**PLAYFAIR, JOHN** (1748–1819), Scottish mathematician and
physicist, was born at Benvie, Forfarshire, where his father was
parish minister, on the 10th of March 1748. He was educated
at home until the age of fourteen, when he entered the university
of St Andrews. In 1766, when only eighteen, he was candidate
for the chair of mathematics in Marischal College, Aberdeen,
and, although he was unsuccessful, his claims were admitted
to be high. Six years later he made application for the chair
of natural philosophy in his own university, but again without
success, and in 1773 he was offered and accepted the living of
the united parishes of Liff and Benvie, vacant by the death of
his father. He continued, however, to carry on his mathematical
and physical studies, and in 1782 he resigned his charge in order
to become the tutor of Ferguson of Raith. By this arrangement
he was able to be frequently in Edinburgh, and to cultivate the
literary and scientific society for which it was at that time
specially distinguished; and through Maskelyne, whose acquaintance
he had first made in the course of the celebrated Schiehallion
experiments in 1774, he also gained access to the scientific circles
of London. In 1785 when Dugald Stewart succeeded Ferguson
in the Edinburgh chair of moral philosophy, Playfair succeeded
the former in that of mathematics. In 1802 he published his
celebrated volume entitled *Illustrations of the Huttonian Theory*
*of the Earth*. To its publication the influence exerted by James
Hutton on the progress of geological knowledge is largely due.
In 1805 he exchanged the chair of mathematics for that of
natural philosophy in succession to Dr John Robison, whom also
he succeeded as general secretary to the Royal Society of
Edinburgh. He took a prominent part, on the Liberal side,
in the ecclesiastical controversy which arose in connexion with
Leslie's appointment to the post he had vacated, and published
a satirical *Letter* (1806) which was greatly admired by his friends.
He was elected F.R.S. in 1807. He died in Edinburgh on the
20th of July 1819.

A collected edition of Playfair's works, with a memoir by James
G. Playfair, appeared at Edinburgh in 4 vols. 8vo. His writings
include a number of essays contributed to the *Edinburgh Review*
from 1804 onwards, various papers in the *Phil. Trans.* (including his
earliest publication, “On the Arithmetic of Impossible Quantities,”
1779, and an “Account of the Lithological Survey of Schiehallion,”
1811) and in the *Transactions of the Royal Society of Edinburgh*
(“On the Causes which affect the Accuracy of Barometrical
Measurements,” &c.), also the articles “Aepinus” and “Physical
Astronomy,” and a “Dissertation on the Progress of Mathematical
and Physical Science since the Revival of Learning in Europe,” in
the *Encyclopaedia Britannica* (Supplement to fourth, fifth and
sixth editions). His *Elements of Geometry* first appeared in 1795
and have passed through many editions; his *Outlines of Natural*
*Philosophy* (2 vols., 1812–1816) consist of the propositions and
formulae which were the basis of his class lectures. Playfair's contributions
to pure mathematics were not considerable, his paper
“On the Arithmetic of Impossible Quantities,” that “On the
Causes which affect the Accuracy of Barometrical Measurements,”
and his *Elements of Geometry*, all already referred to, being the
most important. His lives of Matthew Stewart, Hutton, Robison,
many of his reviews, and above all his “Dissertation” are of the
utmost value.