The French mathematician Urbain Le Verrier, co-predictor with
J.C. Adams of the position of Neptune before it was seen, in an 1860
lecture announced that the problem of observed deviations of the
motion of Mercury could be solved by assuming a planet or a second
asteroid belt inside Mercury's orbit. The only ways to observe this
planet (or asteroids) was if/when it transited the Sun or during total
solar eclipses.

In 1859, Le Verrier had received a letter from the amateur astronomer
Lescarbault, who reported having seen a round black spot on the Sun on
1859 March 26, looking like a planet transiting the Sun.  From
Lescarbault's observations, Le Verrier estimated a mean distance from
the Sun of 0.1427 AU (period of 19.3 days).  The diameter was
considerably smaller than Mercury's and its mass was estimated at 1/17
of Mercury. This was too small to account for the deviations of
Mercury's orbit, but perhaps this was the largest member of an
asteroid belt?  Additional support for such objects was provided by
Prof. Wolf and others at the Zurich sunspot data center, who
identified a total of two dozen spots on the Sun which fit the pattern
of two intra-Mercurial orbits, one with a period of 26 days and the
other of 38 days.

Le Verrier fell in love with the planet and named it Vulcan.  In 1860
Le Verrier mobilized all French and some other astronomers to find
Vulcan during a total solar eclipses---nobody did. Wolf's suspicious
"spots" revived Le Verrier's interest, and just before Le Verrier's
death in 1877, there were more "detections."  On 1875 April 4, a
German astronomer, H. Weber, saw a round spot on the Sun. Le Verrier's
orbit indicated a possible transit on April 3 that year, and Wolf
noticed that his 38-day orbit also could have performed a transit at
about that time. That "round dot" was also photographed at Greenwich
and Madrid.

There was one more flurry of "detections" after the total solar
eclipse at 1878 July 29: Small illuminated disks which could only be
small planets inside Mercury's orbit.  J.C. Watson (professor of
astronomy at the Univ. of Michigan) believed he'd found *two*
intra-Mercurial planets! Lewis Swift (co-discoverer of Comet
Swift-Tuttle, which returned 1992) also saw "Vulcan"---but at a
different position than either of Watson's two "intra-Mercurials." In
addition, neither Watson's nor Swift's Vulcans could be reconciled
with Le Verrier's or Lescarbault's Vulcan.

After this, nobody ever saw Vulcan again, in spite of several searches
at different total solar eclipses.  In 1916, Albert Einstein published
his General Theory of Relativity, which explained the deviations in
the motions of Mercury without invoking an additional planet. In 1929
Erwin Freundlich photographed the total solar eclipse in Sumatra.  A
comparison with plates taken six months later showed no unknown object
brighter than 9th magnitude near the Sun.

What did these people really see? Lescarbault had no reason to tell a
fairy tale, and even Le Verrier believed him. It is possible that
Lescarbault happened to see a small asteroid passing just inside
Earth's orbit. Such asteroids were unknown at that time.  Swift and
Watson could, during the hurry to obtain observations during totality,
have misidentified some stars, believing they had seen Vulcan.

"Vulcan" was briefly revived around 1970-1971, when a few researchers
thought they had detected several faint objects close to the Sun
during a total solar eclipse. These objects might have been faint
comets, and comets have been observed to collide with the Sun.