42 ACCELERATION. [SECT. v. 



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 performs her revolution round the earth 

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

 and that the acceleration in her mean motion has been in- 

 creasing 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 per- 

 vading 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 connected with variations 

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

 matician, in studying the theory of Jupiter's satellites, per- 

 ceived 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 ter- 

 restrial 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 at- 

 traction 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 in- 



