3] NUMERICAL DEVELOPMENTS IN THE LUNAR THEORY. 107 



in which we take 6' = n't, and a has the same definition as before. We 

 find 



u= 1-00097,52861,50 



+ 0-00718,66609,56 cos 2(l-w)0 

 -0-00002,20516,12 cos 4(l-m)0 

 + 0-00000,01410,92 cos 6(l-m)6> 

 -0-00000,00011,34 cos B(l-m)0 

 + 0-00000,00000,10 cos 10(1 -m)0. 

 ^ = 0-0-01021,13075,60 sin 2(l-m)0 

 + 0-00005,40981,47 sin 4(l-m)6> 

 -0-00000,04037,26 sin 6(l-w)0 

 + 0-00000,00034,98 sin 8(l-m)0 

 -0-00000,00000,33 sin 10 (1 -m) 0. 



Forming the functions required for a second approximation, it appears 

 that they all agree with the former values to 11 or 12 places of decimals; 

 hence no corrections are required. 



Dec. I '60 and Jan./ 61. 



[The next investigations were the papers on the latitude, which lead 

 to an infinite determinant, and are abstracted on p. 85 et seqq. The 

 formulae, including the determination of the motion of the node as far 

 as it is independent of e, e' and y, as well as the corresponding parts 

 of the coefficients of the evection in latitude, were reduced numerically 

 and determined, the former to 15 places of decimals and the latter to 

 11 or 12, in 1877. 



In 1880 Adams availed himself of an offer of a friend and former 

 pupil, Miss Fanny Harrison, in order to carry on these calculations. The 

 calculations were made by Miss Harrison from formulae supplied by 

 Adams, and were examined and, where necessary, corrected, refined, or 

 transformed by Adams.] 



If we take the numbers given on p. 106 as approximations to the 



values of and - in terms of t and correct the solution by the method 

 r 



142 



