LOCAL LATITUDE 75 hemisphere. By the Rsine of that (sum or difference) multiply the day-radius and then divide (the product) by the radius. In the resulting quantity apply the earthsine reversely to the application of the ascensional difference (i.e., subtract the earth- sine when the Sun is in the southern hemisphere and add the earthsine when the Sun is in the nothern hemisphere). Then multiply that (i.e., the resulting difference or sum) by the Rsine of the colatitude of the local place and then divide (the product) by the radius again. Thus is obtained the Rsine of the Sun's altitude for the given time in ghatis.¹ The square root of the difference between the squares of the radius and that (Rsine of the Sun's altitude) is known as the (great) shadow.2 The asus elapsed since sunrise in the forenoon or to elapse before sunset in the afternoon are obtained by multiplying the given ghatis³ by 360. These are equivalent to the number of minutes in the arc of the celestial equator lying between the hour circles passing through the Sun and through the Sun's position on the horizon at sunrise or sunset. When these asus are diminished or increased by the asus of the Sun's ascensional difference (according as the Sun is in the northern or southern hemisphere), the asus of the difference or sum correspond to the minutes lying in the arc of the celestial equator intercepted between the Sun's hour circle and the six o'clock circle. The Rsine of that multiplied by the day-radius and divided by the radius gives the distance in minutes of the Sun from the line joining the points of intersection of the six o'clock circle and the Sun's diurnal circle. That increased or diminished by the earthsine (accord- ing as the Sun is in the northern or southern hemisphere) gives the distance of the Sun from the rising-setting line. In Fig. 7, let S be the position of the Sun on the celestial sphere, SA the perpendicular from S on the plane of the horizon, and SB the perpendicular from S on the rising-setting line. Then in the plane triangle SAB, we have ¹ This rule is found also in A, iv. 28; BrSpSi, iii. 25-26; LBh, iii. 7-10; SiDVṛ, I, iii. 24-25; Siśe, iv. 32, 34; Siśi, I, iii. 53-54. 2 This rule is found also in BrSp.Si, iii. 27(ii); and Siśe, iv. 34.
