3. 



NUMERICAL DEVELOPMENTS IN THE LUNAR THEORY. 



[!N a paper " On the Motion of the Moon's Node," Man. Not. xxxvm., 

 Nov. 1877, p. 43 ; Works, Vol. 1, p. 181, Adams gave expression to his views 

 on the most advantageous treatment of the lunar problem, as follows : 



" I have long been convinced that the most advantageous way of 

 treating the Lunar Theory is, first, to determine with all desirable accuracy 

 the inequalities which are independent of the eccentricities e and e', and 

 the inclination 2sin~ a y, and then, in succession, to find the inequalities 

 which are of one dimension, two dimensions, and so on, with respect to 

 those quantities. 



" Thus the coefficient of any inequality in the Moon's coordinates would 

 be represented by a series arranged in powers and products of e, e' and 

 y, and each term in this series would involve a numerical coefficient 

 which is a function of m alone and which may be calculated for any 

 given value of m without the necessity of developing it in powers of m. 

 The variations of these coefficients which would result from a very small 

 change in m might be found either independently or by making the 

 calculation for two values of vn differing by a small quantity. 



" This method is particularly advantageous when we wish to compare 

 our results with those of an analytical theory such as Delaunay's, in 

 which the eccentricities and the inclination are left indeterminate, since 

 each numerical coefficient so obtained could be compared separately with 

 its analytical development in powers of m. 



