The Pentremites, again, are the prophetic type foreshadowing the star-fishes. 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:—

Planet's name.Mean dist. from
the sun in miles.		Mars.Square
root of
Mars		No. of rotations
in one sid.
period.
Mercury,36,814,000277,000526·387·63
Venus,68,787,0002,463,8361·569·6230·90
Earth,95,103,0002,817,4091·678·5366·25
Mars,144,908,000392,735626·7669·60
Jupiter,494,797,000953,570,22230·879·810·471·00
Saturn,907,162,000284,738,00016·874·124·620·00
Uranus,1,824,290,00035,186,0005·931·5

From these data he deduces the following law:—“The square of 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.”