66 DIRECTION, PLACE AND TIME That is to say, it is equal to the ascensional difference of the last point of Taurus minus the ascensional difference of the first point of Taurus. The ascensional difference of Gemini, similarly, is equal to the ascensional difference of the last point of Gemini minus the ascensional difference of the first point of Gemini. The following is the rationale of the above rule: From stanza 7, we have Rsin x Rsin 8 Rsin (asc. diff.) Rsin (90⁰-$) But from stanza 5, assuming gnomon = 12 angulas, equinoctial midday shadow 12 Rsin Rsin (90°-) Therefore Rsin (asc. diff.) - (equinoctial midday shadow) x Rsin 8 x radius 12 x Rcos 8 Hence for a place having one angula for the equinoctial midday shadow Rsin (asc. diff.) - Rsin 8 x R 12 x Rcos 8 radius day-radius X 1397× Rsin λ R R 12 x Rcos & (using stanza 6) where is the sayana longitude, 8 the declination, and R the radius (=3438'). Now we will calculate the ascensional differences of Aries, Taurus, and Gemini for a place having one angula for the equinoctial midday shadow. (1) Calculation of the ascensional difference of Aries. At the last point of Aries, λ = 30°, so that Rsin λ = R/2. Therefore, Rsin 8′=1397/2 = 698' 5 and Rcos 8 = 3366'.
