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. The critical trial depends on the great mass
of computations in Section II. These have been made in duplicate, with
all the care for accuracy that anxiety could supply. Still I cannot
but fear that the error which is the source of discordance must be on
my part. I cannot conjecture whether I may be able to examine
sufficiently into this matter." He resolutely took in hand the
revision of his work, and continued it till October 1888. But it is
clear from the entries in his journal that his powers were now unequal
to the task, and although from time to time he suspected that he had
discovered errors, yet it does not appear that he determined anything
with certainty. He never doubted that there were important errors in
the work, and later on he left the following private note on the
subject: