of which he himself explains. Having a small sum of money left him, which would not have made any serious addition to his income, he determined to employ it in exploring countries, then rarely visited, and deemed almost inaccessible. On his arrival he placed himself in a convent of Copts, till he had become master of the language. Having spent several years in these countries, he produced his well-known Travels. He piques himself on rejecting the mode of writing adopted by the vanity of his predecessors, in which half the work is filled with their personal adventures. We are not fully prepared to admit this as the mode calculated to give the liveliest idea of a country. Still it has no doubt important advantages, and is so managed by him as to produce a valuable work. He combines accurate observation with animated description, and gives certainly a much juster idea of the general character of the country than his predecessor, Savary, though he criticises, perhaps too severely, the gay images called up by the lively imagination of that engaging writer. The Empress of Russia, in testimony of her esteem for this work, sent the author a medal, which, however, he returned after her declaration of war against France, saying, "If I obtained it from her esteem, I can only preserve her esteem by returning it."

On the breaking out of the revolution, Volney embraced with ardour the popular cause, and was elected a deputy in the Assembly of the States General. In 1790, he published a pamphlet, strongly recommending the division of landed property into small partitions, as the most favourable to its productiveness and the general prosperity of the state. He afterwards spent two or three years in Corsica, endeavouring, without success, to improve the political and economical state of that island, which, from its unset

VOL. XIV. PART I.

tled and independent state, has afforded so wide a field to political project

ors.

About this time (1791,) Volney produced his celebrated work, called "The Ruins, or a Survey of the Revolutions of Empires." It is certainly distinguished by several splendid pas sages, though it is to be regretted, that heigives full scope to sceptical opinions on some of the most important subjects. In this view, we cannot consider him as very formidable, as, notwithstanding his powers of diligent research and lively observation, his speculations ap. pear to us usually fanciful and superficial. Dr Priestley wrote an answer, which is charged by Count Daru, as marked by a degree of violence and acrimony unbecoming a philosopher. This, though prompted by good motives, is doubtless blameable, especially in one, who, like Priestley, assumed so wide a latitude in his own opinions.

On returning to Paris, Volney found the reign of terror in full sway; and, like every one whose opinions were at all moderate, became the object of its proscription. He was imprisoned for ten months, but released on the downfall of Robespierre. The Directory were then seeking to repair the wrecks made by jacobinical madness. One of their plans was to form a normal school, destined to become the centre of French instruction; and here Volney was appointed to lecture on history. His lectures were greatly admired, and attended by immense crowds; but, the institution not succeeding as had been expected, was soon closed, and he was forced to interrupt the course of a labour so gratifying to his taste.

Thus left at leisure, Volney again left his country in pursuit of knowledge. Having seen man in the East in a state of decay, and in Europe of maturity, he now sought to view him in infancy, and therefore went to observe the savages of America. His impres

sion, as communicated in a volume published after his return, is very unfavourable, and, in our opinion, somewhat tinctured by disappointment and prejudice.

While Volney was absent in America, he was named an original member of the French National Institute, then founded. After his return, he enrich ed its Transactions with a justification of the chronology of Herodotus. In 1818, he produced his most elaborate work, entitled, "Researches into the History of the most Ancient Nations," which Daru pronounces his master piece. We have not yet perused it. He then engaged in three works, illustrative of the oriental languages, but was interrupted by death on the 20th

April, 1820. He left, however, a premium for the prosecution of these in quiries.

Having, in the biography of this volume, had occasion to embrace both the present and the former years, we have included only political and literary names of the first rank. Even in this view, some omissions may be observed, more particularly in regard to Scotland (Reunie, Gregory, Brown, &c.) The delay is founded on the hope of obtaining more ample information than has yet been communicated to the public, but which we found it impossible to include in the present volume, without retarding its publication be yond the desired period.

formation of lunar tables, founded solely upon the theory of universal gravitation, a number of attempts have been made, which, though not altogether successful, can scarcely fail to be of service in ultimately bringing to perfection a subject of so great importance to navigation. In the Annales de Chimie, (x111. 250.) M. de Laplace has shewn, with great clearness and precision, the advantages which the lunar theory may derive from the concu rent labours of astronomers, as well as the points in which it is incomplete, and to which their labours should be directed. By the labours of geometers, the lunar theory had already made such advancement, that, in the seventh book of the Mécanique Celeste, the greatest difference between the coefficients of the inequalities of the analysis there given, and those of the tables of M. Burg, was reduced to 8.5". Hence it was natural to conclude, that, by means of approximations carried still farther, the theory would represent observations within the limits of the errors of which they are susceptible. The two papers to which the Academy adjudged a reward in 1820, fulfil this condition, and are the result of immense labour; leaving no doubt, that, on a comparison with our present lunar tables, the formula they contain, when reduced to tables, will agree with observation within the limits already indicated. This is directly established by the author of the first paper, M. Damoiseau, who, according to his theory, has formed new tables, which, compared with sixty observations of Bradley, and sixty observations made since the year 1802, only produce slight errors of the same order with those of the tables of Burg and Burckhardt. We may therefore hope, that, by the examination of a great number of observations, the author will improve still farther the arbitrary elements of the theory, and at

length give to his tables all the accuracy which can be desired.

The authors of both these Memoirs have set out from diferential equations of the celebrated problem of the three bodies, in which the differential of the true movement of the moon, referred to the ecliptic, is supposed constant; and they have determined the mean longitude, the latitude, and parallax of that body, in series of sines and co-sines of the angles, inc easing popo ionally to its tave movement. This is the method employed by Laplace, in the seventh book of the Mecanique Celeste already referred to, and appears to give the most converging approximations. Indeed, the disturbing forces present themselves under that form, or are easily reducible to it. To reduce them to another form,-for example, that of the series of sines and co-sines of the angles, increasing proportionally to the time, the approximations would require to be carried very far, by reason of the considerable inequalities of the lunar orbit; which would render the analysis more complicated, and the approximations less convergent. Other forms of series have been tried, and it would be easy to imagine a great number; but none appears better calcu lated to give the coefficients of the lu nar inequalities. Nevertheless, some very small inequalities, of which the argument increases with great slowness, may be better determined by other methods. In the preceding, these inequalities, in virtue of repeated integrations, acquire, as divisors, the squares of the very small coefficients of the true longitude of their arguments. In the final result, these square divisors disappear, and are reduced to the first power; so that this result, being the difference of quantities very great in relation to itself, becomes inexact, unless we are careful to preserve, in the course of the computation, all the

quantities of its order. By neglecting this circumstance, several geometers have failed in determining the inequality depending on the longitude of the node of the lunar orbit. Uniformity of method certainly gives elegance to analysis; but when it is proposed to approximate, as nearly as possible, ana lysis to observation, the methods employed must be varied according to the nature of the inequalities; for it is in the selection of these methods, and in foreseeing the quantities that may become sensible by successive integrations, that the art of approximation consists, an art no less useful to the progress of science, than the discovery of analytical methods.

Laplace having discovered, by theotry, the cause of the inequalities in the secular motion of the moon, the two papers above referred to have verified and conûrmed the results to which that eminent philosopher was conducted by his profound analysis, particularly that relative to the motion of the perigee in proportion to its magnitude. The form

of the analytical expressions of the first, being the same which he had adopted in the seventh book of the Mécanique Celeste already referred to, he was enabled to compare these expressions with his own; and he found, that they agreed in the degrees of approxima tion which are common to both, but that the authors of the papers having carried these approximations farther, the new terms introduced by them have produced differences, inconsiderable, indeed, in regard to the secular equations of the mean motion, and of the perigee, but sensible in relation to the motion of the nodes. The following table exhibits the numerical coefficients, by which, in order to find the secular equations, we must multiply the integral of the product of the differential of the time by the excess of the square of the eccentricity of the terrestrial orbit above the same square at any arbitrary epoch of time, which, in this case, was fixed at the commencement of 1801 :

The authors of the Second Memoir, MM. Plana and Carlini, in the expression of the secular inequality of the mean motion, have not attended to the terms depending on the square of the eccentricity of the lunar orbit; and which, rendered sensible by the small divisors which they acquire in the course of the integrations, produce the difference of results observable in the two communications. Laplace thinks that the difference, in regard to the secular inequality of the perigee, proceeds from the nature of the approximations employed, by the authors' having reduced their expressions to series, disposed according to the ascending powers of the relation of the motion

Mécan. Celeste. 0.0083660

-0.0229890 -0.0251023 0.0051936

0.0061528

2d Memoir. 0.00760102 -0.0311110 0.0053877

of the sun to that of the moon, a relation less than a twelfth. MM. Plana and Carlini find, in the mean lunar motion, a secular inequality equal to the product of -0.1398", by the cube of the number of periods elapsed since 1801. This inequality, which would increase the longitude of the moon at the moment of its eclipses, in the years 719 and 720 before our era, about 37, depends, according to them, on supposing the true ecliptic transposed to a fixed ecliptic, for example, that of 1801; but they have not attended to the secular transposition of the lunar orbit to the same ecliptic, which would have destroyed the result at which they have arrived. have arrived. Laplace has shewn,