The work to which he chiefly devoted himself in his retirement was the completion of his Numerical Lunar Theory. This was a vast work, involving the subtlest considerations of principle, very long and elaborate mathematical investigations of a high order, and an enormous amount of arithmetical computation. The issue of it was unfortunate: he concluded that there was an error in some of the early work, which vitiated the results obtained: and although the whole process was published, and was left in such a state that it would be a comparatively simple task for a future astronomer to correct and complete it, yet it was not permitted to the original author of it to do this. To avoid the necessity of frequent reference to this work in the history of Airy's remaining years, it will be convenient to summarize it here. It was commenced in 1872: "On Feb. 23rd in this year I first (privately) formed the notion of preparing a Numerical Lunar Theory by substituting Delaunay's numbers in the proper Equations and seeing what would come of it." From this time forward till his power to continue it absolutely failed, he pursued the subject with his usual tenacity of purpose. During his tenure of office every available opportunity was seized for making progress with his Lunar Theory, and in every Report to the Visitors a careful statement was inserted of the state in which it then stood. And, after his resignation of office, it formed the bulk of his occupation. In 1873 the Theory was formed, and by 1874 it was so far advanced that he published in the Monthly Notices of the Royal Astronomical Society a statement of the fundamental points of the Theory. In 1875, the Theory having advanced to a stage where extensive arithmetical computation was required, he obtained a small grant from the Government in aid of the expense of the work, and other grants were made in subsequent years. By 1878 the calculations were so far advanced that an opinion could be formed as to the probable accuracy of the Theory, and the following remark is made: "A cursory collation of the terms relating to the Areas (in the Ecliptic) led me to suppose that there might be some error in the computations of the Annual Equation and related terms;" but no error could be discovered and the work proceeded. The complex character of the Theory, and the extreme care required in the mathematical processes, are well illustrated by the following statement, which occurs in the Report of 1879, "An important error in the theoretical formulae for Variations of Radius Vector, Longitude, and Latitude, was discovered; some calculations depending on them are cancelled." In 1880 and 1881 the work was continued, but was "sadly interrupted by the pressure of the Transit of Venus work and other business." After his resignation of the Office of Astronomer Royal he had no further public assistance, and did much of the computations himself, but a sum of _£100_ was contributed by Mr