his office, and to take possession of his dominions, his taste for magnificence was openly displayed: while his appointment of Sadoleti and Bembo, to be his secretaries, was considered as a proof of his predilection in favour of learned men. He employed his utmost exertions to avert from Italy the storm which threatened it from the invasion of Louis XII.; and on the signal discomfiture of the arms of that monarch at Novara, as well as on occasion of the other disasters which crowded on him, the Pope endeavoured to moderate the resentment of his enemies, and to effect a reconciliation between them and him. At this period, the flames of war over-ran nearly the whole of Europe; while the sovereign pontiff, exercising the duties of the common father of christian princes, made every exertion in his power to allay and extinguish them. We find him creating new cardinals; and in the list appears the name of his cousin Giulio, afterward Clement VII. He also regulated the go. vernment of Florence, and entrusted it to Lorenzo his nephew. The moderation of Leo is strikingly exhibited in the pardon which, in opposition to very powerful remonstrances, he extended to the refractory cardinals, the schismatic fathers of the council of Pisa. That nothing might be wanting to complete the splendour of the commencement of the new Pontiff, Louis XII. sued for absolution from the sentence of excommunication passed on him by Julius XII., which he obtained on submitting to the humiliating terms which were prescribed to him.

Much credit is allowed to Leo by his biographer, on the score of his having prevented the execution of a projected league between Louis XII., Ferdinand, and Maximilian. Mr. Roscoe is also of opinion that his holiness was intitled to great praise for effecting a peace between Louis and Henry VIII.; a peace in which, he contends, the interests of the latter were well consulted, whatever were the motives by which the negotiator of it (Wolsey) might have been actuated. The author admits that, at this period, the Pope was devising bold plans for the aggrandizement of his house; and that he aimed at nothing less than the establishment of his brother Giuliano on the throne of Naples, with the addition of Urbino and Ferrara to Florence, which was to be a provision for his nephew Lorenzo. He also states that, in order to realize these brilliant schemes, Leo sought the alliance of the king of France; and it is supposed that these dreams of a disordered imagination formed the heads of a treaty, which he at this time submitted to that monarch. Because Louis took a longer time than the impatience of his holiness would allow to be necessary before he returned an answer, the Pope concluded that his proposals were rejected,

rejected, and renewed his treaties of mutual defence with the Emperor and the king of Spain: when on the day after the signing of these compacts, he received the ratification of his proposals by the king of France. We have here a character. istic trait of Leo as a temporal sovereign: since we find him, shortly after he had lost sight of these splendid projects, exerting all his influence to prevent the Duchy of Milan from falling into the hands of the French.

Every reader of history is acquainted with the manner in which the infidelity of Maximilian, and the jealousies between the Spanish and Papal troops, occasioned Milan to become the easy prey of Francis I. The conduct of the Pope was marked by uncertainty and hesitation; and he seemed more anxious to keep open the door to reconciliation with France, than to at tain the objects of the league of which he was the prime mover. His behaviour was throughout pusillanimous, and his fears induced him to agree to a hard treaty with Francis. This decision led to an interview between the two potentates, at which the pragmatic sanction was abolished, and the celebrated concordat was settled.

Commendation is bestowed on the Pope for counteracting the treaty of Noyon, by a league between the Emperor, the kings of England and Spain, and his holiness. The peace of Europe was established at this time, the Emperor and Venice came to an understanding, Francis and the Swiss were reconciled, and the treaty called the perpetual alliance was settled at Friburgh. While these great transactions were carrying on, the Pope, by arms and negociations, subjugated the Duchy of Urbino, in which he established his nephew Lorenzo. Having suppressed a most dangerous conspiracy among his Cardinals against his life, he added thirty-one new members to the college, and thus ensured tranquillity and security during the remainder of his reign.

The victories of Sultan Selim, in Persia and Egypt, now excited considerable alarm in this quarter of the globe; and we find the Pope, as the first potentate of Christendom, taking measures to prepare a barrier against the inroads which it was apprehended this powerful enemy of the cross would attempt. The proposals of his holiness were respectfully received by the leading christian powers, and promises were liberally made to him that they would zealously co-operate for the common defence. He now availed himself of this period of tranquillity in Europe to aggrandize the holy see, by adding to it several of the neighbouring territories. Treachery of the blackest dye, and stratagems of the most dishonourable kind, seemed to cost him little effort, provided that he could attain his object. His

behaviour

behaviour in this respect shews that he disregarded fame and reputation; and that, if he fell short of the worst of his predecessors in unjust aggressions, it was because he was less able and active, and more pusillanimous.

We have now gone over the civil history which these volumes embrace; and we would only observe here, that, considering the object of the work, the admirable histories of the period which already exist, and the comparative little influence which this celebrated pontiff appears to have possessed in the civil affairs of the time, a more brief relation of them might have sufficed. In the remaining part of this article, we shall touch briefly on the author's narrative of the ecclesiastical transactions which render this period so remarkable, in order to enter more at large into his account of the progress of letters in the course of it, which must have been the leading object in his great undertaking, and certainly was that to which the expectations of the public were directed; we shall then advert to his portrait of Leo, observe on his general plan and his style of narration, and conclude with a summary of our sentiments on the pretensions of the work. We abstain from all such remarks till our readers are in possession of the whole outline of the performance.

[To be continued.]

ART. II. A complete Collection of Tables for Navigation and Nautical Astronomy; with simple, concise, and accurate Methods for all the Calculations useful at Sea: particularly for deducing the Longitude from Lunar Distances, and the Latitude from two Altitudes of the Sun and the Interval of Time between the Observations. By Joseph de Mendoza Rios, Esq. F.R.S. 4to. pp. 717. l. 18. Boards. Faulder, &c. 1806.

IT

T is known, and it would be a species of ingratitude not to recollect the illustrious fact, that Dr. Maskelyne, the Astronomer Royal, published a set of Requisite Tables with the first nautical Ephemeris, viz. that of 1767: the design of these two works being to enable the mariner, expeditiously and with a great degree of precision, to find the latitude and longitude, after he had made the necessary observations with an Hadley's quadrant or sextant. Ten thousand copies formed the first edition of the Requisite Tables, which were sold off in a few years; and in consequence a new impression, much altered and improved, appeared in 1781.

The chief and important object, contemplated by the Astronomer Royal in the publication of the Ephemeris and Tables, was the determination of the longitude by means of the Moon's

distance

distance from the Sun, or from a fixed Star. This distance can be measured by a quadrant: but, from the effects of Parallax and Refraction, the observed distance is only apparent, and not true. It was necessary, then, to possess an easy method of determining the true from the apparent; or of clearing, according to the usual annunciation of the problem, the moon's distance from the effects of parallax and refraction. With regard to its analytical solution, this problem is not difficult: let a, A be the apparent and true altitudes of the moon, and I, H, the apparent and true altitudes of the sun or star: let d be the observed and D the true distance; then, by the solution of a spherical triangle, the finding the value of an included angle at once gives us this equation:

(1)

cos. D-sin. A. sin. H

cos. A. cos. H

cos. d-sin. a. sin. h
cos, a. cos. h

;

and from it, the value of cos. D is easily expressed, or the problem is analytically solved: but the solution, which could be immediately deduced from the above equation, would not be conveniently adapted to arithmetical operations. The form under which Mr. Dunthorne expressed the value of cos. D was by no means commodious. In the arithmetical operation, it was necessary to employ logarithms and natural cosines; and on this account Dr. Maskelyne altered the form, and enabled the computist to deduce the distance by means of logarithms alone. The same ingenious author, in his preface to Taylor's Logarithms, gave a new rule for clearing the moon's distance, founded on a formula easily deduced from the equation (1) which we have already exhibited: the formula is this;

where is an angle, such that tan. 0 =

I

cos. Acos. H

플 § `cos. sin.),d=H)▼ { {sin. £ d+(a−b)){(sin.§ d—(a−b) `c

(A-H)

Cos. a. cos. h

Similar to this, M. Borda deduced a formula, perhaps rather preferable, viz.

The application of logarithms to either of these two last formule is immediate and easy; and there would be an end of Rav. Oct. 1806.

K

the

the investigation, if we merely required a direct and exact me thod but something more is necessary for the mariner, whose education and employments exact a mode which shall be easy and compendious. Now it is not to be dissembled that the methods of Maskelyne and Borda are rather tedious: they require several logarithms to be taken out; and every one who has used Taylor's logarithms has experienced that logarithmic sines, &c. are not to be taken from them very expeditiously. For these reafons, other formulæ and methods of computing the true distance have been suggested; and since, in such an inquiry, practical utility was the principal object, the Academy of Paris proposed the problem under the following terms: "To find, for reducing the apparent distance of two stars to the true distance, a sure and rigorous method, and which in practice requires only simple calculations within the reach of the greater number of navigators." To solve the problem with these conditions, M. Kraft, in the Nova Acta Petropolitana, Tom. VII. p. 365, published a memoir, in which he put the reduced distance under this form :

vers. sin. D= v. sin. (d+w) + v. sin. (d—w) + v. sin. (A— Hy

-v. sin. (a−btw) — v. sin. (c—b—∞)

in which, cos. w = 0.5001343⋅

cos A

cos. a

;

and after the caculation of w, the true distance by this formula would result from arithmetically combining five versed sines. After the deduction of his formula, M. Kraft gives a slight spe cimen of a table constructed for w, subjoins an instance in which he computes his five arguments, and then by a table of versed sines calculates the distance. The advantages of this method are next stated; and it is clear that it is short, and that its use demands in the mariner no knowlege of logarithms nor of trigonometry. In the latter part of the memoir, two other formulæ are added.

It was probably this memoir of M. Kraft, that directed M. Mendoza de Rios, the author of the present Tables, to the invention of a similar formula, and to the construction of Tables derived from it. We have used the term probably, because, not being apprized of what M. Mendoza has written in the Spanish language, we conceive that the Connoissance des Temps for 1796 contains his first published notions on the problem of the moon's distance. In that ephemeris, the author lays down a formula which is similar, as we have just said, to that of M, Kraft; viz.

(5) v. sin. D=v. sin. (d+w) +v. sin. {d—w}+v.sin. (a+b+w)

+ v. sin.