William George Horner
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Through Optics
Horner died comparatively young, before the establishment of specialist, regular scientific periodicals. So, the way others have written about him has tended to diverge, sometimes markedly, from his own prolific, if dispersed, record of publications and the contemporary reception of them.
Family life
The eldest son of the Rev. William Horner, a Wesleyan minister, Horner was born in Bristol. He was educated at Kingswood School, a Wesleyan foundation near Bristol, and at the age of sixteen became an assistant master there. In four years he rose to be headmaster (1806), but left in 1809, setting up his own school, The Classical Seminary, at Grosvenor Place, Bath, which he kept until he died there 22 September 1837. He and his wife Sarah (1787?–1864) had six daughters and two sons.
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Physical sciences, optics
Although Horner's article on the Dædalum (zoetrope) appeared in Philosophical Magazine only in January, 1834, he had published on Camera lucida as early as August, 1815.
Mathematics
Horner's name first appears in the list of solvers of the mathematical problems in The Ladies' Diary: or, Woman's Almanack for 1811, continuing in the successive annual issues until that for 1817. Up until the issue for 1816, he is listed as solving all but a few of the fifteen problems each year; several of his answers were printed, along with two problems he proposed. He also contributed to other departments of the Diary, not without distinction, reflecting the fact that he was known to be an all-rounder, competent in the classics as well as in mathematics. Horner was ever vigilant in his reading, as shown by his characteristic return to the Diary for 1821 in a discussion of the Prize Problem, where he reminds readers of an item in (Thomson's) Annals of Philosophy for 1817; several other problems in the Diary that year were solved by his youngest brother, Joseph.
His record in The Gentleman's Diary: or, Mathematical Repository for this period is similar, including one of two published modes of proof in the volume for 1815 of a problem posed the previous year by Thomas Scurr (d. 1836), now dubbed the Butterfly theorem. Leaving the headmastership of Kingswood School would have given him more time for this work, while the appearance of his name in these publications, which were favoured by a network of mathematics teachers, would have helped publicize his own school.
At this stage, Horner's efforts turned more to The Mathematical Repository, edited by Thomas Leybourn, but to contributing occasional articles, rather than the problem section, as well as to Annals of Philosophy, where Horner begins by responding to other contributors and works up to independent articles of his own; he has a careful style with acknowledgements and, more often than not, cannot resist adding further detail.
Several contributions pave the way for, or are otherwise related to, his most celebrated mathematical paper, in Philosophical Transactions of the Royal Society of London in 1819, which was read by title at the closing meeting for the session on 1 July 1819, with Davies Gilbert in the Chair. The article, with significant editorial notes by Thomas Stephens Davies, was reprinted as a commemorative tribute in The Ladies' Diary for 1838. The issue of The Gentleman's Diary for that year contains a short obituary notice. A careful analysis of this paper has appeared recently in Craig Smoryński's History of Mathematics: A Supplement.
While a sequel was read before the Royal Society, publication was declined for Philosophical Transactions, having to await appearance in a sequence of parts in the first two volumes of The Mathematician in the mid-1840s, again largely at the instigation of T. S. Davies.
However, Horner published on diverse topics in The Philosophical Magazine well into the 1830s. Davies mooted an edition of Horner's collected papers, but this project never came to fruition, partly on account of Davies' own early death.
Other contemporary literature
- P. Barlow, On the resolution of the irreducible case in cubic equations, Math. Rep., NS IV (1814), 46-57 [includes Table for the solution of the irreducible case in cubic equations (6pp.)].
- P. Barlow, A new method of approximating towards the roots of equations of all dimensions, Math. Rep., NS IV (1814), No. 12, 67–71.
- T. Holdred, A New Method of Solving Equations with Ease and Expedition; by which the True Value of the Unknown Quantity is Found Without Previous Reduction. With a Supplement, Containing Two Other Methods of Solving Equations, Derived from the Same Principle(Richard Watts. Sold by Davis and Dickson, mathematical and philosophical booksellers, 17, St. Martin's-le-Grand; and by the author, 2, Denzel Street, Clare-Market, 1820), 56pp..