He then set to work to consider the perturbations produced by Jupiter and Saturn to see whether they had been accurately allowed for, or whether some minute improvements could be made sufficient to destroy the irregularities. He introduced several fresh terms into these calculations, but none of them of sufficient importance to do more than partly explain the mysterious perturbations. He next examined the various hypotheses that had been suggested to account for them. Were they caused by a failure in the law of gravitation or by the presence of a resisting medium? Were they due to some large but unseen satellite or to a collision with some comet?
All these theories he examined and dismissed for various reasons. The perturbations were due to some 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. Finally he proceeded to determine where this planet was, and what its orbit must be to produce the observed disturbances.
Not without failures and disheartening complications was this part of the process completed. This was, after all, the real tug of war. Many unknown quantities existed: its mass, its distance, its eccentricity, the obliquity of its orbit, its position--nothing was known, in fact, about the planet except the microscopic disturbance it caused in Uranus, several thousand million miles away from it. Without going into further detail, suffice it to say that in June, 1846, he published his last paper, and in it announced to the world his theory as to the situation of the planet.
Professor Airy received a copy of this paper before the end of the month, and was astonished to find that Leverrier's theoretical place for the planet was within 1° of the place Adams had assigned to it eight months before. So striking a coincidence seemed sufficient to justify a Herschelian sweep for a week or two. But a sweep for so distant a planet would be no easy matter. When seen through a large telescope it would still only look like a star, and it would require considerable labor and watching to sift it out from the other stars surrounding it. We know that Uranus had been seen twenty times, and thought to be a star, before its true nature was discovered by Herschel; and Uranus is only about half as far away as Neptune.