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learning considered to be connected with its mysteries. Among these were Cocker's Arithmetic, bound up with a treatise on algebra, and a work, written by Partridge, the famous almanack maker, on the calculation of nativities. During a visit paid by the pedlar to Bristol, Simpson studied these books with such ardour and assiduity, that on the former's return, he was struck with wonder at his progress; and, having cast his nativity, declared that, in two years, he would turn out a greater philosopher than himself. Upon this, Simpson gave up the business of a weaver, for that of fortune-teller, and in this capacity, soon became the oracle of the whole neighbourhood. At the same time, he added to his gains by opening an evening school; and, in a short time, he considered himself in a sufficiently flourishing condition marry. He chose for his wife his landlady, the tailor's widow, who is said to have been three times as old as himself at the time of their marriage. She presented him, however, with two children, having had the same number by her former husband, so that Simpson found himself encumbered with family before he had even commenced that career in which he afterwards became so distinguished. He continued to carry on his trade of fortune-teller and schoolmaster till an unfortunate circumstance, in connexion with the former, compelled him to quit the village, and induced him to relinquish that vocation altogether. A young girl, who was attached to a sailor at sea, applied to him to know what her sweetheart was about, either by having him presented to her in a vision, or by a conference with a spirit who might be able to give her the requisite information. To humour her credulity, Simpson engaged a confederate to attire bimself in the usual stage habiliments Appropriated to a spirit, and, upon a certain sign, to start out and answer such questions as might be put to him. The poor girl, however, was so terrified at the appearance of the pretended spirit, that she almost went out of her senses, and fell into such a state of illness and distraction that her life was despaired of. This excited the popular indignation so much against our conjuror, that he was forced to quit alto

a

gether that part of the country in which he resided, and retire to Derby.

He now resumed his occupation of a weaver, and also gave instructions to pupils in the evening, but still found great difficulty in providing for his family. The cares and vexations of poverty, however, seemed but to stimulate him to the acquisition of further knowledge. He was a constant reader of the Ladies' Diary, and it was in that periodical for 1736, that his first two mathematical questions were printed. They were both written in verse, and shew the author to have made, even at that time, no inconsiderable progress in mathematics. Arithmetic, algebra, and geometry, had been already mastered by him, in a sufficient degree to understand the contents of the Ladies' Diary; but of that branch of mathematical learning, called fluxions, or the differential calculus, he was entirely ignorant. The first account he read of it, was in the publication above-mentioned, and he immediately resolved upon making an attempt to become master of the subject; but here he found some difficulty; the only Treatise on Fluxions which had at that time appeared in English, being a very dear and scarce one, by Hayes; so that he found himself unable to procure a copy of it. In this emergency, he recollected that a friend had in his possession Stone's translation of the Marquis de l'Hopital's Analyse des Infinements Petits; and, having borrowed this book, he devoted himself to the study of it with so much perseverance and zeal, that, in a few years, he was enabled to compose a much more accurate treatise on fluxions than any before published in the English language.

With the manuscript of this treatise, and scarcely anything else, in his pocket, and without any letter of introduction, Simpson left Derby, and removed to London, in his twenty-fifth or

twenty-sixth year. He took up his residence in the neighbourhood of Spitalfields, working at his business by day, and teaching mathematics in the evening. In this latter employment, says his biographer, "his engaging method of instruction, and admirable talent for explaining and simplifying the difficulties of his subject, in a short time procured him notice and friends;

and his success was so considerable, that he was enabled to bring his family to town." His name becoming known, he ventured, in 1737, to announce the publication, by subscription, of his Treatise on Fluxions, and it accordingly appeared in that year, in quarto. His demonstration of the principles of fluxions, in this work, do not essentially differ from the method of Sir Isaac Newton, being entirely expounded by finite qualities.

Simpson now pursued the study of his favorite sciences with an industry worthy of his genius. In 1740, he published A Treatise on the Nature and Laws of Chance; to which are annexed full and clear investigations of two important problems, added to the second edition of Demoivre's Book on Chances, as also two new methods for the summation of series. This was succeeded, in the same year, by a quarto volume of Essays on several Curious and Interesting Subjects in Speculative and Mixed Mathematics. He was, shortly after, elected a member of the Royal Academy, at Stockholm; and, in 1742, appeared his Doctrine of Annuities and Reversions, deduced from evident and general principles, with useful tables, shewing the value of single and joint lives, &c. In the following year, he published An Appendix, containing Remarks on Demoivre's Book on the same subject, with Answers to some Personal and Malignant Representations in the Preface to it; to which Demoivre did not think fit to reply. In the same year, appeared his Mathematical Dissertations on a Variety of Physical and Analytical Subjects, dedicated to Martin Folkes, Esq., president of the Royal Society. In 1745, was printed his Treatise on Algebra; of which a second edition was subsequently published, with additions and improvements; among which was a new general method of resolving all biquadratic equations that are complete, or having all their terms. His next work was his Elements of Geometry, with their Application to the Mensuration of Superficies and Solids, to the Determination of Maxima and Minima, and to the Construction of a great variety of Geometrical Problems. This was first published in 1747; and, shortly

afterwards, its accuracy, in certain parts, was questioned by Dr. Robert Simson, professor of mathematics in the University of Glasgow, in the notes to the second edition of his Euclid. His objections were answered, by the subject of our memoir, in a second edition of the Elements; in the preface to which he also fully refuted a charge made against him by Mr. Muller, the professor of fortification and artillery at Woolwich, of having stolen soine part of his Elements from a work published by him. In 1748, Simpson published his Trigonometry, Plane and Spherical, with the Construction and Application of Logarithms; and, in 1750, his 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. This, we are told by the author, in his preface, is a new book, rather than a second edition of that which was published in 1737; in which he acknowledges that, besides errors of the press, there were several obscurities and defects arising from want of experience, and the many difficulties under which he then laboured. In 1752, appeared his Select Exercises for Young Proficients in the Mathematics; and, in 1757, he gave to the public his last work, entitled Miscellaneous Tracts; "a most valuable bequest," says Dr. Hutton; "whether we consider the dignity and importance of the subjects, or the sublime and accurate manner in which they are treated." Besides the above works, he was also the author of several papers in The Philosophical Transactions; but as the greater part of them will be found in his different publications, we do not here particularize them. He also proposed and solved many questions in The Ladies' Diaries, and was the editor or compiler of them from the year 1754 till 1760; during which time the work attained its highest degree of respectability. He is also said to have had a large share in the editing of two periodical works of a mathematical nature,-The Mathematician, and Tanner's Mathematical Exercises.

Having enumerated the various publications of Simpson, we resume the

narration of his life; the latter part of which, however, affords but few events to record. He was, in 1743, through the interest of Mr. Jones, father of Sir William, appointed professor of mathematics, in the Royal Academy of Woolwich; and, in 1745, he was elected a fellow of the Royal Society, on which occasion he was excused his admission fees, and from giving a bond for the usual future payments. When a plan was in agitation for building Blackfriars' Bridge, in 1760, he was consulted by the committee in regard to the best form of arches; and he gave his opinion, in favour of the semicircular form. His letters on this subject appeared, first, in some of the newspapers, and were afterwards collected and published in The Gentleman's Magazine. He continued to teach at the academy with great success till the approach of ill health, brought on, as it is said, by a too free use of gin and porter, induced his physician to advise him to try the air of his native place. Before, however, he left Woolwich, his constitution had suffered such a decline, and he had sunk into such a depression of spirits, that his mental faculties were, in a degree, impaired; and he was, at last, altogether incapable of performing his duty. He set out for Bosworth, in February, 1761; but, upon his arrival, grew gradually worse, and died on the following 14th of May.

"Simpson," says one of his biographers, "was not a man of much original or inventive talent; nor did he possess any quality of mind which would have made him one of the wonders of his time, if he had set out in life with the ordinary advantages. His writings are all able, generally useful, and sometimes ingenious; but

he is not to be enumerated among those who have carried science forward, or materially assisted in any of its great conquests. Not that he was, in point even of mental capacity, by any means an ordinary man, but there is an immeasurable interval between such men as Simpson, and those whose writings and discoveries are destined to influence and mould their own and all succeeding ages. His chief talent was great clearness and quickness of apprehension; and very much of this he owed to the eagerness and devotion with which he gave himself up to the study of whatever he wished to make himself master of, and the unrelaxed attention which he was consequently enabled to apply to it. His superiority principally lay in that passionate love of knowledge which prompted him to seek it in defiance of all impediments, and in that courage and perseverance with which he encountered and overcame, in their pursuit, a succession of difficulties which many would scarcely have had nerve enough to look in the face."

His private character appears to have been, upon the whole, amiable, though, it is said, he was in the habit of frequenting low company. It must be observed, however, as one of his biographers remarks, that the misconduct of his family put it out of his power to associate with the higher orders, or to procure better liquor than porter and gin. His engaging method of teaching procured him the esteem and friendship of his scholars at the academy, though he often became their butt, in consequence of his mildness and easiness of temper. He was survived by his widow, who was allowed, after his death, a pension of £200 per annum ; and, who, it is said, reached the extraordinary age of one hundred and two.

JAMES FERGUSON, the son of a daily labourer, was born in the year 1710, at a little village near Keith, in Banffshire. He learnt to read by listening to his brother's repetition of the Scotch catechism, and by afterwards

taking the book to a neighbouring old woman to explain to him the difficult words. His father afterwards taught him to write, and he was subsequently placed, for three months, at the grammar-school at Keith, which was all the

education he received. "His taste for mechanics arose," as he says, in an account of his own life, "from an odd accident. When about seven or eight years of age, a part of the roof of the house being decayed, my father, desirous of mending it, applied a prop and lever to an upright spar, to raise it to its former situation; and, to my great astonishment, I saw him, without considering the reason, lift up the ponderous roof, as if it had been a small weight. I attributed this, at first, to a degree of strength, that excited my terror as well as wonder; but thinking farther of the matter, I recollected that he had applied his strength to that end of the lever which was furthest from the prop; and finding, on inquiry, that this was the means whereby the seeming wonder was effected, I began making levers (which I then called bars); and, by applying weights to them different ways, I found the power gained by my bar was just proportion to the lengths of the different parts of the bar, on either side of the prop." Upon the same principle, he correctly imagined that, by appending a weight to the end of a rope, and winding it round the axle of a wheel, the power gained would be just as great as the wheel was broader than the axle was thick. The experiment was tried, and the result found to agree with his conjecture. With the assistance of an old turning lathe, belonging to his father, he made a number of wheels, and employed himself in constructing a variety of these machines. He then prepared an account of them; imagining it, as he says, "to be the first treatise of the kind that ever was written," till a gentleman, to whom the manuscript was shewn, convinced him of his error, by putting into his possession a treatise on mechanics. Ferguson, however, could not but be delighted to find that his own experiments agreed so well with those described in the book above-mentioned; and that he had, by his own unaided genius, discovered two of the most important elementary truths in mechanics -the lever, and the wheel and axle.

The subject of our memoir's first employment in life, was in the capacity of shepherd-boy. Whilst in the fields, he amused himself with making models of various mechanical objects, and at

night, wrapping himself up in a blanket, he lay down on his back, and contrived, by an invention of his own, to ascertain the apparent distances of the fixed stars. "My master," he says, "at first laughed at me; but when I explained my meaning to him, he encouraged me to go on; and, that I might make fair copies in the day-time of what I had done in the night, he often worked for me himself." His talents soon became known to the gentlemen in the neightbourhood; one of whom, Mr. Grant, of Achoynamey, offered to take him into his house, and make his butler give him lessons. The name of this butler was Cantley, under whose instructions Ferguson gladly put himself, and soon discovered his tutor to be a very extraordinary man. He had first fixed his attention by a sun-dial, which he happened to be painting on the village school-house, as Ferguson was passing by it, one day; but, on a further acquaintance with him, he found him conversant both with arithmetic and mathematics; that he played on every known musical instrument, except the harp; understood Latin, French, and Greek; and could let blood and prescribe for diseases. From Cantley, Ferguson received instructions in decimal fractions and algebra; and was just about to begin geometry, when the former quitted Mr. Grant, and the subject of our memoir returned home, in consequence, to his father.

Cantley, at parting with Ferguson, had made him a present of Gordon's Geographical Grammar; and, from a description of a globe, given in this book, though it was not illustrated by any figure, he contrived to make one in three weeks. Having turned a piece of wood into the shape of a ball, he covered it with paper, upon which he delineated a map of the world: the meridian ring and horizon were also made of wood, covered with paper, and graduated; and, with this globe, which was the first he had seen, he proceeded to the solution of various problems.

Finding that he was becoming an incumbrance to his father, Ferguson next entered into the service of a miller, in the hope that, in his employ, he should be enabled to find leisure to continue his studies. His master, however, being more fond of frequenting the ale-house

than the mill, not only threw upon him the entire business, but failed to supply him with sufficient food. At the end of a twelvemonth, therefore, having suffered considerably in his health from fatigue and bad living, he left the miller, and became a labouring servant with a person in the neighbourhood, of the name of Young, who followed the professions of a farmer and a physician. It was agreed, that the service which Ferguson might render in the farming department, was to be repaid by instruction in the practice of physic; but the doctor forgot his share of the contract; and Ferguson, after much ill treatment, returned home again at the end of three months.

He amused himself, during the recovery of his health, in making a wooden clock; and having succeeded in constructing one, which went tolerably well, he determined to try his hand upon a watch; and the manner in which he set about, and completed, his undertaking, is thus related in his own words; to vary or compress them would be an injustice to the subject of our memoir :-"Having, then," he says, "no idea how any time-piece could go but by a weight and a line, I wondered how a watch could go in all positions; and was sorry that I had never thought of asking Mr. Cantley, who could very easily have informed me. But happening, one day, to see a gentleman ride by my father's house (which was close by a public road), I asked him what o'clock it then was? He looked at his watch, and told me. As he did that with so much good-nature, I begged of him to shew me the inside of his watch; and, though he was an entire stranger, he immediately opened it, and put it into my hands. saw the spring-box, with part of the chain round it; and asked him what it was that made the box turn round? He told me that it was turned round by a steel spring within it. Having, then, never seen any other spring than that of my father's gun-lock, I asked how a spring within a box could turn the box so often round as to wind all the chain upon it? He answered, that the spring was long and thin; that one end of it was fastened to the axis of the box, and the other end to the inside of the box; that the axis was fixed, and that the box was

loose upon it. I told him that I did not yet thoroughly understand the matter. Well, my lad,' says he, 'take a long, thin piece of whalebone; hold one end of it fast between your finger and thumb, and wind it round your finger, it will then endeavour to unwind itself; and if you fix the other end of it to the inside of a small hoop, and leave it to itself, it will turn the hoop round and round, and wind up a thread tied to the outside of the hoop.' I thanked the gentleman, and told him that I understood the thing very well. I then tried to make a watch with wooden wheels, and made the spring of whalebone; but found that I could not make the wheel go, when the balance was put on, because the teeth of the wheels were rather too weak to bear the force of a spring sufficient to move the balance, although the wheels would run fast enough when the balance was taken off. I enclosed the whole in a wooden case, very little bigger than a breakfast tea-cup; but a clumsy neighbour, one day, looking at my watch, happened to let it fall; and turning hastily about to pick it up, set his foot upon it, and crushed it all to pieces; which so provoked my father, that he was almost ready to beat the man, and it discouraged me so much, that I never attempted to make such another machine again, especially as I was thoroughly convinced I could never make one that would be of any real use."

Ferguson now turned his attention to clock-repairing, as a means of subsistence, and had the satisfaction to find himself employed and encouraged by the principal gentry of the neighbourhood. One of his chief patrons was Sir James Dunbar, of Durn, at whose mansion he was introduced to the knight's sister, the Honourable Lady Dipple, who employed him to draw needle-work patterns for her. In this he succeeded so well, that other ladies in the neighbourhood gave him similar employment; and he says, "I began to think myself growing very rich, by the money I got for such drawings; out of which I had the pleasure of occasionally supplying the wants of my poor father." From drawing patterns, he proceeded to copying, with pen and ink, several of Sir James's pictures, which he executed with such taste, that