Urban Le Verrier was a French mathematician most famous for discovering the planet Neptune based entirely on observations he made about Uranus’s orbit. As Wikipedia describes it,
Le Verrier’s most famous achievement is his prediction of the existence of the then unknown planet Neptune, using only mathematics and astronomical observations of the known planet Uranus. . . . Le Verrier announced his final predicted position for Uranus’s unseen perturbing planet publicly to the French Academy on 31 August 1846, two days before Adams’s final solution was privately mailed to the Royal Greenwich Observatory. Le Verrier transmitted his own prediction by 18 September in a letter to Johann Galle of the Berlin Observatory. The letter arrived five days later, and the planet was found with the Berlin Fraunhofer refractor that same evening, 23 September 1846, by Galle and Heinrich d’Arrest within 1° of the predicted location near the boundary between Capricorn and Aquarius.
In 1859, Le Verrier published a similar conclusion about Mercury’s orbit. Mercury’s orbit couldn’t be completely explained by the existing planets, so Le Verrier hypothesized another as yet undiscovered planet in the solar system.
In 1859, Le Verrier was the first to report that the slow precession of Mercury’s orbit around the Sun could not be completely explained by Newtonian mechanics and perturbations by the known planets. He suggested, among possible explanations, that another planet (or perhaps, instead, a series of smaller ‘corpuscules’) might exist in an orbit even closer to the Sun than that of Mercury, to account for this perturbation.[10] (Other explanations considered included a slight oblateness of the Sun.) The success of the search for Neptune based on its perturbations of the orbit of Uranus led astronomers to place some faith in this possible explanation, and the hypothetical planet was even named Vulcan.
As Real Clear Science notes, a series of fruitless searches for this “missing” planet then began,
But then problems started to arise. Based on Lescarbault’s data, Le Verrier calculated the orbit and size of Vulcan, and instructed astronomers on when and where to watch for the new planet. But when astronomers across the world looked, most of them found nothing. So Le Verrier recalculated and advised them to try again. Again, the vast majority of astronomers saw nothing except for Mercury and the bright, shining Sun. This saga played out over and over for more than a decade, each time with the same results.
Though evidence was turning against planet Vulcan, much of the scientific community continued to support Le Verrier. His calculations, coupled with Newton’s theories, had proven spectacularly correct in the past. Why would they be wrong this time?
Over time, their faith dwindled, but it persisted even as late as 1876. In that year, a volume of the engineering magazine The Manufacturer and Builder reported that, “Our text-books on astronomy will have to be revised again, as there is no longer any doubt about the existence of a planet between Mercury and the sun.” The author apparently chose to focus on the rare confirmatory sightings of Vulcan and to discount all the negative results. (Even in the 19th century, there was poor science journalism apparently.)
The planet, of course, did not exist. In this case what Le Verrier had discovered was not that there was a missing planet, but rather that Newtonian physics was insufficient to explain the observed motions of the planets. Albert Einstein’s general relativity theory would explain the previously unexplained orbit of Mercury without requiring the existence of another planet.