509 



points) about the former, — as consequences of the general 

 equation (I) : 





dV_ 7n + m" f ( 7-P)-' ^-^ j 



It was remarked, that by regarding m, m', m", as repre- 

 senting respectively the masses of the earth, moon, and sun, 

 /3 and y become the geocentric vectors of the two latter bodies ; 

 and that thus the laws of the disturbed motion of our satellite 

 are contained in the two equations (4) and (5), — but especially 

 in the first of those equations (the second serving chiefly to 

 express the laws of the sun's relative motion). 



The part of this equation (4), which is independent of the 

 sun's mass m", is of the form (2), and contains the laws of the 

 undisturbed elliptic motion of the moon ; the remainder is the 

 disturbing part of the equation, and contains the laws of the 

 chief lunar perturbations. A commencement was made of the 

 development of this disturbing part, according to ascending- 

 powers of the vector of the moon, and descending powers of 

 the vector of the sun ; and an approximate expression was 

 thereby obtained, which may be written thus : 



There was also given a geometrical interpretation of this 

 result, corresponding to a certain decomposition of the sun's 

 disturbing force into two others, of which the greater is triple 

 of the less, while the angle between them is bisected by the 

 geocentric vector of the sun ; and the lesser of these two com- 

 ponent forces is in the direction of the moon's geocentric vec- 

 tor prolonged, so that it is an ablatitious force, which was 

 shown to be one of nearly constant amount. 



Although the foregoing formulae may be found in the Appen- 

 2 Y 2 



