40 DISTUKBING ACTION OF THE SUN. [SECT. v. 



The disturbing action (K 101) of the sun on the moon is 

 equivalent to three forces. The first, acting in the direction 

 of the line joining the moon and earth, increases or diminishes 

 her gravity to the earth. The second, acting in the direction 

 of a 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, or removes her farther, from the plane of the ecliptic 

 than she would otherwise 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 magnitude 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 Varia- 

 tion, and the Annual Equation. The disturbing force which 

 acts in the line joining the moon and earth produces the Evec~ 

 tion : it diminishes the excentricity of the lunar orbit in con- 

 junction 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 

 witTi her distance from the perigee (K 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 dimi- 

 nished by the Evection, assigned too small a value to the el- 

 lipticity 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 



