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1796.]

Mathematical Correfpondence.

the places from the fun; but this hypothefis is not generally true, as the heat communicated by a fiery body feems to depend upon its figure, as well as its diftance from the other body; and as its laws differ very confiderably from thofe of attraction; I fhall therefore, in the prefent paper, confider the proportional effects of fiery bodies of regular figures, upon the moft probable hypothefes, and afterwards compare the conclufions with thofe deduced from experiments.

That the action of a very fmall fiery body upon another fmall body is nearly in the reciprocal duplicate ratio of their diftance, is a fuppofition fo agreeable to reafon and to general experience, that we may fafely found our computations upon it but whether in eftimating the effect of a fiery body, we ought to confider the action of the whole, or only part of the hody; or of the whole, or only part of the furface are queftions which have not yet been determined: we fhall therefore give the refults upon each of thefe fuppolitions.-It is likewife neceffary to remark, that the compofition and refolution of forces can no where take place in eftimating effects produced by heat; in this refpect, it differs materially from attraction.

II. Let P be the centre, and AP (Fig. 1) the radius of a fphere, and let it be required to find the heat communicated to the point P by the convex fuperficies of a fegment, whofe axis equals DE. If 3.14159 equal the circumference of a circle, whofe diameter is

639

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CA-(CP-AP)2. CPX AP

(CP2-CA2). CPXAP

unity, 2pX AP will be the circumfeþ×AP×dAP

rence of the generating circle, and there

СР

xdAP=2p

X dAP

and the effect of the

fore 2px APX DE equals the fuperfi- part AUBE of the fphere =2px AP— cies of the fegments; and as every p(CP-CA),

point in this fuperficies is equally dif tant from P, the effect of the whole is

=

2X APX DE

AP2

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III. Now let HFGBH reprefent a folid, generated by the rotation of the curve HFG about its axis HG, and let ADB be perpendicular to HG, meeting the furface in the points A, B; alfo let P, fituate in the axis GH produced, be the point which receives the heat from the body; and from the centre P and radius PA defcribe the arc PEB, meeting HG in E. Then fuppofing the folid com

This problem may be refolved in feveral dif

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xHyp. Log. AP—..........

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Hyp. Log. PH

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#CP_C.12) CP PH2-AP2

X

There

2 CP

fore, if we put AP PG, we will have the action of the whole globe 2p(PG

ferent ways, but the one we have given is pro- -PH)_2XPHXPG

bably the fimpleft.

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If the point P touch the globe, PH will be o; and the heat communicated to P=2px CA, or directly as the radius of the globe.

V. If the furface of the folid alone communicates the heat, the investigation and the refult will be different. For if if HAGB be the folid, and P the given point (Fig. 1) the action of the circumference of the circle, whofe radius is

25X AD

AD, will be equal to differential of the action

of the fegment AHBA=

and the
1
AP
of the furface

2X AD

X

AP2 dAH. Now in this cafe, if the folid be CAx dfD

a sphere, dAH will be equal

AD
CAXPD

=2px. AP2

CP-CA+AP2

ADX dAH

and 2pX

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2CP
, therefore, 2pX.

AP2

and PD CAXdPD AP2

2pXCA dAP
СР AP
XHyp. Log. AP+C. When

and the integral equal

2pXCA

CP

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-I

CA

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and the action of the whole surface = CA CA CAG

+

&c.) When

(CP2+
CP2 3CP 5PC6'
the radius CA bears a fmall proportion
to the diftance PC, the whole action will
CA

be nearly 4X and, confequent-
CP
ly, the heat as the fquare of the dif
tance: which is the very principle upon
which our reafonings were grounded.---
This rule will answer pretty accurately,
when we want to compare the heat of
the different planets with each other.
When P coincides with H, the expref-
fion becomes infinite.

VII. But there is another hypothefis which appears more probable than any of them: that is, that the point P receives its heat from that part of the furface only which is contained between the tangents drawn from the point to the furface of the fphere. In this cafe, AP =PF, and by the nature of the circle PFPGX PH; but the action of the fuperficies of the fegment FHF (§ V)

is =

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x Hyp. Log. PH

PC

xHy. Log.

PG

PGXPI_pxCA Ex Hyp. Log. PH

[ocr errors]

PC

It is obvious that this laft expreffion is juft half the preceding, where the action of the whole furface was confidered. When P coincides with H, this expreffion likewife becomes infinite.

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**The Conclufion of this valuable Paper, as well as the new Questions, and the Anfiers to the former ones, are deferred, for want of Room, till our Next.

TO CORRESPONDENTS.

THE very curious Papers relative to the Marches of Wales-The ingenious Effays on the Characteristics of Poetry-Anti-Sinboron-D. C. in reply to " A Woman"-The interefing Letter of Sarah Bockett-A Poor Northumbrian on Large Farms-N. O. in reply to "O. N."-T.S. A. T. on Oratory-The Sonnet figned Y--the Poetry, by W. R.-the Reply of" A Woman" to "C. D."-A Layman on Tythes-and fome other accepted and valuable Communications are unavoidably deferred-feveral of them on account of their great Lengths. Is the Paper of W. T. jun. original ?-The frequent and the continued Correspondence of all other literary and ingenious Friends will be thankfully accepted.

$796.]

( 64 )

ORIGINAL ANECDOTES AND REMAINS

OF

EMINENT PERSONS.

[This article is devoted to the reception of Bographical Anecdotes, Papers, Letters, Ec. and we request the Communications of fuch of our Readers as can affift us in these obj, Ets.]

ANECDOTES OF PERSONS CONNECTED WITH THE FRENCH REVOLUTION.

[Continued from cur laft.]

CONDORCET

PPERTAINED to the nobility by birth; to the people from fentiment -although a Marquis, he fcorned not to confider himself as a citizen. He was a philofopher alfo.

The friend and difciple of Voltaire, like him too he was the correfpondent of Frederick, of Pruffia. Neither his title, his fortune, his fituation at the Academy, of which he had been declared perpetual fecretary,' nor his private friendship, could prevent him from facrificing every confideration to his principles. Such was the esteem in which he was held, that before the flight to Varennes, the eyes of all France were fixed on him, as tutor to the Prince Royal; but his love of liberty was fo offenfive in the eves of Royalty, that another perfon was furreptitiously appointed by the King and Queen, in order to prevent his nomina

tion.

After thirty years of study and meditation, confecrated to the fciences and his native country, or rather to all Europe; after labouring four years exclufively for the revolution and liberty, this great man, profcribed under the tyranny of Robespierre, was forced to wander about from place to place, to fhelter himfelf in woods and caverns, and at length to have recourfe to poifon, to put an end to his calamities!

Without books, without friends, frequently without even food, inftead of uttering complaints and execrations against his unjuft country, or rather the bloody and victorious faction, that then governed it, his whole mind was bent on a project beneficial to humanity. This is developed in his work, entitled, " Ef quiffe d'un Tableau Hiftorique des progrès de Efprit Humain," in which, confidering man under three diftinct points of view, he enquires, What he has been? What he is and, What he may be ?

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From count Tilly's work on the French Revolution, an abridged extract occurs in the Monthly Review (vol. xviii. p. 557) in which Condorcet is charged with the murder of his friend, benefactor, and political creator, the duc de la Rochefoucauld. The Count admits, that perhaps he was not privy to the defigns against that nobleman; but alleges that his ingratitude is recorded in the courts of law of his country.

"When he married Madame de Grouchy, he had no fortune but that which the derived from the bounty of the house of La Rochefoucauld: theĎuke gave her a bond for 100,000 livres, and paid the intereft of that fum regularly up to the fecond year of the revolution, when Condorcet put the bond in force, and compelled the Duke to pay the principal." Thofe who with to citimate the effe of literature upon the moral cha

xacter,

rafer, must defire to come at the exact truth in this matter.

A French emigrant, who appeared to know much of the leading families of France and of their private hiftory, was lately mentioning, that Madame de Grouchy univerfally paffed for a caft-off miftrets, who by her complaifance and dexterity, had obtained the bond in queition; and that at the time of her marrige, he was announced as a rich ward of the Rochefoucauld family, whom they had introduced to the attention of Condorcet. Whether he knew or knew not her real relation to them, the charge of ingratitude, in exacting her dower, mug, on this ftatement, fall away. The death of the Duke is known to have been connected with the September maffacre; and cannot, of courfe, be fairly charged, directly or indirectly, upon one of the Girondift party, the leaders of which virtuoufly facrificed their own lives, in the attempt to bring the inftigators of that horror to punishment.

GENSONNE,

Born at Bourdeaux, in 1758, and educated for the bar, was returned a member for the Gironde, and became one of the leaders of that illuftrious body, diftinguished by the name of the department whence they were delegated. He was cool, tranquil, intrepid. He abhorred the mountain party, and was at once dreaded and detefted by that faction, which, on the 31st of October, 1793, revenged all his accufations and farcafms, by means of the guillotine. He was a good father, a good citizen, an excellent man, and a fincere republican; but he was a logi cian rather than an orator.

GUADET

Was an orator, but not a logician; he excelled in what we term a fet fpeech-but few of the men of that day could fpeak extempore. He fat both in the legiflative and conventional affemblies, and efcaped the bloody profcription of the twentyone deputies, only to perifh by a more horrible deftiny! He alfo, was a good father, and a good hufband, for it may be neceffary to inform the ignorant and the prejudiced, that there were good men in France, pofterior to the defertion of the clerical and titled emigrants.

MOREAU

Is a native of Morlaix, in the ci-devant Bretanny, 29 miles diftant from Breft. When about 18 years of age, he was fent

to Rennes, to study the law; and he who might have proved but an indifferent avocat, has, at the age of 33, acquired the character of a skilful commander.

He firft diftinguished himself in Holland, and then ferved with great éclot under Pichegru. The late brilliant paffage across the Rhine, without the lofs of a fingle man, was achieved under his aufpices. His father is faid to have perifhed during the tyranny of Robespierre; the fon is a zealous republican, and fights and conquers in that caufe.

THE ABBE DE LILLE,

Like the bards of old, is at once a poet and a mufician; and, in confequence of a rare union of both characters, he compofed the Marfeillois Hymn, which, by connecting his name with the hiftory of the French Revolution, will render it immortal.

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As Anacharfis Cloots termed himself, "the orator of the human race," fo Lequinio affumed the title "citizen of the globe." The latter was a patriot previoufly to the revolution, and a republican before the decree for the abolition of monarchy. He fat in the convention, and voted for the death of Louis. His celebrated work, Les Préjugés Détruits, abounds every where with marks of genius. It was printed at Paris: " anno eventus, quo reges & facerdotes, ab orbe terrarum obliterandi." (1792) M. Le

6

DE ROME.

Ce

*"Le plus bel epifode de for poëme fur l'imagination, dont le fujet eft l'aventure du célèbre peintre, Robert, perdu pendant quelques heures fans guide fans flambeau dans les immenfes fouterrains nommés les CATACOMBES poëme n'eft point imprimé; fi l'auteur eût péri, nous perdions à la fois & le poëte eft l'ouvrage, car Monf. l'Abbé de Lille fe repofant fur fon excellente mémoire n'écrit jamais les vers qu'il compofe que lorfqu'il veut les livrer à l'impreffion.'-This note was written by Madame de GENLIS a few weeks fince.

1796.]

Original Anecdotes.-Servan... Chamfort.

quinio is one of the philofophical fceptics, to whom Dr. Priestley addreffed a letter, juft before he was driven from a country, by the iron-hand of perfecution, which will hereafter claim him as her own.

643

which levels all family diftinctions, no man could be born a republican more truly than Chamfort. He was the fruit of illicit love, and as it fhould feem of promifcuous amours; for he never knew his father-a circumftance which in no

“Our fons shall blush their fathers were thy degree diminished his affection for his

foes!"

SERVAN

Obtained, by his merit alone, the crofs of St. Louis, and that too at a time when

his

attempt

other men acquired it by the meanest arts, and the most degrading fubmiffions. Be fore the revolution, at a period when a liberal fentiment might have afforded an introduction into the Baftile, he published "le Soldat-Citoyen," in which he endeavoured to inspire a mercenary ftand. ing army with the idea of patriotifm :did not prove wholly abortive. His talents, by fome ftrange fatality, had procured him a place at a diffipated and degenerate court, but he was difmiffed in 1790, as his civism rendered him hateful to M. Guynard St. Priest. When a fucceffor to the minifter, Degrave, was thought of, Servan was pointed out as a proper one by Roland; and being approved of by the council, and the patriotic deputies confulted by it, he was prefented to, and accepted readily by the king. This is the more remarkable, as he was perfonally odious to his Majefty.

Servan hated, and in return was hated by the court. It was then what they

themselves were accuftomed to term a

combat au mort between the royalifts and the patriots: one party was fure to fucceed; and which ever prevailed, blood muft inevitably be fhed. At this period Bourdeaux and Marfeilles (the latter of which is a Greek colony) were the most zealous of all the cities of France, Paris itfelf not excepted, in behalf of freedom: nay, it was thither the friends of freedom had determined to retire, in cafe of a reverfe; that if abfolute monarchy reared its head in the North, they might oppole it by means of a republic in the South.Accordingly we find Servan, Barbaroux, and Madame Roland, drawing a line of demarcation on the map; ftudying the military pofitions, and the courfe of the rivers; invoking the aid of the Bordelais and the Marfelllois; and fwearing on the altar of liberty that they would not belie the hopes of mankind!

CHAMFORT.

If a want of the advantages of birth predispose us to favour a government MONTHLY MAG. NO. VIII.

other parent, to fupply whofe wants he often denied himfelf the neceffaries of

life.

He was taken at a very early age into the College des Graffins, at Paris, in quality of Burfur*, and was known there by his Chriftian name of Nicolas. Nothing during the two first years announced extraordinary talents; but in the third, out of five prizes that were diftributed annu ally, he bore away four, failing in Latin verfes alone. The next year his fuccefs was complete; and he made a remark upon the occafion, which difcovered good tate, a fuperior mind, and the opinion he entertained of the judges: "I loft the prize laft year," faid he, "because I imitated Virgil; this year I obtained it, becaufe I took Buchanan, Sarbievius, and other moderns, for my guides.”

In Greek he made a rapid progress; but his petulance, his wit, and his waggifh tricks, threw the class into fo much diforder, that he was expelled from it by M. Lebeau, the profeffor of that language; and not long after left the college altogether. Thrown upon the wide world, without friends or any point of fupport, he was foon reduced to the lowest pitch of poverty. He bore his misfortunes, however, with philofophic patience, and cheered himself with the

oft flattering hopes: "I am a poor devil now," faid he to Selis, another man of letters; "but do you know what will happen? I fhall obtain a prize from the academy, my play will fucceed, I fhall be courted by the world, and well received by the great, whom I despise : they will make my fortune for me, and I shall afterwards live like a philofopher."

The first part of his prediction was foon verified. He obtained a prize, and fent a copy of his production to the very M. Lebeau who had expelled him from the Greek clafs, accompanied by the following note: "Chamfort fends the work

that

haş obtained the fuffrages of the Academy to his old and refpectable mafter; and at the end of nine years begs his pardon for Nicolas." M Lebeau made

*A kind of inferior ufher, with a fmall ftipend. 4 N anfwer

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