78 DIRECTION, PLACE AND TIME is thus obtained multiply the product of the day-radius and (the Rsine of) the colatitude and then divide (the resulting product) by the square of the radius. The result of this (operation) is the Rsine of the (Sun's) altitude. Or, multiply the result obtained by the inverse applica- tion of Rsine of the (Sun's) ascensional difference (in the above process) by the product of (the length of) the gnomon and the day-radius and then divide by the product of (the length of the hypotenuse of the equinoctial midday shadow and the radius; the result is the Rsine of the (Sun's) altitude.¹ That is to say, (1) MX day-radius Rcos R R where M = Rsin (given ghatisFasc. diff)+Rsin (asc. diff.), the upper or lower sign being taken according as the Sun is in the northern or southern hemisphere. a andare, as usual, the Sun's altitude and the latitude of the place respectively. Or, Rsin a = Rsin a = Mx day-radius R X '" gnomon hypotenuse of equinoctial midday shadow "M multiplied by day-radius and divided by radius" represents in the celestial sphere the perpendicular distance of the Sun from the rising-setting line. A rule for finding the Sun's altitude when the Sun's ascensional difference is greater than the given time: 25. When the (Sun's) ascensional difference (is greater than and) cannot be subtracted from the given asus (elapsed since sunrise in the forenoon or to elapse before sunset in the after- noon), subtract the latter from the former and with the Rsine of the remainder proceed as before (i.e., multiply that by the day- radius and divide by the radius); then subtract the resulting ¹ This rule occurs also in BrSpSi, iii. 27(i); ŚiDVṛ, I, iii. 27; Sise, iv. 37.
