to have been born, therefore, some time previous to the commencement of the seventeenth century. A very interesting account of his early life is to be found in a letter prefixed to a French translation of one of his works, from the Chevalier Ramsay, author of the Travels of Cyrus to Father Castel, a Jesuit, at Paris, and published in the Memoires de Trevoux. From this, it appears that Stone's father was gardener to the Duke of Arygle, and his son was, probably, one of his assistants in the service of that nobleman.

own.

The subject of our memoir had arrived at the age of eighteen, when the duke, walking, one day, in his garden, saw lying upon the grass a Latin copy of Newton's Principia, and, concluding it belonged to his own library, directed it to be carried back and placed there. This was about to be done, when Stone, stepping forward, claimed the book as his "Yours?" replied the duke; "do you understand geometry, Latin, and Newton?" "I know a little of them," answered Stone, modestly. The duke then entered into particular conversation with him, and requested to know how he had obtained his present knowledge. "A servant," said Stone, "taught me, ten years since, to read. Does one need to know any thing more than the twentyfour letters, in order to know every thing else that one wishes ?" The duke's curiosity was redoubled, and sitting down on a bank with Stone. the latter, at his request, thus proceeded in his account of himself:"I first learned to read: 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 general 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 twenty-four letters of the alphabet."

The duke now determined to draw Stone from his obscurity, and immediately provided him with an employment which left him in possession of ample time to follow his favourite pursuits. He, shortly afterwards, came to London, and published there, in 1723, his first work, A Treatise on Mathematical Instruments, chiefly translated from the French. In 1725, he was chosen a fellow of the Royal Society; and, in the following year, appeared his Mathematical Dictionary. In 1730, he published A Treatise on Fluxions; the direct method is a translation from the French of the Marquis de l' Hopital's Analyse des Infinements Petits; and the inverse method was supplied by Stone himself. In 1731, he gave a neat and useful edition of the Elements of Euclid, with an account of the life and writings of Euclid, and a defence of his Elements against modern objectors. Some smaller works came from his pen, which he communicated, together with an account of two species of the third order, not mentioned by Sir Isaac Newton or Mr. Stirling, to the Transactions of the Royal Society. After the year 1742, his name was omitted in the list of this body, in consequence, it is supposed, of his inability to pay the usual annual contribution. Of the manner in which he passed his latter days, we have no precise account; but he would to have died in neglect and poverty, as a writer in The Critical Review for 1760, describes him, notwithstanding his universally acknowledged abilities, and his uncontested services to the public, as "living, at an advanced age, unrewarded, except by a mean employment that reflects dishonour on the donors." His death took place in 1768.

seem

Stone possessed a simple, ingenuous, and upright character, and an ardent and disinterested attachment to science, though his knowledge was somewhat superficial, and his principal work contains many errors. His want of depth and solidity was, probably, owing to the rapid and unassisted manner in

which he pursued his studies, by which he contracted a habit of precipitate procedure, and vague and unphilosophic thinking, in all his speculations. His style was altogether such as might have been expected from a self-taught genius. In the second edition of his book on Mathematical Instruments, published in 1760, he has the following passage:-"The plants and trees of the garden of the arts and sciences, cultivated by the dung of ambition, and nourished with the waters of interest, are very subject to be blasted by the winds of error, and sometimes stunted by the weeds of imposition." Upon the whole, says a writer in The Library

66

of Entertaining Knowledge, Stone seems to have had rather a quick and active, than either a very profound or a very acute understanding;" and, as a proof of the unphilosophical nature of some of his speculations, the same authority notices 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."

JOHN BEVIS, the son of a gentleman who expended great part of his fortune in the service of King William, at the time of the revolution, was born near Old Sarum, in Wiltshire, in 1695. He was sent to complete his education at Christ's College, Oxford, where he studied medicine (for which profession he was intended), astronomy, and optics. Having taken his degree of M.D., he left the university for the continent; and, after making a tour through France and Italy, returned to England, and commenced the practice of his profession in London. Astronomy, however, still continued to occupy much of his time; and after his removal to Stoke Newington, where he had built an observatory, it may be said to have formed his chief pursuit. Here he carried on his researches with indefatigable zeal; and, from the volume he published, containing an account of them, it appears that, in the course of a night, he frequently observed the transits of one hundred and sixty stars. In 1745, he undertook to arrange and publish, by subscription, a work, entitled Uranographia Britannica, or an Exact View of the Heavens, on fiftytwo plates, similar to that of Bayer, representing the constellations and all the fixed stars that had been observed by astronomers, together with a consider able number that had been observed

only by himself. For the engraving of these plates, to each of which he wrote a particular explanation, he engaged one John Neale, who became bankrupt, after he had received several hundred pounds of the subscription money. The plates consequently fell into the hands of Neale's creditors, and afterwards were placed under the care of the court of Chancery, so that the author was deprived of the fruits of his labour, and the world of a most valuable addition to astronomical science. To increase the mortification of Dr. Bevis, the public imputed to him some connexion with Neale in his misconduct; indeed, the whole transaction produced an effect upon him which he ever afterwards felt.

He was more fortunate in his exertions to give to the world the astronomical tables of Dr. Halley, which had been left in the hands of the printer since 1725. Dr. Bevis published them in 1749, having himself supplied the auxiliary tables and precepts necessary in the use of them. The practical rules for finding the aberration of the stars in Mr. Thomas Simpson's Essays, were drawn up by the subject of our memoir, who, as Mr. Simpson remarks, proved, before any other person, that the phenomena are universally as conformable in right ascension, as Dr. Bradley found them to be in declination.

In September, 1764, he was appointed, by the board of longitude, conjointly with Mr. Witchell and Captain Campbell, to compute the observations made at Greenwich, and compare them with those made at Portsmouth, and other places, for the purpose of ascertaining the accuracy of Harrison's timekeepers. To the Philosophical Transactions he contributed twenty-seven valuable papers, containing chiefly astronomical observations, besides several articles to The Mathematical Magazine, particularly a curious paper on the satellite of Venus. His separate publications were two pamphlets, one entitled The Satellite Sliding Rule, for determining the immersions and emersions of the four satellites of Jupiter; and the other, An Experimental Inquiry concerning the Contents, Qualities, and Medicinal Virtues, of the Two Mineral Waters discovered at Bagnigge Wells, &c., with directions for drinking them, and some account of their success in very obstinate cases; which went through two editions. He also prepared, but never printed, a translation of Lalande's Astronomy; and such was his reputation among mathemati

some

cians, that Mr. Crakell dedicated to him his translations of Mauduit's Astronomé Sphérique. It was he who gave the name of achromatic to Dollond's improved telescope; an invention which induced Dr. Bevis to make curious experiments on the refractive power of glass, in the composition of which he had used a quantity of borax, and he found the refrangibility to be about as great as that of English crystal. A few years before his death, he removed from Stoke Newington to the Temple, and died there in November, 1771.

Dr. Bevis was a member of the principal foreign academies, and the names of few astronomers were more celebrated, both at home and abroad!, at the time of his decease. He had, in the course of his researches, discovered that the wire micrometer, the invention of which had been always claimed by the French, for Auzout, was due to Mr. Gascoyne, who had invented it in 1641, whereas Auzout's letter to Mr. Oldenburg, which only mentions his having used it to measure the sun's diameter, bears date the 28th of December, 1666.

THIS distinguished mathematician, descended from an ancient family in Argyleshire, and the son of a clergyman, who was minister of Glenderule, was born at Kilmoddan, in Scotland, in February, 1698. He lost both his parents at a very early age, but was carefully educated by his uncle, Mr. Daniel Maclaurin, minister of Kilfinnan. In 1709, he was sent to the University of Glasgow, where his application was so remarkable, that it introduced him to the society and friendship of many persons of high literary character, who afforded him unrestricted access to their libraries. He was directed to the study of mathematics by an accident; for having taken up a copy of Euclid's Elements, in a friend's chamber, though he had never yet looked into a mathematical work, he, in a few days, made himself master

of the first six books without the least assistance. He became enraptured with the science, and soon engaged himself in solving the most difficult problems. At the age of fifteen, he took the degree of M. A.; delivered publicly, upon the occasion, a thesis On the Power of Gravity; and, by the following year, he had invented many of the propositions which were afterwards published under the title of Geometrica Organica. He remained another twelvemonth in the university, chiefly occupied in the study of divinity, when he quitted Glasgow, and, returning to his uncle, devoted himself, with ardour, to his classical, and particularly his mathematical, studies.

At the end of 1717, he was elected, though only nineteen years of age, professor of mathematics in the Marischal College, at Aberdeen, and raised the

taste for the science he taught, to a height that it had never before attained in the university. In the vacation of 1719, he visited London, where he became acquainted with several eminent men, obtained the friendship of Sir Isaac Newton, and was admitted a member of the Royal Society. About the same time, he published his treatise, entitled Geometria Organica, in which he treats of the description of curve lines, by continued motion, and furnishes the mathematical student with many curious theorems. He again visited London in 1721; and, in the following year, became tutor to Lord Polwarth's eldest son, Mr. Hume, who was about to proceed upon his travels. He accompanied his pupil to Paris, and from thence to Lorraine, where he wrote a paper On the Percussion of Bodies, which, in 1724, gained the prize of the Royal Academy of Sciences, and of which the substance is inserted in his Treatise of Fluxions. From Lorraine they proceeded to Montpelier, where Mr. Hume being seized with a fever that terminated fatally, Mr. Maclaurin returned to Aberdeen, and resumed his professorship. Not long afterwards, he was pre-elected to succeed Mr. James Gregory, as mathematical professor in the University of Edinburgh, principally through the recommendation of Sir Isaac Newton, who offered to contribute £20 a-year towards a provision for Mr. Maclaurin till the chair became vacant. In November, 1725, he entered upon the duties of his office, which he discharged so ably, that the mathematical classes became unusually numerous. More than a hundred students attended his lectures annually; and, as these were of different standings, he was obliged to divide them into four or five classes, and to dedicate a full hour every day to each class, from the 1st of November to the 1st of June. In the first, or lowest class, he taught the first six books of Euclid's Elements, plain trigonometry, practical geometry, &c.; in the second, algebra, the eleventh and twelfth books of Euclid, spherical trigonometry, conic sections, and the general principles of astronomy; in the third, astronomy and perspective, and a part of Newton's Principia; and in the fourth, the system of fluxions, the doctrine of chances, and

His

the remainder of the Principia. lectures on these different subjects "were delivered," says his biographer, "with such perspicuity of method and language, that he seldom was under any necessity of repeating his demonstrations; but, so great was his anxiety for the improvement of his pupils, that if, at any time, they seemed not fully to comprehend his meaning, he would resume the demonstration in some other method, to try if, by laying it before them in a different light, he could give them a better view of it.'

Notwithstanding the close application required in his public avocations, his private studies were pursued with such constancy and ardour, as to make a considerable inroad upon his health. In 1728, he wrote a history of the progress which philosophy had made prior to the time of Newton; and to this he afterwards added proofs and, examples given by himself and others, and the whole was published, after his death, under the title of An Account of Sir Isaac Newton's Philosophical Discoveries. In 1733, he married Anne, daughter of Walter Stuart, solicitorgeneral in Scotland, by whom he had seven children; of whom, two sons and three daughters, together with his wife, survived him. In 1734, Dr. Berkeley endeavoured, in his Analyst, to explode the doctrine concerning the nature of fluxions, and brought against mathematicians generally, the charge of infidelity in religion. Maclaurin undertook a reply, but the performance grew so extensively in his hands, that, instead of a vindicatory pamphlet, he produced, in 1742, an entire Treatise on Fluxions, in two volumes, quarto; being the most profound and elaborate work ever published upon the subject. During the period he was employed in this production, he was also engaged as joint secretary, with Dr. Plummer, to a society in Edinburgh, for the improvement of medical knowledge, and produced many highly interesting papers, which were published in the Medical Essays and Philosophical Transactions. He likewise prepared, at the request of the Earl of Morton, a statement of the instruments and operations requisite in a survey of the Orkney and Shetland Islands; which, at his recommendation, was conducted by Mr. Short, the op

tician. In 1740, he received a second prize from the Royal Academy of Sciences, at Paris; his paper being A Resolution of the Problem relating to the Motion of the Tides from the Theory of Gravity; a question which had been given in the preceding year without receiving any solution.

One of Mr. Maclaurin's schemes for the improvement of geography and navigation, was the discovery of a passage from Greenland to the South Sea, by the north pole, of the existence of which he was so fully persuaded, as to declare that, if his situation would admit of such adventures, he would undertake the voyage, even at his own expense. He was preparing some memorials to government on the subject, but before he could finish them, the premium, offered by parliament, in 1744, was limited to the discovery of a north-west passage.

During the rebellion, in 1745, he exerted himself with remarkable energy to place the Scottish capital in a state of defence against the rebel army; and when the city was taken, an order being issued for all those who had defended it to swear allegiance to the Pretender, privately withdrew to England; but, previous to his escape, found means to convey a good telescope into the castle, and concerted a method of supplying its defenders with provisions. Dr. Herring (then Archbishop of York), hearing that Maclaurin was in England, sent an invitation to reside with him, which he readily accepted, and experienced from his host the greatest hospitality and kindness. In a letter to a friend, he says, "Here I live as happily as a man can do who is ignorant of the state of his family, and who sees the ruin of his country."

A fall from his horse, whilst he was escaping from Edinburgh, and the vicissitudes of weather to which he exposed himself on that occasion, had a baneful influence upon his constitution, which he never recovered. On his arrival in the Scottish metropolis, his disease was discovered to be dropsy in the abdomen; of which, after having several times submitted to the operation of tapping, he died, on the 14th of June, 1746.

Maclaurin was both a great and a

good man. The vigour of his mind was equalled by the benevolence of his heart; and it was justly said of him, that he strictly obeyed the commandments of God, and conformed to the laws of man. As a teacher, he was patient and persuasive; clear in his own ideas, and happy in his mode of communicating them to others. His highest merit, as a philosopher, consisted in his accommodating his studies to general utility; in applying his theories, in every possible case, to the beneficial operations of practice. Whenever any difficulty occurred in the execution of a public work, Mr. Maclaurin was always called upon to resolve it; and he determined some disputes of importance at Glasgow, respecting the gauging of vessels, by laying down rules on which the officers have ever since acted. His fondness for science was not only evinced in his communication of instruction to his pupils, but he often supplied them with money from his private purse, to further the utility of his advice and recommendations. In private life, he was remarkable for his benevolence, and for the warmth and constancy of his friendships, as well as for his sincere and ardent piety, which was strongly evinced in the calm resignation of his latest moments.

Mr. Maclaurin's communications to the Philosophical Transactions will be found in the different volumes of those collections, from Number Thirty to Number Forty-two, both inclusive. They are on the following subjects:on the construction and measure of curves; a new method of describing all kinds of curves; on equations with impossible roots; on the description of curves, with an account of farther improvements, &c.; an account of the annular eclipse of the sun, at Edinburgh, on the 27th of January, 1742-3; a rule for finding the meridional parts of a spheriod with the same exactness as of a sphere; and of the bases of the cells wherein the bees deposit their honey. His Treatise of Algebra, and Account of Sir Isaac Newton's Philosophical Discoveries, were published after his death, by the friends to whose judgment he had submitted the disposal of his manuscripts.