From Leverrier's calculations, it appeared that the time of revolution of the new planet would be 19 days 17 hours, its distance from the sun about 147, the earth's being taken as 1,000; giving for Mars, the earth, Venus, Mercury, and Vulcan (as the new planet was named), the respective distances 1, 524, 1,000, 723, 387, and 147. Leverrier assigned 12-1/5 degrees as Vulcan's inclination, and the places where it crosses the ecliptic he considered to be in line with those occupied by the earth on or about April 3 and October 6. Judging from Lescarbault's statement respecting the apparent size of the dark spot, Leverrier concluded that the volume of the stranger must be about one-seventeenth of Mercury's, the masses being presumably in the same proportion. Hence he inferred that the new planet would be quite incompetent to produce the observed change in the orbit of Mercury. Leverrier further found that the brilliancy of Vulcan when the planet was furthest from the sun on the sky (about eight degrees) would be less than that of Mercury when similarly placed in his orbit, and he hence inferred that Vulcan might readily remain unseen, even during total eclipse. Here, as it seems to me, Leverrier's reasoning was erroneous. If Vulcan really has a volume equal to one-seventeenth of Mercury's, the diameter of Vulcan would be rather less than two fifths of Mercury's and the disc of Vulcan at the same distance about two-thirteenths of Mercury's. But Vulcan, being nearer the sun than Mercury in the ratio of 147 to 387, or say 15 to 39, would be more brightly illuminated in the ratio of 39 times 39 to 15 times 15, or nearly as 20 to 3. Hence if we first diminish Mercury's lustre when at his greatest apparent distance from the sun in the ratio of 2 to 13, and increase the result in the ratio of 20 to 3, we get Vulcan's lustre when he is at his greatest apparent distance from the sun. The result is that his lustre should exceed Mercury's in the same degree that 40 exceeds 39. Or practically, for all the numbers used have been mere approximations, the inference is that Vulcan and Mercury, if both seen when at their greatest distance from the sun during eclipse, would probably shine with equal lustre. But in that case Vulcan would be a very conspicuous object indeed, at such a time; for Mercury when at his greatest distance from the sun, or greatest elongation, is a bright star even on a strongly illuminated twilight sky; moreover, Vulcan, when at either of his greatest elongations, ought to be visible in full daylight in a suitably adjusted telescope. For Mercury is well seen when similarly placed, and even when much nearer to the sun and on the nearer part of his path where he turns much more of his darkened than of his illuminated hemisphere towards us. Venus has been seen when so near the sun that the illuminated portion of her disc is a mere thread-like sickle of light. Nay, Professor Lyman, of Yale College, in