The planet Vulcan
It was known since long that the perihelion of Mercury does not preserve a constant orientation with respect to sun. It revolves the sun at 573'' per century. The phenomenon would never occur were Mercury the only planet in the solar system. Leverrier had computed that the action of the other planets may account for the translation of the perihelion of Mercury, although not for the velocity of the translation. The computations differed from observation by 43''. The natural hypothesis then was that there must be another unknown planet which disturbs the motion of Mercury.
The systematic search for the hypothetical planet started in 1859. The problem was not considered easy, since the new planet should revolve around the sun within the orbit of Mercury, so it would be very hard to see it against sunlight. Every now and then reports about the planet having been found appeared, only to be called off soon after. In spite of this, the planet was quickly given a name: Vulcan. With time the zeal for the search began to fade off and eventually the question died out without having found its solution. The missing 43'' were finally accounted for by the general relativity theory. According to it, the curvature of the space-time continuum caused by the sun is responsible for the fact that the orbit of a planet is not completely closed after one cycle. This is valid for all planets, of course, but the effect could be best seen in the case of Mercury because of its fast motion and relatively strongly flattened orbit.