make his days sufficiently long, of the shortness of which many complain.”

WARING (EDWARD), Lucasian professor of mathematics in the university of Cambridge, was descended from an ancient family at Mitton, in the parish of Fittes, Shropshire, being the eldest son of John Waring of that place. He was born in 1734, and after being educated at the free school at Shrewsbury, under Mr. Hotchkis, was sent on one of Millington's exhibitions to Magdalen college, Cambridge, where he applied himself with such assiduity to the study of mathematics, that in 1757, when he proceeded bachelor of arts, he was the senior wrangler, or most distinguished graduate of the year. This honour, for the securing of which he probably postponed his first degree to the late period of his twenty-third year, led to his election, only two years afterwards, to the office of Lucasian professor. 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 Newton, Saunderson, and Barrow, gave great offence to the senior members of the university, by whom the talents and pretensions of the new professor were severely arraigned. The first chapter of his "Miscellanea Analytica," which Mr. Waring circulated in vindication of his scientific character, gave rise to a controversy of some duration. Dr. Powell, master of St. John's, commenced the attack by a pamphlet of "Observations" upon this specimen of the professor's qualifications for his office. Waring was defended in a very able reply, for which he was indebted to Mr. Wilson, then an under-graduate of Peter House, afterwards sir John Wilson, a judge of the common pleas, and a magistrate justly beloved and revered for his amiable temper, learning, honesty, and independent spirit. 1760, Dr. Powell wrote a defence of his "Observations," and here the controversy ended. Mr. Waring's deficiency of academical honours was supplied in the same year by the degree of M. A. conferred upon him by royal mandate, and he remained in the undisturbed possession of his office. Two years afterwards, his work, a part of which had excited so warm a dispute, was published from the university press, in quarto, under the title of "Miscellanea Analytica

In

1 Godwin de Præsulibus, by Richardson.-Rapin's History.-Jortin's and Knight's Lives of Erasmus.-Burnet's Hist. of the Reformation.-Henry's Hist. of Great Britain, &c.

de Æquationibus Algebraicis et Curvarum Proprietatibus," with a dedication to the duke of Newcastle. It appears from the title-page, that Waring was by this time elected a fellow of his college. The book itself, so intricate and abstruse are its subjects, is understood to have been little studied even by expert mathematicians. Indeed, speaking of this and his other works, in a subsequent publication, he says himself, "I never could hear of any reader in England out of Cambridge, who took the pains to read and understand what I have written."

For his profession in life, Mr. Waring chose the study of medicine, and proceeded a doctor in that faculty in 1767. In 1771 he appears in the list of physicians to Addenbrooke's hospital in Cambridge; and about this time practised in the neighbouring town of St. Ives. But though he followed this pursuit with characteristical assiduity, and attended lectures and hospitals in London, he never enjoyed extensive practice. Of this he was the less careful, as, in addition to the emoluments, which are considerable, of his professorship, he possessed a very handsome patrimonial fortune, while his favourite science supplied him with an inexhausible fund of amusement and occupation. In 1776 he entered into a matrimonial connexion with miss Mary Oswell, sister of Mr. William Oswell, a respectable draper in Shrewsbury; and not many years afterwards retired from the university, first to a house in Shrewsbury, and at length to his own estate at Plealey, near Pontesbury. The mathematical inquiries which had occupied so large a portion of his early life, he still continued to cultivate with undiminished diligence; and he also occasionally indulged in philosophical excursions of a more popular and intelligible class. The result of these he collected in a volume printed at Cambridge, in 1794, with the title of "An Essay on the Principles of Human Knowledge." Under this comprehensive title are contained his opinions on a great variety of subjects. But this book, in the front of which he designates himself as fellow of the Royal Society of London, and of those of Bologna and Gottingen, was never published. Thus passed the even tenour of Dr. Waring's life, interrupted occasionally by a visit to the Board of Longitude, in London, of which he was a member, and from which he always returned with an encreased relish for his country retreat at Plealey and here he might have promised himself many years of life and health, when

his career was terminated by a short illness, produced by a violent cold caught in superintending some additions which he was making to his house. He died on the 15th of August, 1798, in the sixty-fourth year of his age.

Dr. Waring successively produced a number of pieces, of a like abstruse kind as his "Miscellanea Analytica,' such as the "Proprietates Algebraicarum Curvarum," published in 1772, the "Meditationes Algebraica," published in 1770, and the "Meditationes Analytica," which were in the press during 1773, 1774, 1775, and 1776. These were the chief and the most laborious works edited by the professor; and in the Philosophical Transactions is to be found a variety of papers, the nature of which may be seen from the following catalogue.

Vol. LIII. page 294, Mathematical Problems.-LIV. 193, New Properties in Conics.-LV. 143, Two Theorems in Mathematics.-LXIX. Problems concerning Interpolations. Ib. 86, A general Resolution of Algebraical Equations.LXXVI. 81, On Infinite Series-LXXVII. 71, On finding the Values of Algebraical Quantities by converging serieses, and demonstrating and extending propositions given by Pappus and others.-LXXVIII. 67, On Centripetal Forces. Ib. 588, On some Properties of the Sum of the Division of Numbers.-LXXIX. 166, On the Method of correspondent Values, &c. Ib. 185, On the Resolution of attractive Powers.-LXXXI. 146, On infinite Serieses.LXXXIV. 385-415, On the Summation of those Serieses whose general term is a determinate function of %, the distance of the term of the Series. For these papers, the professor was, in 1784, 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 they labour, in common with his other works, under the disadvantage of being clothed in a very unattractive form.

In his disposition and character, Dr. Waring is represented as of inflexible integrity, great modesty, plainness, and simplicity of manners; of a meekness and a diffidence of mind to such a degree, as to be always embarrassed before strangers. His extreme short-sightedness too, joined to a certain want of order and method in his mind, which appeared remarkably even in his hand-writing, rendered his mathematical compositions so confused and embarrassed,

1

that in manuscript they were often utterly inexplicable, a circumstance which may account for the numerous typographical errors in his publications.

We shall sum up this sketch of the life of Dr. Waring, with the concluding words of his "Essay on Human Knowledge," which contain a just and pleasing specimen of his genuine piety and unfeigned humility. "Should it please Providence to deprive me of the use of my Faculties, may I submit with humble resignation! May I for the future lead a life better in practice, and more fervent in devotion to the Supreme Being; and may God grant me his grace here, and pardon for my sins, when the trumpet of the great Archangel shall summon me to life again, and to judgement !"

WARNER (FERDINANDO), a very voluminous writer, was born in 1703, but where we are not told. He was of Jesus college, Cambridge, according to Mr. Cole, but we do not find his name among the graduates of that university. In 1730 he became vicar of Ronde, in Wiltshire; in 1746 rector of St. Michael Queenhithe, London, and in 1758 rector of Barnes, in Surrey. He also styles himself chaplain to the lord chancellor, and LL. D.; the latter title probably obtained from some northern university. He died Oct. 3, 1768, aged sixty-five. Dr. Warner was a laborious man, and having deservedly attained the character of judicious and useful writer, as well as a popular preacher, he was frequently engaged in compilations for the booksellers, which, however, he executed in a very superior manner, and gave many proofs of diligent research and judgment, both in his reflections and in the use he made of his materials. The following we believe to be a complete, or nearly complete list of his publications: 1. "A Sermon preached before the Lord Mayor, January 30, 1748." 2. "A Sermon preached before the Lord Mayor, on September 2," 1749. 3. "A system of Divinity and Morality, containing a series of discourses on the principal and most important points of natural and revealed Religion; compiled from the works of the most eminent divines of the Church of England," 1750, 5 vols. 12mo. This was reprinted in 1756, 4 vols. 8vo. 4. "A scheme for a Fund for the better Maintenance of the Widows and Children of the

1 Account of Shrewsbury, 1810, 12mo.-Gleig's Supplement to the Encyclopedia Britannica.-Hutton's Dict. new, edit.

clergy," 1753, 8vo. For this scheme, when carried into execution, he received the thanks of the London clergy, assembled in Sion college, May 21, 1765, and published another pamphlet, hereafter to be mentioned.

5. "An illustration of the Book of Common Prayer and Administration of the Sacraments, and other rites and ceremonies of the Church of England," &c. 1754, folio. In this year he took the degree of LL. D. probably, as we have already suggested, at some northern university. 6. "Bolingbroke, or a dialogue on the origin and authority of Revelation," 1755, 8vo. 7. "A free and necessary enquiry whether the Church of England in her Liturgy, and many of her learned divines in their writings, have not, by some unwary expressions relating to Transubstantiation and the real presence, given so great an advantage to papists and deists as may prove fatal to true religion, unless some remedy be speedily supplied; with remarks on the power of priestly absolution," 1755, 8vo. 8. In 1756 he published the first volume of his "Ecclesiastical History to the Eighteenth Century," folio; the second volume in 1757. This is the most valuable of all his works, and has frequently been quoted with approbation. 9." Memoirs of the Life of sir Thomas More, lord high chancellor of England in the reign of Henry VIII. 1758," 8vo. This is dedicated to sir Rabert Henley, afterwards lord chancellor Northington, who is complimented for the favours he had conferred on him on his receiving the seals; probably for the rectory of Barnes, with which he held Queenhithe and Trinity the Less. 10. "Remarks on the History of Fingal and other poems of Ossian, translated by Mr. Macpherson, in a letter to the right hon. the lord L- (Lyttelton)," 1762,

Svo.

11. "The History of Ireland, vol. I." 1763, 4to. He published no more of this, being discouraged by a disappointment in his expectations of some parliamentary assistance. Yet in one of those newspaper notices, which Dr. Warner did not disdain, he speaks of the encouragement which he met with when he went to Ireland in 1761 in search of materials for this work. He tells us of "the liberty granted him by the provost and fellows of the university to peruse the books and MSS. in the college library, as also those in the library of St. Sepulchre, founded by the late primate Marsh; and of his free access to the collections of Mr. Harris, which were purchased by the parliament, &c.; that he was likewise complimented with the