Michell was educated at Queens College, Cambridge. His name appears fourth in the Tripos list for 1748-1749; and in 1755 he was moderator in that examination. He became M.A. in 1752, and B.D. in 1761. He was a fellow of his college, and was appointed Woodwardian Professor of Geology in 1762, and in 1767 rector of Thornhill in Yorkshire, where he died.
He was elected a fellow of the Royal Society in the same year as Henry Cavendish (1760). In 1750 he published at Cambridge a work of some eighty pages entitled A Treatise of Artificial Magnets, in which is shown an easy and expeditious method of making them superior to the best natural ones. Besides the description of the method of magnetization which still bears his name, this work contains a variety of accurate magnetic observations, and is distinguished by a lucid exposition of the nature of magnetic induction. He was the original inventor of the torsion balance, which afterwards became so famous in the hands of its second inventor Charles-Augustin de Coulomb. Michell described it in his proposal of a method for obtaining the mean density of the earth. He did not live to put his method into practice; but this was done by Henry Cavendish, who made, by means of Michell's apparatus, the celebrated determination that now goes by the name of Cavendish's experiment (Phil. Trans., 1798).
His most important geological essay was that entitled Conjectures concerning the Cause and Observations upon the Phaenomena of Earthquakes (Phil. Trans., li. 1760), which showed a remarkable knowledge of the strata in various parts of England and abroad.
Michell's other contributions to science are:
Observations On the Comet of January 1760 at Cambridge, Phil. Trans. (1760)
A Recommendation of Hadley's Quadrant for Surveying, ibid. (1765)
Proposal of a Method for measuring Degrees of Longitude upon Parallels of the Equator, ibid. (1766)
An Inquiry into the Probable Parallax and Magnitude of the Fixed Stars, ibid. (1767)
On the Twinkling of the Fixed Stars, ibid. (1767)
On the Means of Discovering the Distance, Magnitude, &c., of the Fixed Stars, ibid. (1784).