difference of exactly six hours in time, or ninety degrees in space, from the meridian of Greenwich. These round numbers are easy in their use and application. They can be taken from or added to the headings of charts, the readings of chronometers, or the values in the astronomical ephemeris, without delay, and with little danger of mistake. The selection of the meridian of Washington, which, as the capital of the country, it will first occur to us to select, would be unsuitable, as the difference between it and the meridian of Greenwich is an inconvenient sum to add or subtract. The meridian of New Orleans cuts the great valley of the West, and approaches the central line of our territory on this side of the Rocky Mountains. It has also the practical recommendation, that between the American and English mendians, the degrees and minutes on the chart will be the complements of each other."

This communication of Mr. Davis was referred by the Association to a committee of mathematical gentlemen, from various parts of the Union, for consideration and report.

THE LONGITUDE OF BOSTON.

Ir will be noticed, that, in his paper on the American Prime Meridian, Lieutenant Davis states that, though the longitude of Boston west from Greenwich is better known than that of any other place on this side of the Atlantic, yet after the lapse of a hundred years, during which observations have been continually going on, there is a probable error of two seconds in the comparative longitude of that place. For some months, however, another means of determining our longitude has been in operation, and it is hoped that, in the course of a year, the longitude of Cambridge, and therefore of any other place in America, west from Greenwich, will be very accurately ascertained. Since the spring of 1849, forty chronometers have been carried to and fro from Greenwich to Cambridge, by every Cunard steamer, and the mean of the variations of the chronometers for each trip being taken, and then the mean for all the trips, it will evidently give the approximate longitude of Cambridge, by giving the difference between the time of the two places, which is easily converted into the difference of longitude.-Editors.

THE PLANET HYGEA.

M. GASPARIS, of Naples, who discovered this planet on April 12, 1849, has furnished the following elements of its orbit, derived from several observations:

This newly discovered planet belongs to the same group with Astræa, Hebe, Iris, Flora, and Metis, all of which are, as will be seen

below, of very recent discovery. The planets known from high antiquity are Mercury, Venus, Earth, Mars, Jupiter, and Saturn. To these, in 1781, was added Uranus, or Herschel, as it is sometimes called, from the name of its discoverer. Early in the present century, astronomers became convinced that a planet existed between Mars and Jupiter, and an association of twenty-four observers was formed to examine the whole heavens. But, early in January, 1801, the present planet Ceres was accidentally discovered by Piazzi, in Sicily. În March, 1802, Pallas was discovered by Olbers, in Bremen, and this was followed, in 1804, by the discovery of Juno, and, in 1807, by that of Vesta. On December 8, 1845, Astrea was discovered by Professor Hencke, and on July 1, 1847, he also discovered Hebe. Iris was discovered August 13, 1847, and Flora, October 18 of the same year, both by Mr. Hind. Metis was, we believe, discovered by Mr. Graham, in Ireland, on April 25, 1848. The recent extraordinary discovery of Neptune is familiar to all. The total number of primary planets discovered, up to the present time, is, it will be seen, 18. Many of them are never visible to the naked eye.-Editors.

INTERESTING ANALOGY IN BOTANY AND ASTRONOMY.

PROF. PEIRCE described to the American Association a curious analogy, which has been more fully developed by the Rev. Thomas Hill, of Waltham, Mass., in a recent review. "If, on any twig of a cherry-tree, we count the leaves from the bottom upwards, we shall find that the sixth leaf is over the first, the seventh over the second, &c. That is, two successive leaves, viewed from above, make an angle with each other equal to two fifths of a circle, and it requires five such intervals to make two complete revolutions. On a twig of the elm, the third leaf is over the first; or the angle between two successive leaves, viewed from above, is half a circle. In the currant, the angle is usually three eighths; that is, eight leaves are required to make three turns, and the ninth leaf is over the first. The angle which two successive leaves, viewed from above, make with each other, in any plant, is generally found to be one of the following series of fractions of a circumference:-,,, 3, 15, 27, 14, 21, 34, &c. Sometimes, however, this angle is one of the following:— 4, 4, 3, 4, &c.; and occasionally we have found, in the golden-rod, fractions of the series 4, 1, 3, &c. Other fractions are found, but we believe that, in a healthy plant, the fractions always belong to a similar series, that is, to a series in which the two first fractions have the numerators each 1, and the denominators differing by 1, and the terms of any other fraction are formed by adding those of the two preceding. Such a series, the higher it is carried, approximates more and more nearly to an aliquot part of the difference between the square root of five and some odd number. Now, if we divide the year of the planet Uranus by that of Neptune, the year of Saturn by that of Uranus, that of Jupiter by that of Saturn, &c., we shall obtain nearly the following frac tions, 103, 1, 25, 131, 12, 13, . The close coincidence of these

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fractions with the successive approximations of the common series for leaves is rendered still more significant by the fact, that one of those two which differs most from the common series, namely, the ratio between the year of Venus and that of the Earth, is one of a series which, in vegetable life, cannot be distinguished from the common, except by the spiral running in the opposite direction; the series, namely, beginning with 1, 1, 3, 2, 5, 3, &c. The year of Venus differs by only about one hour and a half from of the Earth's.

Among the periods of Jupiter's moons, also, we find three ratios, among those of Saturn six, among those of Herschel four, which are nearly approximations in these series. They do not, however, follow the proper order of approximation as they approach the primary_planet.

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Here, then, are two problems, one in astronomy, the other in botany, and both solved by the same arithmetical law. The botanical' problem is, to distribute the leaves, buds, petals, &c. of plants in such wise as to secure a graceful variety of symmetry. The astronomical problem is, to proportion the years of the planets in such wise as to render the conjunction of any considerable number a rare occurrence; to secure, that is, the system from too great mutual interference, by keeping the planets scattered round the sun. This is done by making the years incommensurable, and nearly in the ratio which is measured by approximations to an aliquot part of the difference between some odd number and the square root of five. The botanical problem is solved by setting the leaves at an angle, which is to the whole circle in a ratio measured by the same approximations. And, in both cases, the odd number usually employed is three, and the aliquot part is one half. The ratio between the Earth's year and that of Mars does not conform to this rule."

SECOND COMET OF 1849.

Ir now appears that the telescopic comet discovered in April, 1849, by Geo. P. Bond, of the Cambridge (Mass.) Observatory, was detected the same night by M. Schweizer, of Moscow. Its elements agree quite well with those of the second comet of 1748, so that it may be another instance of the return of a comet after a lapse of a certain period.

CONNECTION OF COMETS WITH THE SOLAR SYSTEM.

THE following is an abstract of a paper presented to the American Association, by Prof. Peirce, on the connection of comets with the solar system. Prof. Peirce stated that there had been a century of exact observations upon comets, so that it seemed worth while to in-` quire if we could not now ascertain whether they are component parts of the solar system, or strangers visiting us from other systems. He believed that the facts were sufficient to decide this question.

If any form of the nebular hypothesis was to be adopted, it was necessary to consider their origin. Upon that theory, the readiest way to account for their existence would be to suppose them strangers to all systems, being produced from portions of the nebulous fluid left between the spheres of stellar attraction. His own opinion was, however, that they are component parts of our system, and that the comets within every system belong to that system.

There were two classes of arguments which might be produced. The first arising from the nature of their orbits, from their not being hyperbolical. Of the hundred comets which had been carefully observed, and whose orbits had been accurately computed during the last century, not one had been shown to have a decidedly hyperbolical orbit. But if the comets do not belong to our system, one half of them, upon the average, ought to move in orbits decidedly hyperbolical. He came to this conclusion upon the ground that our system is moving in space. The very point towards which we are moving had been determined, and very recently, in a paper upon stellar astronomy, by Struve, the deduction had been given of the very amount of the motion of this system in space. Its velocity was computed as about one fourth of the velocity of the earth's motion in its orbit. It would amount to the same thing, to suppose the solar system to be placed in a stream of stars to which the comets belong, and the average velocity of which the comets would possess. Now, by the laws of motion, if the comet came into the solar system with no velocity at all, its orbit would be a parabola; but if its velocity was sensible, it would move in a hyperbola, the form of which would be exactly dependent upon the amount of this velocity. It had been shown by Laplace, that the direction does not influence the character of the form of the orbit, but that from the velocity alone, at a given distance from the sun, it can be determined. But if the comets did not belong to the solar system, there ought to be some of them with very remarkable hyperbolical eccentricity; so that the fact that there are no comets with hyperbolic orbits seemed to be in itself almost decisive proof that they do belong to the solar system. Another effect of this motion in space would be, that the comets would more frequently enter the system upon that side towards which we are moving; which was not found to be the case.

Prof. Peirce then showed, that, according to the doctrine of chances by Laplace, the chance was 71 to 1 that there was an actual law regulating the distribution of comets, and that they really belong to the solar system. A question would then oceur, How are the comets connected with the nebular hypothesis? If a comet had been sent out from the sun by expansion, when it came back it could hardly escape from falling again into the sun, even if thrown tangentially. If sent off from the planets,—and Lagrange had found the necessary force to be comparatively small,-the inclination and direction of the orbits would be about what they actually are: with a tendency towards the plane of the ecliptic, and towards direct motion. The great difficulty was in making the force exactly sufficient to produce the parabola, or lengthened ellipse; for if it was more than this,

however minute the excess, they would pass from the system. Leverrier has shown that the action of Jupiter upon Lexell's comet had changed its orbit into the hyperbolic form. So, with this excess

of motion, they would pass into another system, and thus pass from system to system, until they would pass so near some planet as to have their orbit reduced to the parabola or ellipse.

One remark with regard to the direction from which they come. Out of 90 direct comets, there were 57 which came from the south, and 33 from the north. The retrograde comets were nearly in the same proportion. Out of 94, there were 55 from the south, and 39 from the north. This difference, however, might simply be the accident of observation.

AMERICAN NAUTICAL ALMANAC.

CONGRESS at its last session passed an act authorizing the preparation of a Nautical Almanac, and appropriating $6,000 to commence the work. Lieut. Charles H. Davis was appointed, by the Secretary of the Navy, to take charge of it, and he entered upon his duties as soon as possible. The office is at present situated in Cambridge, Mass., but it will probably soon be removed to Washington. We learn from the report of the Secretary of the Navy, that Lieut. Davis asks for an appropriation of $13,000 to defray the expenses of the work during the ensuing year; this sum will enable him to enlarge considerably the present corps of computers. Lieut. D. has, we are informed, secured the valuable services of Prof. Peirce, of Harvard University, whose acknowledged ability as a man of science, and worldwide reputation as a mathematician, cannot fail to inspire increased confidence in the correctness of the work. Two such men as Lieut. Davis and Prof. Peirce cannot fail to produce a valuable volume. The theory of Mars is now in progress. In the first number, which, on account of the immense amount of labor to be performed, cannot be published till about 1852, the ephemerides of some of the planets will be based upon new theories, which will make them much more reliable than any heretofore published.-Editors.

ASTRONOMICAL JOURNAL.

THE American Association, at its meeting at Cambridge, voted that a journal is needed in this country, to be devoted especially to recording the results obtained by our astronomers, and they referred the subject to a committee, who drew up a prospectus. They say," An Astronomical Journal for the publication of original researches has long been needed in the United States, and the want is growing more urgent every day. American astronomy demands an organ, in which important investigations and observations may be published without delay, and which may serve especially as a magazine for astronomical researches made in this country, as a vehicle of information concerning the labors of individuals, and as an exponent of the general progress of science." They