36 DISTURBING ACTION OF PLANETS. SECT. V. 



moon's orbit contracts, and less time is necessary 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 Centre of the terrestrial orbit, so that ancient 

 astronomers imagined the earth's orbit to have a greater excen- 

 tricity 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 disturbing the earth, indirectly disturbs her own motion. 

 Neither the excentricity of the lunar orbit, nor its mean inclina- 

 tion 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 subject to very remarkable variations. 



From the eclipse observed 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 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 per- 

 forms her revolution round the earth more rapidly and in a 

 shorter time now than she did formerly, and that the accelera- 

 tion in her mean motion has been increasing from age to age as 

 the square of the time (N. 105). All ancient and intermediate 

 eclipses confirm this result. As the mean motions of the planets 

 have no secular inequalities, this seemed to be an unaccountable 

 anomaly. It was at one time attributed to the resistance of an 

 ethereal medium pervading space, and at another to the succes- 

 sive transmission of the gravitating force. But, as La Place 

 proved that neither of these causes, even if they exist, have any 

 influence on the motions of the lunar perigee (N". 102) or nodes, 



