MOO 



arising from an increase of the eccentricity of the moon's orbit at tho 

 quadratures, and a diminution of it at the sy/ygics. Let M and S be the 

 mean longitudes of the moon and sun, A' the mean anomaly of the moon, 

 then the evection is 



1. 21'. 5",5 X sin. ( 2 (M S) x ) 



The evection runs through all its changes in 3ld. Wh. 2Stn. nearly. It 

 is called the second lunar inequality, the equation of the centre being the 

 first. 



2. Variation. i.e. a variation in the moon's velocity, which is nothing 

 in syzygy and quadratures, and greatest at the octants. It = 



35'. 42" X sin. 2 (M S). 

 Its period is half a lunar month. This is the third lunar inequality. 



3. The annual equation or fourth lunar inequality, is an irregularity 

 in the moon's motion, arising from the variation of the sun's distance 

 from the earth. It is 



11'. 11",9 X sin, mean anomaly of sun. 



Its period is an anomalistic year. 



These three inequalities were known before Newton's time : they are 

 applied as corrections to the equation of the centre in determining the 

 moon's longitude. 



Other inequalities there are which have a much longer period ; one for 

 instance, discovered by Laplace, depending upon the position of three 

 lines, the axis of the moon's orbit, the axis of the earth's orbit, and the 

 line of the moon's nodes which takes up a period of 85 years, and amounts 

 to 



14" X sin. (2 longitude node X longitude perigee of moon 3 longi- 

 tude perigee of sun). 



Others again there are which do not run through the circle of their 

 changes but in the course of several thousand years, and are usually ex- 

 pounded by their aggregate in 100 years. The moon's nodes, the apogee, 

 the eccentricity, the inclination of the orbit, the moon's mean motion, 

 are all subject to secular inequalities. Of these, the most remarkable is 

 the acceleration of the moon's mean motion (depending on a change in 

 the eccentricity of the earth's orbit), by which her velocity continually 

 cncreases, and periodic time decreases from age to age. For many ages 

 to come, it may be nearly expressed by this formula, where n denotes 

 the number of centuries from 1700. 



10". 181621268 n* + 0". 0185384408 n*. 



The tables of the moon's motion contain at present 28 equations for 

 the moon's longitude, 12 for her latitude, and 13 for the horizontal pa- 

 183 



