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Mathematical Correspondence.

639 the places from the fun; but this hypo- posed of an indefinite number of sphethesis is not generaily true, as the heat rical surfaces, of which the common communicated by a fiery body seems to centre is P, the effect of one of these depend upon its figure, as well as its dir

DE tance from the other body; and as its surfaces ($ II) will be equal 2px laws differ very considerably from those and the differential of the whole action of attraction ; I shall therefore, in the

GAP present paper, consider the proportional equal 2px DEX But as CD is

AP effects of fiery bodies of regular figures, given, and from the nature of the geneupon the most probable hypotheses, and rating curve the relation between CD afterwards compare the conclusions, with those deduced from experiments.

and AD, PD will be given, in terms of That the action of a very small fiery

AP; and, consequently, the integral of

DAP body upon another finall body is nearly the expression 2px DEXAP, or the in the reciprocal duplicate ratio of thcir distance, is a supposition fo agreeable to

a&tion of the part of the folid AHBE reason and to general experience, that upon the point P. we may safely found our computations upon it: but whether in estimating the

Fis:) effect of a fiery body, we ought to consider the action of the whole, or only part of the hody; or of the whole, or only part

HDE of the surface! are questions which liave not yet been determined : we shall therefore give the results upon each of these suppölitions. It is likewise necef IV. Suppose, for example, the fiery bg. fary to remark, that the composition and dy to be a iphere, whose centre is C and resolution of forces can no where take radius CA ; then will 2 PCXPD=CPplace in estimating effects produced by C A2+-AP2 ; PDF

CP-AP2-CA2, heat; in this respect, it differs materially

2CP from attraction.

and DE=AP-PD-II. Let P be the centre, and AP


Hence, 2pX DEX (Fig. 1) the radius of a 1phere, and let

2CP it be required to tind the heat communi. dAP CA-(CP-:P) cated to the point P by the convex su


CP X AP perficies of a segment, whose axis equals DE. If p=3.14159 equal the circum- XDAP


XDAP ference of a circle, whose diameter is

CP ХАР unity, 2pXAP will be : the circumfe


and the effect of the rence of the generating circle, and there

CP fore 2px APX DE cquals the fuperfi- part AUBE of the sphere =2pXAPcies of the fegments; and as every PCPP-CAP) point in this fuperficies is equally dil

x Hyp. Log. AP-....

CP tant from P, the effect of the whole is pXAP? 25 X AP DE DE



But when AP=PH=CP-CA, the III. ^ Now let HFGBH reprefent a

effect should be =0 ; therefore, C=folid, generated by the rotation of the

CP2_CA curve HFG about its axis HG, and let

2 x rg)

X Hyp. Log.

CA ADB be perpendicular to HG, mecting the surface in the points A, B; also let P,

PH+ and the foregoing value

2CP situate in the axis GH produced, be the point which /receives the heat from the equal 24(AP-PH)

(CP-C.1) body; and froin the centre P and radius

CP PA describe the arc PEB, meeting HG Hyp. Log.


Therein E. Then supposing the folid com


fore, if we put AP=PG, we will have This problem may be resolved in several dif

the action of the whole globe =27(PG ways, but the one we have given is pro


PG bably the simplest.



[ocr errors]

=25* AP





x Hyp. Log. PH

* Hyp. Log.PH






and 2px


nature of logarithms, the Hyp. Log. S2' X CA.. 2CP




2CA , 2CA3 2CAS is = +

& Cw CP

CA PC 3PC37 5PCS If the point P touch the globe, PH PC will be =0; and the heat communicated and the action of the whole surface = to P=2pxCA, or directly as the radius

CA? CA* CAG of the globe.

&c.) When V. If the surface of the solid alone the radius CA bears a small proportion

CP2' 3CP+ '5PC6' communicates the heat, the investigation to the distance PC, the whole action will and the result will be different. For if

CA? if HAGB be the folid, and P the given be ncarly = 4oXmand, consequentpoint (Fig. I) the action of the circumference of the circle, whose radius is ly, the heat as the square of the dir.

tance: which is the very principle upon

25 X AD AD, will be equal to and the which our reasonings were grounded.--differential of the action of the surface when we want to compare the heat of

This rule will answer pretty accurately,

AD of the segment AHBA=22X1


the different planets with each other. AP

When P coincides with H, the expresa dAH. Now in this case, if the solid be fion becomes infinite.

CAXDID a sphere, dAH will be equal

VII. But there is another hypothesis AD

which appear's more probable than any AD X DANI CAXIPD of them that is, that the point Pre

= 2 px AP2

AP2 clives its heat from that part of the sur. CP-CA2+AP

fice only which is contained between the but PD=


and PD= tangents drawn from the point to the

CAXWPD СР therefore, 2px

furface of the sphere. In this case, AP

AP2 =P!, and by the nature of the circle 2PX CA GAY

PF2=PGXPH; bur the action of the and the integral equal CP AN

fuperficies of the feginent FHÉ (V) 2px CA



рҳ СА СР, -X Hyp. Log. AP+C. When is

x. H. Log. CP


ic AP=PH, this expression should be =0;

PF? AXCA conscquently, the correct integral

x .

x Hy. Log.

CP-X Hyp. Log.
and the ac-

PG x P pxCA

Pha PC
tion of the whole spherical surface =

It is obvious that this last expreffion is
X Hyp. Log.

just halt the preceding, where the action PHI CP

of the whole furface was considered. VI. Now as PG=PC+CA, and PH When P coincides with H, this ex. PG

is equal

preliion likewise becomes infinite.

[To be continued.]
and 2p/ CAXH. Log.


Aberdeen, June 24. B. CYGNI. CA CP


** The Conclusion of this valuable Papír, PC CA

as well as the new Queft.ons, and the XH. Log.

But by the

Answers io the former ones, are deferred, CP


for want of Room, till 0:« Next.

2px CA

[ocr errors]

x Hyp. Log. PH

[ocr errors]

2px CA .



TO CORRESPONDEN T S. THE very curious Papers relative to the Marches of Wales--Tie ingenicus Elays on the Charnéierijtıcs of Poeir;--jinti- Sinboron-D. C. in reply to A Woman"--The interefing Letter of Sarah Bocketi-A Poor Northumbrian on Large Farnes-N. 0. in reply io “ 0. N."-T.S.A.T. on OraloryThe Sonnel signed Y-the Poetry, by W. R.-be Reply of " A Womanto "C. D.- Á Layman on Tythes--and some other accepied and valuable C:mmunications are unavoidably cleferred--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 of ber literary and ingesious Friends will be thankfully accepted.


( 641)




[This article is devoted 10 the reception of Biographical Axecdotes, Papers, Letters, &c. and

we request the Communications of such of our Reuders as can olift us in these obje&ts.] Axecdotes OF PERSONS CONNECTED The Convention, sensible of the merit WITH THE FRENCH REVOLUTION. of this work, on the 13th Germinal,

1796, decreed as follows: [Continued from cur luft.]

“ Art. I. La commillion exécutive de CONDORCET

l'instruction publique acquerera sur les PPERTAINED to the nobility by fonds mis à la dispotition 3000 exemplaires

birth; to the people from sentiment de l'ouvrage posthume de Condorcet, inti-althcugh a Marquis, he scorned not to tuls, Efquiffe, &c." consider himself as a citizen. He was a

“ 11. Le comité d'instruction public philosopher also.

que est chargé de veiller à ce que ces The friend and disciple of Voltaire, 3000 exemplaires soient distribués dans like him too he was the correspondent of l'étendue de la republique, & de la maFrederick, of Pruisia. Neither his title, nière la plus utile a l'instruction. Chaque his fortune, his ficuation at the Academy, membre de la convention en recevra un of which he had been declared perpe

exemplaire." tual secretary,' nor his private friendlhip,

It is impossible to contemplate could prevent him from facrificing every “A brave man struggling’midit the forms of faten consideration to his principles. Such was * And greatly falling,– the esteem in which he was held, that before the fight to Varennes, the eyes Roman Moralist :

without recollecting the passage in the of all France were fixed on him, as tutor to the Prince Royal ; but his love of li

“ Ecce par Deo dignum, vir fortis



cum mala fortunâ compositus ! berty was fu offensive in the of Royalty, that another person was furs video, inquam, quid habeat in terris Jureptitiously appointed by the King and piter pulchrius, fi convertère animum Queen, in order to prevent his nomina- velit, quàm ut spectet Catonem, jam tion.

partibus non semel fractis, nihilominùs After thirty years of study and medi

inter ruinas publicas erectuin."

Seneca de Divin. Prov. tation, confecrated to the sciences and his native country, or rather to all Europe ; From count Tilly's work on the French after labouring four years exclusively for Revolution, an abridged extract occurs in the revolution and liberty, this great the Monthly Review (vol. xviii. p. 557) in man, proscribed under the Yyranny of which Condorcet is charged with the Robespierre, was forced to wander about murder of his friend, benefactor, and pofrom place to place, to shelter himself in litical creator, the duc de la Rochefouwoods and caverns, and at length to have cauld. The Count admits, that perhaps recourse to poison, to put an end to his he was not privy to the designs against calamities!

that nobleman ; but alleges that his inWithout books, without friends, fre- gratitude is recorded in the courts of law quently without even food, instead of of his country. uttering complaints and execrations a “ When he married Madame de gainst his unjust country, or rather the Grouchy, she had no fortune, but that bloody and victorious faction, that then which the derived from the bounty of governed it, his whole mind was bent the house of La Rochefoucauld: the Duke on a project beneficial to humanity. This gave her a bond for 100,000 livres, and is developed in his work, entitled, “ Es paid the interest of that fum regularly quifle d'un Tableau Historique des progrès ve up to the second year of the revolution, Elprit Humain," in which, considering when Condorcet put the bond in force, man under three distinct points of view, and compelled the Duke to pay the prin he enquires, What he has been ? What cipal." Those who will tú eitimate the he is : and, What he may be?

effcüt of literature upon the moral cha


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ramer, must desire to come at the exact to Rennes, to study the law; and he who truth in this matter.

imight have proved but an indifferent A French emigrant, who appeared to avocat, has, at the age of 33, acquired know much of the leading families of the character of a skitful commander. France and of their private history, was He first distinguish: d himself in Hollately mentirning, that Madame de land, and then served with great éclat Grouchy universally passed for a cast-oit under Pichegru. The late brilliant pafmistrets, who by her complaisance and fage across the Rhine, without the loss dexterity, had obtained the bond in ques of a fingle man, was achieved under his tion; and that at the time of her marri aufpices. His father is said to have pesre, the was announced as a rich ward of rished during the tyranny of Robespierre; the Rochefoucauld family, whom they the son is a zcalous republican, and fights had introduced to the attention of Cen and


in that cause. dorcei. Whether he knew or knew not

THE ABBE DE LILLE, her real relation to them, the charge of ingratitude, in exacting her dow'er, inus,

Like the bards of old, is at once a poet on this statement, fall away. The death and a musician ; and, in consequence of of the Duke is known to have been con a rare union of both characters, he comnocled with the September matsacre ; pored the Marseillois Hymn, which, by and cannot, of course, be fairly charged,

conneēting his name with the history of directly or indirectly, upon one of the

the French Revolution, will render it Girondist party, the leaders of which

immortal. virtuously facrificed their own lives, in In addition to his other works, he has the attempt to bring the instigators of meditated a poem on the “ Imagination," that horror to punishment.

for what is fingular enough, this has

never as yet been commitred to paper. GENSONNE,

The truth is, that the Abbé, relying on Born at Bourdeaux, in 1758, and educat his extraordinary memory, never copies ed for the bar, was returned a member out any of his verses, until they are about for the Gironde, and became one of the to be printed *. leaders of that illustrious body, diftin He was arrested during the short-lived guished by the name of the department tyranny of Robespierre ; and if he had whence they were delegated. ' He was perished on that occasion, both the poem cool, tranquil, intrepid. He abhorred and the poet would have been lost tothe mountain party, and was at once dreaded gether! and detested by that faction, which, on

LEQUINIO. the 31st of October, 1793, revenged all As Anacharsis Cloots termed himself, his accusations and sarcasms, by means of " the orator of the human race," fo Lethe guillotine. He iras a good father, a quinio assumed the title “ citizen of the good citizen, an excellent man, and a globe.” The latter was a patriot previlincere republican; but he was a logi- ously to the revolution, and a republican cian rather than an orator.

before the decrce for the abolition of moGUADET

narchy. He fat in the convention, and

voted for the death of Louis. His celeWas an orator, but not a logician ; he ex brated work, · Les Préjugés Détruits,' celled in what we term a jet speech--but abounds every where with marks of gefew of the men of that day could spcak 'nius. It was printed at Paris : “ extempore. He fat both in the legislative eventus, quo reges & facerdotes, ab orbe and conventional assemblies, and cfcaped terrarum obliterandi." (1792) M. Lethe bloody profcription of the twentyone deputies, only to perith by a more horrible destiny! He also, was a good *Lc plus bel episode de for. poëme sur l'imafather, and a good husband, for it may gination, dont le sujet est l'aventure du célèbre be necessary to inform the ignorant and peintre, Robert, perde pendant quelques heures sans the prejudiced, that there were good guide & fans flambeau dans les immenses souterrains

DI ROME. Ce men in France, posterior to the defertion nommés les CATACOMBES of the clerical and titled emigrants.

poëme n'eft point imprimé ; fi l'auteur eût péri,

nous perdions à la fois & le poëte eft l'ouvrage, MOREAU

car Mons. l'Abbé de Lille se repsfant sur son ex

cellente mémcire n'écrit jamais les vers qu'il compose Is a native of Morlaix, in the ci-devant que lorsqu'il veut les livrer à l'impression.'--This Bretanny, 29 miles distant from Brest.

note was written by Madame de Genlis a few When about'i8 years of age, he was sent weeks fince.




1796.] Original Anecdotes.-Servan. . . Chamfort: . quinio is one of the philofophical sceptics, which levels all family distinctions, no to whom Dr. Priestley addressed a letter, man could be born a republican more just before he was driven from a country, truly than Chamfort. He was the fruit by the iron-hand of persecution, which of illicit love, and as it should seem of will hereafter claim him as her own. promiscuous amours; for he never knew " Our fons shall blush their fathers were thy degree diminished his affection for his

his father-a circumstance which in no foes !”

other parent, to supply whole wants he SERVAN

often denied himself the necessaries of Obtained, by his mcrit alone, the cross life. of St. Louis, and that too at a time when

He was taken at a very early age into the other men acquired it by the meanest arts, Collége des Grassins, at Paris, in quality and the most degrading submiílions. Be- of Burfur*, and was known there by his fore the revolution, at a period when a

Christian name of Nicolas. Nothing dür-, liberal sentiment might have afforded an ing the two first years announced extraintroduction into the Baltile, he publish- ordinary talents ; but in the third, out ed “ le Soldat-Citoyen," in which he en

of five prizes that were distributed annu. deavoured to inspire a mercenary itanei ally, he bore away four, failing in Latin ing army with the idea of patriotism :

verles alone. The next year his success his attempt did not prove wholly abor was complete; and he made a remark tive. His talents, by fome strange fata- upon the occasion, which discovered good lity, had procured him a place at a dilli- taste, a fuperior mind, and the opinion pated and degenerate court, but he was

he entertained of the judges : " I lost the dismissed in 1790, as his civism rendered prize last year,” said he, “ because I him hateful to M. Guynard St. Priest.

imitated Virgil; this year I obtained it, When a successor to the minister, De. because I took Buchanan, Sarbievius, grave, was thought of, Servan was point- and other moderns, for my guides.' ed cut as a proper one by Roland; and

In Greek he made a rapid progress ; being approved of by the council, and

but his petulance, his wit, and his wagthe patriotic deputies consulted by it, he gifh tricks, threw the class into so much was presented to, and accepted readily by diforder, that he was expelled from it

This is the more remarkable, by M. Lebeau, the professor of that lanas he was personally odious to his 'Ma- guage; an not long after left the col. jefty.

lege altogether. Thrown upon the wide Servan hated, and in return was hared world, without friends or any point of by the court. It was then what they support, he was soon reduced to the themselves were accustomed to term a

lowest pitch of poverty. He bore his combat au mord between the royalists and misfortunes, however, with philofophic the patriots: one party was fure to patience, and cheered himself with the succeed; and which ever prevailed, blood moit Hattering hopes : “I am a poor muft inevitably be lhed. At this period devil now,” said he to Sclis, another Bourdeaux and Marseilles (the latter of man of letters; “ but do you know what which is a Greek colony) were the most will happen? I shall obtain a prize from zealous of all the cities of France, Paris the academy, my play will succeed, I itself not excepted, in behalf of freedom: shall be courted by the world, and well pay, it was thither the friends of free- received by the great, whom I despise : dom had determined to retire, in case of a

they will make my fortune for me, and reverse; that if absolute monarchy reared I shall afterwards”live like a philosoa its head in the North, they' might oppole

pher." it by means of a republic in the Soutn.- The first part of his prediction was Accordingly we find Servan, Barbaroux, foon verified. He ebrained a prize, and and Madame Roland, drawing a line of fent a copy of his production to the very demarcation on the map; studying the M. Lebeau who had expelled him from military positions, and the course of the the Greek class, accompanied by the folrivers; invoking the aid of the Bordelais lowing noçe : "Chamfort sends the work and the Marseillois; and swearing on

that has obtained the suffrages of the Arathe altar of liberty that they would not demy to his old and respectable master; belie the hopes of mankind !

and at the end of nine years begs his

pardon for Nicolas." M Lebcau made CHAMFORT. If a want of the advantages of birth * A kind of inferior ulher, with a {mall predispose us to favour a government stipend. MONTHLY MAG. No. VIII.


the king.

4 N

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