SBCT. V. DISTURBING ACTION OF THE PLANETS. 35 



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 ac- 

 tion of the sun ; therefore, the moon requires more 

 time to perform her revolution. But, as the earth ap- 

 proaches its aphelion, the moon's orbit contracts, and 

 less time is necessaiy to accomplish her motion its 

 period, consequently, depends upon the time of the 

 year. In the eclipses, the annual equation combines 

 with the equation of the center of the terrestrial orbit, 

 so that ancient astronomers imagined the earth's orbit 

 to have a greater eccentricity 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 inequalities in the moon's motion, which 

 are more considerable than those arising from their 

 direct action ; for the same reason the moon, by disturb- 

 ing the earth, indirectly disturbs her own motion. Nei- 

 ther the eccentricity 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 mo- 

 tion, the nodes, and the perigee, however, are subject 

 to very remarkable variations. 



From the eclipse observed by the Chaldeans at Baby- 

 lon, on the 19th of March, seven hundred and twenty- 

 one years before the Christian era, the place of the 

 moon is known from that of the sun at the instant of 

 opposition (N. 83), whence her mean longitude may be 

 found. But the comparison of this mean longitude with 

 another mean longitude, computed back for the instant 

 of the eclipse from modern observations, shows that the 

 moon performs her revolution round the earth more 



