16 Aug. 1790. After his father's death in 1803 he lived with his uncle, Dr. James Gregory (1753-1821) [q. v.], in Edinburgh, and studied medicine in 1806-9 in Edinburgh University, and afterwards at St. George's Hospital, London, and the Windmill Street School of Medicine. He graduated M.D. Edinb. in 1811, became M.R.C.S. Engl. in 1812, and in 1813 was sent as assistant-surgeon to the forces in the Mediterranean, where he served in Sicily and at the capture of Genoa. At the close of the war he retired on half-pay, and commenced to practise in London, giving lectures on medicine at the Windmill Street School, and later at St. Thomas's Hospital. He was physician to the Small-pox and Vaccination Hospital from 1824, and to the General Dispensary, was a fellow of the Royal Society, and was elected a licentiate (30 Sept. 1816) and a fellow (30 Sept. 1839) of the Royal College of Physicians. He died at Camden Square, London, on 25 Jan. 1853. Gregory wrote largely in the medical journals, and was a contributor to the ‘Cyclopædia of Practical Medicine’ and to the ‘Library of Medicine.’ His principal works are: 1. ‘Elements of the Theory and Practice of Physic,’ 1820, 2 vols.; 6th ed. 1846; 3rd American ed. 1831. 2. ‘Lectures on the Eruptive Fevers,’ 1843.
[Munk's Coll. of Phys. iii. 152; Gent. Mag. 1853, new ser. xxxix. 444.]
GREGORY, JAMES (1638–1675), mathematician, was born at the manse of Drumoak, twelve miles from Aberdeen, in November 1638. His father, the Rev. John Gregory, minister of Drumoak, was fined, deposed, and imprisoned by the covenanters, and died in 1653 (Hew Scott, Fasti Ecclesiæ Scoticanæ, iii. ii. 497). His maternal grandfather, David Anderson of Finyhaugh, nicknamed ‘Davie-do-a'-thing,’ was said to have constructed the spire of St. Nicholas, and removed ‘Knock Maitland’ from the entrance to the harbour of Aberdeen. By the marriage of his daughter, Janet, with John Gregory, the hereditary mathematical genius of the Andersons was transmitted to the Gregorys and their descendants. James Gregory's education, begun at the grammar school of Aberdeen, was completed at Marischal College. His scientific talent was discovered and encouraged by his elder brother David (1627-1720) [q. v.], and he published at the age of twenty-four ‘Optica Promota’ (London, 1663), containing the first feasible description of a reflecting telescope, his invention of which dated from 1661. It consisted essentially of a perforated parabolic speculum in which the eye-piece was inserted with a small elliptical mirror, placed in front to turn back the image. Gregory went to London and ordered one of six feet from the celebrated optician Reive, but the figure proved so bad that the attempt was abandoned. The first Gregorian telescope was presented to the Royal Society by Robert Hooke [q. v.] in February 1674, and the same form was universally employed in the eighteenth century.
From 1664 to 1667 Gregory prosecuted his mathematical studies at Padua, and there printed in 1667 one hundred and fifty copies of ‘Vera Circuli et Hyperbolæ Quadratura,’ in which he showed how to find the areas of the circle, ellipse, and hyperbola by means of converging series, and applied the same new method to the calculation of logarithms. The validity of some of his demonstrations was impugned by Huygens, and a controversy ensued, the warmth of which, on Gregory's side, was regretted by his friends (Journal des Sçavans, July and November 1668: Phil. Trans. iii. 732, 882; Hugenii Op. Varia, ii. 463, 1724). The work, however, gained him a high reputation; it was commended by Lords Brouncker and Wallis, and analysed by Collins in the ‘Philosophical Transactions’ (iii. 640). Reprinted at Padua in 1668, he appended to it ' Geometriæ Pars Universalis,’ a collection of elegant theorems relating to the transmutation of curves and the mensuration of their solids of revolution (ib. p. 685). He was the first to treat the subject expressly; and his originality, attacked by the Abbé Gallois in the Paris ‘Memoirs’ for 1693 and 1703, was successfully vindicated by his nephew, David Gregory (1661-1708) [q. v.] (Phil. Trans. xviii. 233, xxv. 2336).
On his return to England Gregory was elected, on 11 June 1668, a fellow of the Royal Society, and communicated on 15 June an ‘Account of a Controversy betwixt Stephano de Angelis and John Baptist Riccioli,’ respecting the motion of the earth (ib. iii. 693). He shortly after published ‘Exercitationes Geometricæ’ (London, 1668), in which he extended his method of quadratures to the cissoid and conchoid, and gave a geometrical demonstration of Mercator's quadrature of the hyperbola. In the preface he complained of ‘unjust censures’ upon his earlier tract, and replied to some of Huygens's outstanding objections. Appointed, late in 1668, professor of mathematics in the university of St. Andrews, he thenceforth imparted his inventions only by letter to Collins in return for some of Newton's sent to him. Through the same channel he carried on with Newton in 1672-3 a friendly debate as to the merits of their respective telescopes, in the course of
