In the year 1669, a work was published at Rotterdam, by Mr George Sinclair, professor of philosophy in the univer sity of Glasgow, entitled Ars Nova et Magna Gravitatis et Levitatis ; and another work on hydrostatics, by the same author, appeared at Edinburgh in 1672. Mr Sinclair had been dismissed from his professorship soon after the resto ration, on account of his political principles, and had given offence to the Royal Society of London, by charging them with negligence and injustice. He appears also to have act ed improperly towards one of Mr Gregory's colleagues, and thus. to have incurred the displeasure of that mathema tician. In the year Gregory, under the assumed name of Patrick Mothers, archbedal to the university of St An drew's, attacked Sinclair, in a tract, entitled The great and new art of weighing Vanity, or a discovery of the Ignorance and Arrogance of the great and new Artist, in his Pseudo philosophical writings. To this work is annexed Tentamina de mote penduli et projectorzim.
In 1674, Gregory was called to the mathematical chair in the university of Edinburgh, a situation which he did not live long to enjoy. In the month of October 1675, when he was walking home from supper, he was struck suddenly blind, and expired a few days afterwards, in the 36th year of his age.
The following is a list of the inventions and discoveries of James Gregory, as given by Dr Hutton. The reflecting telescope; burning mirror;' quadrature of the circle, el lipse, and hyperbola ; method for the transmutation of curves ; geometrical demonstration of Lord Brouncker's seriesfor squaring the hyperbola ; demonstration that the meridian line is analogous to a scale of logarithmic tan gents, of the half complements of the latitude ; a simple converging series for making logarithms ; solution of the famous Keplerian problem, by an infinite series ; method of drawing tangents to curves geometrically, without previous calculation ; a rule for the direct and inverse method of tangents, depending on the principle of exhaustions ; a se ries for the length of the arc of a circle from the tangent, and vice versa, and also for the secant and logarithmic tan gent and secant, and vice versa ; and serieses for the length of the elliptic and hyperbolic curves. See Hutton's Ma thenzatical Dictionary, 2d edition, p. 601, Re. and the other works quoted is the article.