Being left in very narrow circumstances by the death of his father, he was obliged for his suppport to give private instruction to pupils; but he still continued his mathematical and astronomical pursuits, and in 1743 took his degree as master of arts, after having maintained two disputations, first, on the satellites of Jupiter, under the presidency of Celsius; and secondly, on the political system of Machiavel. Wargentin's principal object in his studies was to qualify himself for being lecturer on mathematics in the gymnasium of Hernösand. As a preparatory step to this situation, he wished to become a teacher of astronomy in the academy of Upsal; and with that view he maintained a disputation on the improvement made in astronomy from the beginning of the last century. He attained his object, and about this period his merit began to become known to the public in general, and to some of the learned societies in foreign countries. He had already calculated new tables of Jupiter's satellites, which were inserted in the Transactions of the Society of Upsal for the year 1741, and on that account he was admitted a member. These and a literary correspondence, which after the death of Celsius, he began with some of the French astronomers, such as Monnier, De l'Isle, and others, procured him in 1743 the honour of being appointed by the Royal Academy of Sciences at Paris one of its correspondents, and in the same year he was nominated a member. In 1748 he was appointed by King Adolphus Frederic to the place of a philosophical adjunct in the Academy of Upsal; and on the death of Elvius, secretary to the academy of sciences, in 1749, he was chosen his successor, and continued to discharge the duties of this post with great diligence for thirty-four years. So early as 1741 Wargentin had calculated tables for the four satellites of Jupiter, taking those of Cassini the elder as the foundation, and correcting them by a multitude of observations collected from different works or made by himself and Celsius; but having occasion to go to Stockholm, his trunk was unfortunately stolen by the way, and along with it his tables, together with the greater part of the property which he then possessed. He had now no other resource than to resume his labour, which he accordingly did; and with the help of a few memorandums and scraps of paper left at Upsal, he was at length

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printed in the Transactions of the Society for the year 1741; and were received with much approbation by all foreign astronomers, in consequence of the exactness with which they represented the actual motion of that planet. When these tables were published, Wargentin promised to communicate separately the obser vations he had used in the construction of them, in order that a comparison might be made between them. This promise, in regard to the first satellite, he performed in the Transactions of the Society for 1742, in which he gave above a thousand observations made by various astronomers, which he compared with his tables, and found that the difference seldom amounted to a minute of time, but for the most part to less. In the same Transactions, for 1743, he inserted about four hundred observations of the other satellites, also compared with the tables, in which the difference seldom amounted to four minutes of time, but for the most part to less. After this period, the theory of Jupiter and his moons, and the improvement of it, continued to be the chief object of his labour and industry, during the remainder of his life, so that when he had any leisure from his other occupations, he employed it in bringing his tables to a greater degree of perfection. A longer course of observations and the comparison of them with preceding ones could not fail to suggest to him new changes, by which it was necessary that his tables should be corrected. On this account he undertook a revision of them with improvements, up to the year 1753; and when these new tables of the four satellites were completed, he transmitted a copy of them to De la Lande, who in 1759 inserted them in a new edition of Halley's tables published at Paris. These tables he still farther improved afterwards; and in 1769 sent a copy of them to Dr. Maskelyne, by whom they were published in the Nautical Almanac for 1771. They were published also, with farther improvements, the same year, by De la Lande, along with his own astronomical tables; and another edition of them, but somewhat different from the latest Paris edition, appeared at Berlin in 1776. Farther proofs of Wargentin's assiduity and zeal for the advancement of this part of astronomy may be seen in the Connoissance des Mouvements celestes for 1766, the Nautical Almanac for 1771 and 1779, and the Astronomisches Jahr-buch for the years 1777, 1779, 1781, and 1782, in which he gives an account of the new changes he found it neces-sary to make in the equations of some of the

satellites. The result of his last labour, in regard to these tables, was communicated to the public in the fourth volume of the Nova Acta Societatis Litteraria Upsaliensis, in which he gave 1250 observations of the third satellite, with various remarks on the irregularities of its motion indicated by them. Besides the above works, Wargentin contributed to the Transactions of the Royal Academy of Sciences a number of papers on different subjects, amounting all together to sixty. In one of the first he undertook to compare the periods of the revolution of Jupiter's moons; their conjunctions, quadratures, and other phenomena with each other, and with the equation which, in such cases, he had found by the tables to correspond with them; in order that he might thence discover how far they perturbed each other in their motion. All the rest of his papers, besides the above, and another written in 1744, on the velocity of the rays of light, were composed by him after he became secretary to the Academy. A great part of them relate to the history of the sciences; such as on thermometers and the best kinds of them; on the attempt made to determine the real figure of the earth; on the parallax of the fixed stars and the experiment made to discover it; on logarithms; on the flux and reflux of the sea; on comets; on the use of ventilators on board ship; on the northern lights. All these papers, which are written in an easy and familiar style, suited to such subjects, display great soundness of judgment, as well as extensive knowledge. Another part of them treats of climate and the differences of it. In these, besides other useful observations, Wargentin remarks, in general, that milder and colder winters, summers more or less warm, earlier or later springs and autumns, depend not only on the greater or less degree of latitude of the place, but also on other circumstances; such as the vicinity of the sea, lakes, marshes, large woods, uninhabited desarts, and other things; from which he deduces this conclusion, that the climate of Sweden is much more temperate than many others lying under the same parallel. Other papers contain observations of solar and lunar eclipses, and of the comets of the years 1769 and 1771. In some also he treats of parallactic observations of the sun and moon, together with calculations in regard to the distance of these luminaries from the earth, undertaken in consequence of De la Caille's corresponding observations made at the Cape of Good Hope, in the year 1751. In these he discusses with great ability the principles of such parallactic

VOL. X.

researches, and the precautions necessary to be observed in them. Though the parallax of the sun, as calculated by Mr. Wargentin from his own and De la Caille's corresponding observa-* tions, and which he found to be 10" 50", was too large by 2" 40", as was afterwards proved by the transit of Venus over the sun's disk ob served in 1769, it was the most accurate ever before obtained, and on that account was published in the third volume of the Memoires de Mathematique et de Physique presentés à l'Academie Royale des Sciences. Wargentin's observations of the transit of Mercury over the sun, on the 3d of May 1753, which were inserted in the Swedish Transactions of that year, deserve also to be mentioned. In the same work may be found two papers on the transits of Venus over the sun's disk, in the years 1761 and 1769, and the arrangements made in Sweden for observing them. Wargentin turned his attention likewise to magnetic phenomena; and in the Transactions for 1750. gave some observations on the variation of the magnetic needle, during an extraordinary bright appearance of the northern lights, and pointed out some connection between these two phenomena, from which it appears that the varia tions are violent in proportion to the intensity of the lights. A similar remark was made by Celsius at Upsal in 1740, and published in the Transactions of the Academy. Wargentin communicated his observations to Mr. Morton, who caused them to be published in the Philosophical Transactions. He furnished also to the Academy of Sciences a great many tables in regard to births and deaths, as well as population in general, collected from observations made not only at Stockholm, but in various other places, and by these means rendered considerable service to this important branch of political economy. He maintained an epistolary correspondence with many of the European literati, during the whole time of his being secretary to the Academy; and his astronomical labours procured him so much respect, that all those who applied to the practical part of that science were careful to communicate to him their observations, and in particular those relating to the satellites of Jupiter. Other mathematicians also were happy in transmitting to him their discoveries, and by these means his correspondence was considerably increased. Wargentin was a man of great integrity, modest and friendly in his disposition; zealous for the advancement of science, and ever ready to make any sacrifice which could tend to promote the good of his country. In consequence of his

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merit he was created by King Adolphus Frederic, in the year 1759, a knight of the Polar Star; and he was a Fellow of the Royal Society of London and member of the Academies of Petersburgh, Paris, Gottingen, Copenhagen, and of other learned bodies. Wargentin was not distinguished by great brilliancy of genius; but he possessed an excellent understanding, combined with great readiness in comprehending every thing which required patient or laborious examination. He was exceedingly diligent, and seldom indulged even in those innocent amusements which are necessary to recreate the mind after intense labour. By regularity and temperance he preserved good health to an advanced period of life; but in his latter years his sight and hearing began to fail, which is not surprising, when it is considered how much he exposed himself to the open air in a severe climate, while making observations. Neither his spirits nor strength, however, seemed to decline till the summer of 1783, when he was attacked by a diabetes, which, notwithstanding every medical assistance, terminated in his death, in the month of December the same year. The following papers by him were printed in the Philosophical Transactions. On the Variation of the Magnetic Needle, vol. xlvii.; Observations on the Transit of Venusover the Sun, on June 6th, 1761, and on the Eclipse of the Moon, May 8th, 1761, taken in Sweden, vol. lii.; An Account of the Observations made on the Transit of Venus over the Sun, June 6th, 1761, at Ajaneburg in Sweden, ibid.; Relation of the Transit of Venus, vol. liii.; An Essay on a new Method of determining the Longitude of Places from Observations of the Eclipses of Jupiter's Satellites vol. Ivi.; Meteorological Observations made at Stockholm, in the Winter of 1767-8, vol. lviii. ; Observations on the Transit of Venus, June 3d, 1769, in Sweden, vol. lix.; Observations on the Occultation of some Stars by the Moon, vol. lxv.; On the Difference of Longitude of the Royal Observatories of Paris and Greenwich, resulting from the Eclipse of Jupiter's first Satellite, observed during ten Years, with a comparative Table of the corresponding Observations of the first Satellite, made in the principal Observatories, vol. lxvii.; Aminnelse-Tal hällit för Kongl. Vetenskaps Academien. Philosoph. Transactions. - J.

WARING, EDWARD, M.D. Lucasian professor of mathematics in the University of Cambridge, was descended from an ancient family at Milton, in the county of Salop. He was born in 1734, and after being educated at

Shrewsbury free-school, was sent to Magdalencollege, Cambridge, where he applied himself with so much diligence to the study of the mathematics, that when he took his first degree, in 1757, he was considered as a prodigy in those branches of science which form the subject of the bachelor's examination. Two years after he was elected Lucasian professor, but the appointment of a young man, scarcely twenty-five years of age, and still only a bachelor of arts, to a chair which had been honoured by the names of a Newton, a Saunderson, and a Barrow, gave great offence to some of the senior members of the university; and the first chapter of his "Miscellanea Analytica," which he circulated in vindication of his scientific character, produced a controversy of some duration. Dr. Powell, master of St. John's, commenced the attack, by a pamphlet containing observations upon this specimen of the professor's qualifications for his office. Waring was defended in a very able reply by Mr. Wilson, afterwards Sir John Wilson, a judge of the common pleas, and a magistrate justly esteemed for his eminent and amiable qualities. In 1760, Dr Powell wrote a defence of his observations, with which the controversy terminated; and Waring's deficiency of academical honours was supplied, the same year, by the degree of master of arts, which was conferred upon him by royal mandate. In 1762 his "Miscellanea Analytica," a part of which had excited so warm a dispute, was published from the university press in quarto, with a dedication to the Duke of Newcastle. This work, written upon the abstrusest parts of algebra, extended his fame over all Europe. He was elected, without solicitation, member of the societies of Bologna and Gottingen, and he received very flattering marks of esteem from the most eminent mathematicians, both at home and abroad. Of the nature of this miscellany the best idea will be formed from the author's own words: "I have myself wrote," says he, " on most subjects in pure mathematics, and in these books inserted nearly all the inventions of the moderns with which I was acquainted. In my prefaces I have given a history of the inventions of the different writers, and ascribed them to their respective authors, and likewise some account of my own. To every one of these sciences I have been able to make some additions, and in the whole, if I am not mistaken in enumerating them, somewhere between three and four hundred new propositions of one kind or other, considerably more than

have been given by any English writer; and in novelty and difficulty not inferior; I wish I could subjoin, in utility. Many more might have been added, but I never could hear of any reader in England out of Cambridge, who took the pains to read and understand what I have written. But I must congratulate myself that D'Alembert, Euler, and Le Grange, three of the greatest men in pure mathematics of this or any other age, have since published and demonstrated some of the propositions contained in my "Meditationes Algebraicæ," or "Miscellanea Analytica," the only book of mine they could have seen at that time; and D'Alembert and Le Grange mention it as a book full of excellent and interesting discoveries in algebra. Some other mathematicians have inserted some of them in their publications. The reader will excuse my saying so much, there being some particular reasons which influenced me." But notwithstanding the early and uncommon progress which Mr. Waring made in mathematics, they did not engross the whole of his attention. He devoted some part of his time to the study of medicine, which he intended to be his future profession, and in 1767 he took his degree as doctor; but though he followed this pursuit with his usual assiduity, and attended lectures and hospitals in London, it does not appear that he ever enjoyed extensive practice. It is indeed said, that he was so embarrassed in his manners before strangers, that he could not have made his way in a profession, in which so much depends on address. But this was of the less consequence, as, in addition to the emoluments of his office, he possessed a very handsome patrimonial fortune, and his favourite science supplied him with an inexhaustible fund of amusement and occupation. His time was spent chiefly in scientific discoveries, and in attending to the publication of them, either in the Philosophical Transactions, or in separate volumes. He resided some years after taking his doctor's degree at St. Ives in Huntingdonshire, and in 1776 married; but the air of Cambridge, to which he had then removed, not agreeing with Mrs. Waring's constitution, he went to live on his own estate at Plaisley, about eight miles from Shrewsbury, where he continued to cultivate with unabated diligence those mathematical enquiries which had occupied so considerable a portion of his early life. He applied also occasionally to studies of a more popular and familiar nature, the result of which he collected and printed at Cambridge

in 1794, under the title of "An Essay on the Principles of Human Knowledge." But this work, which contains his opinions on a great variety of subjects, was never published. The general tenor of Dr. Waring's life was seldom interrupted, except by a visit now and then to the Board of Longitude in London, of which he was a member, and from which he always returned with an increased relish for his country retreat. A violent cold, caught while superintending some additions he was making to his house, caused his death, after a short illness in August 1798, in the sixtyfourth year of his age. Dr. Waring was a man of inflexible integrity as well as great modesty, and in his manners exceedingly simple and plain. Those who knew the superiority of his understanding from his writings, looked up to him with reverence; but he enjoyed himself in domestic circles with those chiefly among whom his talents could not be the object of either admiration or envy.

In regard to his writings, he is, according to his own account, the discoverer of nearly four hundred propositions in the analytics. This may appear as a vain-glorious boast, especially as the greater part of these discoveries, from their abstruse nature, are likely to sink into oblivion; but he was in a manner compelled to make it, by the insolence of Lalande, the celebrated French astronomer, who in his Life of Condorcet asserts, that, in 1764, there was no first-rate analyst in England. In reply to this assertion, the professor, in a letter to Dr. Maskelyne, first mentions with proper respect the inventions and writings of several celebrated British mathematicians, of whom two were living in 1764; and then gives a full and impartial detail of his own discoveries, many of which were published prior to 1764. By mathematicians, this account which was not published by the professor himself, is allowed to be very little if at all exaggerated. Yet, if according to his own acknowledgement, "few thought it worth while to read even half of his works," there must be some ground for this neglect, either in the difficulty of the subject, the unimportance of the discoveries, or some defect in the communication of them to the public. The subjects are certainly of a difficult nature, and the calculations are abstruse, but Europe contained many persons who were not to be deterred by the most abstruse calculations. The neglect, therefore, complained of, is to be ascribed chiefly to a perplexity both in the style and manner. The reader is stopped at

every instant, first to make out the author's meaning, and then to fill up some chasm in the demonstration. He must invent anew every invention; for after the enunciation of the theorem or problem, and the mention of a few leading steps, little farther assistance is afforded. His principal works, besides those already mentioned, are "Meditationes Algebraica," published in 1770; " Proprietates Algebraicarum Curvarum," 1772; and "Meditationes Analytica," which were in the press during the years 1773, 1774, 1775, and 1776. To the Philosophical Transactions he contributed a variety of papers, which alone would be sufficient to give him a conspicuous place in the scale of mathematicians. They are under the following titles: Mathematical Problems, vol. liii. p. 294.; New Properties in Conics, vol. liv. p. 193.; Two Theorems in Mathematics, vol. lv. p. 143.; Problems concerning Interpolations, vol. lxix. p. 86.; A General Resolution of Algebraical Equations, vol.lxxvi. p. 80.; On Infinite Series, vol. lxxvii. p. 71.; On finding the Values of Algebraical Quantities by Converging Serieses, and demonstrating and extending Propositions given by Pappus and others, vol. lxxviii. p. 67.; On Centripetal Forces, ibid. 588.; On some Properties of the Sum of the Division of Numbers, vol. lxxix. p. 166.; On the Method of Correspondent Values, &c. ibid. p. 185.; On the Resolution of Attractive Powers, vol. Ixxxi. p. 146.; On Infinite Serieses, vol. lxxxiv. p. 385-415. For these papers the professor, in 1784, was deservedly honoured by the Royal Society with Sir Godfrey Copley's medal, and most of them afford very strong proofs of the powers of his mind both in abstract science and the application of it to philosophy, though in common with his other works they have the disadvantage of being clothed in a very unengaging dress. Nichols's Literary Anecdotes of the Eighteenth Century. Pantalogia.-J.

WARNERY, CHARLES EMANUEL, a writer on military tactics, was born at Morges in the Pays de Vaud, in 1719. At the age of fourteen he entered into the service of Sardinia, and some time after quitted it for that of Prussia, in which he was a lieutenant-colonel at the commencement of the seven years' war. He distinguished himself so much, that he was decorated with the order of merit; but having been in Schweidnitz in 1758, along with Generals Sers and Grumkow, who gave up that fortress, he thought himself obliged to request leave to resign, and he quitted the service of

Prussia for that of Poland, in which he obtained the rank of Major-general. After this, he purchased an estate in Silesia to which he retired, and devoting his time to study and rural economy, lived as a private individual. In 1771 he caused to be printed at Breslau, "Remarks on the Military System of the Turks and on their Method of Fighting, with Observations on the Austrian and Russian Expeditions into Turkey." Three years after, he sent some memoirs of the same nature to Busching, who inserted them in the sixteenth volume of his magazine. In 1782 he published at Warsaw, "Remarks on the Tactics. of Guibert," and afterwards "Remarks on the Commentaries of Count Turpin on the Memoirs of Montecuculi." He died in 1786, a few months before Frederic II. His history of the seven years' war was published after his death, under the following title: "Campagnes de Frederic II. Roi de Prusse de 1756 à 1762," à Vienne, 1788, 8vo. This work, though not well written, is curious and interesting. Frederic II. always appears in it with that strength of mind which he was universally allowed to possess; but it is seen, at the same time, that he was inclined to listen to advice and to consult persons of talent and skill. La Prusse Littéraire sous Frederic II. par l'Abbé Denina. — J.

WARTON, JOSEPH, D.D. a distinguished writer in poetry and polite literature, born in 1722, was the eldest son of the Rev. Thomas Warton, poetry-professor at Oxford, and vicar of Basingstoke. He received his early education chiefly under his father; and at the age of 14 was admitted on the foundation at Winchester-school, where he continued till 1740, when he was entered of Oriel-college, Oxford. In this situation he studiously cultivated his literary taste, and composed some pieces of poetry which afterwards appeared in print. After taking the degree of B.D. he became curate to his father at Basingstoke, where he officiated two years; and in 1746 he removed to a similar employment at Chelsea. In the same year he published a small volume of "Odes," one purpose of which he represented in his preface to be, to wean the public from an exclusive taste for moral and didactic poetry, which was then prevalent, and bring back the art to its proper channel of invention and description. In 1748 he was presented by the Duke of Bolton to the rectory of Winslade, and soon after married. He accompanied his patron in 1751 on a tour to the south of France; before which period he had com