eter--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 noti