So the next thing was to calculate backwards, and see if by any possibility the planet could have been in that place at that time. Examined in this way the tabulated observations of Flamsteed showed that he had unwittingly observed Uranus five distinct times, the first time in 1690, nearly a century before Herschel discovered its true nature. But more remarkable still, Le Monnier, of Paris, had observed it eight times in one month, cataloguing it each time as a different star. If only he had reduced and compared his observations, he would have anticipated Herschel by twelve years. As it was, he missed it altogether. It was seen once by Bradley also. Altogether it had been seen twenty times. 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. It was not an _exact_ ellipse, of course: none of the planets describe _exact_ ellipses--each perturbs all the rest, and these small perturbations must be taken into account, those of Jupiter and Saturn being by far the most important. 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 at first thought 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 would not accurately obey even these. The error amounted to some 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. [Illustration: FIG. 93.--Perturbations of Uranus.