In the year 1795, Mr. Playfair published his Elements of Geometry, which consisted of the first six books of Eu clid, with three additional ones containing the rectification and quadrature of the circle, the intersection of planes, and the geometry of solids, with plane and spherical trigono metry, and the arithmetic of sines. The notes to this work possess a peculiar value ; and hence the work itself has been held in high estimation for the purposes of elemen tary instruction.
During the same year, Mr. Playfair communicated to the Royal Society his Observations on the Trigonometrical Tables of the Brahmins ;§ and some time afterwards, on the 5th February, 1798, he read to the same body his In vestigation of certain Theorems relative to the Figure of the Earth.}1 one of the principal objects of which, was to consider the advantages of comparing a degree of the me ridian with a degree of the circle perpendicular to it, and also with a degree of the parallel of latitude by which it is crossed.
The death of Dr. James Hutton in the winter of 1797, gave a new direction to Mr. Playfair's studies; and, with some exceptions, rendered necessary by his professional occupations, the rest of his life was devoted to geological investigations, or to those kindred pursuits from which 'his fascinating study derives either support or illustra tion. Attached by long acquaintance and similarity of opinion to the celebrated author of the Huttonian theory, Mr. Playfair was led by inclination, as well as by duty, to compose a biographical memoir of his departed friend. Having been in the daily habit of discussing with Dr. Hut ton the difficult questions which this theory involved, Mr. Playfair had acquired a more correct knowledge of its principles than could have been derived from the writings of its author; and he was therefore peculiarly qualified to appear as its illustrator and defender.
After five years' labour, Mr. Playfair produced, in 1802, his Illustrations of the Huttonian Theory, in one volume 8vo.; and on the 10th January, 1803, he read to the Royal Society of Edinburgh his Biographical Account of the late 1)r. James Hutton. These two works added greatly to the fame of their author; and whether we consider them as models of composition ur of argument, we cannot but re gard them as the productions by which the name of Mr. Mayfair must be handed down to posterity. All his other writings, beautiful and profound as they are, can be con sidered in no other light than as able and perspicuous ex positions, which illuminate the obscurities of science with out extending her domains. But his illustrations of the Huttonian theory are marked with a higher character. Though brought out under the modest appellation of a commentary, it is unquestionably entitled to be regarded as an original work; and though the theory which it ex pounds must always retain the name of the philosopher who first suggested it, yet Mr. Playfair has in a great measure made it his own, by the philosophical generalisa tions which he has thrown around it; by the numerous phenomena which he has enabled it to embrace ; by the able defences with which its weakest parts have been sus tamed; and by the relation which he has shown it to bear to some of the best established doctrines, both in chemis try and astronomy. In the execution of this great work,
and in the subsequent improvements which it had under gone during the last seventeen years of the life of its au thor, he received great assistance from Sir James Hall, Lord Webb Seymour, Dr. Hope, Sir George Mackenzie, Mr. Allan, and Mr. Jardine; and many of the happiest of his days were spent in the society of these eminent indi viduals, who either accompanied or aided him in all his geological journeys and investigations. The deep interest which these gentlemen, in common with all Mr. Playfair's scientific friends, took in the appearance of the second edition of the Illustrations, may therefore be readily con ceived ; and it is not easy to express the regret which they feel, that literary labours of a more fleeting kind should have interfered with the completion of a work, which would have shed a new lustre over his already honuured name.
Upon the death of Dr. Robison, in 1805, Mr. Playfair was elected General Secretary to the Royal Society, and he was also appointed his successor in the chair of natural philosophy,—a situation which his mathematical acquire ments, and his powers of perspicuous illustration, render ed him peculiarly qualified to fill. This event, however, though in every respect advantageous to himself, inter rupted in no slight degree the progress of his general studies. The preparation of a course of lectures on sub jects which he had only indirectly pursued, and the com position of his Outlines of Natural Philosophy, which he considered necessary for the use of his students,' occupied much of that valuable time on which the higher interests of science possessed so many claims. Notwithstanding these avocations, however, he read to the Royal Society, in January, 1807, his paper On the Solids of greatest At traction,t--a subject to which his attention had been ne cessarily directed during his Ethological survey of Sche hallien, which he made in conjunction with Lord Webb Seymour, and of which he has given an account in the Philosophical Transactions for 18114 The object of this survey was, to obtain an estimate of the specific gravity of the mountain, in order to correct the deductions of Dr. Maskelyne respecting the mean density of the earth ; and the conclusions which this survey authorized, were de duced by means of the formulae investigated in the memoir already alluded to on the solids of greatest attraction. The leading problem in this paper had been previously treated by Boscovich, and also by M. Sylvabellc ; but Mr. Play fair had never seen the labours of either of these mathe maticians.