CONTRIBUTIONS TO THE THEORY OF THE MOTION OF THE MOON. 235 
of such magnitude that he felt convinced that there must still 
exist some serious defect in the lunar theory as developed in the 
theoretical basis of the tables. 
Professor Newcomb has lately completed an elaborate investi- 
gation of the earlier observations of the moon. He takes for 
his data a number of eclipses of the moon, which are quoted by 
Ptolemy in his 44 Almagest,” a still larger number which were 
observed by the Arabians during the ninth and tenth centuries, 
and a number of observations of eclipses and occupations which 
were made by different astronomers during the seventeenth and 
early part of the eighteenth centuries. The greater number of 
these last have remained unpublished since the time they were 
made, and were discovered by Professor Newcomb when examin- 
ing the archives of the Paris observatory. These last constitute 
the basis of a most important contribution to astronomy, for by 
carefully reducing them Professor Newcomb has been enabled to 
deduce with considerable accuracy the observed place of the 
moon for epochs much anterior to 1750, where previously had 
terminated our exact observations of the moon. In fact, by 
means of this investigation of Professor Newcomb, astronomers 
can trace back the observed path of the moon with some 
exactitude to 1675, and with less certainty to 1620. Professor 
Newcomb has made use of the data furnished him by this inves- 
tigation for the purpose of ascertaining how far the observed place 
of the moon agrees with Hansen’s tables for the period anterior 
to 1750. He shows that they fail to do so, and that for epochs 
prior to 1750 Hansen’s tables are as discordant with observation 
as they have proved to be for epochs subsequent to 1850. 
Assuming with the Astronomer Royal that one of Hansen’s terms 
of long period ought to be rejected, Professor Newcomb then 
endeavours to ascertain what corrections must be introduced to 
make the tables best represent the observations. He shows that 
the mean motion of the moon must be decreased by nearly 
thirty seconds in a century, and the value of the secular 
acceleration of the mean motion be decreased by nearly one- 
third of the amount assigned to it by Hausen. Even, however, 
when the tables are thus corrected in the best possible manner, 
there remain such large outstanding errors that Professor New- 
comb comes to the same conclusion as Sir Gr. Airy, that there 
is still some serious defect in the luuar theory. 
Professor Newcomb draws attention to the fact that these out- 
standing errors can be entirely accounted for by supposing that 
the earth is subject to periodical inequalities in its rotation on 
its axis. For some years it had seemed to Professor Newcomb 
that this was the most probable hypothesis on which to explain 
these deviations between theory and observation. As he points 
out, it would be a most serious and unwelcome one, for, granting 
