William, an eminent mathematician, was born on the 14th May 1701, at Hurworth, a village about three miles south of Darlington; at least it is certain that he resided here from his childhood. His father Dudley Emerson taught a school, and was a tolerable proficient in mathematics; and without his books and instructions, perhaps his son's genius, though eminently fitted for mathematical disquisitions, would have never been unfolded. The latter was instructed in the learned languages by a young clergyman, then curate of Hurworth, who was boarded at his father's house. In the earlier part of his life he attempted to teach a few scholars; but, whether from his concise method of explaining his ideas, in which he was not happy, or from the warmth of his natural temper, he made no progress in his school; he therefore soon left it off, and, satisfied with a moderate competence left him by his parents, he devoted himself to a studious retirement. Towards the close of the year 1791, being sensible of his approaching dissolution, he disposed of the whole of his mathematical library to a bookseller at York; and on the 20th of May 1782 he died of a lingering and painful disorder, at his native village, in the eighty-first year of his age.

Mr Emerson in his person was rather short, but strong and well made, with an open countenance and ruddy complexion. He was exceedingly singular in his dress and manners, and his appearance, which was rather clownish, if not boorish, did not bespeak the man of science; but his eccentricities were more than atoned for by the uncompromising independence of his character, and by the possession of strong natural parts, of which he has left ample evidence in his writings. He always walked up to London when he had any thing to publish, and revised it sheet by sheet himself. It was a favourite maxim with him to trust no eyes but his own. He never advanced any mathematical proposition which he had not first tried in practice, constantly making all the different parts himself on a small scale, so that his house was filled with all kinds of mechanical instruments together or disjointed. Fishing was a diversion which he was remarkably fond of, and while engaged in it he would frequently stand up to his middle in water. He used to study incessantly for some time, and then seek relaxation by taking a ramble to any potable-house where he could get any body to drink with and talk to. The Duke of Manchester was highly pleased with his company, and used often to come to him in the fields and accompany him home, but could never persuade him to get into a carriage. He was a married man, and his wife used to spin on an old-fashioned wheel, of which a very accurate drawing is given in his Mechanics. He was deeply skilled in the science of music, the theory of sounds, and the various scales both ancient and modern, but as a performer he had nothing to boast of.

The following is a list of Mr Emerson's works: 1. The Doctrine of Fluxions, 1748, 8vo; 2. The Projection of the Sphere, orthographic, stereographic, and gnomical, 1749, 8vo; 3. The Elements of Trigonometry, 1749, 8vo; 4. The Principles of Mechanics, 1754, 8vo; 5. A Treatise of Navigation, 1755, 12mo; 6. A Treatise of Algebra, in two books, 1765, 8vo; 7. The Arithmetic of Infinites, and the Differential Method, illustrated by Examples, 1767, 8vo; 8. Mechanics, or the Doctrine of Motion, 1769, 8vo; 9. The Elements of Optics, in four books, 1768, 8vo; 10. A System of Astronomy, 1769, 8vo; 11. The Laws of Centripetal and Centrifugal Force, 1769, 8vo; 12. The Mathematical Principles of Geography, 1770, 8vo; 13. Tracts, 1770, 8vo; 14. Cyclomathesis, or an easy Introduction to the several branches of the Mathematics, 1770, in 10 vols. 8vo; 15. 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, 8vo; 16. A Miscellaneous Treatise, containing several Mathematical Subjects, 1776, 8vo.