ACCELERATION*. 37 



they could not affect the mean motion ; a variation in the mean 

 motion from such causes being inseparably connected with varia- 

 tions in the motions of the perigee and nodes. That great mathe- 

 matician, in studying the theory of Jupiter's satellites, perceived 

 that the secular variation in the elements of Jupiter's orbit, from 

 the action of the planets, occasions corresponding changes in the 

 motions of the satellites, which led him to suspect that the 

 acceleration in the mean motion of the moon might be connected 

 with the secular variation in the excentricity of the terrestrial 

 orbit. Analysis has shown that he assigned the true cause of the 

 acceleration. 



It is proved that the greater the excentricity of the terrestrial 

 orbit, the greater is the disturbing action of the sun on the moon. 

 Now, as the excentricity has been decreasing for ages, the effect 

 of the sun in disturbing the moon has been diminishing during 

 that time. Consequently the attraction of the earth has had a 

 more and more powerful effect on the moon, and has been con- 

 tinually diminishing the size of the lunar orbit. So that the 

 moon's velocity has been gradually augmenting for many centu- 

 ries to balance the increase 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 

 excentricity 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 (N. 106). 

 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 1 48' in the moon's longitude, 

 and of 7 12' in her mean anomaly (N. 107). 



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 revolu- 

 tion in 6793 d 9 h 23 m 9 B '3, or about 18 6-10 years; and the 



