26. 



NOTE ON SIR GEORGE AIRY'S INVESTIGATION OF THE THEORETICAL 

 VALUE OF THE ACCELERATION OF THE MOON'S MEAN MOTION. 



[From the Monthly Notices of the Royal Astronomical Society (1880), Vol. XL.] 



I LOSE no time in pointing out briefly the reason why the Astronomer 

 Royal, in the investigation which he communicated to the Society at the 

 last Meeting, has failed to find my value of the coefficient of the Lunar 

 Acceleration. 



It may be useful, in the first place, to recall to mind that, according 

 to my theory, the secular changes of 



n, the Moon's mean motion, 

 and e', the eccentricity of the Earth's orbit, 

 are connected by the following relation : 



dn e'de' ( 3771 . 34047 



ndt~ dt { 32 42 



where m denotes, as usual, the ratio of the Sun's mean motion to that of 

 the Moon. 



If we stop at the first term of the series within the brackets the 

 result is identical with that found by Laplace. 



We do not know why Laplace did not carry his investigations further 

 than this first term ; but he probably thought that the succeeding terms 

 would prove to be inconsiderable. 



