PLAYFAIR, JOHN, an eminent mathematician and natural philosopher, born March 10, 1748, at Benvie in Forfarshire, was the eldest son of the Rev. James Playfair, minister of the united parishes of Liff and Benvie. He received the rudimentary part of his education at home; and, at the age of fourteen, was sent to the university of St. Andrews, where he soon became distinguished for his love of study, and especially for the rapid progress which he made in mathematical learning. While yet a mere student, he was usually selected by Dr. Wilkie, author of ‘The Epigoniad,’ then professor of natural philosophy, to deliver the lectures to his class during his own absence from indisposition. In 1766, when only eighteen years old, he became a candidate for the professorship of mathematics in Marischal college, Aberdeen. After a lengthened and very strict examination, only two out of six rival competitors were judged to have excelled him, namely, Dr. Trail, who was appointed to the chair, and Dr. Hamilton, who subsequently succeeded to it. In 1769 he went to reside at Edinburgh; and on the death of Dr. Wilkie, in 1772, he offered himself as his successor, but was again unsuccessful. The same year his father died; and the care of providing for the support of his mother and her young family having in consequence devolved upon him, he considered it his duty to enter upon the ministry, for which he had been educated, notwithstanding his strong predilection for scientific pursuits. He accordingly applied to Lord Gray, the joint patron with the Crown, for the vacant living of Liff and Benvie, and his request was at once complied with; but his lordship’s right of presentation being disputed, he did not obtain induction till August 1773.
During the nine following years his time was chiefly occupied with his pastoral duties, and the superintendence of the education of his brothers. He did not neglect, however, the prosecution of his own philosophical researches. In 1774 he visited Schichallion, in Perthshire, to witness the experiments of Dr. Maskelyne, the astronomer royal, on the attraction of the mountains in that district, on which occasion he formed a permanent friendship with that celebrated philosopher. His earliest contribution to science was a paper communicated to the Royal Society of London, and inserted in their Transactions for 1779, ‘On the Arithmetic of Impossible Quantities,’ which is said to exhibit a greater taste for purely analytical investigation than had been shown by any of the British mathematicians of that age.

In 1782 he was induced, by an advantageous offer made to him by Mr. Ferguson of Raith, to resign his charge, and to become the tutor of his two sons, Mr. Robert Ferguson, subsequently a member of parliament, and his brother, afterwards Sir Ronald. In consequence of this arrangement, he removed to Edinburgh with his pupils.

In 1785, when Dr. Adam Ferguson exchanged his chair of moral philosophy for that of mathematics, taught by Mr. Dugald Stewart, and, in consequence of declining health, retired from the duties of the professorship, Mr. Playfair was admitted into the university of Edinburgh as his assistant, being appointed joint professor of mathematics. On the institution of the Royal Society of Edinburgh, in 1783, he became one of its original Fellows, and in subsequent years he contributed many valuable papers to its Transactions. In 1789 he communicated his ‘Remarks on the Astronomy of the Brahmins,’ which excited considerable attention both in Europe and India, and gave rise to much speculation and controversial discussion. The same year he succeeded Dr. Gregory as secretary to the physical class of the society; and, owing to the illness of Dr. Robison, the duties of general secretary, with the arrangement of the Society’s Memoirs for publication, were for many years chiefly performed by him. In 1792 he communicated to the Society’s Transactions a learned treatise ‘On the Origin and Investigation of Porisms.’ In which he gives a clear and beautiful philosophical analysis of this class of geometrical propositions.

In 1795 he published his ‘Elements of Geometry,’ for the use of the pupils attending his class, a work which has gone through numerous editions. In 1802 he published his ‘Illustrations of the Huttonian Theory of the Earth,’ in one vol. 8vo, a work on which he had been engaged for five years, and in which he powerfully, and with all the arguments he could derive from reason, science, and philosophy, effectively supports the geological system of his friend Dr. James Hutton, an admirable biographical account of whom he communicated in 1803 to the Transactions of the Royal Society.

On the death of Dr. Robison in 1805, Mr. Playfair succeeded him as general secretary to the Royal Society, and also as professor of natural philosophy in the university of Edinburgh. He resigned, in consequence, his former chair of mathematics, on which occasion his class presented him with a valuable astronomical circle, not in the Observatory of the Astronomical Institution at Edinburgh. The opposition of the clergy to the appointment of Mr. Leslie as his successor in the vacant chair, induced Mr. Playfair to come forward in his vindication, which he did, first, in a Letter to the lord provost, and afterwards in a strongly-written pamphlet, published in 1806, neither of which have been reprinted in the collection of his works.

In 1807 he was elected a Fellow of the Royal Society of London, and soon afterwards communicated to that learned body his ‘Lithological Survey of Schichallion,’ which appeared in the Philosophical Transactions for 1811.

In 1814 appeared, in two vols. 8vo, his ‘Outlines of Natural Philosophy,’ being the heads of lectures delivered to his class, an elementary work of great value. In 1815 he drew up for the Royal Society of Edinburgh a very interesting memoir of his distinguished predecessor, Dr. John Robison, which was published in their Transactions. To the Supplement of the ‘Encyclopaedia Britannica’ he contributed an Introductory Dissertation on ‘The Progress of Mathematical and Physical Science since the Revival of Letters in Europe;’ which masterly production comprises not only a succinct history of the sciences, but also gives comprehensive biographical sketches of those persons by whom they have been principally cultivated in this and other countries. For the same work he also wrote the valuable biographical account of Æpinus, and the learned article on ‘Physical Astronomy.’

Having planned a greatly enlarged edition of his ‘Illustrations of the Huttonian Theory,’ he had at different times made excursions to various parts of Scotland and England, for the purpose of extending his geological inquiries, besides deriving materials for his intended republication, from the most approved works on geology; but he had no opportunity of visiting the Continent till the general peace of 1815 threw it open to travelers from Britain. At the age of sixty-eight he undertook a long journey through France and Switzerland into Italy, and spent a considerable time in exploring the mineralogical and geological phenomena of the Alps. On his return, after eighteen months’ absence, other occupations unfortunately prevented him from maturing for publication the vast body of valuable materials he had collected for the proposed second edition of his Illustrations. For some time before his death he suffered much from a severe attack of disease is the bladder, which occasionally interrupted his literary labours, and of which at last he died on the morning of July 19, 1819, in the 72d year of his age. A monument has been erected to his memory on the Calton Hill, Edinburgh. His portrait is subjoined:

[portrait of John Playfair]

His works are:

Elements of Geometry, containing the first six books of Euclid, with two books on the Geometry of Solids; to which are added, Elements of Plain and Spherical Trigonometry. Edin. 1794, 8vo. Numerous editions.
Illustrations of the Huttonian Theory of the Earth. Edin. 1802, 8vo.
A Letter to the Author of the Examination of Professor Stewart’s Statement. 1806, 8vo.
Outlines of Natural Philosophy, being Heads of Lectures delivered in the University of Edinburgh. Edin. 1812, 1816, 2 vols. 8vo.
On the Arithmetic of Impossible Quantities, Phil. Trans. 1778, Abr. Xiv. 356.
An Account of a Lithological Survey of Schichallion, made in order to determine the Specific Gravity of the Rocks which compose that Mountain. Ib. 1811, 347.
On the Causes which affect the Accuracy of Barometrical Measurements. Trans. Soc. Edin. 1786, vol. i. 87.
The Life of Matthew Stewart. Ib. vol. i. p. 57.
Remarks on the Astronomy of the Brahmins. Ib. 1789, vol. ii. 135.
On the Origin and Investigation of Porisms. Ib. 1792, vol. iii. 154.
On the Trigonometrical Tables of the Brahmins. Ib. 1795, vol. iv. 83.
Meteorological Abstract for the years 1794, 1795, 1796. Ib. 213.
Investigation of certain Theorems relating to the Figure of the Earth. Ib. 1798, vol. v. 1; and in Nicholson’s Journal, vii. 102.
Meteorological Abstract for the years 1797, 1798, and 1799. Ib. 193.
Biographical Account of the late Dr. James Hutton. Ib. 1803, vol. v. 39.
On Solids of Greatest Attraction. Ib. 1807, vol. vi. 187.
On the Progress of Heat when communicated to Spherical Bodies from their Centres. Ib. 353.
Biographical Account of the late John Robison, LL.D., &c. Ib. 1815, vol. vii. 495. The same, in Thom. Ann. Philos. Vii. 169, 1816.
Dissertation second; exhibiting a general view of the Progress of Mathematical and Physical Science since the revival of letters in Europe. Part I. Part II. unfinished, in the Supplement to the enclyclopaedia Britannica. 1816 and 1819.

From 1804 Professor Playfair was a frequent contributor to the Edinburgh Review, the majority of his articles being of a scientific nature. The most celebrated of these is his admirable analysis of the ‘Mecanique Celeste’ of Laplace, and his masterly review of ‘Leslie’s Geometry.’ In general literature he wrote for the same periodical an able and interesting paper on Madame de Stael’s ‘Corinne.’ The whole of his articles are reprinted in the fourth volume of the collected edition of his works published at Edinburgh in 1822, in four vols. 8vo, with a Life prefixed by his nephew, Dr. James G. Playfair. An unfinished Memoir of John Clerk of Eldin, the inventor of the Naval Tactics, left by him in manuscript, was published, after his death, in the 9th volume of the Edinburgh Transactions. An interesting account of the character and merits of this illustrious mathematician, from the pen of Lord Jeffrey, has been inserted in the Encyclopaedia Britannica, and in the Memoir prefixed to his works by his nephew.

PLAYFAIR, WILLIAM, an ingenious mechanic and miscellaneous writer, brother of the preceding, was born in 1759. His father dying when he was very young, his education and support devolved on his brother. He early discovered a strong predilection for mechanical science, and when of sufficient age was apprenticed for a short period to a millwright of the name of Meikle, in Dundee, where he had for his fellow-apprentice John Rennie, the celebrated engineer. He subsequently went to Birmingham, and was engaged, in 1780, as a draughtsman, at the Soho Works, in the employment of Mr. James Watt. Being ambitious to be known as an author, he turned his attention to politics and political economy, and published a great variety of pamphlets connected therewith. During the early period of his literary career, however, he did not altogether neglect his mechanical pursuits, having successively obtained five patents for various inventions. He also invented a machine to complete the ornamental part or fretwork of silver tea-boards and sugar-tongs, which had hitherto been executed by the hand only. The same machine was applicable to the manufacture of coach ornaments, buckles and even horse shoes.

After residing some time at Birmingham he went to London, where he opened a silversmith’s shop for the sale of plate of his own manufacture; but this he soon relinquished, and proceeded to Paris, where he entered on some mechanical speculations, particularly a rolling-mill on a new plan, for the manufacture of which he obtained an exclusive privilege. One of the most important of his discoveries was that of the plan of the telegraph, then in constant use in France, which, with an alphabet invented by himself, he communicated to the British government; though the great service he thus rendered to his country was not only totally unrewarded, but was even very tardily acknowledged. He happened to be at Frankfort-on-the-Maine, when a member of the parliament of Bordeaux arrived at the same inn, and described to him a telegraph which had been erected on the mountain of Belville. Having at once comprehended the plan, in the course of the next day he executed two working models of the instrument, which he sent to the duke of York; “and hence,” says the Encyclopaedia Britannica, “the plan and alphabet of the machine came to England.”

While residing in Paris, Mr. Playfair became acquainted with Mr. Joel Barlow, who had been sent to France as agent for the sale of about three million of acres of land, on the banks of the Scioto, a river falling into the Ohio, which had been purchased by a company at New York, to be disposed of in lots to intending emigrants. As Mr. Barlow was without connections in Paris, and unacquainted with the French language, Playfair undertook the management of the business. The lands were to be sold at five shillings per acre, one-half to be paid on signing the act of sale, and the other half to remain on mortgage to the United States, to be paid within two years after taking possession. In November 1789 he opened an office in a street contiguous to the Palais Royal, and in less than two months fifty thousand acres of land were disposed of. Two vessels sailed from Havre laden with the first settlers in the colony of Scioto, which was thus formed by Mr. Playfair. Having soon after unfortunately expressed himself in an unguarded manner concerning the French Revolution, he incurred the hostility of Barrere, the president of the National Convention, who obtained an order for his arrest. Being, however, seasonably apprized of his danger, he succeeded in escaping into Holland, and thence returned to England. On his arrival in London, he projected a Bank, under the name of the Security Bank, which was opened in Cornhill. Its object was to divide large securities, so as to facilitate the negotiation of small loans; but sufficient attention not being paid to the nature of the securities, bankruptcy ensued. He now devoted himself more closely than ever to literary pursuits, and his life, like that of most authors, was henceforth much chequered. His pamphlets and other publications, which are chiefly on subjects of temporary interest, amount to nearly a hundred distinct works. In politics he was a firm supporter of government, and able vindicator of its measures towards France.

On the restoration of the Bourbons, he went again to Paris, and was for some time editor of Galignani’s Messenger, until obliged to quit France by a prosecution for libel. From that period he picked up a precarious living in London by essay-writing and translating. He died February 11, 1823, in the 64th year of his age; leaving a widow, two sons, and two daughters, one of the latter being unfortunately blind.

His principal works are:

Regulations for the Interest of Money. 1785, 8vo.
The Commercial and Political Atlas. Lond. 1786, 4to.
On the National Debt, with copperplate Charts. 1787, 4to.
The Inevitable Consequences of a Reform in Parliament. 1792, 8vo.
A General View of the Actual Force and Resources of France in 1793; to which is added, a Table, showing the Depreciation of Assignats, arising from their increase in quantity. Lond. 1793, 8vo.
Better Prospects to the Merchants and Manufacturers of Great Britain. Lond. 1793, 8vo.
Thoughts on the Present State of French Politics. Lond. 1793, 8vo.
Peace with the Jacobins impossible. 1794, 8vo.
Letter to Earl Fitzwilliam, occasioned by his two Letters to the Earl of Carlisle. 1795, 8vo.
The History of Jacobinism, its Crimes, Cruelties, and Perfidies; comprising an Inquiry into the manner of disseminating, under the appearance of philosophy and virtue, principles which are equally subversive of order, virtue, religion, liberty, and happiness. Lond. 1795, 8vo.
A Real Statement of the Resources and Finances of Great Britain. 1796, 8vo.
Letter to Sir W. Pulteney, Bart., on the Establishment of another Public Bank in London. Lond. 1797, 8vo.
Statistical Tables, exhibiting View of all the States of Europe; translated from the German of Boetticher, with a Supplementary Table containing the changes since the publication of the original Work. Lond. 1800, 4to.
Strictures on the Asiatic Establishments of Great Britain, with a view to an Inquiry to the true Interests of the East India Company. Lond. 1800, 4to.
The Statistical Breviary, on a principle entirely new; the Resources of every State and Kingdom in Europe, illustrated with Plates; to which is added, a similar exhibition of the Ruling Powers in Hindostan. Lond. 1801, 8vo.
Proofs relative to the Falsification by the French of the intercepted Letters found on board the Admiral Aplin East Indiaman. Lond. 1804, 8vo.
An Inquiry into the permanent Causes of the Decline and Fall of Powerful and Wealthy Nations, illustrated by four engraved Charts. Lond. 1805, 4to.
Smith’s Wealth of Nations, with Notes, Supplementary Chapters, &c. Eleventh Edition, 1805, 3 vols. 8vo.
A Statistical Account of the United States of America, translated from the French. 1807, 8vo.
British Family Antiquity. Lond. 1809-10, 5 vols. 5to.
Plan for establishing the Balance of Power in Europe. 1813, 8vo.
Political Portraits of this new Era, with Notes Historical and Biographical. 1814, 2 vols. 8vo.
The Statement of Buonaparte’s Plot made to Earl Bathurst and the French Ambassador. 1815, 8vo.
Supplementary Volume to Political Reports in this new Era, with Explanatory Notes, Historical and Biographical. Lond. 1816, 8vo.
France as it is; not Lady Morgan’s France. 1820, 2 vols. 8vo.