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Shortly after their separation, Lauzun writer of these pages was then at Paris);-was ordered with his regiment to 'Ame- Versailles was the temple of delight; and rica. It was now that the ardour of his Lauzun was the idol of the day. His foui biazed forth unftified : he panted for name was re echoed hy all ranks of peo glory, he fighed for military diftin&tion; ple; and the surrender of York-Town was he was eager to entwine the lauret of vic- considered as the most promiling event tory with the infignia of nobility. But which had been recorded on the annals of Lauzun was destined through life to be the American war. But the French peothe vakil of his fenóbility; and the more ple, particularly those who were blinded delicate, the more refined paflions of his by courtly splendour, did not forelee, that heart perpetually interrupted his progre's thofe, who by their valour had contributed towards fame.

towards the establishment of liberty in AmeWhile he was preparing to embark for rica, would scarcely permit the ardent efAmerica, intelligence reached him, that fects which it produced to lie dormant in the lady for whom he had once cherished their bosoms. the mori ardent affection, was at that mo The Duc de Lauzun, at this period, ment expcied to some pecuniary difficulties, pofseffed a linall villa at Mont-rouge, in the and labouring under the anxiety of ne- vicinity of Paris. It was completely fitted glect even from those in whom she had re- up after the English fashion; all the dopoled anbounded confidence. The suscep- mestics, excepting one or two, were of this tibili'y of Lauzun's heart could not calmly country, and even his table was arranged endure the inquietude occasioned by such after the manner of the English. This reevents; therefore, after obtaining leave of treat was the scene of rational festivity, abience for a short interval, he collected very unlike the temples of some illuftrithe remnants of his pecuniary resources, ous personages, who dedicated their villas inclosed the sum in a small pori-folio, and, to the most profligate debasement. on a post horse, unartended, set out from The late Duke of Orleans, then Duc Paris. Thus did he travel many hun- de Chartres, followed the example of dred miles, with little corporeal and fill Lauzun; and the fairy palace of Mouceau less mental rest, till he arrived at the abode was inhabited by English domeftics.of the fair recluse. It was in the dreary There English liberty was enthusiastically season of the year ; the situation wild and extolled, and French despotism daily dilbarren ; and nothing less eccentric than cussed without reserve ; till a fpirit of rethe feelings of such a character could form, and a glow of newly awakened inhave prompted or performed so romantic dependence, fastened on every mind, aan expedition.

mong the inferior classes of society. He was immediately admitted; he found Shortly after the commencement of the the lady alone; he had not power to atter revolution, the subject of these pages, then a syllable; but, after placing the port-folio Duc de Biron, having succeeded his uncle on a table which Itood before her, he in fortune and title, let out for England. quitted the room, remounted his horse, His personal attachment to the Queen in and remeasured back his route towards a great degree kept down the spirit of reParis ; shortly after he embarked for publican ardour, --and suppressed that acAmerica, where by his gallant conduct tive zeal which would otherwise have inbe foon became highly distinguished. He fluenced his conduct in the cause of free. was the friend of the Marquis de la Fayette; dom. Biron was the very loul of chivaland he alio enjoyed the elteem even of his ry:--The Queen of France was beautiful, military adverlaries, among whom may and persecuted. The event of his deparhe named the Earl of Moira, then Lord ture terminated unfortunately. Biron's

no less distinguished for resources were locked up by the strong
rtue, for political know- hand of anarchy: he had many debts in Eng-
iuine philanthropy! land: his creditors, either under the suppo-
own was surrendered by fition that he was become opulent by the
an was dispatched to the death of his uncle or that he would
les, with the important shortly be exposed to indigence by the con-
arrival at Paris, he was vullions of political changes, arrested him;
lamations of transport; and he was, for several weeks, confined in
conqueft, the harbinger the houle of a sheriff's officer.
ich was in a great degree It was there that the enterprising foul of
s important capitulation. Biron indulged in the varying emotions
f France now became a which his chequered destiny gave birth to;
: brilliant festivity--(the and, while his bolom glowed with the ena

thutiarm

thusiasm of liberty, it also ached under honour to distinguis one who fo far outthe severe humiliations of a constrained hone his cotemporaries; and the merits of captivity.

John Jebb were sufficiently acknowledged, In this distressing embarrassment, the by being the second in the list. Waring Earl of Moira, whole mind and whole took his first, or bachelor's degree, in conduet do honour to human nature, re 1757, and the Lucafian Professorship beceived intimation of the Duke's confine came vacant before he was of sufficient ment; and, by his interference and iriend. standing for the next, or Master's degree, Mip, Biron was liberated. But the pow. which is a necessary qualification for that er of legal prosecution had only augmented office. This defect was supplied by a the enthufialm of freedom; and he re- royal mandate, through which he became turned to Paris, to unite with the most po. Master of Arts in 1760; and, Mortly after pular leaders of the revolution,

his admission to this degree, the Lucasian There he renewed his friendship with professor. the Duke of Orleans (who had assumed the The royal mandate is too frequently a title of Egalité); and, by his influence, screen for indolence; and it is now become was prevailed on to take the command of almost a custom, that heads of colleges, who the army of La Vendée. Whether Biron ought to set the example in discipline toothers felt the dreadful effects of anarchy, while are the chief violaters ofit, by making their he hourly received accounts of masacres office a pretext for taking their Doctor's deand horrors; or whether the sufferings of gree in Divinity, without performing the ill. fated and persecuted Marie An- those exercises which were designed as toinette impressed his sensible and philan- proofs of their qualifications. Such indo. thropic mind, is not clearly ascertained ; lence cannot be imputed to Waring; yet but he certainly evinced an inactivity of several circumftances previous to his elecfoul, which terminated in his destruction. tion into the professorial chair, discovered He was recalled to Paris, deprived of the that there was, at least, one person in the rank which he held in the ariny; impri- University who disapproved of the anticisoned ; and executed!

pation of degrees by external influence. Here let the sensible reader bestow a Waring, before his election, gave a small tear, while reflection Thews the progress of specimen of his abilities, as proof of his Biron's fall from power to degradation ; qualifications for the officewhich he was then from the most splendid altitudes of fame soliciting; and a controversy on his merits and fortune, to the gloomy platform of ensued : Dr. Powell, the master of St. the guillotine! and, while memery tran. John's College, attacking, in two pamscribes his many virtues, his gallant ac- phlets, the Professor ; and his friend, aftertions, his amiable sensibility, and his ro wards Judge Wilson, defending. The mantic enthusiasm on the page of Time, let attack was scarcely warranted by the erPity efface with her spontaneous tears, rors in the specimen; and the abundant the frailties of human nature, and the last proofs of talents in the exercise of the profelfad close of his unfortunate destiny. forial office are the best answers to the

M. R. farcasms which the learned divine amused

himself in casting on rising merit. An of50ME ACCOUNT OF DOCTOR WARING, fice held by a Barrow, a Newton, a

MATHE- Whiston, a Cotes, and a Sanderson, 'moft

excite an ingenuous mind to the greateft EDWARD WARING, Lucasian Pro- exertions; and the new professor, whatever feffor of Mathematics in the University may have been his success, did not fall of Cambridge, was the son of a wealthy far behind any of his predecessors, in either mer, of the Old Heath, near Shrewsbury. zeal for the science, or application of the The early part of his education he re powers of his mind to extend its bounda. ceived at the free-school in Shrewsbury; ries. In 1762, he published his Miscella. whence he removed to Cambridge, and nea Analytica, one of the most abiiruse was admitted on the 24th of March 1753 books written on the abstruseft parts of Ala member of Magdalen College. Here his gebra. This work extended his fame over talents for abtruse calculation soon dee all Europe. He was elected, without loveloped themselves, and, at the time of licitation on his part, member of the fo. taking his degree, he was confidered as a cieties of Bononia and Göttingen ; and prodigy in shode Iciences which i ake the received flattering marks of esteem from subject of the bachelor's examination. Tlie the most eminent mathematicians at home name of Senior Wrangler or the first of and abroad. The difficulty of this work thw year was thought icarcely a sufficient may be presumed from the writer's own

worus,

CELEBRATED

THE LATE
MATICIAN.

words, “ I cannot say that I know any swering, viva voce, or writing down anone who thought it worth while to read swers to the professor's questions, from the through the whole, and perhaps not the first rudiments of philosophy, to the deephalf of it."

est parts of his own and Sir Isaac Newton's Mathematics did not, however, engross works. Perhaps no part of Europe affords the whole of his attention. He could de- an instance of so severé a process; and dicate some time to the study of his future there was never any ground for fuspecting profeffion ; and in 1767, he was admitted the professor of partiality. The zeal and to the degree of Doctor of Physic; but, judgment with which he performed this whether from the incapacity of uniting to- part of his office cannot be obliterated gether the employments of active life with from the memory of those who passed abstruse speculation, or from the natural through his fiery ordeal. diffidence of his temper, for which he was Withing to do ample justice to the tamost peculiarly remarkable; the degree lents and virtue of the professor, we feel which gave him the right of exercising his ourselves somewhat at a loss in (peaking talents in medicine, was to him merely a of the writings by wltich alone he will be barren title. Indeed, he was so embar- known to posterity. He is the discoverer, raised in his manners before strangers, that according to his own account, of nearly be could not have made his way in a pro- four hundred propositions in the analytics, feffion in which so much is done by address; and the account is scarcely exaggerated ; and it was fortunate that the ease of his yet we have reason to believe, that the circumstances permitted him to devote the greater part of these discoveries will fink whole of his time to his favourite pursuit. into oblivion; and that pofterity will be His life passed on, marked out by disco. as little attentive to them as his own coveries, chiefly in abstract science; and by temporaries. If, according to his own the publication of them in the Philosophi- confeffion, “few thought it worth their cal Transactions, or in separate volumes, while to read even half of his works,” wder his own inspection. He lived some there must be some grounds for this neyears after taking his doctor's degree, at glect, either from the difficulty of the fub. Št

. læs, in Huntingdonshire: while at ject, the unimportance of the discoveCambridge he married-quitted Cam- ries, or a defect in the communication of bridge with a view of living at Shrewsbu- them to the public. The subjects are cerry; but the air or smoke of the town be- tainly of a difficult nature, the calculaing injurious to Mrs. Waring's health, he sions are abstruse, yet Europe contained removed to his own estate at Plaisley, a many persons not to be deterred by the bout eight miles from Shrewsbury, where most intricate theorems.

Shall we say he died, universally esteemed for infexible then, that the discoveries were unimportintegrity, modesty, plainnels, and fim- ant? If this were really the case, the want plicity of manners. They who knew the of utility, would be a very small disparagegreatness of his mind from his writings, ment among those who cultivate science looked up to him with reverence every with a view chiefly to entertainment and where; but he enjoyed himself in domestic the exercise of their rational powers. We circles, with those chiefly among whom are compelled then to attribute much of kis pursuits could not be the object either this neglect to a perplexity in style, manner, of admiration or envy. The outward pomp and language; the reader is stopped at which is affected frequently in the higher every instant, first to make out the writer's departments in academic life, was no gra- : meaning, then to fill up the chafm in the tification to one whose habits were of a demonftration. He must invent anew Very opposite nature; and he was too much every invention ; for, after the enunciaoccupied in science, to attend to the in- tion of the theorem or problem, and the trigues of the university. There, in all mention of a few steps, little assistance is questions of science, his word was the law; derived from the professor's powers of exand at the annual examination of the can- planation. Indeed, an anonymous writer, didates for the prize instituted by Dr. Smith, certainly of very contiderable abilities, has be appeared to the greatest advantage.- aptly compared the works of Waring to The candidates were generally three or four the heavy appendages of a Gothic build. of the best proficients in the mathematics ing, which add little of either beauty or at the previous annual examination for the stability to the structure. bachelor's degree, who were employed A great part of the discoveries relate to from nine o'clock in the morning to ten at an affumption in Algebra, that' equations bight, with the exception of two hours for may be generated by multiplying together dianes, and twenty minutes for tea, in an. Others of inferior diinenfions. The roots

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of these latter equations are frequently when x = a, P is equal to
terms called negative, or impoffible; and
the relation of these terms to the coefficients

they, is equal to of the principal equation is a great ob

a t* ject of inquiry. In this art the professor that is, when x is equal to a, P= was very successful, though little aslistance

at * is to be derived from his writings, in looking for the real roots. We shall not, per

But when x is equal to a, the nu.' haps, be deemed to depreciate his merits, merator and denominator of the fraction if we place the series for the sum of the powers of the roots of any equation, among

are both, in their language, equal the most ingenious of his discoveries; yet

to nothing. Therefore, nothing divided we cannot add, that it has very usefully enlarged the bounds of science, or that by nothing, is equal to In the same the algebraift will ever find occasion to in. troduce it into practice. We may say the manner

which, same on many ingenious transformations

taxt* of equations, on the discovery of impossi

wheu x is equal to a, becomes • There. ble roots, and similar exertions of undoubt. edly great talents. They have carried the fore, nothing divided by nothing is equal assumption to its utmost limits; and the

=_, that is, which difficulty attending the speculation has

3 u2

34 rendered persons more anxious to ascer is abfurd. But we need only trace back tain its real utility; yet they who reject it our steps to see the fallacy in this mode of may occasionally receive useful hints from

i

reasoning. For P is equal to some num-the Miscellanea Analytica. The first time of Waring's appearing in

ber multiplied into that is, when public as an author, was, we believe, in

x is equal to a, P is equal to fome numThe latter end of the year 1759, when he ber multiplied into nothing, and divided published the first chapter of the Miscella.

by nothing ; that is, Pis, in that cale, nica Analytica, is a specimen of his quali no number at all. For a- a cannot be fications for the protefloihip; and this divided by a—x when x is equal to a, chapter he defended, in a reply to a pam; fince, in that case, a - * is no number plet entitled, Oblervations on the First

at all. Chapter of a book called Miscellanea Ana

If, in the beginning of his career, the lyrica. Here the profesor was strangely profesor could admit such paralegilins inpuzzled with the common paradox, that

io his speculations; and the writings of nothing divided by nothing may be equal the mathematicians, for nearly a ctntury to various finite quantities, and has re before him, may plead in his excule; we course to unquestionable authorities in

are not to be surprised that his discoveries proof of this pontion. The names of Mac- fhould be built rather on the affumptions faurin, Saunderson, De Moivre, Bernou- of others, than on any new principles of illi, Monmort, are ranged in favour of his his own. Acquiefcing in the strange noopinion: but Dr. Powell was not so tasily tion, that nothing could be divided by noconvinced, and returns to the charge, in the thing, and produce a variety of numbers, Detince of the Observations; to which the he as easily adopted the position, that an prcfeffor replied in a Letter to the Rev. equation has as many roois as it has diDi. Powell, Fellow of St. John's College, mensions. Thus 2 and 4 are said to be Cambridge, in antwer to his observations, roots of the equation x? 2x ---8, though &r. In this controveriy, it is certain that

4 can be the root only of the equation ; the profeffor gave evident proofs of his

*2-24-3, which differs so materially from abilities; though it is equally certain that the preceding, that in one cale 2x is added, he followed to implicitly ihe decisions in the other cate it is subtracted from x2. of his predeceffors. No apparent advan. Allowances being made for this error in tage, no authority, whatever, should in the principles, the dicuctions are, dice mathematicians to fwerve from the neral, legitimately made; and any one principles of right reasoning, on which who can give himself the trouble of demontheir science is fupposed to be peculiarly ftrating the propofitions, may find suifounded. According to Maclaurin, the cient imployment in the profeflor's ana. Prafeffor, and others, If P= then,

lytics. Perhaps it will be fulficient for a student to devote his time to the fimpleft

cale

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contents.

cak ro+1=0; and when he has found a lution to go through them, will not only few thousand roots of + 1 and I the add much to his own knowledge, but be publicatien of them may afford to posterity usefully employed in dilating on those ar2 ftrang proof of the ingenuity of their ticles for the benefit of the more general predecessors, and the application of the reader. We might add in this place a powers of their mind to uleful and import work written on morals and metaphysics ant truths. In this exercise may be con- in the English language : but as a few co. iulted the method given by the professor, pies only were presented to his friends, of finding a quantiiy, which, multiplied and it was the professor's wish that they into a given irrational quantity, will pro- should not have a more extensive circuladuce a rational product, or consequently tion, we Mall not here enlarge upon its exterminate irrational quantities out of a gives equation ; but if an irratio al In the mathematical world the life of quantity cannot coine into an equation, the Waring may be confidered as a ditina utility of this invention will not be ad- guished æra. The itrictness of demonstramitted without heftation.

tion required by the ancients had graThe Proprietates Algebraicarum Cur. dually fallen into disuse, and a more comvarum, publihed in 1772, necessarily la- modious though almost mechanical moce bour under the same defects with the Mif: by Algebra and Fluxions took its place, cellanea Analytica, the Meditationes Al. and was carried to the utmost limit by the gebraicæ, publified in 1770, and the professor. Hence many new demonstraMeditationes Analyticæ, which were in tions may be attributed to him, but four the press during the years 1773, 1774, hundred discoveries can ícarcely fall to the 1775, and 1776. These were the chief lot of a human being. If we examine and the most laborious works edited by the thoroughly those which our professor profelior ; and in the Philosophical Tranf- would distinguish by such names, we shall , actions is to be found a variety of pa- find many to be mere deductions, others, pers, which alone would be sufficient to

as in the solution of biquadratics, antiplace him in the first rank in the mathe- cipated by former writers. But if we canmatical world. The nature of them may

not allow to him the merit of lo inventive be feen from the following catalogue.

a genius, we must applaud his affiduity; Vol

. LIII. page 294, Mathematical and, distinguished as he was in the scienProblems.-LIV. 193, New Properties tific world, the purity of his life, the fimin Conics.-LV. 143, Two, Theorems in plicity of his manners, and the zeal which Mathematics. - LXIX. Problems con- he always manifested for the truths of the cerning. Interpolations—86, A general Gospel, will intitle him to the respect of Resolution of Algebraical Equations, all who do not esteem the good qualities LXXVI. 81, On Infinite Series.

of the heart inferior to those of the head. LXXVII. 71, On finding the Values of

London, Nov. 1799.

F. Algebraical Quantities by converging feriekes, and demonstrating and extending ORIGINAL LETTER OF H. BAKER, AUpropofi-ions given by Pappus and others.

"MICROSCOPE MADE LXXVIII. 67, On Centripetal Forces. EASY," TO DR. DODDRIDGE. ib. 588, On fome Properties of the Sum DEAR SIR, of the Division of Nunbers.-LXXIX. Your last favour came

to London 166, On the Method of correspondent Va. whilst I was at Ditton with his Grace lues, &c. ib. 185, On the Resolution of the Duke of Montague, where and attractive Powers.--LXXXI. 146, On with whom I constantly spend a weck or infinite Seriefes.- LXXXIV. 385—415, ten days every Christmas and Eailer; and On the Summation of those Serieses whole I have no other holidays during the whole gederal term is a determinate funétion year. At these time's feveral noblemen of 2, the distance of the term of the and gentlemen meet there to enjoy a perfect

frecidom, and throw off that ceremony and . For these papers, the profesior was, in restraint which their rank fubjets them to 1784,deservedly honoured by the Royal at London. Our company this Christmas Society with Sir Godfrey Copley's medal; was his Grace, the Earls of Pembroke and most of them afford very strong proofs and Cardigan, the Lorus Tyrawley, Edgof the powers of bis mind, both in abstract cumbe, and Herbert, the Marquis NicoScience, and the application of it to philo. lini, our worthy president of the Royal fophy; though they labour in common Society, and seven or eight gentlemen of with his other works under the diiadvan- ditinétion. The rules of the duke's heuse fige of being clothed in a very unattractive are, for every body to go to bed and rile torm. The mathematician who has relu. at his ovn time, and amule himself in NOKTALY MAG. NO. 55.

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