Somebody else (can't remember who) drew attention to this fact and I want to highlight it again:
Neptune was actually seen by other astronomers, and the honour of the theorist obtained additional lustre. But it appears, from a communication of M. Babinet, that this is not the planet of M. Le Verrier. He had placed his planet at a distance from the sun equal to thirty-six times the limit of the terrestrial orbit. Neptune revolves at a distance equal to thirty times of these limits, which makes a difference of nearly two hundred millions of leagues!
Le Verrier predicted that the radius (one of the eliptical axes, probably) of Neptune's orbit was 36 Astronomical Units (the Sun-Earth distance), but Neptune was found to orbit at only 30 Astronimical Units; as reported by Babinet. A *huge* error, I agree.
But ... Both Le Verrier and Babinet agreed that both The Earth and Neptune are in orbit around The Sun. So neither of them were Flat Earth proponents. So the discrepancy between Neptune's predicted and true orbit, huge as it is, does not support a flat Earth.
Babinet supports the observation that the difference between the orbits of Neptune and The Earth is (30-1) Astronomical Units. Converting to miles that's 29 x 92,955,807 = 2,695,718,403 miles. Far, far, far in excess of the distance to the Sun and the planets in Flat Earth Theory (which is only 3,000 miles, I believe).
Whichever way you look at it: the discovery of Neptune is a triumph for the Heliocentric Model of The Solar System and Newton's Law of Universal Gravitation.