SECT. V. DISTURBING ACTION OF THE SUN. 35 



tangent to her orbit, disturbs her motion in longitude. And the 

 third, acting perpendicularly to the plane of her orbit, disturbs 

 her motion in latitude ; that is, it brings her nearer to, or removes 

 her farther from, the plane of the ecliptic than she would other- 

 wise be. The periodic perturbations in the moon, arising from 

 these forces, are perfectly similar to the periodic perturbations of 

 the planets. But they are much greater and more numerous ; 

 because the sun is so large, that many inequalities which are 

 quite insensible in the motions of the planets, are of great mag- 

 nitude in those of the moon. Among the innumerable periodic 

 inequalities to which the moon's motion in longitude is liable, 

 the most remarkable are, the Equation of the Centre, which is the 

 difference between the moon's mean and true longitude, the 

 Evection, the Variation, and the Annual Equation. The dis- 

 turbing force which acts in the line joining the moon and earth 

 produces the Evection : it diminishes the excentricity of the lunar 

 orbit in conjunction and opposition, thereby making it more 

 circular, and augments it in quadrature, which consequently 

 renders it more elliptical. The period of this inequality is less 

 than thirty-two days. Were the increase and diminution always 

 the same, the Evection would only depend upon the distance of 

 the moon from the sun ; but its absolute value also varies with 

 her distance from the perigee (N. 102) of her orbit. Ancient 

 astronomers, who observed the moon solely with a view to the 

 prediction of eclipses, which can only happen in conjunction and 

 opposition, where the excentricity is diminished by the Evection, 

 assigned too small a value to the ellipticity of her orbit (N. 103). 

 The Evection was discovered by Ptolemy from observation, about 

 A.D. 140. The Variation produced by the tangential disturbing 

 force, which is at its maximum when the moon is 45 distant 

 from the sun, vanishes when that distance amounts to a quadrant, 

 and also when the moon is in conjunction and opposition ; conse- 

 quently, that inequality never could have been discovered from 

 the eclipses : its period is half a lunar month (N. 104). The 

 Annual Equation depends upon the sun's distance from the 

 earth : it arises from the moon's motion being accelerated when 

 that of the earth is retarded, and vice versa for, when the earth 

 is in its perihelion, the lunar orbit is enlarged by the action of 

 the sun; therefore, the moon requires more time to perform 

 her revolution. But, as the earth approaches its aphelion, the 



