
The sightings were apparently spurious.  There is no planet inside of
the orbit of Mercury.

The idea of Vulcan came from the differences between Mercury's observed
perihelion precession and the value it should have had according to
Newtonian physics.  Leverrier made an extensive set of observations
and calculations during the mid 19th century, and Simon Newcombe later
improved on the observations and re-calculated using Leverrier's system
of equations.  Now Leverrier was one of the co-discoverers of Neptune
and since he had predicted its existence based on anomalies in the orbit
of Uranus his inclination was to believe the same sort of thing was
afoot with Mercury.

But alas, 'twere not so.  Mercury's perihelion precesses at the rate
it does because the space where it resides near the sun is significantly
curved due to the sun's mass.  This explanation had to wait until 1915
and Albert Einstein's synthesis of his earlier theory of the electrodynamics
of moving bodies (commonly called Special Relativity) with Reimanian 
geometry.  The result was the General Theory of Relativity, and one of
it's most noteworthy strengths is that it accounts for the precession
of Mercury's perihelion almost exactly.  (Exactly if you use Newcomb's
numbers rather than Leverrier's.)

Of course not everybody believes Einstein, and that's fine.  But subsequent
efforts to find any planets closer to the sun than Mercury using radar
have been fruitless.

-Bill Gawne

 "Forgive him, he is a barbarian, who thinks the customs of his tribe
  are the laws of the universe."                       - G. J. Caesar