and the catalogue would by that entry be wrong.  The thing to do, therefore, was to examine all the catalogues for errors, to see whether the stars entered there actually existed, or whether any were missing.  If a wrong entry were discovered, it might of course have been due to some clerical error, though that is hardly probable considering the care spent in making these records, or it might have been a tailless comet, or possibly the newly found planet.

The next thing to do was to calculate backward, to see whether 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.  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.  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.