SIMPSON, (THOMAS,) in biography, professor of mathematics at the Royal Academy at Woolwich, fellow of the Roy al Society, and member of the Royal Aca demy, at Stockholm, was born at Market Bosworth, in Leicestershire, in 1710. His father, a stuff-weaver, taught him on ly to read English, and brought him up to his own business; but meeting with a scientific pedlar, who also practised for tune-telling, young Simpson, by his assist ance and advice, left off weaving, and professed astrology. As he improved in knowledge, however, he grew disgusted with his pretended art, and renouncing it, was driven to such difficulties for the subsistence of his family, that he came up to London, where he worked as a weaver, and taught mathematics at his spare hours. As his scholars increased, his abilities became better known, and he published his Treatise on Fluxions, by subscription, in 1737; in 1740, he publish ed his Treatise on the Nature and Laws of Chance ; and Essay in Speculative and Mixed Mathematics. After these appear ed his Doctrine of Annuities and Rever sions; Mathematical Dissertations ; Trea tise on Algebra ; Elements of Geometry; Trigonometry, Plane and Spherical ; Se lect Exercise ; and his Doctrine and Ap plication of Fluxions, which he professes to be rather a new work, than a second edition of his former publication on flux ions: In 1743, he obtained the mathe matical professorship at Woolwich Acade my; and soon after was chosen a member of the Royal Society, when the president and council, in consideration of his mo derate circumstances, were pleased to ex cuse his admission-fees, and his giving bonds for the settled future payments. At the Academy he exerted all his abili ties in instructing the pupils who *ere the immediate objects of his duty, as well as others whom the superior officers of the ordnance permitted to be boarded and lodged in his house. In his manner of teaching he bad a peculiar and happy ad dress, a certain dignity and perspicuity, tempered with such a degree of mildness, as engaged the attention, esteem, and friendship of his scholars. He therefore acquired great applause from his supe riors in the discharge of his duty.
Mr. Simpson's Miscellaneous Tracts, printed in 4to, 1757, were his last legacy to the public : a moat valuable bequest, whether we consider the dignity and importance of the subjects, or his sub lime and accurate manner of treating them.
The first of these papers is concerned in determining the precession of the Equinox, and the different motions of the Earth's Axis, arising from the Attraction of the Sun and Moon. It was drawn up about the year 1752, in consequence of another on the same subject, by M. de
Sylvabelle, a French gentleman. Though this gentleman had gone through one part of the subject with success and per spicuity, and his conclusions were per fectly conformable to Dr. Bradley's ob servations, it nevertheless appeared to Mr. Simpson that he had greatly failed in a very material part, and that indeed the only very difficult one ; that is, in the determination of the momentary altera tion of the position of the Earth's axis, caused by the forces of the Sun and Moon ; of which forces, the quantities, but not the effects, are truly investigated. The second paper contains the Investi gation of a very exact Method or Rule for finding the Place of a Planet in its Orbit, from a correction of Bishop Ward's circular Hypothesis, by means of certain Equations applied to the Motion about the upper Focus of the Ellipse. By this method the result, even in the orbit of Mercury, may be found within a second of the truth, and that without repeating the operation. The third shows the Manner of transferring the Motion of a Comet from a parabolic Orbit to an elliptic one ; being of great use, when the observed places of a (new) comet are found to differ sensibly from those com puted on the Hypothesis of a parabolic orbit. The fourth is an attempt to show, from Mathematical Principles, the Advan tage arising. from taking the Mean of a Number of Observations, in practical As tronomy ; wherein the odds, that the re sult in this way is more exact than from one single observation, is evinced, and the utility of the method in practice clearly made appear. The fifth contains the Determination of certain Fluents, and the Resolution of some very useful Equa tions in the higher Orders of Fluxions, by means of the measures of angles and ratios, and the right and versed sines of circular arcs. The sixth treats of the Resolution of algebraical Equations, by the Method of Surd divisors ; in which the grounds of that method, as laid down by Sir Isaac Newton, are investigated and explained. The seventh exhibits the In vestigation of a general Rule for the Resolution of Isoperimetrical Problems of all Orders, with some examples of the use and application of the said rule. The eighth, or last part, comprehends the Resolution of some general and very im portant Problems in Mechanics and Phy sical Astronomy ; in which, among other things, the principal parts of the third and ninth sections of the first book of Newton's Principia are demonstrated in a new and concise manner. But what may perhaps best recommend this excellent tract is, the application of the general equations, thus derived, to the determi nation of the lunar orbit.