**EMERSON, WILLIAM** (1701–1782), English mathematician, was born on the 14th of May 1701 at Hurworth, near Darlington, where his father, Dudley Emerson, also a mathematician, taught a school. Unsuccessful as a teacher he devoted himself entirely to studious retirement, and published many works which are singularly free from errata. In mechanics he never advanced a proposition which he had not previously tested in practice, nor published an invention without first proving its effects by a model. He was skilled in the science of music, the theory of sounds, and the ancient and modern scales; but he never attained any excellence as a performer. He died on the 20th of May 1782 at his native village. Emerson was eccentric and indeed clownish, but he possessed remarkable independence of character and intellectual energy. The boldness with which he expressed his opinions on religious subjects led to his being charged with scepticism, but for this there was no foundation.

Emerson’s works include *The Doctrine of Fluxions* (1748); *The Projection of the Sphere, Orthographic, Stereographic and Gnomical* (1749); *The Elements of Trigonometry* (1749); *The Principles of Mechanics* (1754); *A Treatise of Navigation* (1755); *A Treatise of Algebra*, in two books (1765); *The Arithmetic of Infinites, and the Differential Method, illustrated by Examples* (1767); *Mechanics, or the Doctrine of Motion* (1769); *The Elements of Optics*, in four books (1768); *A System of Astronomy* (1769); *The Laws of Centripetal and Centrifugal Force* (1769); *The Mathematical Principles of Geography* (1770); *Tracts* (1770); *Cyclomathesis, or an Easy Introduction to the several branches of the Mathematics* (1770), in ten vols.; *A Short Comment on Sir Isaac Newton’s Principia*; to which is added, *A Defence of Sir Isaac against the objections that have been made to several parts of his works* (1770); *A Miscellaneous Treatise containing several Mathematical Subjects* (1776).