CONTRIBUTIONS TO THE THEORY OF THE MOTION OF THE MOON. 241 
Then correcting Hansen’s terms of long period in the manner 
suggested by Professor Newcomb, diminishing Hansen’s value of 
the mean motion by about forty seconds per century, and em- 
ploying the theoretical value of the secular acceleration, the 
modified tables will completely represent the observations both 
ancient and modern. Indeed, by slightly altering the period of 
the term of long period, its coefficient might be much reduced, 
and it would still represent, with tolerable accuracy, the ob- 
servations. 
These considerations show that recent investigations go far 
to remove the supposed discrepancy between the value of the 
secular acceleration in the mean motion of the moon which is 
given by theory and by observation. They are sufficient to 
show that there is no necessity to assume any retardation in the 
rotation of the earth due to friction produced by the tides of 
the ocean. 
In connection with the American expeditions for observing 
the transit of Venus, it became necessary to examine the cor- 
rections to Hansen’s tables of the moon given by the observations 
made during the period 1862-1874. After applying various 
slight corrections to the differences between the observed and 
tabular places of the moon, Professor Newcomb was surprised to 
find systematic errors outstanding which could not be repre- 
sented by corrections to the elements of the lunar orbit. At 
first he was inclined to attribute them to irregularities on the 
surface of the moon, but a more careful examination showed 
that they were periodic. F urther investigation showed Professor 
Newcomb that they arose from small variation in the eccen- 
tricity and longitude of the perigee of the lunar orbit, this 
variation going through all its changes in a period of nearly 
seventeen years. Owing to these variations the moon would be 
periodically accelerated or retarded in its orbital motion by 
about three seconds of time. Professor Newcomb was unable 
to offer any explanation of the origin of these periodical vari- 
ations. It has since been shown that they arise from the 
attraction of Jupiter on the moon in its revolution around the 
earth. 
From the attraction of the sun upon the moon in its revo- 
lution around the earth, a great inequality is produced in the 
motion of the moon, from which its position in its orbit is 
alternately increased or decreased by nearly three hours. This 
great inequality was discovered by Ptolemy, and was subse- 
quently named the evection. Every planet, by its attraction, 
produces a similar term, although much smaller ; so much 
smaller, indeed, that it was generally thought that they would 
be too small to be ever detected. In general, this view is per- 
fectly correct, and it would also be the case with Jupiter were 
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