36 ACCELERATION. SECT. V. 



rapidly and in a shorter time now than she did formerly, 

 and that the acceleration 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 unaccount- 

 able anomaly. It was at one time attributed to the re- 

 sistance of an ethereal medium pervading space, and at 

 another to the successive 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, they 

 could not affect the mean motion ; a variation in the 

 mean motion from such causes being inseparably con- 

 nected with the variations in the motions of the perigee 

 and nodes. That great mathematician, 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 sus- 

 pect that the acceleration in the mean motion of the 

 moon might be connected with the secular variation in 

 the eccentricity of the terrestrial orbit. Analysis has 

 shown that he assigned the true cause of the acceleration. 

 It is proved that the greater the eccentricity of the 

 terrestrial orbit, the greater is the disturbing action of 

 the sun on the moon. Now as the eccentricity has 

 been decreasing for ages, the effect of the sun in dis- 

 turbing 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 

 continually diminishing the size of the lunar orbit. So 

 that the moon's velocity has been gradually augmenting 

 for many centuries 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 eccen- 

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

 celerated ; but when the eccentricity has passed its 

 minimum, and begins to increase, the mean motion will 

 be retarded from age to age. The secular acceleration 



