LECTURE XVII. 



ON HILL'S METHOD OF TREATING THE LUNAR THEORY. 



LET us suppose the Moon to move in the plane of the ecliptic, and 

 let us refer its motion to rectangular axes in rotation, the rotation being 

 such that the axis of x passes always through the mean position of the 

 Sun ; that is, the axes rotate with angular velocity n', and if we suppose 

 the Sun describes a circular orbit about the origin, its coordinates ai'e 



x' = a', y' = 0. 

 Let x, y be the coordinates of the Moon. 



Then the disturbing forces of the Sun upon the Moon, relative to the 

 Earth are 



in' x a! m' m' y 



~ P* P ~ a " ' P* P 

 parallel to the axes of x and y respectively, where 



p' = (x-ay + y>, 

 and the forces of the Earth on the Moon relative to the Earth are 



w 



here 



Now these forces may be written 



dfl dfl 

 dx ' dy ' 



m' m'x 



where fl = - -\ 



r p a' 



