ASTRONOMY AND METEOROLOGY.

KIRKWOOD'S ANALOGY.

Ar the recent meeting of the Association for the Advancement of Science, an announcement was made, which, if it is found to be correct, will be regarded as relating to one of the most important discoveries which have been made in astronomy for years. It is no less than a new law of the solar system, closely resembling those of Kepler, which form the groundwork of many of the problems of astronomy. Mr. S. C. Walker read to the Association a letter from Mr. Daniel Kirkwood, of Pottsville, Pa., the discoverer of this new law, from which we make some extracts, omitting all that refers to the higher branches of mathematics.

"While we have in the law of Kepler a bond of mutual relationship between the planets, as regards their revolutions around the sun, it is remarkable that no law regulating their_rotations on their axes has ever been discovered. For several years I have had little doubt of the existence of such a law in nature, and have been engaged, as circumstances would permit, in attempting its development. I have at length arrived at results, which, if they do not justify me in announcing the solution of this important and interesting problem, must at least be regarded as astonishing coincidences."

After stating some equations, he gives the following tables as the data on which he has proceeded.

From these data he deduces the following law:

the number of a primary planet's days in its year, is as the cube of the diameter of its sphere of attraction in the nebular hypothesis."

"The square of

"The points of equal attraction between the planets severally (when in conjunction) are situated as follows: —

Between Mercury and Venus,

Miles from the former. Miles from the latter.

66 Venus and Earth,

"It will be seen from the above, that the diameter of the earth's sphere of attraction is 49,864,000 miles. Hence the diameters of the respective spheres of attraction of the other planets, according to my empirical law, will be found to be as follows:

Mercury
Venus

Mars

Diam. of Sph. of Attr.

19,238,000

36,660,000

74,560,000

466,200,000

824,300,000

Jupiter
Saturn

"The volumes of the sphere of attraction of Venus, Mars, and Saturn, in this table, correspond with those obtained from the preceding one; that of Mars extending sixty-one million miles beyond his orbit, or to the distance of two hundred and six million miles from the sun. This is about two or three million miles less than the mean distance of Flora, the nearest discovered asteroid. That of Mercury extends about eleven million miles within the orbit; consequently, if there be an undiscovered planet interior to Mercury, its distance from the sun, according to my hypothesis, must be less than twenty-six million miles. Jupiter's sphere of attraction extends only about two hundred million miles within his orbit, leaving eighty-nine million miles for the asteroids. It is only in the most distant portion of this space, where small bodies would be less likely to be detected, that none have yet been discovered."

Mr. Kirkwood then modestly concludes:

"The foregoing is submitted to your inspection with much diffidence. An author, you know, can hardly be expected to form a proper estimate of his own performance. When it is considered, however, that my formula involves the distances, masses, annual revolutions, and axial rotations, of all the primary planets in the system, I must confess I find it difficult to resist the conclusion, that the law is founded in nature."

After this letter had been read, Mr. Walker said, that, induced by the importance of the subject, he had at once proceeded to verify the data and conclusions of Mr. Kirkwood, and had found that there was nothing in them requiring modification, except, perhaps, the substitution of some more recent values for the masses of Mercury and Ura

nus.

This theory, and that of Laplace with reference to nebulæ, mutually strengthen each other, although the latter has been a mere supposition, while the former rests upon a mathematical basis. later letter, which was also read, Mr. Kirkwood says that he has pur

In a

sued this subject for the last ten years, it having been first suggested to him by the nebular hypothesis, which he thought could be established by some law of rotation.

Mr. Walker then entered into a lengthened examination of the data on which the law rests, and seemed to come to the conclusion, that, as far as we know at present, every thing is in favor of the truth of the law, except that it requires the assumption of another planet between Jupiter and Mars.

Mr. Walker closed his examination by saying,-" We may therefore conclude, that, whether Kirkwood's analogy is or is not the expression of a physical law, it is at least that of a physical fact in the mechanism of the universe. The quantity on which the analogy is based has such immediate dependence upon the nebular hypothesis, that it lends strength to the latter, and gives new plausibility to the presumption that this, also, is a fact in the past history of the solar system.

"Such, then, is the present state of the question. Thirty-six elements of nine planets (four being hypothetical) appear to harmonize with Kirkwood's analogy in all the four fundamental equations of condition for each planet.

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"To suppose that so many independent variable quantities should harmonize together by accident, is a more strained construction of the premises than the frank admission that they follow a law of nature. If, in the course of time, the hypotheses of Laplace and Kirkwood shall be found to be laws of nature, they will throw new light on the internal organization of the planets, in their present and in any more primitive state through which they may have passed.

"For instance, we may compute the distance from the centre at which any planet must have received its projectile force in order to produce at the same time its double movement of translation and rotation.

"If the planet in a more primitive state existed in the form of a ring revolving round the sun, having its present orbit for that of the centre of gravity of the ring, the momentum of rotation must, by virtue of the principle of conservation of movement, have existed in some form in the ring. It is easy to perceive that this momentum is precisely the amount which must be distributed among the particles of the ring, in order to preserve to all the condition of dynamical equilibrium, while those of each generating surface of the ring were wheeling round with the same angular velocity.

If the planets have really passed from the shape of a revolving ring to their present state, the prevalence of Kirkwood's analogy shows a nice adaptation of parts in every stage of the transition.

"If the primitive quantity of caloric (free and latent) had undergone a very great change beyond that now indicated in the cooling of their crusts; if the primitive quantity of movement of rotation had been different from its actual value for any planet; if the law of elasticity of particles for a given temperature and distance from each other varied from one planet to another in the primitive or present states; in either of these cases, the analogy of Kirkwood might have failed. As it is, no such failure is noticed; we are authorized, therefore, to conclude, that the primitive quantity of caloric, the law of elasticity, the

quantity of movement of rotation, the past and present radii of per-cussion, the primitive diameter of the generating surface of the rings, and the present dimensions and density of the planets, have been regulated by a general law, which has fulfilled for all of them the four fundamental conditions of Kirkwood's hypothesis.

"We may extend the nebular hypothesis and Kirkwood's analogy to the secondary systems. If they are laws of nature, they must apply to both. In the secondary systems, the day and month are the same. This fact has remained hitherto unexplained. Lagrange showed that if these values were once nearly equal, a libration sets in round a state of perfect equality; but he offered no conjecture as to the cause of the primitive equality. On the nebular and Kirkwood's hypothesis, it would only be necessary that, upon the breaking up of the ring, the primitive diameter of the generating figure and law of relative density of layers should be preserved."

Professor Peirce, whose opinion will probably be regarded as of more value on such a subject than that of any other man in this country, especially since his successful discussion with Leverrier, remarked, that Kirkwood's analogy was the only discovery of the kind since Kepler's time, that approached near to the character of his three physical laws. Bode's law, so called, was at best only an imperfect analogy. Kirkwood's analogy was more comprehensive and more in harmony with the known elements of the system. The diameter of the sphere of attraction, a fundamental element in this analogy, now for the first time gave an appearance of reality to Laplace's nebular hypothesis, which it never had before. The positive testimony in its favor would now outweigh the former negative evidence in the case, however strong it may have been. It follows at least from Kirkwood's analogy, that the planets were dependent upon each other, and therefore connected in their origin, whatever may have been the form of the connection, whether that of the nebular hypothesis, or some other not yet imagined.

At a later period of the meeting, Mr. B. A. Gould, Jr., stated that he had gone through the necessary calculations, using different quantities, and had come to the same conclusions as Mr. Walker. He expressed his opinion, that at some future day the world will " speak of Kepler and Kirkwood as the discoverers of great planetary laws.' The members generally expressed the opinion, that Laplace's nebular hypothesis, from its furnishing one of the elements of Kirkwood's law, may now be regarded as an established fact in the past history of the solar system.

SHOOTING STARS OBSERVED IN 1849.

THE following observations on the periodical occurrence of shooting stars have been made in various parts of the country during the year 1849. On the night of the 20th of April, 54 different meteors were observed in New Haven, as follows: - in the northwest, 23; in the south, 21; in the northeast, 10. There was nothing remarkable in these as to brilliancy, nor was there any decided point of radiation.

As usual, there was a general motion towards the west. The conclusion arrived at by the observers was, that the number of meteors was not greatly beyond the average.

The meteors, however, of the 10th of August, seem to have appeared in their usual numbers. At Canonsburg, Penn., between the hours of 10 P. M. and 12 A. M., 260 meteors were observed in all. They appeared with great regularity, about an equal number in each quarter of the heavens, and each successive half-hour. About nine tenths of all observed moved towards the southwest, the remaining tenth traversing the heavens in all directions. There was no central point of emanation, though a majority, perhaps, of the whole, appeared to originate in the directions of Cassiopeia and Ursa Major. On the night of the 11th of August, also, meteors were more than usually abundant, but by no means so numerous as on the evening of the 10th. At Mineral Point, Wisconsin, numerous shooting stars were observed on the night of the 9th of August.

At the Cambridge (Mass.) Observatory, although the sky was clear, very few meteors were observed on the 12th and 13th of November. In France, M. Coulvier-Gravier's observations for the August period of shooting stars again this year confirm his views, that the phenomenon is progressive, and not a sudden appearance in great numbers about the 10th of the month. It will be seen, by the subjoined table of his observations, that the increase continued from the 10th of July to the 10th of August, diminishing on the night of the 11th.

In November, the maximum number noticed by M. Gravier amounted to only 40, but they lasted for several days.

The series of observations made by M. Coulvier-Gravier from July, 1841, leads to the general result, that, from December 21st to June 21st, the number of meteors is much smaller than in the second half of the year.

AN AMERICAN PRIME MERIDIAN.

AT the meeting of the American Scientific Association, in August, 1849, a paper on the subject of an American Prime Meridian was presented by Lieut. Davis, U. S. N., from which the following extracts are taken.

"It is a question whether, having a National Observatory, and being about to publish an American Nautical Almanac, we shall still continue to count our longitude from the meridian of Greenwich, or whether it is preferable for convenience, for accuracy, or for other reasons, to establish a new prime meridian on this continent. It would