4] THE SECULAR ACCELERATION OF THE MOON'S MEAN MOTION. 129 

 Coefficient of cos 2 <', 



de' 

 = T- (-0930002) + raBoj ( - -0014134) + w8a 8 ( - 3'551 19) 



+ nSb, (-0073983) + nSb s ( - 3'1529 1). 

 Coefficient of si 



de' 

 = -T. (- -0009612) + na, ('0314059) + nSa s (671480) 



b, (-0098053) +S& 9 (3-85040). 

 Coefficient of cos (2 +<'), 

 -- ( - -0124702) + nBa. ( - '0014134) + n&a, ( - 3'85040) 



, (-0093859) + nb(- 3'70656). 

 These equations give 



(-0017349), *_* (-2-58480), 



= j- (--0377033), 86 g = ("0658969). 



' 



(-0237240), 8b,= di ' (-'0345550), 

 and 



If we take 



the last gives the secular acceleration 



5"'7041. 



The value found by including terms of the series which represents 

 the same up to m 7 or m s , and estimating the remainder is 5"70. 



Dec. 1859. 



A. II. 17 



