PLAYFAIE, Jcars, a Scottish mathematician and natural philosopher, was b. at Ben vie in Forfarshire, March 10, 1748. His father, who was minister of the united parishes of Lill and Benvie, sent hint to the university of St. Andrews at the age of 14, to study with a view to the ministry; and here Playfair gained great reputation as a diligent and successful student, especially in mathematics and natural philosophy; so much so that, while a student, be for some time discharged the duties of the natural philosophy chair daring the illness of the professor. In 1773 he entered the ministry, and succeeded his father in the parish of Ulf and Ben vie. Duping his leisure hours, he still prosecuted his favorite studies, the fruits of these labors being two memoirs, On the Arithmetic of Impos sible Quantities and Account of the Lithological Survey of Schaallion, which were cominu nicated to the royal society of London. Iu 1782 he resigned his parochial charge to superintend the education of the sons of Mr. Ferguson of Math; and in 1785 he became joint-professor of mathematics along with Adam Ferguson in the university of Edin burgh; but exchanged his chair for that of natural philosophy in 1805. Ile took the part of Mr. (afterwards sir John) Leslio (q.v.), his successor in the mathematical chair, and published a pamphlet full of biting satire against the " new-sprung zeal for ortho doxy." Ile became a strenuous supporter of the " Huttonian theory" in geology, and after publishing his Llastiwtians of the Huttonian Theory of the Earth (Ediu. 1802), he made many journeys for the sake of more extensive observations, particularly in 1815, when he visited France, Switzerland, and Italy. He died at Edinburgh, July 19, 1819.
Playfair, according to Jeffrey (Annual Biography, 1820), " possessed in the highest degree all the characteristics both of a fine and a powerful understanding; at once pene trating and vigilant, but more distinguished, perhaps, by the caution and success of its march, than by the brilliancy or rapidity of its movements." Playfair was, during the later part of his life, secretary to the royal society of Edinburgh. From 1801 he was a frequent contributor to the Edinburgh Review, criticising the works of Laplace, `Lath. and Hater, and the great trigonometrical surveys, both French and English, which had just been completed. He also wrote the articles "YEpinus" and " Physical Astronomy," and an incomplete " Dissertation on the Progress of Mathematical and Physical Science" for the Encyclopedia Britannica. His contributions to the Transactions of the Royal Society of Edinburgh are numerous and exceedingly varied, a treatise on "Naval Tactics" even appearing among them. His separate works are the Elements of Geometry (Edin 1795), containing the first six books of Euclid, with supplementary articles on trigonom etry, solid geometry, and the quadrature of the circle; and his Outlines of Natural Phil osophy (Ellin. 1812 and 1816), being the heads of his lectures delivered in the university on that subject. A third volumes of the Outlines, completing the work, was promised, but never appeared.