These old observations of Flamsteed and those of Le Monnier, combined with those made after Herschel's discovery, were very useful in determining an exact orbit for the new planet, and its motion was considered thoroughly known. For a time Uranus seemed to travel regularly, and as expected, in the orbit which had been calculated for it; but early in the present century it began to be slightly refractory, and by 1820 its actual place showed quite a distinct discrepancy from its position as calculated with the aid of the old observations. It was thought at first that this discrepancy must be due to inaccuracies in the older observations, and they were accordingly rejected, and tables prepared for the planet based on the newer and more accurate observations only. But by 1830 it became apparent that it did not coincide with even these. The error amounted to about 20". By 1840 it was as much as 90", or a minute and a half. This discrepancy is quite distinct, but still it is very small; and had two objects been in the heavens at once, the actual Uranus and the theoretical Uranus, no unaided eye could possibly have distinguished them or detected that they were other than a single star. The errors of Uranus, though small, were enormously greater than other things which had certainly been observed; there was an unmistakable discrepancy between theory and observation. Some cause was evidently at work on this distant planet, causing it to disagree with its motion as calculated according to the law of gravitation. If the law of gravitation held exactly at so great a distance from the sun, there must be some perturbing force acting on it besides all the known forces that had been fully taken into account. Could it be an outer planet? The question occurred to several, and one or two tried to solve the problem, but were soon stopped by the tremendous difficulties of calculation. The ordinary problem of perturbation is difficult enough: Given a disturbing planet in such and such a position, to find the perturbations it produces. This was the problem that Laplace worked out in the _Mécanique Céleste_. But the inverse problem--given the perturbations, to find the planet that causes them--such a problem had never yet been attacked, and by only a few had its possibility been conceived. Friedrich Bessel made preparations for solving this mystery in 1840, but he was prevented by fatal illness.