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calculated was found to agree well with the value empirically- 
assigned to it by Hansen, so that this part of Hansen’s tables 
was confirmed. It is true it differed from the complete theo- 
retical value which Hansen had found for this term, but this 
was of slighter moment, for Hansen himself had expressed a 
strong doubt of its accuracy. 
Delaunay proceeded next to the determination of the value 
of the second term of long period, namely, that which results- 
from the indirect action of Venus. He calculated the value of 
this by the same method as before, but taking care to consider 
the effect of the inclination of the orbit of Venus, he announced 
that he made the value of this term less than one-hundredth of 
that assigned to it by Hansen. This was a most important 
matter, for if Delaunay was right in his conclusion, the tables 
of the moon calculated by Hansen must be seriously inaccurate, 
for without this term which Delaunay declared was so greatly 
in error, these tables would not represent the motion of the 
moon with any accuracy at all. At this period, however, the 
tables of the moon did represent its motion with considerable 
accuracy, which appeared to be a strong indication that Hansen 
was right, and not Delaunay. Moreover, it has been mentioned 
that Delaunay employed his new method of attacking the lunar 
theory in determining the value of these inequalities, and this 
rendered it difficult for those unfamiliar with it to follow his 
calculations. It was only when Hansen’s tables of the moon 
were seen to be developing serious errors that general attention 
was turned to Delaunay’s investigations. 
Professor Newcomb, of Washington, was the next to take 
up the subject, which he in turn examined by a method of con- 
siderable novelty, but he has not published the details of his 
investigations. He was able, however, to completely confirm 
the results which had been arrived at by Delaunay. It appeared 
certain, therefore, that Hansen’s tables were wrong. By this 
time, however, this last fact was unquestionable, for the tables 
were rapidly deviating from the real place of the moon, and it 
was obvious that there was some grave imperfection in Hansen’s 
work. 
In 1873 Sir Gr. Airy pointed out that the theoretical inves- 
tigations of Delaunay and Newcomb appeared to render it 
certain that Hansen’s second term of long period, namely, that 
mainly due to the indirect action of Venus, had no right to be 
present in his tables. He therefore directed his attention to 
determining whether it was possible after removing this term 
to make the tables represent the motion of the moon by suitably 
correcting certain of the elements of its orbit. Sir Gr. Airy 
found, however, that this was not possible. Even after applying 
the best possible corrections, there remained outstanding errors 
