mathematician to fill the chair of Barrow, Newton, Whiston, Cotes, and Saunderson; and the defect in his honorary titles was supplied by royal mandate, through which he became master of arts in 1760, and shortly afterwards was appointed Lucasian professor.

Mr Waring was originally intended for the medical profession, and took his degree of M. D. in 1767; he never attempted, however, to practise a profession for which he could not acknowledge any enthusiasm, and for which, indeed, he was in a great measure unqualified by a certain mauvaise honte of manner which he never could get over. He passed his life in the study of the abstract sciences, and chiefly on his own estate at Plaisley near Shrewsbury, where he died in August, 1798. "Wishing to do ample justice to the talents and virtue of the professor," says an able cotemporary of his own, "we feel ourselves somewhat at a loss in speaking of the writings by which alone he will be known to posterity. He is the discoverer, according to his own account, of nearly four hundred propositions in the analytics, and the account is scarcely exaggerated; yet we have reason to believe that the greater part of these discoveries will sink into oblivion; and that posterity will be as little attentive to them as his own cotemporaries. If, according to his own confession, few thought it worth their while to read even half of his works,' there must be some grounds for this neglect, either from the difficulty of the subject, the unimportance of the discoveries, or a defect in the communication of them to the public. The subjects are certainly of a difficult nature, the calculations are abstruse, yet Europe contained many persons not to be deterred by the most intricate theorems. Shall we say then that the discoveries were unimportant? If this were really the case, the want of utility would be a very small disparagement among those who cultivate science with a view chiefly to entertainment and the exercise of their rational powers. We are compelled then to attribute much of this neglect to a perplexity in style, manner, and language; the reader is stopped at every instant, first to make out the writer's meaning, then to fill up the 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 steps, little assistance is derived from the professor's powers of explanation. Indeed, an anonymous writer, certainly of very considerable abilities, has aptly compared the works of Waring to the heavy appendages of a Gothic building, which add little of either beauty or stability to the

structure.

"A great part of the discoveries relate to an assumption in Algebra, that equations may be generated by multiplying together others of inferior dimensions. The roots of these latter equations are frequently terms called negative, or impossible; and the relation of these terms to the coefficients of the principal equation is a great object of inquiry. In this art the professor was very successful, though little assistance is to be derived from his writings, in looking for the real roots. We shall not, perhaps, be deemed to depreciate his merits, if we place the series for the sum of the powers of the roots of any equation, among the most ingenious of his discoveries; yet we cannot add, that it has very usefully enlarged the bounds of science, or that the algebraist will ever find occasion to introduce it into practice. We may say the same on many ingenious transformations of equations, on the discovery of im

possible roots, and similar exertions of undoubtedly great talents. They have carried the assumption to its utmost limits; and the difficulty attending the speculation has rendered persons more anxious to ascertain its real utility; yet they who reject it may occasionally receive useful hints from the Miscellanea Analytica.'

"The first time of Waring's appearing in public as an author, was, we believe, in the latter end of the year 1759, when he published the first chapter of the Miscellanea Analytica,' as a specimen of his quali fications for the professorship; and this chapter he defended, in a reply to a pamphlet (by Dr Powell) entitled, 'Observations on the first Chapter of a book called Miscellanea Analytica.' Here the professor was strangely puzzled with the common paradox, that nothing divided by nothing may be equal to various finite quantities, and has recourse to unquestionable authorities in proof of this position. The names of Maclaurin, Saunderson, De Moivre, Bernouilli, Monmort, are ranged in favour of his opinion; but Dr Powell was not so easily convinced, and returns to the charge, in the Defence of the Observations;' to which the professor replied in a 'Letter to the Rev. Dr Powell, Fellow of St John's College, Cambridge, in answer to his Observations, &c.' In this controversy, it is certain that the professor gave evident proofs of his abilities; though it is equally certain that he followed too implicitly the decisions of his predecessors. No apparent advantage, no authority whatever, should induce mathematicians to swerve from the principles of right reasoning, on which their science is supposed to be peculiarly founded.

"The Proprietates Algebraicarum Curvarum,' published in 1772, necessarily labour under the same defects with the Miscellanea Analytica, the Meditationes Algebraicæ,' published in 1770, and the Meditationes Analytica,' which were in the press during the years 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, which alone would be sufficient to place him in the first rank in the mathematical world.'

"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. The mathematician who has resolution to go through them, will not only add much to his own knowledge, but be usefully employed in dilating on those articles for the benefit of the more general reader. We might add in this place a work written on

The nature of them 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-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 Series -lxxxiv. 385-415, On the Summation of those Series whose general term is a determinate function of z, the distance of the term of the Series.

morals and metaphysics in the English language; but as a few copies only were presented to his friends, and it was the professor's wish that they should not have a more extensive circulation, we shall not here enlarge upon its contents.

"In the mathematical world the life of Waring may be considered as a distinguished era. The strictness of demonstration required by the ancients had gradually fallen into disuse, and a more commodious though almost mechanical mode by Algebra and Fluxions took its place, and was carried to the utmost limit by the professor. Hence many new demonstrations may be attributed to him, but four hundred discoveries can scarcely fall to the lot of a human being. If we examine thoroughly those which our professor would distinguish by such names, we shall find many to be mere deductions,-others, as in the solution of biquadratics, anticipated by former writers. But if we cannot allow to him the merit of so inventive a genius, we must applaud his assiduity; and, distinguished as he was in the scientific world, the purity of his life, the simplicity of his manners, and the zeal which he always manifested for the truths of the gospel, will entitle him to the respect of all who do not esteem the good qualities of the heart inferior to those of the head."

James Boswell.

BORN A. D. 1740.-DIED A. D. 1799.

JAMES BOSWELL was born at Edinburgh, on the 29th October, 1740. He was the eldest son of Alexander Boswell of Auchinleck, the representative of a very ancient and respectable family, and one of the senators of the college of justice, the supreme civil court in Scotland. He received his early education at the schools and in the university of Edinburgh, where his father's professional pursuits necessarily fixed his residence. During his attendance at the university, the powers which he displayed in his exercises, and in the societies of his fellow-students, excited an applause which warmed his opening mind with hopes of future literary greatness.

Some eminent Scotsmen, such as Hume, Kames, and Robertson, had about this time distinguished themselves in literature. Those ancient prejudices by which the Scots had been too long withheld from the liberal cultivation of art were beginning to disappear; and a theatre for the exhibition of the works of the English drama had, in spite of presbyterian prejudices, been established at Edinburgh. Passionately desirous to flutter and shine among the young and fashionable, as well as ambitious to merit the esteem of the learned, Boswell, the farther be entered upon the scenes of life, became still more ardently the votary of wit and of the literary arts. The vanity of literary and colloquial eminence was thus early rooted in Boswell's bosom, and became his ruling passion. He learned to account it the supreme felicity of life to sparkle in gay convivial converse over wine, and to mingle with passionate delight in the society of professed wits. He was encouraged to

Its title is: An Essay on the Principles of Human Knowledge.'

try his fortune, far too rashly, as a youthful author; and to send to the press various levities in poetry and prose which had been much more wisely condemned to the fire. Of these several appeared in a small collection of original poems, by Scottish gentlemen, which was, about this time, published at Edinburgh. Boswell's pieces in this collection possess scarcely any other merit than that of a giddy vivacity. It was fortunately enriched with some more precious materials, the composi tions of Dr Thomas Blacklock, Gilbert Gordon, Esq. of Halleaths, and Jerome Stone, rector of the school of Dunkeld. A series of letters between Boswell and his friend, the Hon. Andrew Erskine, were, with similar imprudence, published about the same time, but certainly not at all to the honour of either of the young gentlemen.

Thus far young Boswell's life had been gay and flattering: he was now to launch farther out upon the ocean of the world. In the choice of a professional destination, he hesitated between a life of literature and business, and one of idleness and fashion. Had it not been for his father's authority, the latter would have gained his preference; but Lord Auchinleck, believing that the lively talents of his son could not fail of success at the bar, urged him to become a lawyer, with flatteries, promises, and some threats, which at last subdued James's pas sion for a red coat, a cockade, and a commission in the Guards. A sort of compromise took place between the father and the son; in consequence of which, the latter obtained permission, with a suitable pecuniary allowance, to visit London, to study the civil law at Utrecht, and to make the tour of Europe before he should finally fix himself at home as a practising advocate. On his arrival in the metropolis, his passion. for the acquaintance of men of great intellectual eminence had, in the first instance, the merit of saving him from the emptiness of mere foppery, as well as from brutal and profligate debauchery. Even in the society of a Wilkes and a Foote, in their loosest and most convivial hours, it was not possible that there should not be more of "the feast of reason and the flow of soul" than of sensual grossness.

The eloquence of the Ramblers,' being of that gorgeous and strongly discriminated character which most easily engages the attention of youth, had powerfully impressed the imagination of Boswell during his studies at Edinburgh. Johnson's 'Dictionary,' presenting its author in the character of the great censor and dictator of the English language, aided and confirmed the impression. When, in addition to this, he learned that Johnson's conversation was not less rich and original than his books, there needed nothing more to make him earnestly ambitious of the great lexicographer's acquaintance. He found in Johnson, when the desired introduction was at last obtained, not precisely what he had imagined, but something of a different cast altogether from that which his hopes and wishes had taught him to expect. Almost from the very first days of their acquaintance, he gladly haunted the presence of the illustrious moralist, and watched and preserved the treasures which fell from his lips as if he had already determined to become his biographer. Attentions so respectfully flattering are not easily resisted by either philosophers or heroes; Johnson could not but become partial to an admirer who professed to court his company almost with the humble devotion of a mortal attending the footsteps of a divinity, who was himself a youth of genius,. fortune, and fashion, and who ardently

professed to be ambitious of nothing so much as of making eminent improvement in piety, virtue, and liberal intelligence.

Satiated at length with the enjoyments of London, Boswell departed, with a new flutter of hopes and wishes, to pursue knowledge and pleasure in those new varieties of form in which they might present themselves on the continent. At Utrecht he studied law for some time under an eminent civilian. From Utrecht, he, after a while, continued his travels through Germany into Switzerland. The ambition of becoming known to eminent men, was still one of his predominant foibles; and to the unspeakable gratification of that passion of his, he had the felicity of being, in his tour through Germany, the travelling companion of the Right Honourable George Keith, the last Earl Marischal of Scotland. In Switzerland, the Lord Marischal introduced his young countryman to Rousseau, who then, an exile from France and Geneva, resided at Motiers in Neufchatel, under the protection of the great king of Prussia. Boswell, in due time, found occasion to tell the world how fondly he had visited Jean-Jaques-Rousseau; how kindly he had been received by the solitary philosopher; and with what flattering and confidential commendations a man so discerning and so suspicious had deigned to honour his merits! Boswell had also the pleasure of visiting the patriarch of Ferney, and the delight of hearing him deal out sarcasms and malicious fictions, the inspirations of fear and envy, against a rival wit and philosopher who was as vain and jealous as himself.

Having seen the lions in Germany and Switzerland, Boswell hastened away over the Alps to Italy. Addison had visited and celebrated the republic of San Marino; Boswell resolved to visit that of Corsica. The Corsicans, after struggling with various success, for a long course of years, to throw off the yoke of the Genoese, were at last about to be transferred to masters against whose power their efforts would be vain ; at this moment they enjoyed, in the interior parts of the isle, a miserable independence purchased at the expense of almost all besides that was precious in life. Their last generous exertions to secure the prize of liberty had, more than all the former, drawn upon them the admiration and the eager sympathy of Europe. The fame of Paoli and the Corsicans had greatly interested the curiosity of Boswell, as a young Scottish whig, even before he saw Rousseau; Rousseau's conversation and eulogy of Paoli completed the charm. The Genevan philosopher was too cautious, however, to give Boswell more than an indirect letter of introduction to the Corsican general, who received him with kindness and respect, and entertained him with liberal hospitality. Paoli and his Corsicans could not help expressing, in Boswell's hearing, their wishes that they might obtain the protection and aid of Britain; and Boswell, in the Don Quixote-like fervour of his imagination, was almost moved, when these wishes met his ear, and when he saw himself lodged, feasted, and attended in ceremonious state, to believe himself a British ambassador, deputed to declare Britain the tutelar divinity of Corsican freedom. After he retired from the court of Paoli, he was politely received, and entertained with courteous hospitality, by the French officers on the isle. He returned at last to the Italian continent, vain of his expedition, and gratefully boasting of all the favours and honours which it had procured him.