srct. iv.J DISSERTATION SECOND. 103 



same force which was sufficient to bend the orbit of the earth 

 into an ellipse, could not but have a sensible effect on the 

 orbit of the moon. Here Newton immediately observed^ 

 that it is not the whole of the force which the sun exerts on 

 the moon, that disturbs her motion round the earth, but only 

 the difference between the force just mentioned, and that 

 which the sun exerts on the earth, — for it is only that diffe- 

 rence that affects the relative positions of the two bodies. To 

 have exact measures of the disturbing forces, he supposed 

 the entire force of the sun on the moon to be resolved into 

 two, of which one always passed through the centre of the 

 earth, and the other was always parallel to the line joining 

 the sun and earth, — consequently, to the direction of the 

 force of the sun on the earth. The former of these forces 

 being directed to the centre of the earth, did not prevent the 

 moon from describing equal areas in equal times round the 

 earth. The effect of it on the whole, however, he showed 

 to be, to diminish the gravity of the moon to the earth 

 by about one 358th part, and to increase her mean distance 

 in the same proportion, and her angular motion by about a 

 179th. 



From the moon thus gravitating to the centre of the earth, 

 not by a force that is altogether inversely as the square of 

 the distance, but by such a force diminished by a small part 

 that varies simply as the distance, it Avas found, from a very 

 subtle investigation, that the dimensions of the elliptic orbit 

 would not be sensibly changed, but that the orbit itself 

 would be rendered moveable, its longer axis having an angu- 

 lar and progressive motion, by which it advanced over a 

 certain ate during each revolution of the moon. This af- 

 forded an explanation of the motion of the apsides of the 

 lunar orbit, which had been observed to go forward at the 

 rate of 3° 4', nearly, during the time of the moon's revolu- 

 tion, in respect of the fixed stars. 



