PHYSICAL ASTRONOMY. 



in a contrary direction to the motion of the MOOD, 

 that is, a retrograde motion, or in antecedentia. 



258. From this, NEWTON has shewn, that the 

 horary motion of the node at any time is to 

 33". 177, as the product of the sines of these 

 three angles, the distance of the Moon from the 

 quadrature, the distance of the Moon from the 

 node, and the distance of the node from the 

 Sun, to the cube of the radius. 



Princip. lib. in. prop. 31. 



When any one of the above three sines becomes ne- 

 gative, the motion of the node, from being retro- 

 grade, becomes progressive* 



The mean horary motion of the node, 

 which arises from taking the average of all the 

 horary motions, is to 16".2771 as the, square of 

 the sine of the distance of the node from the 

 Sun to the square of the radius. 



Ibid. cor. 



Hence the mean motion of the nodes for a siderial 

 year is 19 .1S'.1".4-, which is not far from the re- 

 sult of astronomical observation. 



VOL. II. R 260. From 



