SECT, v.] MOTION OF NODES AND PERIGEE. 43 



crease of the earth's attraction. This secular increase in the 

 moon's velocity is called the Acceleration, a name peculiarly 

 appropriate at present, and which will continue to be so for a 

 vast number of ages ; because, as long as the earth's excen- 

 tricity diminishes, the moon's mean motion will be accele- 

 rated ; but when the excentricity has passed its minimum, and 

 begins to increase, the mean motion will be retarded from age 

 to age. The secular acceleration is now about 11"'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 diminution 

 in the excentricity, which has not altered the equation of the 

 centre of the sun by eight minutes since the earliest recorded 

 eclipses, has produced a variation of about l48 f 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 their sidereal 

 revolution in 6793 d 9 h 23 m 9 S> 3 ; and the perigee accomplishes 

 a revolution in 3232 d 13 h 48 m 29 8< 6, or a little more than nine 

 years, notwithstanding its motion is sometimes retrograde 

 and sometimes 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 11"'8 annually. The form of the earth has no sen- 

 sible effect either on the lunar nodes or apsides. It is evident 

 that the same secular variation which changes the sun's dis- 

 tance from the earth, and occasions the acceleration in the 

 moon's mean motion, must affect the nodes and perigee. It 

 consequently appears, from theory as well as observation, 

 that both these elements are subject to a secular inequality, 

 arising from the variation in the excentricity of the earth's 

 orbit, which connects them with the Acceleration, so that 



