MILLER, WILLIAM HALLOWES

(b. Llandovery, Carmarthenshire, Wales, 6 April 1801; d. Cambridge, England, 20 May 1880)

crystallography, mineralogy.

His father, Captain Francis Miller, who served in the American war, had a long military ancestry. By his first wife Captain Miller had three sons, all of whom entered the army, and two daughters. After losing his estate near Boston, Massachusetts, he retired to Wales to the small estate of Velindre near Llandovery and in 1800 married Ann Davies, the daughter of a Welsh vicar. William was the only child of this second marriage; his mother died a few days after his birth, but his father lived to the age of eighty-six, dying in 1820.

William was educated privately until he entered St. John’s College, Cambridge, where he graduated B.A. as fifth wrangler in mathematics in 1826. In 1829 he became a fellow of St. John’s and in 1831 published his first book—written in his characteristically lucid but terse style— The Elements of Hydrostatics and Hydrodynamics, which survived as a standard, though difficult, textbook into the fifties. Another mathematical textbook, An Elementary Treatise on the Differential Calculus, appeared in 1833 and passed through several editions. By then Miller had, in 1832, succeeded William Whewell as professor of mineralogy. He was elected F.R.S. in 1838. In 1841 came a curious diversion: the statutes of St, John’s College required all fellows to proceed in time to holy orders except for four who should be doctors of medicine, and in order to retain his fellowship, Miller prepared himself for and took the M.D. He was obliged to vacate his fellowship on his marriage (5 November 1844) to Harriet Susan Minty, the daughter of R. V. Minty, a retired civil servant. They had two sons and four daughters. In 1875 he became a fellow of St. John’s again under new statutes. In 1876 he suffered a stroke, which effectively brought his scientific life to a close four years before his death.

Miller’s significant contribution to crystallography was made in A Treatise on Crystallography published in 1839 (translated into French by H. de Senarmont [1842], and into German with two new chapters by J. Grailich [1856], and again into German in abbreviated form by P. Joerres [1864]). Miller started with the fundamental assertion that crystallographic reference axes should be parallel to possible crystal edges; his system of indexing, a derivative from Whewell (Philosophical Transactions of the Royal Society, 1825), was based on a parametral plane (111) making intercepts a, b, c on such reference axes and was such that indices (hkl) were assigned to a plane making intercepts on the reference axes in the ratio a/h : b/k : c/l where h, k. l are integers. The established German school of C. F. Naumann and C. S. Weiss had, to use the same nomenclature, assigned indices (hkl) to a plane making intercepts in the ratio ah : bk : cl on reference axes not restricted to parallelism with possible crystal edges. The algebraic advantages of “Millerian indices” were immediately apparent; the crystallographic superiority of Miller’s reciprocal indices over Weiss’s direct indices did not become apparent until Bravais’s development of Haüy’s rudimentary lattice concept in 1848, and not fully appreciated until Bragg’s interpretation of the diffraction of X rays by crystals in 1912. But Miller’s notation had quickly found favor with his contemporaries on grounds of convenience and had already served to codify an immense corpus of morphological observations in a thoroughly well-understood manner.

In the Treatise Miller had little to say about symmetry, but he explored crystal geometry to the full. The zone law of Weiss was simplified by the new notation, and zone symbols were defined in familiar form; the equations to the normal and the cos θ formula were developed; and the rational sine ratio, which was to be further developed in A Tract on Crystallography (1863), made its first appearance here. For the representation of three-dimensional angular relationships Miller followed F. E. Neumann in using spherical projection, but the stereographic projection, which subsequently acquired greater currency, and the gnomonic projection were discussed in the final chapter.

The new edition (1852) of William Phillips’ Elementary Introduction to Mineralogy by H. J. Brooke and W. H. Miller was an entirely new book largely written, as Brooke states in the preface, by Miller, and it represents his principal contribution to mineralogy. It incorporated a vast amount of accurate goniometric data provided by Miller himself; it followed the Treatise in using spherical projection; and it made a tentative start in the use of polarized light for the characterization of transparent minerals. The Introduction, like the Treatise, soon eclipsed its contemporaries; it inspired Des Cloizeaux to produce his more elaborate Manuel de minéralogie (Paris, 1862–1893), and determined the form of all subsequent texts on descriptive mineralogy.

In 1843 Miller branched out into a new field on appointment to the parliamentary committee concerned with the preparation of new standards of length and weight consequent on the destruction of the old standards in the burning of the Houses of Parliament in 1834. His exceptionally accurate work was responsible for the construction of the new standard of weight (Philosophical Transactions of the Royal Society, 1856). In 1870 he was appointed to the Commission Internationale du Mètre. Many honors fell to Miller in his lifetime. He was president of the Cambridge Philosophical Society (1857–1859) and foreign secretary of the Royal Society (1856–1873), being awarded a Royal Medal in 1870.

The exceptional breadth of Miller’s scientific knowledge was recognized by his contemporaries. He was generous and hospitable to a point, yet remarkably spartan in his way of life. His ingenuity in constructing surprisingly accurate apparatus from simple, often homely, materials was notable. While no great traveler, he obviously enjoyed his trips to Paris for meetings of the Meter Commission, and he regularly holidayed in the Italian Tirol, where he simply enjoyed the scenery while his wife sketched it.

BIBLIOGRAPHY

I. Original Works. Miller’s works include The Elements of Hydrostatics and Hydrodynamics (Cambridge, 1831); An Elementary Treatise on the Differential Calculus (Cambridge, 1833); A Table of Mineralogical Species (Cambridge, 1833); A Treatise on Crystallography (Cambridge, 1839); and William Phillips, An Elementary Introduction to Mineralogy, new ed, by H. J. Brooke and W. H. Miller (London, 1852).

II. Secondary Literature. On Miller or his work see R Storey Maskelyne, Nature, 22 (1880), 247–249; T. G. Bonney, Proceedings of the Royal Society, 31 (1881), ii–vii; and J. P. Cooke, Proceedings of the American Academy of Arts and Sciences, 16 (1881), 460–468. Memorial of William Hallowes Miller by his wife (privately printed, Cambridge, 1881[?]).

Duncan Mckie

William Miller

William Miller (1782-1849), American clergyman, founded a movement which involved thousands in eagerly awaiting the Second Coming of Christ.

William Miller was born on Feb. 15, 1782, near Pittsfield, Mass. His family soon moved to western New York, where he received a rudimentary education. Battle experience during the War of 1812 aroused his concern with religious questions. Converted from deism by a revival meeting in 1816, he became a Baptist. Gradually, the subject of the Second Coming attracted his attention, and eventually, after laborious biblical investigation, he concluded that Christ would reappear about 1843.

Most enthusiastic Christians of the period were seeking to establish the date of the Second Advent. Doctrinally orthodox, Miller made only one innovation, suggesting that Christ would appear before (rather than after) the millennium. A reserved, somewhat shy man, he hesitated to publish his convictions, but the nearness of the event made it urgent to save as many souls as possible by publishing his news to the world. As a boy preacher, he discovered an unexpected eloquence, and in 1833 the Baptist Church ordained him as a minister.

Miller's message attracted increasing attention in New England and western New York. In 1838 he published Evidence from Scripture and History of the Second Coming of Christ about the Year 1843. Two years later another Baptist cleric, the Reverend Joshua Himes, seeing Miller as a tool to further the cause of evangelism, took over management of Miller's campaign.

Miller's enthusiasm, plus the pressures of an economic depression, drew thousands of converts. As his following grew, so did controversy over his activities. Orthodox ministers condemned but could not silence him. Miller had avoided naming a day for the Advent, but, as 1843 approached, pressures for a precise prediction increased. He chose March 1843. When March passed, he still insisted that 1843 was the fateful year. Others in his movement chose October 22 as the last day; Miller agreed. Some people sold their goods, not expecting to need them after October 22; others took a holiday to watch the Millerites gather to await the Advent. According to older accounts, the undisturbed arrival of October 23 drove some of the faithful to suicide and others to insanity; recent scholars have discounted such tales. Meanwhile, the Baptist Church disowned Miller, and he joined others to form the Advent Society, ancestor of several modern Adventist churches. He died on Dec. 20, 1849, in Hampton, N.Y.

Further Reading

The principal source for Miller's life is Sylvester Bliss, Memoirs of William Miller (1853). Alice Felt Tyler, Freedom's Ferment: Phases of American Social History from the Colonial Period to the Outbreak of the Civil War (new ed. 1962), accepts traditional views emphasizing the bizarre aspects of Millerite behavior. Whitney R. Cross, The Burned-over District: The Social and Intellectual History of Enthusiastic Religion in Western New York, 1800-1850 (1950), gives a broader view of the movement based on additional sources, including Miller's own papers at Aurora College.

Additional Sources

Gale, Robert, The urgent voice: the story of William Miller, Washington: Review and Herald Pub. Association, 1975.

Gordon, Paul A., Herald of the midnight cry, Boise, Idaho: Pacific Press Pub. Association, 1990.

White, Ellen Gould Harmon, William Miller: herald of the blessed hope, Hagerstown, MD: Review and Herald Pub. Association, 1994. □

Miller, William Hallowes (1801–80) The mathematician W. H. Miller graduated as fifth wrangler at Cambridge in 1826 and was awarded a fellowship at St. John's College. In the early years he published treatises on hydrodynamics and hydrostatics, but in 1832 he succeeded W. Whewell as Professor of Mineralogy, a post he held until 1870.

His mineralogical work was essentially crystallographic and in 1839 he published his Treatise on crystallography, a classic work in which, following a suggestion by Whewell, he introduced what became known as the Millerian system of notation of crystal faces using Miller symbols or Miller indices. This is a method for specifying the positions of crystal faces in space by reference to three (sometimes four) crystallographic axes. In this same work he formalized the law of rational sine ratios (Miller's law) after its recognition by several earlier workers. This law is concerned with the angular relation of crystal faces and their Miller indices. In order to give graphical expression to the system of facial indices and to facilitate calculations, Miller introduced the use of the stereographic projection which underpins much of his 1839 treatise.

Accurate determination of the angles between crystal faces is essential for detailed crystallographic work and for mineral identification. Using an adaptation of a single-circle goniometer which utilizes reflections of light from crystal faces, Miller in 1874 devised a two-circle instrument with which angles could be measured to within a few seconds of arc.

With H. J. Brookes he published in 1852 a new edition of Elementary introduction to minerals by W. Phillips, which introduced much new crystallographic data.

R. Bradshaw

William Miller 1782–1849, American sectarian leader, b. Pittsfield, Mass. He was the founder of the sect of Second Adventists , sometimes called Millerites. In 1831, convinced from study of the Bible that the prophecies pointed to the second coming of Christ in 1843, he went about spreading his belief among large audiences. Many prepared for the Day of Judgment, and when the year passed without a fulfillment of Miller's prophecy, a date in 1844 was set. In 1845 Miller and his followers founded the Adventist Church.

Miller, William Hallowes (1801–80) A British mineralogist from the University of Cambridge, Miller developed a classification system for crystallography, based on crystal axes. His method was published in Treatise on Crystallography (1839). See MILLER INDICES.