"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.