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 service 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; Poly. bius; 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 contempo rary, 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

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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 any thing more than the twenty-four letters in order to learn every thing else that one wishes?' The Duke's curiosity re-doubled: he sat down on a bank, and requested a detail of the whole process by which he had become so learned.

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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 I 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 every thing when we know the twentyfour 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 universally acknowledged abilities, and his uncontested services to the public," living, at an advanced age, unrewarded, except by a mean employment that reflects dishonour on the donors." Ramsay, in the letter already quoted, speaks in the strongest terms of Stone's simple, ingenuous, and upright character, and of his ardent and disinterested attachment to science. He was, however, by no means a man of the same powers of mind with Simpson. Even in those departments of learning in which he chiefly excelled, his knowledge appears to have been somewhat superficial; and his principal works have been characterized as abounding in errors, He seems, upon the whole, to have had rather a quick and active, than either a very profound or a very acute understanding; and some of his speculations are singularly unphilosophical, especially that contained in the last work he gave to the world, in which he attempts to expose the insufficiency of the proofs on which the spherical form of the earth has been assumed, arguing, with incredible absurdity, that it is just as likely to be an angular figure, as if the waters of the sea, for example, could any where maintain themselves in a position like that of the rafters of a house.

We may, perhaps, trace something of all this to the entirely unassisted and solitary efforts to which he owed his first acquaintance with science and literature. A want of depth and solidity is by no means the necessary or uniform characteristic of the attainments of the self-educated scholar; who, on the contrary, is apt to be distinguished for a more than usually perfect acquaintance with the subjects which he has studied with more than usual effort and application. But a mind gifted in a remarkable degree with the capacity of rapid apprehension, is just that which is likely to suffer most from being left to be altogether its own instructor; and especially when placed in circumstances which shut it out from that most salutary and strengthening of all intellectual exercises, communication and encounter with other intellects. This was Stone's case. He had not only no master, but no companions in his studies-no one even to put his knowledge to the proof, or with whom, by trying it, as it were, in conflict, he might discover either its strength or its weakness. Then, his facility in possessing himself of the outlines of a subject deceived and betrayed him: he skimmed its surface with so much ease and expedition, that he had no time to think of what was beneath, or that any thing was beneath; and thus he acquired a habit of precipitate procedure, and vague and unphilosophic thinking, in all his speculations. If he had had a few associates in his early pursuits, he probably would have escaped all this, as well as some other deficiencies under which he laboured during his life.

Our readers will be amused by a specimen of the ambitious rhetoric of his English style. He is talking, in the second edition of his book on Mathematical Instruments, published in 1760, of a newly-invented mariner's compass; and the following are the terms in which, at the close of his description, he expresses