can leave no doubt in our mind that these prophetic types really foreshadowed that diversity of forms which has been created since they have gone by. We may also say that these prophetic types lay before us the course of thoughts which has been carried out in the plan of creation by the Supreme intelligence, who called them into existence in rich order of succession, and in so diversified relations. The recognition of this prophetic character of certain types of extinct animals is not only important in a philosophical point of view; I have no doubt it will ultimately and rapidly lead to a better, fuller, higher, and deeper understanding of the various relations which exist between animals. Let me at once point to some of these relations which might never have been understood but for this appreciation.

Among Crinoids, we have not only progressive types, as I have already quoted, but we have also prophetic ones. The Cystidæ are truly prophetic of the Echini proper. I may only mention the genus Echinocrinus to shew the link.

The Pentremites, again, are the prophetic type foreshadowing the starfishes. And often in subordinate groups we may find such close relations between genera of the same minor divisions; such, for instance, as the genus Encrinus, in which the genera Apiocrinus and Pentacrinus, are simultaneously foreshadowed. Perhaps, in this case, a distinction might be introduced between truly prophetic types and synthetic types, in which the characters of later groups are rather more combined than really foreshadowed.

As for the relation between older types and the embryos of the living representatives of the same families which are so extensively observed in almost all groups of the animal kingdom, which have existed during earlier periods, it may best be expressed if we call those fossils which exemplify, in full grown animals, forms which exist at present only in the earliest stages of growth of our living animals, Embryonic Types, in counterdistinction from the progressive types, and from the prophetic types. These embryonic types may be purely such, or they may be at the same time either progressive types, or even prophetic types. I shall call purely embryonic types those in which we recognise peculiarities characteristic of the embryo of the same family. For instance, the older Sauroids, which have the upper lobe of the tail prolonged, or the common Crinoids provided with a stem, which resemble the young Comatulæ, &c., &c. I shall distinguish, as progressive embryonic types, those in which we recognise simultaneously a relation to the embryo of the same family, when they form besides a link in the natural chain of progressive development. Such, for instance, as the oldest Salamanders, or the earliest Sirenoid Pachyderm. Finally, I shall call prophetic embryonic types those in which we have embryonic characters, combined with the peculiarities which stamp the type as a prophetic one,

such, for instance, as the Echinoid and Asteroid Crinoids of the former ages.

The fact that these different types may thus present complications of their character, or appear more or less pure and typical, goes further to shew how deeply diversified the plan of creation is, and how many relations should be simultaneously understood before we are prepared to have a full insight into the plan of creation. There we see one type forming simply, and alone, the first link of a progressive series. There we see another which foreshadows types, which appear isolate afterwards. There we see a third, which, in its full development, exemplifies a state which is transient only in higher representatives of the same family. And then, again, we see these different relations running into each other, and reminding us that, however difficult it may be for us to see at one glance all this diversity of relations, there is, notwithstanding, an intelligence which not only conceived these various combinations, but called them into real existence in a long succession of ages.-L. Agassiz in the American Association for the Advancement of Science, August 1849.

On a new Analogy in the Periods of Rotation of the Primary Planets discovered by Daniel Kirkwood of Pottsville, Pennsylvania.

At 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 :

:-" The square of

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 points of equal attraction between the planets severally (when in conjunction), are situated as follows:--

"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 emperical law, will be found to be as follows:

"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 61,000,000 miles beyond his orbit, or to the distance of 206,000,000 miles from the sun. This is about 2,000,000 or 3,000,000 miles less than the mean distance of Flora, the nearest discovered asteroid. That of Mercury extends about 11,000,000 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 26,000,000 miles. Jupiter's sphere of attraction extends only about 200,000,000 of miles within his orbit, and leaving 89,000,000 miles for the asteroids. It is only in the most distant portion of this space, where small bodies would be 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 Uranus. 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. In a later letter, which was also read, Mr Kirkwood says that he has pursued 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, everything is in favour 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.

"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 should be found to be the 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 shews a nice adaptation of parts in every stage of the transition.

If the primitive quantity of coloric (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 state; in either of these cases, the analogy of Kirkwood might have failed. As it is, no such failure is noticed; we are authorised, therefore, to conclude, that the primitive quantity of coloric, the law of elasticity, the quantity of movement of rotation, the past and present radii of percussion, 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 hypothethis.

"We may extend the nebular hypothesis and Kirkwood's analogy to the secondary system. 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 shewed 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 opinions 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