PHYSICAL ASTRONOMY. 259 



same time, and will not come to intersect the ra- 

 dius vector at right angles, till this last has moved 

 over a greater arch than 180. Hence the solar 

 force, by lessening the Moon's gravitation to the 

 Earth, produces an advance in the place of the 

 apsides, in the direction of the Moon's motion. 

 If the same force had been added, it would have 

 produced a motion in antecedentia* 



The precise quantity of the motion of the apsides is 

 not, however, easily determined. NEWTON left this 

 part of the theory almost untouched ; and the only 

 theorem which he gave, having any reference to 

 it, made the motion only half of what it is found in 

 reality to be. MACHIN was, I believe, the first, 

 who, after NEWTON, attempted this investigation ; 

 he has only mentioned the result, which is very 

 exact, and the principles on which his reasoning 

 was founded, viz. that from the disturbing force in 

 the direction of the radius vector, he determined 

 the Moon's nearest approach to the Earth, and 

 farthest recess from it, supposing that but for such 

 disturbance, the Moon's orbit would have been a 

 circle : from this also he found the time from the 

 lowest to the highest apsis. 



This method was afterwards adopted by Dom. 

 WALMSLEY, and by Dr MATHEW STEWART, who 

 both derived from it the true motion of the ap- 

 sides, by investigations extremely ingenious, and 



that 



