96
moon ’s mean motion, is not equal in tlie two halvesM 4 Mj M 2 and M 2 M 3 M 4 (fig. 19). It is greater in theformer semicircle, on the whole, than in the latter;but the points where the tangential force vanisheslie outside the extremities of this latter semicircle.Thus the points where the variation attains its maxi-mum value lie on the sides of m 1 and m 4 towards M uand on the sides of and m, s away from Jf 3 ;and the amount of the maxima at the two formerstations is greater than the amount at the two latter.Moreover, when the earth is in perihelion these effectsare greater, while when she is in aphelion they areless than when she is at her mean distance. Themaximum inequality thus produced, a variation ofthe variation as it were, amounts to about twominutes, or about the sixteenth part of the moon’sapparent diameter. It is called the parallacticinequality, because of its dependence on the sun’sdistance, which, as we know, is usually expressedby a reference to the solar parallax. And as theinequality depends on the sun’s distance, so itsobserved amount obviously supplies a means of de-termining the sun’s distance. It was, in fact, adetermination of the sun’s distance, deduced byHansen from the observed amount of the moon’smaximum parallactic inequality, which recently ledastronomers to question a value of the distance,based on observations of Venus in transit, whichhad been for many years adopted in our text-booksand national ephemerides.