# Dictionary of National Biography, 1885-1900/Gregory, James (1638-1675)

​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 ​which he described burning mirrors composed of 'glass leaded behind,' which afterwards came into general use (Rigaud, Corr. of Scientific Men, ii. 249). The theory of equations and the search for a general method of quadratures by infinite series occupied his few leisure moments. He complains to Collins (17 May 1671) of the interruptions caused by his lectures and the inquiries of the ignorant (ib. p. 224). In the same year some members of the French Academy were desirous to obtain a pension for him from Louis XIV, but the project fell through. Gregory had never believed it serious, and easily resigned himself to its failure. Under the pseudonym of ‘Patrick Mathers, Arch-Bedal of the university of St. Andrews,’ he attacked Sinclair, ex-professor of philosophy at Glasgow, in ‘The Great and New Art of Weighing Vanity’ (Glasgow, 1672), worth remembering only for a short appendix, ‘Tentamina quædam Geometrica de Motu Penduli et Projectorum,’ giving the first series for the motion of a pendulum in a circular arc. Sinclair in his reply reproached Gregory with want of skill in the use of astronomical instruments which he had erected at St. Andrews.
Gregory was the first exclusively mathematical professor in the university of Edinburgh. He was elected on 3 July 1674, and delivered his inaugural address before a crowded audience in November. One night in the following October, while showing Jupiter's satellites to his students, he was struck blind by an attack of amaurosis, and died of apoplexy three days later, before he had completed his thirty-seventh year. He had till then enjoyed almost unbroken health. He married at St. Andrews in 1669 Mary, daughter of George Jameson [q. v.] the painter, and widow of Peter Burnet of Elrick, Aberdeen, and had by her two daughters and a son, James, afterwards professor of physic in King's College, Aberdeen (d. 1731).
Gregory's genius was rapidly developing, and the comparative simplicity of his later series showed the profit derived by him from Newton's example. Among his discoveries were a solution by infinite series of the Keplerian problem, a method of drawing tangents to curves geometrically, and a rule, founded on the principle of exhaustions, for the direct and inverse method of tangents. He independently suggested, in a letter to Oldenburg of 8 June 1675, the differential method of stellar parallaxes (Rigaud, Corresp. of Scient. Men, ii. 262; Birch, Hist. Roy. Soc. iii. 225); pointed out the use of transits of Mercury and Venus for ascertaining the distance of the sun (Optica Promota, p. 130), and originated the photometric mode of estimating the distances of the stars, concluding Sirius to be 83,190 times more remote than the sun (Geom. Pars Universalis, p. 148). The word ‘series’ was first by him applied to designate continual approximations (Commercium Epistolicum, No. lxxv). Leibnitz thought highly of his abilities (ib. No. liii), and by his desire Collins drew up an account of the inventions scattered through his correspondence (ib. No. xlvii). The collection of ‘Excerpta’ thus formed was sent by Oldenburg to Paris on 26 June 1676, and eventually found its way to the archives of the Royal Society. Most of the series sent by Gregory to Collins were included in his nephew David Gregory's ‘Exercitatio,’ and his correspondence with Newton about the reflecting telescope was reprinted as an appendix to the same writer's ‘Elements of Catoptrics’ (ed. 1735). His ‘Optica Promota’ and ‘Art of Weighing Vanity’ were republished at the expense of Baron Maseres in 1823 among ‘Scriptores Optici.’ Open and unassuming with his friends, Gregory was of warm temper, and keenly sensitive to criticism. He was devoid of ambition, and found ready amusement in the incidents of college life. A portrait of him in Marischal College shows a refined and intellectual countenance.
A. M. C.