their rectification and quadrature, the cubature and complanation of solids formed by the rotation of conic sections upon their axes and other lines, the method of equidistant ordinates and sections, the centro-baryc method of determining the measure of planes and solids by means of their centre of gravity, &c. The practical rules are presented in an orderly series, and applied to the solution of numeral examples; the demonstrations of the several rules are thrown into the notes, which are very extensive, and present a most valuable and instructive series of investigations and deductions connected with the successive topics of the work. These are followed by comprehensive and elegant treatises on landsurveying, gauging, artificers' works, and timber measuring. The volume concludes with an extensive table of the areas of circular segments; useful both in the computations of mensuration, and in the determination of fluents of certain kinds.

About the years 1771 and 1772, Dr. Hutton was employed by the magistrates of Newcastle as the most proper person in that place to make an accurate survey of the town and county of the town of Newcastle-upon-Tyne; a tract of many miles in circuit, and a town which, from the crookedness of the streets, and the unevenness of the ground, is perhaps the most difficult of any one in the island to measure. Of this tract he made a most accurate survey and plan, which was soon after engraved, and published in a map, consisting of two very large sheets of paper; containing also a neat abridged account of the history, trade, and population of the place.

The overthrow of Newcastle bridge, and other bridges across the river Tyne, in November, 1771, by reason of a very high and rapid flood in that river, drew our author's attention to another subject, that is to say, the theory of the equilibration of arches and piers. The result of his investigations was laid before the public in 1772, in an octavo tract, on “The Principles of Bridges; containing the Mathematical Demonstrations of the Properties of the Arches, the Thickness of the Piers, the Force of the Water against them,

&c. together with practical Observations and Directions drawn from the Whole." This performance was entirely out of print, when, on occasion of Telford and Douglas's project for erecting an iron bridge over the Thames at London, it was republished in 1801, verbatim from the Newcastle edition. Dr. Hutton had for several years been collecting materials for an enlarged and improved edition of this treatise, among which were theoretical and practical observations on several of the most celebrated bridges in Italy and other parts of continental Europe; but these, unfortunately for the world, were lost. He however made several improvements, though by no means to the extent which he had contemplated, in the edition of this essay which appears in his Collection of Tracts in 1812.

About the year 1772, also, the indefatigable subject of this memoir commenced the republication of the "Ladies' Diaries," from the origin of the series. It may be necessary to inform readers who are not Englishmen, that, more than a century ago, some of the almanacks published in England were devoted to other purposes than those which relate to the mere calendar. So early as the year 1704, Mr John Tipper, with some ingenious associates, determined to publish a yearly almanack, which should have the farther object of promoting literature, science, and taste. To effect this, they introduced into the almanac smart jeux d'esprits, enigmas, charades, and other lively compositions in prose and poetry, together with a series of well-selected problems in criticism, philosophy, and different branches of mathematical science; which were to be proposed for investigation in one almanack, and their solutions published in the next. This happy plan for the excitement of emulation, and the promotion of science, was found to be highly beneficial. In 1741, a similar annual publication appeared, under the title of the "Gentleman's Diary." Both this and the Ladies' Diary have ever since been published annually; and, as several thousand copies of each are sold, they have been found to be exceedingly instrumental in exciting and augmenting a love

of literature and science among the middle classes of society in England. From a full persuasion of the utility of such an undertaking, Dr. Hutton determined to republish the whole of the poetical and mathematical departments of the Ladies' Diaries periodically. As he proceeded, he gave new and improved solutions to many of the problems. He also inserted in each successive number of his publication a series of new and curious problems; while, in several numbers, there appeared valuable disquisitions, by himself and his correspondents, on a variety of subjects, connected both with pure and with mixed mathematics. These were afterwards published separately, under the title of "The Mathematical Miscellany," in a single volume: the poetical and mathematical parts of the Ladies' Diaries, down to the year 1773, constitute five additional volumes. Though humble in their appearance, they are by no means despicable in value. They contain many interesting and useful investigations, by Emerson, Simpson, Dunthorne, Heath, Rollinson, Hutton, Wildbore, Vince, Landen, and others who have contributed to the advancement of mathematical science in Britain.

It is remarkable that the printing of the foregoing works at Newcastle happily proved the occasion of bringing into public notice one of the most admirable wood-engravers that the world ever beheld, in the person of the ingenious Mr. Bewick. There was no artist at that time in Newcastle professedly capable of engraving in wood the necessary figures. There was, however, a very ingenious young man, Mr. Ralph Beilby, a seal-engraver, who, assisted by Dr. Hutton, produced such excellent specimens in these works, that the Bishop of Norwich employed him, in consequence, to execute the engravings for his complete edition of Newton. So great a quantity of business of this kind, both for the works of Newton, and for Dr. Hutton's three books, induced Mr. Beilby to unite with himself in the execution of it his pupil and assistant Mr. Bewick, who afterwards rose to such eminence in the art, and laid the foundation of its present perfection.

To return to Dr. Hutton: labours like those which we have already enumerated soon led him into a most extensive correspondence, and procured for him a very exalted reputation; such, indeed, as occasioned his removal to a situation of great importance, as well as respectability. The Professorship of Mathematics in the Royal Military Academy at Woolwich became vacant, in consequence of the resignation of Mr. J. L. Cowley; and the Marquis Townsend, at that time Master-General of the Ordnance, formed the laudable determination of giving the appointment to the individual, who, by a public examination, should prove himself best qualified to discharge the duties of a mathematical professor. Dr. Hutton was persuaded by his friend Colonel Edward Williams, of the Royal Artillery, himself a mathematician of considerable acquirements, to become a candidate for the situation. His natural diffidence, which was at all times as remarkable as his talents, caused him at first to shrink from all desire to obtain a professorial chair, which had previously been occupied by one so deservedly eminent as Thomas Simpson: but his friends at length overcame his scruples, and he travelled from Newcastle to Woolwich, a distance of 300 miles, to propose himself as a candidate. He had no less than ten competitors, among whom were Mr. Benjamin Donn, the author of "The Geometrician," and other well-known works, and Mr. Hugh Brown, the able translator and commentator upon "Euler's Gunnery." The gentlemen appointed to conduct the examination were, Dr. Maskelyne, then Astronomer Royal; Bishop Horsley, the learned editor of Newton's works; and Col. Henry Watson, translator of Euler's Treatise on the Construction of Ships, and afterwards Chief Engineer in Bengal. To all these gentlemen Dr. Hutton was entirely unknown, except by character. At the time appointed, the competitors attended the Board of Examiners, by whom they were separately examined, to prevent any one from taking advantage of the examination of the others. Indeed nothing could be fairer, nor apparently more impartial on the part of the examiners,

nor could any examination be better conducted to answer completely the good and wise intentions of the Master-general. Every candidate was closely questioned in the several branches of the mathematical sciences; concerning their principles and properties; the knowledge and choice of books and authors, both ancient and modern; the various and best modes of teaching those sciences, with every other requisite that seemed necessary in the qualification for such an office. This examination occupied the whole day till late in the evening, and at its conclusion the examiners delivered to every candidate a large collection of very difficult problems, in the more abstruse parts of the mathematical and philosophical sciences, requesting their attendance again at the end of a week, with such solutions to those problems as they might be able to make out.

They met again accordingly; and though all his competitors were in a manner at home, among their friends, and in the midst of their books, to assist them in making out solutions to their problems, advantages of which Dr. Hutton was debarred by his peculiar situation, yet his knowledge and talents triumphed over all difficulties. In conclusion, the Board of Examiners drew up an unanimous report of their proceedings to the Master-general and board officers, stating, that though most of the candidates were sufficiently well qualified for the discharge of the duties of the office which was the object of their competition, yet that there was one among them, a Mr. Charles Hutton, whom they found it their duty in a more particular manner to recommend to his Lordship's notice, on account of the very able manner in which he had answered all their questions, and on account of his very extensive reading and acquirements.

A few days after, namely, on the 24th of May, 1773, Dr. Hutton received at his lodgings notice of his appointment to the office from the Master-general, who had never so much as heard of his name before. A noble example! and one well worthy of imitation.