James Patrick Muirhead (26 July 1813 – 15 October 1898) was a Scottish lawyer and author, known as the biographer of James Watt.
Born at The Grove, Hamilton, Lanarkshire, he was son of Lockhart Muirhead; George Muirhead was his great-uncle. He was educated first at Glasgow College. Gaining on 3 February 1832 a Snell exhibition at Balliol College, Oxford, he matriculated there on 6 April 1832; spending his long vacations in Alpine expeditions, and in the study of German rather than in working for honours, he took a third class in lit. hum. on graduating B.A. in 1835 (M.A. 1838).
Admitted advocate at Edinburgh in 1838, Muirhead practised law in Edinburgh. His wife found the climate of Edinburgh uncongenial, and in 1846 he gave up his career at the Scottish bar, and in 1847 settled at Haseley Court, Oxfordshire, a property in his wife's family.
Muirhead died in his eighty-sixth year, on 15 October 1898.
While at Oxford, he had become acquainted with his kinsman James Watt the younger, who decided not to write a memoir of his father, and gave the task to Muirhead. His grandfather, Patrick Muirhead of Glasgow University, had married in 1804 a cousin Anne Campbell, whose mother (née Muirhead) was a first cousin of James Watt.
Muirhead in 1839 translated François Arago's Eloge Historique de James Watt for the Académie des Sciences, given in1834. In the priority dispute of Watt with Henry Cavendish over the discovery of the chemical composition of water, he visited Paris in 1842 to confer with savants there, and in 1846 published a vindication of Watt, The Correspondence of the late James Watt on his Discovery of the Theory of the Composition of Water. This was followed in 1854 by The Mechanical Inventions of James Watt (3 vols.). The third volume, illustrated with engravings of machinery by Wilson Lowry, dealt with patent specifications; the second with extracts from correspondence. The introductory memoir (vol. i.) was the basis of the fuller Life of James Watt that Muirhead published in 1858 (2nd edit. 1859).