PHYSICAL ASTRONOMY. 31J 



320. The action of the Moon produces also 

 an inequality which diminishes the precession 

 by a quantity proportional to the sign of the dis- 

 tance of the Moon's ascending node from the 

 vernal equinox ; and, besides this, a diminution 

 in the obliquity of the ecliptic, proportional to 

 the cosine of the said distance. 



These two inequalities constitute the Nutation j and 

 the result here stated from the theory of gravita- 

 tion, is conformable to that which was before gi- 

 ven from observation, 218. Conformably to 

 what is said there, these two inequalities may be 

 expressed by the revolution of the extremity of 

 the Earth's axis produced to the Heavens, and 

 describing an ellipse, as there represented ; of 

 which the greater axis is to the less, as the cosine 

 of the obliquity of the ecliptic to the cosine of twice 

 that obliquity. 



. The precession, on account of variations 

 in the solar action, as well as in the lunar, is 

 subject to some inequalities, not included in 

 the preceding theorems. 



The amount of the precession, including all these ine- 

 qualities, may be calculated for any period of time, 

 by a formula given in the Mecanique Celeste, which, 

 reduced to the sexagesimal notation, is 



50".412 X t - 4626" sin. 1".394. X t + 

 12954" sin 1".4298 X t. 

 t is the number of years reckoned from 1750. 



As 



