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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,

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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 de

sire 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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passing day; but, on the contrary, when he wished to make himself acquainted with any new subject, he could with difficulty find a book out of which to study it, and had a family to support at an age when many have scarcely begun even to maintain themselves. Yet, with both his days and his evenings employed in toiling for a subsistence, he found time for intellectual acquisitions, such as to a less industrious and ardent student would have sufficed for the occupation of a whole life. This is a striking proof how independent we really are, if we choose, of those external circumstances which seem to make so vast a difference between the situation of man and man; and how possible it is for us in any situation at least to enrich our minds, if fortune refuse us all other riches. It is the general ignorance of this great truth, or indifference to it, that prevents it from being oftener exemplified; and it would be rendering a high ser vice to the human species, if we could awaken men's minds to a sufficiently lively trust in it, and a steady sense of its importance.

CHAPTER VII.

Self-educated Men continued. E. Stone; J. Stone.-Pursuits of Knowledge and Business united. Cicero; Jones; Cæsar; Scipio; Polybius; Frederick II.; Sully; De Thou; More; Selden; Hale; Grotius.

We have remarked that the book from which Simpson acquired his first knowledge of fluxions was a work by EDMUND STONE. Stone affords us another instance of a self-educated mathematician. Neither the place

nor the time of his birth is exactly known; but he was probably a native of Argyleshire, and born a few years before the close of the seventeenth century. He is spoken of as having reached an advanced age in 1760, and he died in 1768. The only account we have of his early life is contained in a letter, which is to be found prefixed to a French translation of one of his works, from his contemporary, the Chevalier Ramsay, who knew him. His father, Ramsay tells us, was gardener to the Duke of Argyle, who, walking one day in his garden, observed a Latin copy of Newton's 'Principia' lying on the grass, and thinking it had been brought from his own library, called some one to carry it back to its place. Upon this," (the narrative proceeds) "Stone, who was then in his eighteenth year, claimed the book as his own. 'Yours?' replied the Duke. Do you understand Geometry, Latin, and Newton?' I know a little of them,' replied the young The Duke was surprised; and, having a taste for the sciences, he entered into conversation with the

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