260 OUTLINES OF NATURAL PHILOSOPHY. 



that of the latter, particularly distinguished for its 

 geometrical elegance. Dr STEWART has demon- 

 strated this theorem : 



261. If r be the radius of the Moon's orbit, 

 supposing it to be a circle, and acted on only 

 by F, her gravity to the Earth. Then if a mean 

 disturbing force =f be supposed to diminish 

 the Moon's gravity, the greatest distance she 



__ 



will go to from the Earth is r x ^ - -^ and 



* 5f 



the cube of this distance will be to the cube of 

 r in the duplicate ratio of the angle described 

 by the Moon from one apsis to the next to two 

 right angles. 



Tracts Math. $ Phys. Tract iv. prop. 27. ; also 

 Sun's Distance 9 prop. 9. 



Hence the angle described from one apsis to the 



next = ( F ~ 3 /r X 180. 

 (F-5/r 



FRISI has adopted the principle of MACHIN, inclu- 

 ding also the action of the forces perpendicular t 

 the radius vector. Opera, torn. in. p. 380. 



VINCE, in the 2d volume of his Astronomy, has com- 

 puted the motion of the apsides according to this 

 last method, and makes the quantity of it in a si- 



derial 



