NOTE.--Such, at least, is rather a representation of American opinions than of our own. We are inclined to compare it more with Bode's law than with Kepler's. The former is a mere arithmetical accident, applying indifferently well to a portion only of the planets, and having nothing of reason to advance for its establishment. The latter are essential parts of mechanics and gravitation, and precisely and perfectly, and necessarily true, not only in every part of the solar system, but through the whole universe.
The fact of axial rotations being the groundwork of Kirkwood's analogy seems fatal to it, for gravitation takes no more account of the time of rotation of a planet than it does of specific gravity; all calculations of the movement of the body in space are equally independent of the one and the other.
Under these circumstances, the degree of accuracy with which it may be found to apply is the only saving clause. Messrs Walker and Gould investigating the subject independently, and with better constants of mass and distance than Kirkwood had been able to procure, declare that it appears _perfectly_! We are sorry that the late hour at which we have received this paper has prevented us either from giving it in full, or from testing the theory rigidly.
It will be observed that, according to Kirkwood's theory, in order to compute the time of axial rotations of any planet, it is necessary to have its mass and mean distance, together with the same quantities for the planets on either side of it. Now, these quantities are only obtainable for Venus, the Earth, Saturn, and Uranus (a planet being lost between Mars and Jupiter); and the rotation of Uranus not having been obtained as yet, there remains only the three first by which the theory can be tested.
In a preliminary calculation which we have instituted, we do not find the results so accordant as we had been led to expect, but still sufficiently so to give a certain probability of the approach to truth, in a case where the quantity had not been observed.
Viewed in this light, some very interesting results are obtained.
_1st_, The idea entertained by Bianchini and other observers, that the rotation of Venus is nearly 24 times as long as hitherto supposed, is utterly untenable.