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 treatise 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 any thing 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. He now also ventured to announce the publication of his Treatise 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 exertions as a writer on his favourite

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.

Here, then, is an inspiring example, shewing how a man may triumph over almost any outward circumstances. Nor let it be said that such victories are reserved only for persons of extraordinary intellectual powers. We repeat that it is not genius, but resolution and perseverance, that are wanted. Simpson 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. This, indeed; is rather a habit of mind which may be acquired, than a talent that one must be born with; or at least it depends much more than many other sorts of talent on those moral qualities which may be excited and strengthened by proper discipline in every man. was here that Simpson's 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 this pursuit, a succession of difficulties, which many would scarcely have had nerve enough to look in the face. Among those

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born in the same rank of life to which he originally belonged, there are, undoubtedly, at all times, numbers who occasionally feel something of the ambition that animated him; and would at least be very glad if, without much trouble, they could secure for themselves the profit, and power, and enjoyment, attendant upon intellectual cultivation. But the desire dies away in them, and ends in nothing, because they have not fortitude enough to set earnestly and resolvedly about combating the obstacles which oppose its gratification. These obstacles appear, to their indolence and timidity, far more formidable than they really are. There are few cases in which they can be actually combined in greater force than they were in that of him whose history we have just sketched. It may be hoped, that it does not often happen in the present day, that a parent shall obstinately oppose his child's innocent and most praise-worthy efforts in the work of self-improvement. Instruction in the elements of learning, in reading, writing, and the rudiments of arithmetic, is already, or we trust soon will be, in our own country, within the reach of all; so that even the son of the poorest artisan or labourer has scarcely now, in any case, to begin life unprovided with what we may call the great passkeys to all literary and scientific knowledge. Thus furnished, his future progress depends upon himself; and any degree of proficiency is within his reach. Let those who doubt this reflect on what Thomas Simpson accomplished, in circumstances as unfavourable as can well be imagined. His first acquaintance with books was formed during moments stolen from almost incessant labour, and cost him his domestic peace, the favour of his friends, and, finally, the shelter of his father's roof. He never had afterwards either any master to instruct him, or any friend to assist him in providing for the necessities of the

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