38 Sryt-shadata . as was emptoyed in the case of the other planets--they apply the equation of blhe apsis, the result of the third process, to the mean place of the enjunction only leteas before, by an indirect process instead of applying it to the conjunction itseli, they apply it with a contrary sign to \be node, the effect upon the seletive position of the ywo being the same. Thus, for instance, the longitude of Mercury's conjunction at the given time is (see p. 80). 4 16° 5' frorr this subtract 2° ?', the equa tion of the 2psis found by the third process. Ind its equated longitude is 44 14ी 55 no ' deducting the longitude of the mode at the same time, which is 20° 41, we ascertain the planet's distance from the node to be 3 24 Or, by the Gindu method. dd the same equation to the mean position of the node and its equatbed longitude i8 22° 48; Bubtract this from the mean longitute ot he conjunction, and the distance is, as before, B° 24' The planet's djs Hey on h; note being determined, its latitude would be found by process sinmilar to that proseribed in verse 28 of this chapte, if the earth were at the centre of motion, and that rule is accordingly applied in the use of the mon; the proportion being, 1B Pradiug is to the sine of be distinct from the node, Ro is the sine of. ax brenme latitude (or the latitude itself, the lik»rence between the sine and tho are being of little count when the arc is $o small) to the latitude at the given point. In (Fe of the other planets, however, this pro portion is modified by com ination with anothe namely is the last variable hypotenuxo (cle how), which is the line ajawn from the earth to the finally determined place of the planet, or its true distance, is to radius, its mean distance, so i8 its apparent latitude at the mean distance fo its apparent latitude at its true distance That is, with R : Hin ned, list. externe lot. : १actual lat. at dist. R combine var, hyp |at. at djat. 12 at. at the dist, wo h®ve va. hyp. in nod. dis: extreme lat. actual lat, at true dist , which, durmed into an equation, is the rule in the latter halft of v. 57. The latitude, as thus found, is measurea. Of course. upon a se७OIId• ary to the ecliptic. By the rule in verse 58, howevor, it is treated as it measured upon a circle of foclination, and is, without modification, added to or subtracted from the declination. ecordlip; t; the direction of the two He ahe sac OF ifferent. "he cormmentary take note of this error, but explains it, as in other similar ta888, as being, x for fear of giving men , touble, and on tuccount of the very slighi inteeracy, overlooked by the ble88ed Sun, moved with compassion . We present in the annexad t.bla the results of the processes for cal culating the latitude, the declination, and the true declination as Rfected by latitude, of all the planets, at the time for which thei; longitude has already been found. The declination is calculated by the rule in veB
