108 NUMERICAL DEVELOPMENTS IN THE LUNAR THEORY. [3 



given in Lecture VII., we at length obtain the values of the following 

 functions to 15 places of decimals. 



= ^ + 0-01021,13629,54071,22 sin 2(n-n')t 

 + 4,23732,68757,73 sin 4(n-?i') 



+ 2375,68231,26 sin 6(n-ri)t 



+ 15,07977,03 sin 8(n-n')t 



+ 10246,17 sin W(n-n')t 



+ 72,68 sin I2(n-n')t. 



\= 1-00090,73880,47512,46 



+ 718,64751,59794,38 cos 2(n-n')t 



+ 4,58429,07983,33 cos 4(n-n')t 



+ 3268,81854,41 cos 6(n-n')t 



+ 24,50530,00 cos 8(n-n')t 



+ 18904,15 cos W(n-n')t 



+ 148,58 cos 12 (n-n')t 



,21 cos 14 (n n'} t. 



Moreover 



cos (6 - nt) = I - 0-00002,60682,62341,65 



2163,47566,91 cos 2(n-n r )t 

 + 2,60665,43862,72 cos 4(n-n')t 



+ 2163,33894,18 cos 6(n-n')t 



+ 17,18369,39 cos 8(n-n')t 



+ 13671,84 cos W(n-n')t 



+ 109,54 cos 12 (n-n')t 



+ ,88 cosl4:(n-ri)t. 



aw(e-nt)= 0-01021,12298,58342,60 sin 2(n-n')t 

 + 4,23721,64162,51 sin 4(n-n') 



+ 2819,24397,22 sin 6(n-n')t 



+ 20,60200,05 sin 8(n-n')t 



+ 15691,70 sin W(n-n')t 



+ 122,40 sin I2(n-n')t 



+ ,99 sin I4(n-ri)t. 



