Now the errors in the motion of Uranus, _i.e._ the discrepancy between its observed and calculated longitudes--all known disturbing causes, such as Jupiter and Saturn, being allowed for--are as follows (as quoted by Dr. Haughton) in seconds of arc:-- ANCIENT OBSERVATIONS (casually made, as of a star). Flamsteed 1690 +61·2 " 1712 +92·7 " 1715 +73·8 Le Monnier 1750 -47·6 Bradley 1753 -39·5 Mayer 1756 -45·7 Le Monnier 1764 -34·9 " 1769 -19·3 " 1771 -2·3 MODERN OBSERVATIONS. 1780 +3·46 1783 +8·45 1786 +12·36 1789 +19·02 1801 +22·21 1810 +23·16 1822 +20·97 1825 +18·16 1828 +10·82 1831 -3·98 1834 -20·80 1837 -42·66 1840 -66·64 These are the numbers plotted in the above diagram (Fig. 92), where H marks the discovery of the planet and the beginning of its regular observation. Something was evidently the matter with the planet. 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 those known ones which had been fully taken into account. Could it be an outer planet? The question occurred to several, and one or two tried if they could 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 problem it was that Laplace worked out in the _Mécanique Céleste_. But the inverse problem: Given the perturbations, to find the planet which causes them--such a problem had never yet been attacked, and by only a few had its possibility been conceived. Bessel made preparations for trying what he could do at it in 1840, but he was prevented by fatal illness. In 1841 the difficulties of the problem presented by these residual perturbations of Uranus excited the imagination of a young student, an undergraduate of St. John's College, Cambridge--John Couch Adams by name--and he determined to have a try at it as soon as he was through his Tripos. In January, 1843, he graduated as Senior Wrangler, and shortly afterwards he set to work. In less than two years he reached a definite conclusion; and in October, 1845, he wrote to the Astronomer-Royal, at Greenwich, Professor Airy, saying that the perturbations of Uranus would be explained by assuming the existence of an outer planet, which he reckoned was now situated in a specified latitude and longitude.