Meanwhile, and quite independently, something of the same sort was going on in France. A brilliant young mathematician, born in Normandy in 1811, had accepted the post of Astronomical Professor at the École Polytechnique, then recently founded by Napoleon. His first published papers directed attention to his wonderful powers; and the official head of astronomy in France, the famous Arago, suggested to him the unexplained perturbations of Uranus as a worthy object for his fresh and well-armed vigour. At once he set to work in a thorough and systematic way. He first considered whether the discrepancies could be due to errors in the tables or errors in the old observations. He discussed them with minute care, and came to the conclusion that they were not thus to be explained away. This part of the work he published in November, 1845. He then set to work to consider the perturbations produced by Jupiter and Saturn, to see if they had been with perfect accuracy allowed for, or whether some minute improvements could be made sufficient to destroy the irregularities. He introduced several fresh terms into these perturbations, but none of them of sufficient magnitude to do more than slightly lessen the unexplained perturbations. He next examined the various hypotheses that had been suggested to account for them:--Was it a failure in the law of gravitation? Was it due to the presence of a resisting medium? Was it due to some unseen but large satellite? Or was it due to a collision with some comet? All these he examined and dismissed for various reasons one after the other. It was due to some steady continuous cause--for instance, some unknown planet. Could this planet be inside the orbit of Uranus? No, for then it would perturb Saturn and Jupiter also, and they were not perturbed by it. It must, therefore, be some planet outside the orbit of Uranus, and in all probability, according to Bode's empirical law, at nearly double the distance from the sun that Uranus is. Lastly he proceeded to examine where this planet was, and what its orbit must be to produce the observed disturbances. [Illustration: FIG. 94.--Uranus's and Neptune's relative positions. The above diagram, drawn to scale by Dr. Haughton, shows the paths of Uranus and Neptune, and their positions from 1781 to 1840, and illustrates the _direction_ of their mutual perturbing force. In 1822 the planets were in conjunction, and the force would then perturb the radius vector (or distance from the sun), but not the longitude (or place in orbit). Before that date Uranus had been hurried along, and after that date it had been retarded, by the pull of Neptune, and thus the observed discrepancies from its computed place were produced. The problem was first to disentangle the outstanding perturbations from those which would be caused by Jupiter and Saturn and all other known causes, and then to assign the place of an outer planet able to produce precisely those perturbations in Uranus.]