CONTRIBUTIONS TO THE THEORY OF THE MOTION OF THE MOON. 231 
inequality. That it did not arise from the attraction of the 
sun appeared to be certain from the investigations of Laplace, 
Plana, Poisson, and Pontecoulant ; that so large an inequality 
as this was due to the attraction of the planets seemed to be out 
of the question ; and it did not appear possible that it could be 
due to the attraction of the earth. It was left for Professor 
Hansen to discover its origin in an unlooked for source, namely, 
in the attraction of the planet Venus. He showed that this 
planet, from its attraction on the earth and its satellite, pro- 
duced two terms of long period in the motion of the moon ; by a 
long and laborious calculation he computed the value of these 
terms ; and he showed that the combined effect of these two 
terms of long period exactly accounted for that observed in- 
equality in the motion of the moon which had so long perplexed 
astronomers. 
The first of the two new terms in the motion of the moon 
which were discovered by Professor Hansen was principally due 
to the direct attraction of Venus upon the moon. From a 
remarkable numerical relation between the motion of the moon 
in its orbit and the motion of Venus and the earth around the 
sun, for one hundred and forty years at a time the action of 
Venus on the moon tends to increase its distance from the earth 
and so render its motion around the earth slower, whilst for the 
next one hundred and forty years exactly the reverse action takes 
place. Thus from the direct attraction of Venus on the moon, 
our satellite moves slower round the earth for one hundred and 
forty years, so that at the end of this period it is behind its 
mean place ; and then for the next one hundred and forty years 
it moves quicker round the earth, and gets correspondingly 
before its mean place. This may be called the direct term of 
long period. The second term of long period discovered by 
Professor Hansen arises from the indirect action of Venus upon 
the moon. Sir Gr. Airy had discovered in 1828 that from the 
attraction of Venus upon the earth, this last body would alter- 
nately move in a rather larger or smaller orbit than it would 
have were it not for the attraction of Venus. He showed that 
for one hundred and twenty years the earth would be rather 
more distant from the sun, and for the next one hundred and 
twenty years, rather less distant from the sun, than would be 
otherwise the case. Professor Hansen now showed that this 
would cause a sensible variation in the motion of the moon. 
From the disturbing action exercised by the attraction of the 
sun, the moon cannot move round the earth so quickly as it 
would otherwise do. During then the term of one hundred and 
twenty years, when the earth had its distance from the sun in- 
creased from the attraction of Venus, the action of the sun is 
decreased, and the moon is enabled to move more quickly round 
