3] NUMERICAL DEVELOPMENTS IN THE LUNAR THEORY. 113 



s / 



Y=_ \\ 0-02192,93435,69543,96 sin 2(n-n')t 



n L 



+ 22,15097,16543,17 sin 4(n-n') 



+ 20403,69529,98 sin 6(n-n')t 



+ 182,50089,05 sin 8(n-n')t 



+ 1,61025,56 sin 10 (ft -ft')? 



+ 1409,92 sin 12(n-n')t 



+ 12,29 sin 14 (ft -ft')?], 

 and thence 



CJ / 



81= -f [-0-00157,07440,23063,65 

 n 



1503,04573,28666,23 cos 2(n-n')t 



13,85178,94754,61 cos 4 (ft -ft')? 



12198,71210,26 cos 6 (ft -ft')? 



106,12235,10 cos 8(ft-ft')? 



91844,94 cos 10 (n- ')? 



792,73 cos 12 (ft -ft')? 



6,89 cos 14 (ft -ft')?], 



Cs / 



8a= , f 0-02172,72068,72058,04 sin 2(n-n')t 

 n 



+ 17,93852,23118,97 sin 4(w-n') 



+ 15064,30388,89 sin 6 (ft -ft')? 



+ 127,41426,27 sin 8(n-n')t 



+ 1,08179,31 sin 10 (ft -ft')? 



+ 920,61 sin 12 (ft -ft')? 



+ 7,92 sin 14 (ft -ft,')?]. 



In the values of 81, 8w the fifteenth figure is in some cases doubtful, 

 especially in the coefficients with the argument 2 (n n') t. 



Dec. 1881. 

 A. II. 15 



