पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

IV. 48 IV. THREE PROBLEMS 121 From the sin degrees of time, and thence by dividing by 6, the time in nāḍīs after the Sun has touched the unmaṇḍala is obtained. The addition or subtraction of the half-cara to this gives the time from sunrise, to obtain which sin half-cara is got from the Earth-sine, and then its arc, viz the degrees of half-cara. षड्घ्नेऽथ स्वद्युमिते छिन्ने सद्धादशैर्विमाध्याह्नैः । छायाङ्गुलैर्गतास्ता नाड्यः प्राक् पृष्ठतः शेषाः ॥ ४८ ॥ Time for sunset 48. Or roughly, multiply the duration of daytime in nāḍīs by 6, and divide by the shadow increased by 12 and decreased by the midday shadow of date. The time from sunrise is got in the forenoon, and the time to elapse for sunset is obtained in the afternoon. The shadows mentioned here are those of the twelve-digit gnomon and not the shadows of a person measured by his foot. The rule is the time in nāḍīs = 6 × daytime in nāḍīs ÷ (shadow + 12 − mid-day shadow). Example 18. Given the duration of daytime, nāḍīs 33-20, and mid-day shadow, 2 aṅg 50 vyaṅg. Find the time when the gnomonic shadow is 13 aṅg 56 vyaṅg. The time = 6 × 33 1/3 ÷ (13 14/15 + 12 − 2 5/6) = 200 ÷ 23 1/10 = nāḍīs 8-37. The data given in the example are for the place and day in Example 16 (a), and we must get nāḍīs 8, as the time. But we get nāḍīs 8-37. From this we can have an idea of the roughness of this method. Evidently VM wants us to use this rule if we feel that this accuracy is sufficient, for, this is easy to use, provided the daytime and the midday shadow are tabulated beforehand and kept ready. The rule may be explained in the manner we explained the similar rule with Vāsiṣṭha Siddhānta. Let us assume, time = x × day-time ÷ (shadow − mid-day shadow + y), where x and y are two con- stants to be determined. (The daytime occurs as a multiplier in the rule because, other things being equal, the time must vary with the daytime. For the deduction of the mid-day shadow from the shadow, see the explanation in the Vāsiṣṭha.) At noon the shadow is equal to the mid-day shadow of date, and the time is daytime/2. Therefore we have: x × day time ÷ (mid-day shadow − mid-day shadow + y) = daytime/2. ∴ 2x × daytime = daytime × y. ∴ 2x = y. Therefore, whatever be the multiplier for the daytime, twice that is the constant additive to the shadow, as in the author's rule here, 6 and 12, respectively. Only so far can we go in the explanation 48. Quoted by Utpala on BS 2, p.62 48a. A. षट्प्रोथवा द्युमाने; C.D. षड्घ्नेऽथवा द्युमाने c. A1. गतास्था; A2. गतास्थे b. A. ०दशे विमध्याह्ने d. A. नाद्यः. A. प्रष्टतो