PLAYFAIR, JOHN, a celebrated Scotch mathematician and natural philosopher, was the eldest son of the Rev. James Playfair, minister of the united parishes of Liff and Benvie, in the county of Forfar. He was born at I3envie, on the 10th of March, 1743 ; and after receiving a classi cal education under the roof of his father, he entered the univerity of St. Andrews at the age of fourteen. At this ancient seat of learning Mr. Playfair soon distinguished himself by the excellence of his conduct, as well as the ardour of his application ; and so great was his progress in natural philosophy, that Professor (the author of the Epigoniad) who taught that branch of knowledge in the university, selected him to teach his class during his indisposition.
In the year 1766, upon the death of Mr. Stewart, Profes sor of Mathematics in Marischal College, Aberdeen, seven candidates appeared for the vacant chair. Among these were the Rev. Dr. Trail, Dr. Hamilton, and Mr. Playfair. The professorship was a private foundation, by Dr. Liddel, and a clause in the deed of foundation was considered as a direetion to fill up the vacancy by a disputation or com parative trial. Dr. Reid of Glasgow, Mr. Vilant of St. Andrews, 1)r. Skene, of Marischal College, and Professor Gordon of King's College, accepted the office of judges on this occasion ; and after a severe examination, which lasted for a fortnight, Dr. Trail was appointed to the chair. Mr. Playfair was excelled only by two, out of six candidates, DI'. Trail and Dr. Hamilton, who now fills the same chair; but when it is considered, that Mr. Play fair was two years younger than Dr. Trail, the result of the election must have been greatly affected by that cir cumstance alone; and Dr. Trail himself has modestly re marked, in a letter to the writer of this article, that he has always attributed his own success to this disyarity of years.
In the year 1772, when the chair of natural philosophy became vacant by the death of Dr. yrilkie, Mr. Playfair again cherished the hopes of a permanent appointment ; but his expectations were a seceod time frustrated ; a dis store severe, as the death of appointment which was the his father in the same year had devolved open hint the charge of his mother net family. This circumstance
appears to have determ;ried Mr. Playfair to the pro fession of his father, to which he had been educated, but which his ardent atrachment to mathematical pursuits had induced him to Mink or abandoning. Having been pre seoted by Lord Gray to his father's living of Liff and Ben vie, of which. however, he did not obtain possession till August, 1773, in consequence of a dispute respecting the right of proronage. Mr. Playfair devoted his time to the duties of I,;s sawed office, to the education of his younger brothers, and to the occasional prosecution of his own favourite studies. In 1774 he went to Schehallicn, where Dr. Maskelyne was carrying on his interesting experi ments on the attraction of the mountains ; and while he was enjoying the acquaintance of that eminent astronomer, he was little aware that he should himself contribute, at some distant period, to the perfection of the result which it was the object of this experiment to obtain.
In the year 1777, Mr. Playfair communicated to the Royal Society of London an essay On the Arithmetic of Im possible Quantities, which appeared in the Transactions for that year, and which was the first display of his mathe matical acquirements. In this ingenious paper, which is strongly marked with the peculiar talent of its author, Mr. Playfair has pointed out the insufficiency of the explana tion of the doctrine of negative quantities given by John Bernouilli and Maclaurin, viz. that the imaginary charac ters which are involved in the expression compensate or destroy each other ; • and he has endeavoured to show that the arithmetic of impossible quantities is nothing more than a particular method of tracing the affinity of the measures of ratios and of angles, and that they can never be of any use as an instrument of discovery, unless when the subject of investigation is a property common to the measures both of ratios and of angles.