there was a sixth edition in 1790. His next work was, "Elements of Geometry, with their application to Mensuration of Superficies and Solids, to the determination of Maxima and Minima, and to the construction of a great variety of Geometrical Problems," 1747, 8vo, reprinted in 1760, with large alterations and additions, designed for young beginners; particularly for the gentlemen at the king's academy at Woolwich, and dedicated to Charles Frederick, esq. surveyor-general of the ordnance; and other editions have appeared since *. In 1748 came out his "Trigonometry, Plane and Spherical, with the construction and application of Logarithms," 8vo. This little book contains several things new and useful. In 1750 appeared in 2 vols. 8vo, "The doctrine and application of Fluxions, containing, besides what is common on the subject, a number of new improvements in the Theory, and the solution of a variety of new and very interesting Problems, in different branches. of the Mathematics." In the preface the author offers this to the world as a new book rather than a second edition of that published in 1737; in which he acknowledges, that, besides errors of the press, there are several obscurities and defects, for want of experience, in his first attempt. This work is dedicated to George earl of Macclesfield. In 1752 appeared in 8vo, "Select Exercises for young proficients in Mathematics," dedicated to John Bacon, esq. F. R. S. His "Miscellaneous Tracts," printed in 1757, 4to, was his last legacy to the public; a most valuable bequest, whether we consider the dignity and importance of the subjects, or his sublime and accurate manner of treating them. These are inscribed to the earl of Macclesfield, and are ably analyzed in Dr. Hutton's Dictionary.

Besides the foregoing, which are the whole of the regular books or treatises that were published by Mr. Simpson,

* Mr. Simpson met with some trouble and vexation in consequence of the first edition of his Geometry. First, from some reflections made upon it, as to the accuracy of certain parts of it, by Dr. Robert Simson, the learned professor of mathematics in the university of Glasgow, in the notes subjoined to his edition of Euclid's Elements. This brought an answer to those remarks from Mr. Simpson, in the notes added to the second edition as above; to some parts of which Dr. Simson again replied in his notes on

the next edition of the said Elements of Euclid. The second was by an illiberal charge of having stolen his Elements from Mr. Muller, the professor of fortification and artillery at the same academy at Woolwich where our author was professor of geometry and mathematics. This charge was made at the end of the preface to Mr. Muller's Elements of Mathematics, m two volumes, printed in 1748; which was fully refuted by Mr. Simpson in the preface to the second edition of his Geometry.

he wrote several papers which were read at the meetings of the Royal Society, and printed in their Transactions; but as most, if not all of them, were afterwards inserted, with alterations or additions, in his printed volumes, it is needless to take any farther notice of them here. He also proposed, and resolved many questions in the "Ladies Diaries," &c.; sometimes under his own name, as in 1735 and 1736; and sometimes under feigned or fictitious names; such as, it is thought, Hurlothrumbo, Kubernetes, Patrick O'Cavenah, Marmaduke Hodgson, Anthony Shallow, esq. and probably several others; see the Diaries for 1735, 36, 42, 43, 53, 54, 55, 56, 57, 58, 59, and 60. Mr. Simpson was also the editor or compiler of the Diaries from 1754 till 1760, both inclusive, during which time he raised that work to the highest degree of respect. He was succeeded in the editorship by Mr. Edw. Rollinson.

It has also been commonly supposed that he was the real editor of, or had a principal share in, two other periodical works of a miscellaneous mathematical nature; viz. the "Mathematician," and "Turner's Mathematical Exercises," two volumes, in Svo, which came out in periodical numbers, in 1750 and 1751, &c. The latter of these seems especially to have been set on foot to afford a proper place for exposing the errors and absurdities of Mr. Robert Heath, the then conductor of the "Ladies Diary" and the "Palladium;" and which controversy between them ended in the disgrace of Mr. Heath, and expulsion from his office of editor to the "Ladies Diary," and the substitution of Mr. Simpson in his stead, in 1753.

In 1760, when the plans proposed for erecting a new bridge at Blackfriars were in agitation, Mr. Simpson, among other gentlemen, was consulted upon the best form for the arches, by the New-bridge Committee. Upon this occasion he gave a preference to the semicircular form;" and, besides his report to the Committee, some letters also appeared, by himself and others, on the same subject, in the public newspapers, particularly in the Daily Advertiser, and in Lloyd's Evening Post, which were collected in the Gentleman's Magazine for that year. It is probable that this reference to him, induced him to turn his thoughts more seriously to this subject, so as to form the design of composing a regular treatise upon it; for his family often informed Dr. Hutton, that he laboured hard upon this work for some time before his death, and was very anxious to

have completed it, frequently remarking to them, that when published, it would procure him more credit than any of his former publications. But he lived not to put the finishing hand to it. Whatever he wrote upon this subject, probably fell, together with all his other remaining papers, into the hands of major Henry Watson, of the engineers, in the service of the India company, being in all a large chest full of papers. This gentleman had been a pupil of Mr. Simpson's, and bad lodged in his house. After Mr. Simpson's death, Mr. Watson prevailed upon the widow to let him have the papers, promising either to give her a sum of money for them, or else to print and publish them for her benefit. But neither of these was ever done; this gentleman always declaring, when urged on this point by Dr. Hutton and others, that no use could be made of any of the papers, owing to the very imperfect state in which he said they were left. And yet he persisted in his refusal to give them up again.

Through the interest and solicitations of William Jones, esq. he was, in 1743, appointed professor of mathematics, then vacant by the death of Mr. Derham, in the Royal academy at Woolwich; his warrant bearing date August 25th. And in 1745 he was admitted a fellow of the Royal Society, having been proposed as a candidate by Martin Folkes, esq. president, William Jones, esq. Mr. George Graham, and Mr. John Machin, secretary; all very eminent mathematicians. The president and council, in consideration of his very moderate circumstances, were pleased to excuse his admission fees, and likewise his giving bond for the settled future payments.

At the academy he exerted his faculties to the utmost, in instructing the pupils who were 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 had a peculiar and happy address; a certain dignity and perspicuity, tempered with such a degree of mildness, as engaged both the attention, esteem, and friendship of his scholars; of which the good of the service, as well as of the community, was a necessary consequence.

In the latter stage of his existence, when his life was in danger, exercise and a proper regimen were prescribed him, but to little purpose; for he sunk gradually into such a lowness of spirits as seemed to injure his mental faculties, and at

last rendered him incapable of performing his duty, or even of reading the letters of his friends; and so trifling an accident as the dropping of a tea-cup would flurry him as much as if a house had tumbled down. The physicians advised his native air for his recovery; and, Feb. 1761, he set out, with much reluctance (believing he should never return), for Bosworth, along with some relations. The journey fatigued him to such a degree, that upon his arrival, he betook himself to his chamber, where he died, May 14, in his fifty-first year.

He left a widow and a son and a daughter; the former an officer in the royal regiment of artillery. The king, at the instance of lord Ligonier, in consideration of Mr. Simpson's great merits, granted a pension to his widow, together with handsome apartments adjoining to the academy; a favour never conferred on any before. His widow died at Woolwich Dec. 19, 1782, aged one hundred and two.'

SIMSON (ROBERT), an eminent mathematician, was the eldest son of Mr. John Simson, of Kirton-hall in Ayrshire, and was born Oct. 14, 1687. Being intended for the church, he was sent to the university of Glasgow in 1701, where he made great progress in classical learning and the sciences, and also contracted a fondness for the study of geometry, although at this time, from a temporary cause, no mathematical lectures were given in the college. Hav ing procured a copy of Euclid's Elements, with the aid only of a few preliminary explanations from some more advanced students, he soon came to understand them, and laid the foundation of his future eminence. He did not, however, neglect the other sciences then taught in college, but in proceeding through the regular course of academic study, acquired that variety of knowledge which was visi→ ble in his conversation throughout life. In the mean time his reputation as a mathematician became so high, that in 1710, when only twenty-two years of age, the members of the college voluntarily made him an offer of the mathematical chair, in which a vacancy in a short time was expected to take place. From his natural modesty, however, he felt much reluctance, at so early an age to advance abruptly from the state of a student, to that of a professor in the same college, and therefore solicited permission to spend

Gent, Mag. vol. LIII.-Hutton's Dictionary.-Nichols' Leicestershire.

one year at least in London. Being indulged in this, be proceeded to the metropolis, and there diligently employed himself in improving his mathematical knowledge. He also enjoyed the opportunity of forming an acquaintance · with some eminent mathematicians of that day, particularly Mr. Jones, Mr. Caswell, Dr. Jurin, and Mr. Ditton. With the latter, indeed, who was then mathematical master of Christ's Hospital, and well esteemed for his learning, &c. he was more particularly connected. It appears from Mr. Simson's own account, in his letter, dated London, Nov. 1710, that he expected to have had an assistant in his studies chosen by Mr. Caswell; but, from some mistake, it was omitted, and Mr. Simson himself applied to Mr. Ditton. He went to him not as a scholar (his own words), but to have general information and advice about his mathematical studies. Mr. Caswell afterwards mentioned to Mr. Simson that he meant to have procured Mr. Jones's assistance, if he had not been engaged.

When the vacancy in the professorship of mathematics at Glasgow did occur, in the following year, by the resignation of Dr. Robert Sinclair, or Sinclare (a descendant or other relative probably of Mr. George Sinclare, who died in that office in 1696), the university, while Mr. Simson was still in London, appointed him to fill it; and the minute of election, which is dated March 11, 1711, concluded with this very proper condition, "That they will admit the said Mr. Robert Simson, providing always, that he give satisfactory proof of his skill in mathematics, previous to his admission." He returned to Glasgow before the ensu ing session of the college, and having gone through the form of a trial, by resolving a geometrical problem proposed to him, and also by giving "a satisfactory specimen of his skill in mathematics, and dexterity in teaching geometry and algebra;" having produced also respectable certificates of his knowledge of the science, from Mr. Caswell and others, he was duly admitted professor of mathematics, on the 20th of November of that year.

Mr. Simson, immediately after his admission, entered on the duties of his office; and his first occupation necessarily was the arrangement of a proper course of instruction for the students who attended his lectures, in two distinct classes. Accordingly he prepared elementary sketches of some branches on which there were not suitable treatises in general use. Both from a sense of duty and from inclina