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ƒ (b) ƒ (c) denoting forces parallel to the Axes of b and ‹,

Again, by deducing the value of

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&c. from equation 1,

This is the fluxionary or differential equation of which we have spoken; and, as it cannot be integrated, M. La Place transforms it, and interprets it so as thence to deduce several curious theorems.-This is the equation, also, which M. BIOT interprets in the present memoir; and he transforms it by making a, b, c, three quantities introduced, the functions of a, b, c, thus:

a'=f (a, b, c,)

b'=f. (a, b, c,)
c=f1 (a, b, c,)

He then finds the equation, Lo, by substituting for the values of

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&c. in the equation,

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in which , 4, &c. are functions of b' and ' without 4'. Now, if the fluxionary co-efficients of are formed from this series, and substituted in the equation Lo, it will appear that the functions 2, 3, &c. depend on the functions, which are indeterminate. Again, forming from the expanded series

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it easily appears that the series representing their value are completely determined when the first terms of the series are known; that is, when the values of

V. V.

are

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of &c.; and the one can be known from the other in the case when ao; and since the values of the co-efficients

i

&c. are known in all cases when the values are known

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in the particular case of do, the values of

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• &c.

will be completely known also. But do is the equation to

any surface, and consequently

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&c. express

the attraction of the spheroid on the points in space that belong to the surface of which the equation is a'o. Hence M. BIoT deduces this general theorem :

In order to know the attraction of any spheroid whatever on any points whatever in space, it is sufficient to know the attractions of the same spheriod on all the points of a surface that may, at pleasure, be assumed.'

This is a very curious theorem: the simplest case would be to assume ao, the equation to the surface of the attracting spheroid. In this case, from the theorem, we may affirm that the attraction of the spheroid on all points in space may be determined, when the attraction of the spheroid on all points situated on its surface is known.

We shall attend to the papers in this volume which be long to other divisions of science, at a future opportunity.

ART. XV.

[To be continued.]

Mémoires et Lettres, &c. Memoirs and Letters of the Marshal DE TESSÉ, containing ancedotes and facts never before published; relating to the reigns of Louis XIV and Louis XV. 2 Vols. 8vo. Paris. 1806. Imported by De Boffe. Price 148.

No

statement is made by the editor of these volumes, from which we can learn where the manuscripts of this military courtier, who made a considerable figure in his day, have. been thus long concealed, nor how they have been at length obtained: neither have we the means of ascertaining in what degree they have been followed in drawing up the narrative before us. It is said, however, that no papers are Inserted but those of which the originals can be produced, or at least authentic copies of

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them. The publication rests its claim to notice on the ground of its anecdotes and facts relating to the two reigns mentioned in the title page, and which it pretends for the first time to present to the public.

The Comte DE TESSÉ was born in the year 1651, and was devoted from his infancy to the profession of arms; in which he repeatedly distinguished himself, and arrived at the highest rank: but his success was not wholly owing to his military services, since a very considerable share of address, and an early introduction to the mighty Louvois must have in no slight degree aided and accelerated his promotion. He was regarded in his time as a man of talents, of eminent valour, and distinguished by many good qualities, with which was mixed no small portion of alloy. He was little scrupulous about the means of advancement, but executed most of the charges which he undertook with ability and fidelity; and many of them were important as well in the diplomatic as the military line. He was engaged in several negotiations at the court of Turin and Madrid, and was employed in some considerable military commands.

Early in his career, we find him sent on one of those missions of conversion which so deeply tarnish the memory of Louis XIV; we mean the famous dragooning expeditions against the Protestants. M. DE TESSE appears to have undertaken this object as he would have fulfilled any other duty which his profession imposed on him, and to have mixed good humour and pleasantry with the tragic service assigned to him. From a letter which he wrote to Lauvais on this occasion, we shall translate a few passages respecting the city of Orange; which Louis held under the pretence of sequestration, but which was not formally ceded to him till a considerable time later.

The success of the conversions fully answers the expectations which I had formed, and imparted to you; the whole city of Orange is converted, and the state has adopted the same resolution; the gentlemen of the long robe, who shewed a little more resistance, came to the same determination twenty-four hours later; and the whole has been effected peaceably, without violence or confusion. The minister C., the patriarch of the country, alone refuses to hear rea. son; the president of the court of law, who seemed disposed to aspire to martyrdom, as well as the rest of the legal corps, would have become Mohammedans if I had desired it. As to points of faith, the bishop is fully satisfied.'

It is related that the Count sent a detachment to a village, in order to oblige the inhabitants to become converts: but the poor people, terrified by the sight of the soldiers, instantly declared that they were ready to abjure, and consequently the troops were withdrawn. The captain of the party, regretting

that

that his prey was taken from him, on his return said to the Count, "I fancy that they only deceive you; they did not allow us time even to instruct them."

This business, though bad enough, was not the worst in which M. DE T. was employed; for under the Maréchal de Lorges, he was engaged in burning the towns of the Palatinate. He afterward served with repute in Italy, under the brave and magnanimous Catinat. As the plenipotentiary of Louis XIV. he concluded a treaty of peace with the Duke of Savoy, and he successfully negotiated a marriage between a Princess of Savoy and the Duke of Burgundy.

On the authority of the Count, it is here said that Charles of Spain sent the Duke of Uzeda, the first gentleman of his bedchamber, to Rome, in order to consult his Holiness, assisted by such of his cardinals as he deemed most capable of giving advice on the subject of the succession to his crown: a measure which was taken privately, without the knowlege of his queen, or any of his courtiers. The reigning Pope was Pignatelli, who had assumed the name of Innocent XII. After some difficulties, he at length consented to take the matter into consideration in his council, at which attended the cardinals Albano, (afterward Clement XI.) Spinola, and Spada, who advised him to appoint the Duke of Anjou as Charles's successor. The Count states this communication as having been made to him by the Duke of Uzeda himself.

Though M. DE TESSÉ acquired distinction in the Italian campaigas, he stained his reputation with a foul intrigue, grounded equally on ingratitude and injustice; we mean, by an attempt to disgrace at court his friend and benefactor, the Maréchal Catinat, in hopes of superseding him, and being raised to the chief command. In both these aims he was disappointed, but he so far succeeded in injuring Catinat, that, though the latter remained with the army, the weak Villeroi was sent to take the post of honour. This is a foul blot on the memory of the Count.

The Duke of Berwick, who commanded the forces of the two kings in Spain, having differences with the Duke de Grammont, and being out of favour with the queen, the Maréchal DE TESSE was sent there to replace him; and we find a curious paper written by the latter, dated in 1705, giving an account of the state of the court of Madrid at that period. The king (Philip V.) is represented as in the highest degree indolent, as possessing no decision, and never continuing long in the same mind; and as entirely governed by the queen, who, though of good capacity, was a total stranger to state affairs, and never would attend to them, unless some person, male or female, obtained

her whole confidence, and thus rendered them interesting to her. She did not relish the form which was observed in Spain, and would soon have broken through it, in order to live in that free manner which was allowed in France and Piedmont, but the king loved solitude more than the Spaniards themselves, and would have abandoned himself to it altogether, if etiquette had permitted.

The picture which the French commander gives of the Spanish ministers is indicative of a government in the last stage of decrepitude. One is old and incapable, and another is unacquainted with his particular province; a third has some general knowego, but is a stranger to detail; and another refuses all responsibility, and only acts the part of a ommis. • These mer, (says the lively Gallican,) together with a young king wholly governed by his wife, form the envied councils of the court of Madrid; and these four ministers are always at variance, never uniting except to oppose any measure that may establish the authority of the king.' The manner of holding the council, and the state of the war department, are represented in the same ludicrous light; and he speaks of all orders of the state as feeling extreme indifference respecting the choice which was to be made from among the candidates for the crown. The Duke of Medina Celi, the Count of Aguilar, and two archbishops, are stated to be the only persons, besides the ministers, who concerned themselves in political affairs; and M. DE TESSÉ says that the rest of the grandees devoted themselves wholly to their private intrigues and cabals, and were' incapable of being roused, unless a change in their usages was attempted, to which they would on no account submit. Every thing in Spain is in an eternal state of suspence; all is doing and undoing; and the minister is changed every six months.'

It would seem that this Maréchal was more distinguished' by an insight into men and manners, than by the higher attainments in the science of war; and that he was better calculated to excel in diplomacy, than to execute succesfully the duties of a commander. He is no sooner elevated to superior rank than his laurels fade. He attempted, without success, to raise the siege of Barcelona, and became the object of epigrams and pasquinades. If he drove the Duke of Savoy from Toulon, he suffered Suza to be taken before his eyes; and he experienced, on the part of his second in command, the Count de Medavi, the same treatment which the revered Catinat had received from himself: with this difference only, that Medavi could not be reproached with secretly doing ill offices to a

patron

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