188 ON THE MOTION OF THE MOON'S NODE IN A PARTICULAR CASE. [24 



In powers of m. In powers of m. 



m 2 -00419,64258,6 m' '00490,24088 



m 3 294,27947,8 m s 292,31135 



m 4 99,56981,8 m 4 55,37745 



m 5 30,35769,9 m 5 14,37162 



m 6 9,13946,6 m 6 3,49278 



m' 2,82999,6 m 7 ,99062 



m" ,98356,5 m 8 ,42111 



w 9 ,34684,2 m 9 ,08515 



00857,14945,0 '00857,29096 



The true value reduced from Mr Hill's, so as to correspond to the 

 value of m which we have employed, is 



00857,25645. 



Hence, as in the former case, the advantage of developing in powers of m 

 is very evident. 



I have found that a similar advantage results from the employment 

 of m instead of m in the development of the coefficients of the Moon's 

 periodic inequalities. 



