It is, in the first place, clear from Lescarbault's account that Vulcan must have a considerable diameter--certainly if Vulcan's diameter in miles were only half the diameter of Mercury, it would have been all but impossible for Lescarbault with his small telescope to see Vulcan at all, whereas he saw the black spot very distinctly. Say Vulcan has half the diameter of Mercury, and let us compare the brightness of these two planets when at their greatest apparent distances from the sun, that is, when each looks like a half-moon. The distance of Mercury exceeds the estimated distance of Vulcan from the sun as 27 exceeds 10, so that Vulcan is more strongly illuminated in the proportion of 27 times 27 to 10 times 10, or 729 to 100--say at least 7 to 1. But having a diameter but half as large the disc of Vulcan could be but about a fourth of Mercury's at the same distance from us (and they would be at about the same distance from us when seen as half-moons). Hence Vulcan would be brighter than Mercury in the proportion of 7 to 4. Of course being so near the sun he would not be so easily seen; and we could never expect to see him at all, perhaps, with the naked eye--though even this is not certain. But Mercury, when at the same apparent distance from the sun, and giving less light than at his greatest seeming distance, is quite easily seen in the telescope. Much more easily, then, should Vulcan be seen, if a telescope were rightly directed at such a time, or when Vulcan was anywhere near his greatest seeming distance from the sun. Now it is true astronomers do not know precisely when or where to look for him. But he passes from his greatest distance on one side of the sun to his greatest distance on the other in less than ten days, according to the computed period, and certainly (that is, if the planet exists) in a very short time. The astronomer has then only to examine day after day a region of small extent on either side of the sun, for ten or twelve days in succession (an hour's observation each day would suffice), to be sure of seeing Vulcan. Yet many astronomers have made such search many times over, without seeing any trace of the planet. During total solar eclipses, again, the planet has been repeatedly looked for unsuccessfully--though it should at such a time be a very conspicuous object, when favourably placed, and could scarcely fail of being very distinctly seen wherever placed. The fourth argument of Lescarbault's is not so effective, and in fact he gets beyond his depth in dealing with it. But it is to be noticed that a considerable portion of the discrepancy between Mercury's observed and calculated motions has long since been accounted for by the changed estimate of the earth's mass as compared with the sun's, resulting from the new determination of the sun's distance. However, the arguments depending on this consideration would not be suited to these pages.