SUN'S PRIME VERTICAL ALTITUDE AND ZENITH DISTANCE respectively, and C the point where SB meets the line joining the points of intersection of the Sun's diurnal circle and the six o'clock circle. Naturally, SB is perpendicular to that line. In the triangle ACB, we have LABC and LACB Therefore AC = Rsin 8, AB= where is the declination the latitude of the place. Therefore = Rsin (Sun's agrā), 90° - $, 90°, of the Sun, and Rsin (Sun's agrā) But (vide stanza 6 above) Rsin = Therefore Rsin 8 x R Rcos Rsin λx 1397 R Rsin (Sun's agrā) where is the Sun's sayana longitude. and LSBA - 90°- $. Now in the triangle SAB, right-angled at A, we have SA Rsin a, AB= Rsin (Sun's agrā), S A Rsina x 1397 Rcos Rsin (Sun's agrā) x Rcos Rsin 85 Fig. 8 (1) (2) B Rsin a = where a is the Sun's altitude. The necessary conditions for the existence of the prime vertical altitude of the Sun are: (i) that the Sun should be in the northern hemi- sphere, and (ii) that the Sun's declination should be less than the latitude of the place. The condition laid down in the above rule that the Sun's agrā should be less than the latitude is incorrect. This error is, in fact, due to Aryabhata I, whom the author is following in this work. But the 1 See A, iv. 30-31,
