WILLIAM MILLER (1801 - 1880). Treatise on Crystallography. Cambridge: For J. & J.J. Deighton, [etc.], 1839.
Miller was educated at St. John's College, Cambridge, where he graduated in 1826 as fifth "wrangler", (i.e., he received the fifth-highest score of all the graduating students on the mathematics examination given at Cambridge that year). For a few years Miller acted as a college tutor, during which time he published treatises on hydrodynamics and hydrostatics. In 1832 he was appointed to the chair of mineralogy at Cambridge, a post which he occupied until 1870. Miller was elected a Fellow of the Royal Society of London in 1838. In 1843, he assisted the committee appointed to superintend new standards in weights and measures.
René Just Haüy was the first to recognize that each face of a crystal could be assigned a sequence of three numbers specific to that face, but his law of rational indices suffered from certain ambiguities and deficiencies. Later crystallographers and mathematicians proposed various alternatives in attempts to remedy these deficiencies. The system in current use was first proposed by the Cambridge polymath William Whewell (1794 - 1866) in 1825, and independently by Moritz Frankenheim in 1826. But this system did not come into common use until Miller adopted it in his Treatise.
Miller's Treatise is divided into ten chapters: I. General Geometrical Properties of Crystals, II. Octahedral System, III. Pyramidal System, IV. Rhombohedral System, V. Prismatic System, VI. Oblique Prismatic System, VII. Doubly-Oblique Prismatic System, VIII. Twin Crystals, IX. Goniometers, &c., and X. Drawing Crystals and Projections. In the first chapter, Miller described an improved way to define the crystallographic reference axes on which the crystal faces could be indexed (i.e., assigned its sequence of three numbers). In succeeding chapters, he showed how his method could be applied to crystals of different shapes.
Schuh, Curtis P. Mineralogy & Crystallography: An Annotated Bibliography of Books Published 1469 through 1919. Tucson: privately published, 2005, p1045.