Vulcan was actually "observed" quite a few times through the telescope by both professional and amateur astronomers. But, Vulcan never really did exist. It was a theoretical construct created to solve a problem in planetary dynamics that never would be solved by the then-standard Newtonian model of planetary motion. The story, with its fascinating twists and turns, the fleeting and ambiguous sightings of Vulcan, and the lengths to which supporters of Vulcan's existence went to explain away the lack of evidence make this story of interest to skeptics.
The story actually starts in 1781 with the discovery by William Herschel of the planet Uranus. It soon became clear to astronomers that Uranus was behaving badly -- it wasn't moving along the orbit predicted for it by Newtonian physics. What could be the matter? Was Newton wrong? Impossible! If Newton wasn't wrong, then he had to be right, and something else had to be causing the odd orbit of Uranus -- something doing so in obedience to Newton's laws. The obvious answer was that there was another planet beyond Uranus, the gravitational influence of which was causing Uranus to orbit as it did.
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