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its truth, it would be no longer possible to predict the apparent 
motion of the moon, since the changes in the rotation of the 
earth could not be expected to follow any determinate law. 
Further investigations have led Professor Newcomb to the 
gratifying conclusion that we may yet hope to find the source 
of these deviations in *the effects of the attraction of some 
member of the solar system. Closer examination of the out- 
standing errors showed Professor Newcomb that they could be 
explained by a new periodical term with a period of about 260 
years. This is very nearly the period of the term of long period 
which was discovered by Professor Hansen to be produced by the 
direct action of Venus on the moon. It occurred to Professor 
Newcomb that by slightly changing the constants in this term 
the outstanding errors might be reduced. The result was most 
striking. This term, like the other inequality in the motion of 
the moon, has for its argument a quantity proportional to the 
time added to a constant quantity; and Professor Newcomb 
found that merely by changing the sign of this constant part of 
the argument, all the considerable outstanding errors dis- 
appeared. It is, in fact, merely necessary to make this slight 
change, and Hansen’s tables, when corrected as previously men- 
tioned, well represent the motion of the moon from 1625 to 
1875. This led Professor Newcomb to examine whether there 
was not some accidental mistake in the sign of this constant 
quantity, but he found that it was perfectly correct. It is, 
therefore, a mere chance that this change of sign of this quantity 
causes the outstanding errors to disappear in this way. 
These investigations of Professor Newcomb very clearly 
establish the following conclusions. Firstly, that Hansen was 
entirely wrong in the value which he empirically assigned to 
one, at least, of the terms of long period in the motion of the 
moon, which arose from the attractions of Venus. Secondly, 
that if Delaunay’s value of these terms be correct, there still 
remains to be discovered at least one more term of long period 
in the motion of the moon. Thirdly, that if both Hansen’s 
tabular value and Delaunay’s theoretical value be wrong, it is 
possible to satisfy the observations without supposing any new 
term to exist. 
Quite recently another contribution has been made to this 
subject, which places the theory of these terms of long period 
in an entirely fresh light, and opens a means of reconciling the 
contradictory results obtained by two such distinguished astro- 
nomers as Hansen and Delaunay. Hansen never published an 
account of the manner in which he theoretically calculated the 
complete value of these terms of long period, but finding two 
results arrived at by different methods to be irreconcilable, he 
postponed publishing his investigations until he had completed 
