PHYSICAL ASTRONOMY. 



quadratures, and diminished both at the oppo- 

 sition and the conjunction, and the areas de- 

 scribed by the radius vector, except near the 

 quadratures, are never exactly proportional to 

 the times. 



a. Let ADBC (fig. 25.) be the orbit, nearly circu- 

 lar, in which the Moon M revolves round the 

 Earth at E. Let the Sun be at S, and let the line 

 SE denote the force of the Sun on the Earth , then 



SE 3 



c-\ift * s tne attract i n of the Sun on the Moon at 



M ; let MG be equal to this line, and joining ME, 

 let the parallelogram KF be described, of which 

 GM is the diagonal, and the sides MF, MK are 

 in the directions of ME and ES; and let HS 

 be drawn parallel to ME. 



The force MG may be resolved into the two MF, 

 MK, of which MF, directed toward the centre E, 

 increases the gravity of the Moon to the Earth, 

 and does not hinder the areas described by the 

 radius vector from being proportional to the times. 



The other force MK draws the Moon in the direc- 

 tion of the line joining the centre of the Sun and 

 Earth ; but it is only the excess of this force above 

 that by which the Sun draws the Earth, that dis- 

 turbs the relative position of the Moon and Earth. 

 If, therefore, ES, which denotes the force of the 

 Sun on the Earth be taken from MK, the remain- 

 der KH will be the force by which the Sun 



draws 



