SECT. V. MOTION OF NODES AND PERIGEE. 37 



is now about ll"-9, but its effect on the moon's place 

 increases as the square of the time. It is remarkable 

 that the action of the planets, thus reflected by the sun 

 to the moon, is much more sensible than their direct 

 action either on the earth or moon. The secular dimi- 

 nution in the eccentricity, which has not altered the 

 equation of the center of the sun by eight minutes since 

 the earliest recorded eclipses, has produced a variation 

 of about 1 48' in the moon's longitude, and of 7 12' in 

 her mean anomaly (N. 106). 



The action of the sun occasions a rapid but variable 

 motion in the nodes and perigee of the lunar orbit. 

 Though the nodes recede during the greater part of the 

 moon's revolution, and advance during the smaller, they 

 perform then* sidereal revolution in 6793 d 9 h 23 ra 9"-3 ; 

 and the perigee accomplishes a revolution in 3232 J 13 h 

 48 m 29 s - 6, or a little more thart nine years, notwith- 

 standing its motion is sometimes retrograde and some- 

 times direct : but such is the difference between the 

 disturbing energy of the sun and that of all the planets 

 put together, that it requires no less than 109,830 years 

 for the greater axis of the terrestrial orbit to do the 

 same, moving at the rate of IT'-S annually. The form 

 of the earth has no sensible effect either on the lunar 

 nodes or apsides. It is evident that the same secular 

 variation which changes the sun's distance from the 

 earth, and occasions the acceleration in the moon's mean 

 motion, must affect the nodes and perigee. It conse- 

 quently appears, from theory as well as observation, that 

 both these elements are subject to a secular inequality, 

 arising from the variation in the eccentricity of the 

 earth's orbit, which connects them with the Acceleration, 

 so that both are retarded when the mean motion is an- 

 ticipated. The secular variations in these three ele- 

 ments are in the ratio of the numbers 3, 0-735, and 1 ; 

 whence the three motions of the moon, with regard to 

 the sun, to her perigee, and to her nodes, are continu- 

 ally accelerated, and their secular equations are as the 

 numbers 1, 4-702, and 0-612. A comparison of ancient 

 eclipses observed by the Arabs, Greeks, and Chaldeans, 

 imperfect as they are, with modern observations, con- 

 firms these results of analysis. Future ages will de- 

 D 



