The late Mr. Ferguson of Raith having held out to Mr. Playfair a very advantageous offer to superintend the edu cation of his two eldest sons, the present Robert Ferguson, Esq. of Raith, and Sir Ronald Ferguson, he was induced, in 1782, to resign his living for this purpose, and we be lieve he never afterwards exercised any of the duties of the clerical office.
In the year 1785, when Dr. Adam Ferguson exchanged the chair of Moral Philosophy for that of Mathematics, which was then filled by Mr. Dugald Stewart, Mr. Playfair was appointed Joint Professor of Mathematics, a situation which had been the highest object of his ambition, and which he was in a peculiar manner qualified to fill.
As Mr. Playfair was a member of the Philosophical So ciety of Edinburgh, he became one of the original fellows of the Royal Society at its institution by royal charter in 1783, and, by his services as an office-bearer, as well as by his communications as a member, he contributed most essentially to promote the interests, and to add to the re nown, of this distinguished body. His memoir On the Causes which affect the accuracy of Barometrical Measure ments• was read on the 1st March, 1784, and on the 10th January, 1785. The mensuration of heights by rometer was involved in many errors. M. De Luc had applied the important correction, depending on the tem perature of the atmospherical column; but when the height waz and the difference of temperature at the two exttinities of the column considerable, his me thod of the temperature was liable to consider able error. Mr. obyfair was therefore led to give an accurate formula for 'his purpose, and to investigate new ones, in order to exPrtAs those other circumstances by which the density of the atmosphere is affected. The man ner in which he has this task deserves high praise, and though the memoir is written with much per spicuity, and contains many original and sagacious views, it has not been referred to, as it ought, by those who have followed him in the same field of inquiry.
On the 3d of April, 1786, Mr Playfair read to the Royal Society a Biographical Account of the It•ru. Dr. Matthew Stewart, in which he has displayed those talents for ele gant composition for which he was afterwards so highly distinguished.
In year 1789, Mr. Playful!. succeeded Dr. Gregory as Secretary to the Physical Class of the Royal Society ; and as Dr. Robison, who then filled the office of General Secretary, was unable, from indisposition, to attend to its peculiar duties, the management of the society, and the arrangement of its memoirs for publication, devolved principally upon him.
The appearance, in 1787, of the Traite de I' Astronomic Indienne et Orientate, written by M. Bailly, the eloquent historian of astronomy, attracted the particular notice of Mr. Playfair, who became a complete convert to the fasci nating views which it contains respecting the antiquity of the Indian astronomy. He was therefore desirous of pre senting to his countrymen that particular view of the argu ment which had appeared to himself the most striking, and hence he was led to compose his Remarks on the Astro nomy of the which was read to the Royal So ciety 00 the 2d of March, 1789. The views which this paper contains have given rise to considerable contro versy ; and (though we have maintained the opposite side of the question in our article ASTRONOMY) we believe it is now universally admitted by the most acute, as well as by the most learned astronomers, that the Brahmins had skil fully adapted their tables to the fictitious epoch of the Cal you ghan.
Mr. Playfair's next communication to the Royal Society was his paper On the Origin and Investigation of Porisms.1 which was read on the 2d April, 1792. The account which he has here given of this class of geometrical propositions is in every respect philosophical, and removes all the dif ficulties which had been so long attached to them. This paper, however, contains only their geometrical analysis ; and though the algebraical investigation was promised as a second part, there is no reason to suppose that he ever prosecuted the subject any farther. This loss, however, is the less to be regretted, as, in the article Ponisms, which Mr. Babbage has written for this work, (Vol. XVI.) this distinguished mathematician has endeavoured to supply those observations on the algebraical part of the subject, which might have been expected in the continuation of Mr. Play fair's paper.