ASTRONOMY. 131 



the quadratures, and diminishes when the moon is 

 in the syzygies. 



130. Another irregularity in the moon^s mo- 

 tion, which vanishes at the syzygies and the 

 -quadratures, and is greatest in the middle be- 

 tween them, or in the octants, is called the 

 Moon's Variation. It depends on the differ- 

 ence of longitude of the sun and moon, or on 

 their angular distance, and may foe represented 

 by the formula 



(3,5' 42") sin 2 (<[ 0). 



This inequality was discovered by TYCHO BRAKE'. 

 Its period is 14-d.76.53, or half a lunar month. 



131. The angular motion of the moon is also 

 subject to a third irregularity, by which it is di- 

 minished when the sun approaches the perigee, 

 and increased when he approaches the apogee. 

 This is called the Annual Equation : it depends 

 entirely on the time of the year, or mean ano- 

 maly of the sun, and is equal to 



(1 1' 11".<J) sin Mean Anom.Q. 



TYCHO BRAKE' was acquainted with this inequality, 

 and made an allowance for it in the equation of 

 time. These are the only irregularities in the 

 moon's motion, that were known previously to the 

 theory of Gravitation. That theory not only ex- 

 plains 



