dour and assiduity, that the pedlar, upon returning from his excursion, was quite confounded at his progress; and looked upon him as so marvellous a genius, that he proceeded forthwith to draw his horoscope, (to speak in the jargon of the art,) or, in other words, to calculate the position of the planets on the day he was born, in order that he might ascertain the splendid destiny in store for him. He predicted, that in two years more this miraculous pupil would actually turn out a greater philosopher than himself. After this, it cannot surprise us that our young aspirant should give himself to his occult studies with greater devotion than ever; and we find him, in fact, ere long commencing business as fortune-teller on his own account, and rapidly raising in reputation in that capacity until he became the oracle of the whole neighbourhood. He now gave up working as a weaver; but, to occupy his leisure, he added to his principal profession that of a school-master: so that, his gains being now considerable, he looked upon himself as in the secure high road to prosperity, and accordingly took to himself a wife in the person of his landlady, the tailor's widow, whom we have already mentioned. This was a somewhat singular match; for, if the account commonly given of the lady be correct, which account makes her die in the year 1782, at the age of one hundred and two, she must have been at the time of this her second marriage about three times as old as her husband. deed, as we have already observed, she had (beside a daughter) a son by her former husband two years older than her new one. Nevertheless it is recorded, that she presented the latter with two successive additions to the family-the juvenile portion of which (excluding the father) now consisted, therefore, of four individuals.

In

It is necessary to mention these circumstances, in

order to give a true picture of Simpson's situation at this period of his life, and of the multiplied difficulties through which he must have fought his way to the eminence he eventually attained. No starting-place for a literary career, one should think, could well be more awkward and hopeless, than that of a man who, beside many other disadvantages, had already a family to maintain before he had almost commenced his education, and no other means of doing so except a profession which necessarily excluded him from any association with the literary world in general, much more effectually than if he had eaten the bread of the humblest or most menial industry. It was quite necessary, indeed, that, if he was ever to give himself a chance either of advancement or respectability, he should exchange his trade of a fortune-teller and conjurer for some more reputable vocation, even although it should be, at the same time, a more laborious and less lucrative one. This desirable result, in fact, was at last brought about by one of those accidents, which so often in human life bring with them a temporary inconvenience only to turn a man into some path of permanent prosperity, which, but for this compulsion, he would have overlooked or never entered. Among the credulous persons who applied to Simpson to resolve, by his art, their doubts and misgivings touching the distant or the future, was a young girl, whose sweetheart, a sailor, was at the time at sea, and who wished to learn what he was about, either by having him presented to her in vision, or by a conference with a spirit who might be ble to give her the requisite information. It was resolved, therefore, to use the jargon of imposture, to raise a spirit; and, for this purpose, a confederate of the conjurer's was attired in certain terrific habiliments, and concealed among a quantity of straw in the corner of a hay-loft, that he might step forth on due

invocation. The sublime, however, had been carried a little too far in the decoration of this figure; for so passing hideous was the apparition, that it actually drove the poor girl almost out of her senses, and sent her off in such a state of illness and distraction that for some time her life was despaired of. The popular feeling was so strongly excited against Simpson by this misadventure, that he was obliged to leave that part of the country altogether; upon which he fled to the town of Derby, about thirty miles distant, determined to have nothing more to do with conjuring. Here he wisely returned to his original occupation of a weaver; and joining to his labours at the loom during the day, the teaching of a school at night, contrived for some time, though with much difficulty, to earn in this way a scanty subsistence for himself and his family.

It was during his residence at Derby, amid the fatigues of hard and unceasing labour, and the cares and vexations of poverty, that this extraordinary man made his most important advances in scientific knowledge. His principal source of information was the Ladies Diary,' of which he was a regular and attentive reader. It was in this publication that he first read of that branch of mathematical learning called Fluxions, or the Differential Calculus, the recent discovery of Sir Isaac Newton and Leibnitz; but the places in which it was noticed scarcely informed him of more than its name, and its immense importance in all the higher investigations of mathematics. But this was enough for such a mind as his. He determined to make himself master of the subject, and could not rest until he had possessed himself of the means of commencing the study of it. The only treaties on fluxions which had at that time appeared in English, was a work by an author of the name of Hayes; but it was a dear and somewhat scarce

book, so that he found it impossible to procure a copy of it. Fortunately, however, in the year 1730 appeared Edmund Stone's Translation of the Marquis de l'Hôpital's French work on the subject. This Simpson borrowed from a friend; and, immediately setting about the study of it with his characteristic ardour, prosecuted it with so much success that he not only made himself in a short time familiar with the new science, but qualified himself to compose a work of his own upon it, which, when published a few years after, turned out to be much more complete and valuable than either that of Hayes or that of Stone. When he had finished this performance, he set out for London, leaving his wife and family in the mean time at Derby. He reached the capital without even a letter of introduction, and with scarcely anything except his manuscript in his pocket. He was at this time in his twenty-fifth or twenty-sixth year. Having established himself in humble lodgings in the neighbourhood of Spitalfields, he maintained himself in the first instance, as he had been wont to do in the country, by working at his trade during the day, while he occupied his evenings in teaching mathematics to such pupils as he could procure. In this latter employment, 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. now also ventured to announce the publication of his "Treaties on Fluxions,' by subscription; and it accordingly appeared in quarto, in the year 1737. From this era, his fortunes and his celebrity went on steadily advancing. But the most remarkable and honourable part of his history is that which recounts his unwearied exertion as a writer on his favourite

He

subjects, after he had acquired a station and a regular income, as well as a degree of distinction which would have satisfied the ambition and relaxed the industry of many others whose early struggles had been so severe as his. We will just note the dates of his different publications. In 1737, as we have already observed, appeared his New Treatise of Fluxions.' In 1740 he produced two other works, also in quarto; the first entitled' A Treatise on the Nature and Laws' of Chance;' the second, Essays on several curious and interesting Subjects in Speculative and Mixed Mathematics." In 1742 appeared his 'Doctrine of Annuities and Reversion,' In 1743, he was principally through the interest of Mr. Jones, father of the celebrated Sir William Jones, and himself an able mathematician, appointed Professor of Mathematics at Woolwich; and the same year he gave to the world a large volume, entitled Mathematical Dissertations.' In 1745, he was admitted a Fellow of the Royal Society, on a recommendation signed by four of the most eminent mathematicians in England: and about the same time he published his Treatise on Algebra,' one of the most valuable and best known of his productions. His Elements of Geometry,' another very able work, and which has gone through many editions, appeared in 1747; his Trigonometry, Plane and Spherical,' in 1748; a new work on the differential calculus, called 'The Doctrine and Application of Fluxions,' in 1750; in 1752, his 'Select Exercises for Young Proficients in Mathematics,' another excellent and most useful performance; and finally, in 1757, his Miscellaneous Tracts.' To all these labours are to be added the papers he published in the Philosophical Transactions, and his contributions to the Ladies' Diary, of which he was for several years the editor. He died in 1761, in his fifty-first year.