118 NUMERICAL DEVELOPMENTS IN THE LUNAR THEORY. [3 



Thence we find the expressions 



87 = X[ 0-11388,97944,95676,6 cos (n-n')t 



134,75546,22715,5 cos 3(n-n')t 



1,31065,61724,1 cos 5(n-n')t 



1161,73856,5 cos 7 (n-ri)t 



- 10,10844,5 cos S(n-n')t 



8740,2 cos 11 (n-n')t 



75,3 cos 13 (n-n')t 



,6 cos 15 (n-n')t], 



S W = A.[_ 0-24265, 3781 1,19304,3 sin (n-n')t 



+ 142,30587,09590,8 sin 3(n-n')t 



+ 1,47053,22766,2 sin 5(n-n')t 



+ 1313,75623,3 sin 7(n-n')t 



+ 11,41511,3 sin 9 (n-n')t 



+ 9832,9 sin 11 (n-n')t 



+ 84,4 sin 13 (n-n')t 



+ ,7 sin 15 (n n')t]. 



If these values are substituted in the equations which 81, Sea should 

 satisfy they leave small residuals, in one case reaching 12 units of the 

 fifteenth place of decimals. It does not appear that Adams amended these 

 results as he amended the others ; there is no MS. reference of his to 

 them except an entry in the Diary of 1884 : 



March 27. A large mass of calculations arrived from Miss F. Harrison: 

 apparently very well done. 



Thus these discrepancies remain, as well as others arising from the 

 fact that the values of - , 6, &c. which Miss Harrison employs, differ 



from the definitive values which we have just given, in general slightly, 

 but in one case by nearly a unit in the twelfth place. 



We learn from the words in his paper on the motion of the Moon's 

 node, quoted above, that he had reduced the determination of the ine- 

 qualities of longitude and radius vector which involve the first power of 



