peared 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 perform ance; 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, showing 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 repcat 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. It was here that Simpson's superiority principally lay-in that pas sionate 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 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 praiseworthy 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 artizan or labourer has scarcely now, in any case, to begin life unprovided with what we may call the great pass-keys 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 mo.. ments 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 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 generaĺ ignorance of this great truth, or indifference to it, that prevents it from being oftener exemplified; and it would be rendering a high service to the human species, if we could awaken men's minds to a sufficiently lively trust in ìt, 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 nave 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 man. The Duke was surprised; and having a taste for the sciences, he entered into conversation with the young mathematician. He asked him several questions; and was astonished at the force, the accuracy, and the candour of his answers. But how,'

said the Duke, 'came you by the knowledge of all these things?' Stone replied, "A servant taught me, ten years since, to read. Does one need to know anything

more than the twenty-four letters in order to learn everything else that one wishes?' The Duke's curiosity redoubled he sat down on a bank, and requested a detail of the whole process by which he had become so learned. "I first learned to read,' said Stone; the masons were then at work upon your house. I approached them one day, and observed that the architect used a rule and compasses, and that he made calculations. I inquired what might be the meaning and use of these things, and I was informed that there was a science called arithmetic. I purchased a book of arithmetic, and I learned it. I was told there was another science called geometry; I bought the necessary books, and I learned geometry. By reading, I found that there were good books in these two sciences in Latin; I bought a dictionary, and 1 learned Latin. I understood, also, that there were good books of the same kind in French; I bought a dictionary, and I learned French. And this, my lord, is what I have done; it seems to me that we may learn everything when we know the twenty-four letters of the alphabet.'

Under the patronage of the Duke of Argyle, Stone, some years after this, made his appearance in London, where, in 1723, he published his first work-a "Treatise on Mathematical Instruments," principally translated from the French. In 1725 he was chosen a Fellow of the Royal Society. Next year appeared his Mathematical Dictionary, which was followed by other occasional productions down to the year of his death. Of his private history, however, after he took up his residence in the metropolis, little or nothing is known. It is to be feared that he spent his latter days in neglect and poverty. He had contributed several papers to the Transactions of the Royal Society; but we find his name omitted in the list of members, after the year 1742, probably in consequence of his inability to pay the small annual contribution which, we may remark by-the-bye, was a few years after remitted to Simpson, and which Sir Isaac Newton had, on his own petition, been excused from paying. He is spoken of, by a writer in the Critical Review for 1760, as of unblemished reputation; and yet, notwithstanding his