पृष्ठम्:महाभास्करीयम्.djvu/१५६

SUN'S DECLINATION AND LOCAL LATITUDE hemisphere; then multiply that (sum or difference) by (the Rsine of) the colatitude and divide by the radius. The result thus obtained is the Rsine of the Sun's altitude at midday. Let S (See Fig. 6) be the position of the midday Sun on the celestial sphere. Also let SA and SB be the perpendiculars dropped from S on the plane of the celestial horizon and the Sun's rising-setting line respec- tively. Then in the plane triangle SAB, we have S SA = Rsin a SB = day-radius earthsine, LSBA = 90° - $, and SAB = 90°, where a denotes the Sun's altitude, and the latitude of the place. Therefore SA/SB or Rsin a = A Rsin SBA / Rsin SAB, 71 Fig. 6 (day-radius earthsine) x Rsin (90°-) R B + or - sign being taken according as the Sun is to the north or south of the equator. A rule for determining the Sun's declination with the help of the Sun's meridian zenith distance and the latitude of the local place, when the latitude is greater than the Sun's meridian zenith distance: 1 Vide supra, p. 64 (footnote). 2 This rule is found also in LBh, iii. 30. 13. When the latitude is greater than the arc of the Sun's meridian zenith distance derived from the (midday) shadow (of the gnomon), their difference is the declination of the apparent Sun. The Sun is also, in that case, in the northern hemisphere.2 This rule relates to the case when the midday shadow of the gnomon falls to the north of the gnomon.