OUTLINES OF NATURAL PHILOSOPHY. 



orbit in less time. As the area described by the 

 radius vector in the primitive and the disturbed 

 orbit is the same, it can be shewn, that in conse- 

 quence of the mean disturbing force, the radius 

 vector is increased by a 358th part, and the angu- 

 lar velocity diminished by a 179th part. 



Exposition du Systeme du Monde, chap. v. p. 213. 

 2<*e edit. 



252. The annual equation is an irregularity in 

 the Moon's motion, arising from the variation 

 of the Sun's distance from the Earth, and bear- 

 ing a given ratio to the equation of the Sun's 

 centre, 



Since the Sun's disturbing force is inversely as the 

 cube of his distance, when he approaches the 

 Earth at the perihelion, the Moon's motion is 

 slower, and, for the same reason, at the aphelion, 

 it is quicker than the mean. This produces what 

 is called the annual equation, equal nearly to 

 (H',12") X sin Sun's mean anomaly. It is nearly 

 equal to one-twelfth part of the equations of the 

 Sun's centre, but has the opposite sign, being sub- 

 tracted when that equation is added, and vice versa. 



253. An equality in the same disturbing force, 

 depending on the position of the transverse axis 

 of the Moon's orbit, in respect of the line drawn 

 from the Earth to the Sun, produces the equa- 



tion 



