22. 



ON THE SECULAR VARIATION OF THE ECCENTRICITY AND INCLINATION 



OF THE MOON'S ORBIT. 



[From the Monthly Notices of the Royal Astronomical Society (1859). Vol. xix.] 



IN a memoir read before the Royal Society in June, 1853, I shewed 

 that the secular variation of the Moon's mean motion is given by means of 



the equation 



dn e'de' ( 2 , 3771 t \ 



ndt~ dt \ 32 



in which the coefficient of m 4 is totally different from that in Plana's result. 



I have since carried the approximation to the seventh order in m, and 

 find that 



dn e'de' ( 3771 34047 5 306865 . 17053741 ,) 



7 ' T I *JUV ^ III' ^ rt _ IIV i . rhr/l 



ndt dt 1 32 32 48 576 J 



(t V 

 j , in the expression for the acceleration 



to 5"7, only about one-half of the value hitherto received*. M. Delaunay 



has recently verified my coefficient of m 4 ; and he informs me that he shall 



very soon have carried the approximation to the eighth order in m, and 

 included the terms depending on e~ and y 2 . 



In my memoir above referred to I mentioned that other elements of 

 the Moon's orbit suffer secular changes which had been overlooked. 



* The first part of this Paper was communicated to the French Institute in January, 1859, 

 and was published in the Comptes Rendus. 



