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 L100 was contributed by Mr De La Rue in furtherance of the work, and this sum was spent on computers.  In his retirement the work made good progress, and on Dec. 31st, 1882, he made the following note:  “I finished and put in general order the final tables of Equations of Variations.  This is a definite point in the Lunar Theory....  I hope shortly to take up severely the numerical operations of the Lunar Theory from the very beginning.”  The work was continued steadily through 1883, and on Mar. 24th, 1884, he made application through the Board of Visitors to the Admiralty to print the work:  after the usual enquiries as to the expense this was acceded to, and copy was sent to the printers as soon as it was ready.  The first printed proofs were received on Feb. 5th, 1885, and the whole book was printed by the end of 1886.  From the frequent references in his journal to errors discovered and corrected during the progress of these calculations, it would seem likely that his powers were not what they had been, and that there was a probability that some important errors might escape correction.  He was far too honest to blind himself to this possibility, and in the Preface to his Numerical Lunar Theory he says thus:  “I have explained above that the principle of operations was, to arrange the fundamental mechanical equations in a form suited for the investigations of Lunar Theory; to substitute in the terms of these equations the numerical values furnished by Delaunay’s great work; and to examine whether the equations are thereby satisfied.  With painful alarm, I find that they are not satisfied; and that the discordance, or failure of satisfying the equations, is large.