He was educated at St John's College, Cambridge, where he graduated in 1826 as fifth wrangler, and became a fellow in 1829. For a few years he was occupied as a college tutor and during this time he published treatises on hydrostatics and hydrodynamics.
He also gave special attention to crystallography, and on the resignation of William Whewell he succeeded in 1832 to the professorship of mineralogy, a post which he occupied until 1870. His chief work, on Crystallography, was published in 1838. He was elected FRS in 1838.
Miller Indices are named after him, the method having been described in his Treatise on Crystallography (1839) (Oxford English Dictionary Online, May 2007).
In 1852 he edited a new edition of HJ Brooke's Elementary Introduction to Mineralogy. He assisted in 1843 the committee appointed to superintend the construction of the new Parliamentary standards of length and weight (see Phil. Trans., 1856).