when its force causing precession is nothing- ; at other times more than 

 230 distant, when its force is greatest. Hence the sun's action in produ- 

 cing precession must continually vary from the Equinox in March to the 

 solstice in June. The correction due to this solar inequality is called 

 the semi-annual Solar Equation. In consequence of this solar inequali- 

 ty, the pole of the earth describes, half yearly according to the order of 

 the signs, round the place of the mean pole a circle whose radius = 

 0".434o. 



The solar inequality affects the precession of the stars in longitude, 

 declination, and right ascension, also the obliquity of the ecliptic ; hence 

 the following formulae. 



Equation of precession in longitude. 



This = 1", 1 X sin. 2 sun's longitude. 



Substitute this expression for 50",31 in the above formulae for preces- 

 sion, and we shall have the equations of precession in declination and 

 R. A. 



Correction of the obliquity. 



This = 0",4345 X cos. 2 sun's longitude. 



The variation in the obliquity of the ecliptic arising from the sun, is 

 called the correction of the obliquity ; that from the moon is called the 

 equation of the obliquity. 



III. Precession, lunar inequality of. 



The lunar inequality of precession is called Nutation, to distinguish it 

 from the solar inequality. In consequence of the lunar action, the true 

 pole of the earth describes about the place of the mean pole, in 18 years 

 7 months, contrary to the order of the signs, an ellipse of which the ma- 

 jor axis 19",2, and minor axis 15". 



The nutation affects the precession of the stars in longitude, declina- 

 nation, and R. A. and also the obliquity of the ecliptic ; hence the follow- 

 ing formulae. 



Equation oftJie Equinoxes in R. A. 



The variation in the precession, or in the equinoctial points, usually 

 called the Equation of the Equinoxes in R. A. is 



17",2 sin. longitude moon's node. 

 This affects the longitude of all the stars equally. 



Nutation in declination. 



Let A be the R. A. of a star, D its declination, N the longitude of the 

 moon's node j then nutation in declination , 



1",1 sin. (A + N) + 8",5 sin. (A N). 

 211 M3 



