be induced to learn the songs of various lark species. He however dismissed the idea of long distance migration in birds, and supported the ancient view that swallows went to sleep underwater during winter.