the centre of the system; to give motion to the earth, which the senses declared to be immoveable; to oppose the prevailing opinion of between five and six thousand years; to contradict the reputed truths of revelation; these were obstacles that required a most ardent mind to surmount; and we may rather wonder that Copernicus, a man of science, more attached to his study than to the world, should venture to permit his name to be attached to such heterodox sentiments. Death prevented him from suffering any evil consequences from his doctrine; and it perhaps was favourable to his reputa tion that his book could silently insinuate among the chosen few those notions which must have offended the great and little vulgar of those times, and brought upon the author the censures and punishments of the church.

There were difficulties also in his system which even were too great for some real astronomers to surmount, and these, added to ancient prejudice, gave birth to the system introduced by Tycho Brahe. He perceived clearly that the Ptolemaic system could no longer be maintained; but he was not prepared to dismiss the earth from its ancient station. The circular motion embraced by Copernicus served to keep him in his errors; but his numerous observations were particularly beneficial to science, and prepared the way for the calculations of Kepler, by which a new theory was to be established.

Kepler adopted the Copernican system, and in the year 1600 had the benefit of enjoying the society of Tycho Brahe, at Prague, in Bohemia. Fortunately the Dane was then employed in observations on Mars, with a view to verify its approaching opposition in the sign of Leo; and the degree of excentricity of this planet was a great advantage in discovering the nature of its orbit. Here the opposition between his and his patron's sentiments led to a most laborious examination of ancient tables, and calcula-. tions from them; and the inclination of the orbit, after repeated failures and many injurious methods, was at length. discovered by him to be invariable; and after farther most laborious efforts to make his observations correspond with a circular motion, he found them ineffectual, and was reduced to the necessity of looking out for some other theory.

The labour employed by Kepler in endeavouring to preserve the motion of Mars in a circle is almost incredible, and

the astronomer will appreciate it who gives himself the trouble of considering only the time employed in a few of the calculations which this work contains. From the suspicion that the orbit might not be circular to the conviction that it was not so, neither the time nor the progresses were so long as in previous attempts; yet within this time he had given up his first idea of calculating areas, and might have been lost in the labyrinth of his calculations, if he had not discovered the distances in a circular orbit to be totally inconsistent with those deduced from observation.

But much was to be done before his mind was satisfied, and the necessary steps to obtain this conviction are clearly pointed out; and after all, accident led the way to the great discovery, which was the foundation both of Kepler's and of Newton's fame. He had discovered that the breadth of the lunula, fut off by the real orbit of Mars from the excentric, was but half of that cut off by the oval; and that even at 90° from the apsides, where it was greatest, it did not exceed 660 parts of a semi-diameter, or 152350. His disappointment here was great; but fortunately for him whilst he was contemplating the subject, it occurred to him that these 660 parts were equal to 432 parts of a semi-diameter 100000, that is nearly to 429 the half of 858, which he had found to be in the same parts the extreme breadth of the lunula, cut off in the oval theory; and turning his attention to the greatest optical equation of Mars, which is between 5° 18', and 5o 19', be perceived that 429 was also the excess of the secant of 5° 18′ above the radius 100000. Here new light broke in upon him; he pursued it with ardour; the circular motion was given up for the elliptical, not without extreme perplexity, and "almost approaching to derangement of mind;" and he was occupied in the famous problem afterwards called the Keplerian, from the mean anomaly to find the true, or, by a line drawn from the focus, to divide a semi ellipse in any given ratio.

Nothing but the utmost ardour for science, indefatigable industry, and perfect knowledge of figures, could have enabled the discoverer of the facts relative to the planetary system, to ascertain that the planets moved in elliptical or bits, described equal areas around the sun in equal times, and that the squares of their periodical times varied as the cubes of their mean distances from the

sun. On reviewing his labours we cannot help exclaiming with the poet,

Tante molis erat romanam condere gentem.

To the work before us we would refer our mathematical readers for an insight into these labours; and though there are

some oversights, from the distance we presume of the author from the press, we cannot withhold the tribute of applause for this effort to give the mathematical world a competent idea of the merits of Kepler.

THIS very excellent work cannot fail to be studied with attention by every astronomer. If in the parts which it has in common with our nautical almanac, it can by no means pretend to rival the annual publication of our astronomer royal, the additional parts give it an interest, which must make this work most sought after in foreign countries. The first part contains articles similar to those in the preceding volume; the second part commences with a very interesting history of astronomy for the year 8. In the commencement of it the historian, Jerome Lalande, passes in review various discoveries which have done honour to the eighteenth century. Among them are to be reckoned the discovery of a planet and eight secondaries, sixty-eight comets, the aberration and nutation of the stars, the passage of Venus over the sun, and hence the true distance of the sun and planets, calculations of the irregularities produced by attractions, particularly by those of Jupiter and Saturn, lunar tables exact to a quarter of a minute, and fifty thousand new stars; to these may be added the improvement of instruments, sectors, circles, chronometers, and the telescopes of Short and Herschel.

The commencement of the present century is distinguished by various events. A very curious one is likely to throw some important lights on the theory of the moon's motion. Among the manuscripts of Delisle was found a copy in Arabic of the work of Ebn Jounis, written in the tenth century; the original was discovered to be at Leyden, and the French ambassador, by means usual with the French, procured the transmission of it to Paris. It contains 400 pages in quarto, small character, and Caussin is employed in translating the whole work, which, with the original, will be given it is expected to the public.

The prizes for tables determining the longitude, apogee and node of the moon, were divided between Burg and Bou

vard, who made their calculations from a great number of observations by Maskelyne. These have been increased by Burchhardt, and Parceval and Laplace have both added to the knowledge we have thus acquired on so difficult a subject.

Vidal is remarkable for the number of observations communicated of the planet Mercury, for he sees the planet every day, and even within a few minutes of the sun. This skilful astronomer lives at Mirepoix, where, says our author, "it is probable that no one knows so remarkable à character, whose fame is by this publication to be transmitted to the whole universe, and to posterity."

Mars has given employment to Michael Lalande, to Burchhardt, Triconecher, Oriani, Wurm, who have calculat ed his perturbations; and Bouvard has calculated those of all the planets, by the forms given by La Place.

The grand work on the meridian line from Dunkirk to Rodez has been printed, and Mechain is employed on the southern part. The observations of Vidal on the stars below the tropick, will soon be printed. From the description of the astrolabe found by Gale in Synesius, Delambre has been led to draw up an essay on the history of astrolabes, their construction and properties. Burchhardt has discovered a formula to represent the deviations of the needle observed at Paris since the year 1580, whence it appears that its greatest western deviation is thirty, and its greatest eastern deviation only twenty-three degrees.

The printing of the celestial history has been continued, as well as of the astronomical bibliography. The printing of the table of sines for the thousand parts of a quadrant, begun by Borda, has been completed under Delambre.Triesmacher has collected the calculations of all the eclipses observed since the year 1747; and Goudin has determined all the circumstances which will

take place in the eclipse in the year 1847, the most considerable of the nineteenth century. Duvaucel, who has given delineations of eclipses for the last thirty years, has delineated also this important eclipse for every country, whence it appears that it will be annular in England, France, Turkey, and as far as CochinChina.

Malaspina, whose voyage round the world had been announced, is still in prison, but his observations have been, or will be made use of in the charts now forming in Spain. The king of Denmark has erected a board of longitude, of which Bugge is made director. Schroeter, of Lilienthal, has established a manufactory of telescopes, whence they may be procured, it is said, at a tenth part of the price demanded in London. With his telescopes he has made many observations on Mercury, whose rotation on its axis he calculates at twenty-four hours five minutes. He has frequently seen also through them little streaks of very feeble light, which last two or three seconds; whence it is inferred that the hydrogen and oxygen extend very high in the atmosphere, for the meteors or globes of fire which astonish us at the distance of some hundred rods, become starry streaks at the distance of a league, and telescopical stars at the distance of three or four leagues.

From Egypt we learn the news of the great antiquity of their observations, and the news is eceived without any remark of its incongruity with historical records. We may allow an antiquity of four thousand years; but when they come to seven or fourteen thousand years, nothing but the credulity of French infidelity can entertain the supposition for a moment. The writer, if he has not overcome the prejudices of infidelity, has exhibited the instance of an extraordinary victory over another prejudice, which is very strong in his own country, and not uncommon in ours. He recommended an eminent astronomer for a particular service, but that astronomer was not a Frenchman.

The reason appeared decisive against his being employed; and "in vain did I exert myself," says the writer, "to destroy the prejudice.'

We have thus selected as much as our limits would permit us of this history, which, as it is to be continued annually, will excite an interest among astronomers throughout Europe. The zeal manifest. ed by the French in this respect does them great credit; and it will be followed to the great advantage of science in other nations, if they only follow the French plan of forming a board consisting only of men eminent in the peculiar science which is intended to be encouraged.

A variety of useful tables follows this history: those on Mercury and Mars, and the occultations of some stars, are particularly worthy of notice. The report on the lunar tables, made by La Grange, La Place, Mechain, and Delambre to the board of longitude, is worthy of their high characters. In the History of Astronomy for the year IX. or 18011802, the obliquity of the ecliptic is determined to be 23° 28′ 64", and its secular diminution 36". At Bologna some cu rious experiments on the fall of bodies have been made, to prove the rotation of the earth; and similar preparations are proposed to be made at Hamburgh. Burchhardt has calculated from fifteen thousand barometrical observations, the effects of different winds on their heights; whence he concludes that the mean height with a southern wind is 27 inches 11,3 lines, and with an eastern wind 28 inches 1,9 line. Its height on the shore of the Mediterranean is 28 inches 2,2 lines, and on the shore of the Atlantic 28 inches 2,8 lines.

Two excellent memoirs are given on the new planets Olbers and Piazzi. The longitude of various places is ascertained; and the quantity of 500 pages, which the government has ordered to be annually given to the public, is filled up with matter which must tend very much to promote astronomical researches,

thus enriched the original work with his own observations. His efforts were well received in France, where the mathematics are cultivated with great success, and the readers are not only very numerous, but not to be discouraged by deductions derived from the first elements of arith

metic and geometry. In this country the work will naturally labour under some disadvantages, though the translator has himself added to its utility by inserting several articles omitted by Montucla, and adapting others to the meridian of London. To those who have

made some progress in the mathematics, the Recreations will be really such, and convey beside a great deal of instruction; and the editor deserves well of the mathematical world for giving to so valuable a foreign publication an English dress..

THE several editions of this very valuable work are so well known to the public, that it is not necessary here to enlarge upon the contents of these volumes. It is needless to say that the contents of the former editions are arranged in the best manner, because from the acknowledged talents and abilities of the editor, whose life has been employed in the pursuits recommended by his uncle, and whose investigations, presented to the Royal Society, exceed any thing of the kind in the mathematical world, nothing else could be expected than that this edition should surpass all that have gone before it. The work is absolutely necessary to all who engage in the numerous plans at present for providing for future payments dependent on lives; and the experience the editor has had in one of the greatest magnitude, qualifies him to determine with great precision on the probable stability of those which are born only to wither in a short time, or to take deep root and flourish. Indeed, the advice given by him cannot be too often repeated, that every society of this kind should every five or six years calculate its real value, whence its rise or decline may be determined, or proper correctives be applied. The fluctuating state of property makes a great difference in all these calculations. If the plan is made accurately, according to the Northampton tables, when money is at five per cent. interest, a great change must necessarily take place in the circumstances of the society, if money should rise or fall to six or four per cent. The present state of the country makes these things very precarious; and if Dr. Price was alarmed for the state of the nation, the editor

seems to be justified in his additional fears.

"Had Dr. Price lived to witness the profusion of the last ten years, he would probably have moderated the severity of this censure. The debt which appalled him, when it amounted to 230 millions, has lately swollen to the enormous mass of 540 millions; and the yearly expenditure of a peace-establishment, which he considered insupportable at 16 millions, will in future require an annual taxation of more than $4 millions!The paper-circulation, which he so justly deplored when he first published this work, appears to have been then only in its infancy: it has now completely inundated the country. The coin has disappeared, and the bank, for whose credit he was apprehensive, has for many years ceased to pay its notes in specie. The American war, which he regarded as injurious and disgraceful to the kingdom, has been succeeded by another infinitely more ruinous, and more degrading in its consequences. Had he therefore lived to witness these, and a long train of other calamities, which are too deeply felt to need the recital of them-had he lived to beloid the man, during whose administration they were produced, retiring from office in, triumph, and congratulating the nation on the envied state of prosperity to which it had been lately exalted, he would have changed the object of his resentment, and acknowledged that Lord NORTH had long lost the distinction assigned to him in this preface."

The variety of tables in this work, and the mathematical demonstrations of intricate problems, make it of peculiar advantage to every one engaged in this species of calculation; and the science cannot be under better auspices than those of the editor, who, while he is em balming his uncle's memory, is laying the surest foundation for his own well, deserved fame.

THE heads of a course of lectures are contained in this work, which will be useful only to tutors who are engaged in a similar employment, or those who having gone through a course of natural philosophy, wish to refresh their memory, by reviewing frequently the objects of their studies. Demonstrations are very seldom given to any article; but where they are given, it is done with great taste and judgment. Mechanics, hydrosta tics, aerostatics, hydraulics, pneumatics, acoustics, optics, electricity, magnetism, are analysed in the order specified. The work would have been rendered much more valuable by references to the works where a demonstration might be found of each article: this is done sometimes, but much too sparingly; and we cannot say that the author is always very successful in his definitions. Thus we are told that space is the order of things which co-exist, and time is the order of things which exist in succession; whence few persons, we apprehend, will find any assistance in forming to themselves an idea of the things defined.

In demonstrations we have observed that the author is more successful, and we will insert one on the greatest velocity communicated through an elastic ball to another at rest.

"Let A and C be two given bodies, between which is inserted the body X of intermediate magnitude; if the velocity of A be called a, the velocity of C =

2 A a

2 X

A+~+X+C, a maximum; but the

X

=X, and A C=X2; that is, when X is a mean proportional between A and C."

The difficulties attending the problem of Huygens on the ultimate velocities of bodies descending in fluids are well known. The demonstration of this author is well adapted to the subject.

"Mathematically speaking, bodies descending in fluids will not acquire their ultimate and uniform velocity in any finite time whatever.

=

"The absolute force with which the body descends is the difference between its weight and the weight of an equal bulk of the fluid; and this difference divided by the force, which let us suppose equal to d; now weight of the body will be the accelerating the resisting force increases as the square of the velocity v, and therefore will be equal to some constant quantity multiplied into 2; let this quantity be e, therefore the absolute accelerating force, upon the whole, will be d-ev2. Let the constant force d be repre crement of this force by the resistance, be AK, sented by the given line AC, and let the deand consequently the absolute accelerating force KC; also let the absolute velocity AP of the body be a mean proportional between AC and AK, and therefore in the subduplicate ratio of AK. Let the increment of the resisting force be KL, and the contempo raneous increment of the velocity be PQ; with the centre C, and the rectangular asymptotes AC, CH, let the hyperbola BNS be described, meeting the ordinates AB, KN, LO. Because AK:: AP, the moment of the former KL will be as the increment 2 APQ of the latter; that is, as AP X KC, for the in crement PQ of the velocity is as the absolute accelerating force KC; therefore KLX KN :: AP × KC × KN :: AP, because KC x KN is constant. Therefore the indefinitely little hyperbolic area_KNOL:: AP. And particles KNOL always proportional to the the hyperbolic area ABOLis composed of the space described with that velocity, the particle of time in which KL is generated being given. Consequently, when KC the absolute accelerating force vanishes, that is, when the

motion of the body becomes uniform, the space described ABSHCA, and therefore the time, will be infinite."

TECHNICAL and scientific men are constantly at variance. The technical man, without understanding a single

principle of the art by which he makes his fortune, produces a work whose execution the scientific man neither can nor