In 1805 he quitted the chair of mathematics to succeed Professor Robison in that of natural philosophy. In the contest which ensued upon the appointment of Leslie as his successor in this chair, he took a very active part; and amongst the heaviest blows which Leslie's opponents had to sustain, were those that parted from the hand of Mr. Playfair. In 1807 he was elected a Fellow of the Royal Society, to which learned body he very soon afterwards presented his 'Account of the Lithological Survey of Schehallien;' this was the result of his investigations during the period of Dr. Maskelyne's visit to Schehallien, to measure the attraction of that mountain, on which occasion Playfair shared the shelter of this distinguished astronomer's tent on the side of the mountain, and contracted with him a friendship which lasted during the remainder of their lives. In 1809 he contributed to the 'Edinburgh Transactions' an excellent paper on 'Solids of the Greatest Attraction,' and in 1812, another, on the 'Progress of Heat in Spherical Bodies.' In 1814 he published, in two volumes octavo, for the use of his class, an elementary work of great value, under the title of 'Outlines of Natural Philosophy.' About the same time he drew up for the 'Encyclopædia Britannica' an introductory 'Dissertation on the Progress of Mathematical and Physical Science,' a treatise distinguished for the soundness of judgment, beauty of writing, and extent of knowledge displayed in it. In 1815, Playfair wrote for the Royal Society of Edinburgh a very interesting memoir of his distinguished predecessor, Dr. Robison. In the course of the same year he undertook, at the age of sixty-eight, a long journey through France and Switzerland into Italy, and did not return for a period of nearly eighteen months, during which time his principal attention was directed to the mineralogical and geological phenomena of the different regions which he visited. On his return from this expedition, he was occupied in drawing up a memoir on the 'Naval Tactics of Clerk of Eldin,' which was published after his death in the 'Philosophical Transactions.' Playfair had for several years suffered from a recurrence at different times of a painful affection of the bladder, which appeared with increased seventy in the early part of 1819, but was so far got under as to enable him to complete his course of lectures in the spring. It returned, however, in a still more distressing form in the summer, and at last put a period to his life on the 19th of July. Though suffering great pain during the last part of his confinement, he retained not only his intellectual faculties quite unimpaired, but also the serenity and mildness of his spirit, occupying himself until within a few days of his death in correcting the proof-sheets of the 'Dissertation' before noticed.