was a circle with a radius equal to twice the mean distance of Uranus from the Sun—an assumption suggested by Bode's law. The result showed that a good general agreement between his theory and observation might be obtained. He now in 1844, if not before, acquainted Prof. Challis, Airy's successor with his scientific enterprise; and through him made a request to Airy for the errors of the tabular geocentric longitude of Uranus for 1818-26, with the factors for reducing them to errors of heliocentric longitude. Airy at once supplied all the results of the Greenwich observations of Uranus from 1754 to 1830.
With these improved data Adams now undertook a more elaborate discussion of the problems, retaining however the former assumption with respect to the mean distance; and by September of the following year (1845) he had the investigation completed. He communicated the results to Prof. Challis in the form of a note giving numerical values for the new planet, of its mean longitude at a given epoch, the longitude of its perihelion, the eccentricity of its orbit, its mass and its geocentric longitude for the last day of the month but without any account of his method. Challis on the 22d of September wrote to Airy a letter to introduce Adams; the first sentence in that letter has been already quoted in my lecture on Airy. Challis further said that he considered Adams' deductions to be made in a trustworthy manner. Challis had the best facilities in England to search for the predicted planet, yet he turned the matter over to Airy. Provided with the letter Adams called at the Greenwich Observatory, and met with the experiences described in my last lecture. Adams was naturally of a shy disposition and he felt mortified. In reply to the paper of results that he had left at the Observatory, Airy sent, a fortnight later, a letter to Adams: "I am very much obliged by the paper of results which you left here a few days since, showing the perturbations on the place of Uranus produced by a planet with certain assumed elements. . . . I should be very glad to know whether this assumed perturbation will explain the error of the radius-vector of Uranus." The prin-
