WALLACE, WILLIAM, an eminent Scottish mathematician, was born at Dysart, in Fife-shire, on the 23d of September 1768. He acquired the art of reading at a school in his native town, and was indebted for his instruction in arithmetic to his father's tuition. His father, not succeeding as a leather-merchant in Dysart, removed in 1784 to Edinburgh, where young Wallace was apprenticed to a bookbinder in that city. During his leisure hours, he was busy in the pursuit of knowledge, and on the completion of his apprenticeship he was a tolerable proficient in geometry, algebra, and astronomy. Being introduced by the assistant of Dr Robison to the notice of that distinguished professor, Wallace obtained permission to attend his class for the study of natural philosophy, and received private instructions in the higher geometry from the same generous individual. Professor Playfair likewise contributed much to his advancement in the study of the mathematics. After various changes of situations, dictated mainly by a desire to gain time for his books, he became, in 1794, an assistant teacher of mathematics in the academy of Perth; and ultimately, in 1803, one of the mathematical masters to the Royal Military College in Great Marlow, Bucks, and subsequently in Sandhurst, Berks. In 1819, while Wallace was steadily adding to his fame as a lecturer in England, a more important situation was open for him in Edinburgh, the scene of his early struggles and victories. This was the professorship of mathematics, which he filled with great success till 1838, when, on account of ill health, he was obliged to retire. Wallace received the honorary degree of LL.D. from the university where he had taught for nearly twenty years; and, in consideration of his eminent attainments in science, he received a government pension for life. He died at Edinburgh, after a lingering illness, on the 28th of April 1843. He was fellow or honorary member of numerous scientific societies both in Edinburgh and elsewhere.
The contributions of Dr Wallace to mathematical literature were select and important, if not very extensive. He wrote a considerable number of papers for the Royal Society of Edinburgh, as well as contributing on various subjects to other scientific associations. He produced the principal mathematical articles for the Edinburgh Encyclopædia, and for the fourth edition of the Encyclopædia Britannica, some of which, from their abiding excellence, have still a place in the present issue of that work. The following is a list of his more important papers contributed to the Transactions of the Royal Society of Edinburgh:—
"Geometrical Problems, with Examples of their Applications to the Solution of Problems," was written in 1796; in 1802, "A New Method of expressing the Co-efficients in the Development of the Formula which represents the Mutual Perturbation of two Planets." In 1808, he read an important paper to the Society, entitled "New Series for the Quadrature of the Conic Sections, and the Computation of Logarithms." A fourth paper was read before it, in 1823, on the "Investigation of Formulae for finding the Logarithms of Trigonometrical Quantities from one another;" in 1831, another entitled "Account of the Invention of the Pentograph, and a Description of the Eidograph," the latter being an instrument of his own invention; in 1839, a paper on the "Analogous Properties of Elliptic and Hyperbolic Sectors," and his last contribution to the Transactions of the Society was entitled "Solution of a Functional Equation with its Application to the Parallelogram of Forces, and the Curve of Equilibration." In 1836, he contributed "Two Elementary Solutions of Kepler's Problem by the Angular Calculus" to the Royal Astronomical Society; and, for the Cambridge Philosophical Society, he wrote a paper on "Geometrical Theorems and Formulae, particularly applicable to some Geodetical Problems." At the outset of his career, Wallace was an occasional contributor
to Laybourne's Mathematical Repository, and to the Gentleman's Mathematical Companion.