II.] ACCELERATIONS OF THE MOON RELATIVE TO THE EARTH. 11 



Our problem is to discuss these equations and to obtain from them 

 expressions for the Moon's position at any time. The integration is best 

 effected by observing what kinds of terms will disappear on substitution 

 in the equations, and then assuming for the desired expressions for the 

 coordinates a series of such terms multiplied by undetermined coefficients. 

 Our procedure will be to discuss one by one the irregularities which can 

 be isolated from one another. This will permit a survey of the entire field 

 without involving needless complexity; but if the Lunar Theory is to be 

 accurate, the combinations of such terms with one another must also be 

 included, and the number of terms employed and the labour of manipu- 

 lating them becomes very great. 



22 



