पृष्ठम्:महाभास्करीयम्.djvu/१४८

DECLINATION, DAY-RADIUS, EARTHSINE AND ASCENSIONAL DIFFERENCE That is (1) Rsin 8 = 1397 x Rsin > R (Rsin 8)² x Rsin 8 Rsin (90°-+) (2) Day-radius=√√ R²- Rsin (3) Earthsine earthsine X radius day-radius 63 (4) Rsin (ascensional difference) where R is the radius, is the latitude of the place, and and are the sayana longitude and declination respectively. Definitions. The day-radius is the radius of the small circle parallel to the celestial equator. A small circle parallel to the celestial equator is called a diurnal circle (ahoratra-vṛtta). In particular, the Sun's diurnal circle is the small circle parallel to the equator which the Sun describes in the course of a day. The earthsine is the Rsine of the arc of a diurnal circle intercepted between the local horizon and the six o'clock circle.2 In Hindu astronomy the six o'clock circle is called the equatorial horizon (niraksa-ksitija) as it is the horizon of a places on the equator. The ascensional difference is defined by the arc of the celestial equator lying between (i) the equatorial horizon and (ii) the secondary to the equator passing through the intersection of the diurnal circle and the (eastern or western) horizon. It is measured in time (i.e., in asus). The ascensional difference of the Sun thus denotes the difference between the times of rising of the Sun on the local and equatorial horizons. ¹ By the sayana longitude is meant the celestial longitude measured from the moving vernal equinox. 2 The six o'clock circle is the great circle of the celestial sphere which passes through the east and west points of the celestial horizon and the poles of the celestial equator. 3. This place lies at the intersection of the local meridian and the equator. 4 One așu corresponds to one minute of arc of the celestial equtaro Thus one asu= 4 seconds of sidereal time.