276 GANITASĀRASANGRAHA drawn which will extend from north to south. The straight line running through the middle of the angles of this (fish-shaped figure) represents of itself the northern and the southern direc- tions. The intermediate directions have to be ascertained as being derivable from half the (interspace between these) directions. 4. The (measure of the) equinoctial shadow is indeed half of the sum of the measures of the shadows obtained at the middle of the day-time (or noon) on days when the sun enters the sign of Aries as also the sign of Libra. 5. In Lanka, Yavakoti, Siddhapuri,and Rōmakāpuri, there is no (such) equinoctial shadow at all; and, therefore, the day-time is of 30 ghafis. 63. In other regions, the day-time happens to be longer or shorter hy 30 ghafis. On the days of the entrance (of the sun) into Aries and into Libra, the day-time is everywhere of 30 ghatis (in duration). 7. Having understood the measure of the duration of the day- time and also of the shadow at (noon or) the middle of the day according to the way described in astronomy, one should learn herein the calculations regarding shadows by means of the collec- tion of rules hereafter to be given. The rule for arriving at the time of day, on knowing the measure of the shadow of a given style at a given time (in the forenoon or afternoon) in relation to a place where there is no equinoctial shadow :- 8. One is added to the measure of the shadow (expressed in terms of the height of an object), and (the sum so resulting) 8. If a be the height of the object and the length of its shadow, then the time of the day that has elapsed or has to elapse is, according to the rule given here, equal to where A is the angle repre- 2 (cot. A + 1) 1 1 Vila 2(a + 1) senting the altitude of the sun at the time. It may be seen that this formala gives only the approximate value of the time of the day in all cases except when the altitude is 45', and that the approximation is very rough only in the case of large altitudes, nearing 90° The formula seems to be based on the fact that for small values the angles in a right-angled triangle are approximately proportional to the opposite sides.
