SECT, v.] DISTURBING ACTION OF THE PLANETS. 41 



when that distance amounts to a quadrant, and also when the 

 moon is in conjunction and opposition ; consequently, that in- 

 equality never could have been discovered from the eclipses : 

 its period is half a lunar month (N. 104). The Annual Equa- 

 tion depends upon the sun's distance from the earth : it arises 

 from the moon's motion being accelerated when that of the 

 earth is retarded, and vice versa for, when the earth is in its 

 perihelion, the lunar orbit is enlarged by the action of the 

 sun ; therefore, the moon requires more time to perform her 

 revolution. But, as the earth approaches its aphelion, the 

 moon's orbit contracts, and less time is necessary to accom- 

 plish her motion its period, consequently, depends upon the 

 time of the year. In the eclipses the annual equation com- 

 bines with the equation of the centre of the terrestrial orbit; 

 so that ancient astronomers imagined the earth's orbit to have 

 a greater excentricity than modern astronomers assign to it. 



The planets disturb the motion of the moon both directly 

 and indirectly : their action on the earth alters its relative 

 position with regard to the sun and moon, and occasions in- 

 equalities in the moon's motion, which are more considerable 

 than those arising from their direct action ; for the same reason 

 the moon, by disturbing the earth, indirectly disturbs her own 

 motion. Neither the excentricity of the lunar orbit, nor its 

 mean inclination to the plane of the ecliptic, have experienced 

 any changes from secular inequalities ; for, although the mean 

 action of the sun on the moon depends upon the inclination of 

 the lunar orbit to the ecliptic, and the position of the ecliptic 

 is subject to a secular inequality, yet analysis shows that it 

 does not occasion a secular variation in the inclination of the 

 lunar orbit, because the action of the sun constantly brings 

 the moon's orbit to the same inclination to the ecliptic. The 

 mean motion, the nodes, and the perigee, however, are sub- 

 ject to very remarkable variations. 



From the eclipse observed by the Chaldeans at Babylon, on 

 the 19th of March, seven hundred and twenty-one years 

 before the Christian era, the place of the moon is known from 



