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

210 PAÑCASIDDHĀNTIKĀ IX.11 Example 7. Days, 52931. Benaras is east of Ujjain longitude by 68 yojanas. Find the true Moon at noon at that place. From example 6, the true Moon at Ujjain noon is rā.4-13-29.9. The difference in time for Benaras = nāḍikās (68 ÷ 53 1/3), earlier. From this, the correction for local noon = 729'.1 × 68 ÷ (53 1/3 × 60) = 15'.5, subtractive. (The Moon's daily motion for the day will be shown to be 729'.1 under verse 13.) ∴ The true Moon required = rā.4-13-29.9 − 15′.5 = rā.4-13-14.4. The instruction is explained thus: The author takes it that for the region of Ujjain the length of the latitude circle is 3200 yojanas. The Sun, in its apparent diurnal motion westward goes once round the circle in 60 nāḍikās, crossing all the meridians on the earth. There are thus 3200 ÷ 60 = 53 1/3 yojanas for one nāḍī, and a place east by this distance has its meridian crossed by the Sun, i.e. its noon earlier by one nāḍī, and west, later. The motion for this time is calculated by the proportion, 60 nāḍīs: daily motion :: the nāḍīs got: the motion for the same. That the motion is deductive if the noon is earlier, and vice versa is plain. (This is for direct motion, the Sun and the Moon alone being considered here. If the daily motion is retrograde, as is possible in the case of the star-planets, it is obvious that the subtraction and addition have to be reversed.) But it is to be noted that in the Ārdharātrika of Āryabhaṭa and in the Khaṇḍakhādyaka, the diameter of the earth is given as 1600 yojanas from which the equatorial circumference got is 5027 yojanas. Therefore the Original Saura must have given the same values. The Modern Sūrya Siddhānta, and the Siddhāntas that follow it also give the same. From this the latitude circle at or near Ujjain should be given according to them as 5027 cos 24° = 4600 yojanas. According to the Āryabhaṭīya, which uses a yojana measure one and a half times that of Saura etc., the equatorial circumference would be 3300 yojanas. From this, it is 14° latitude circle that would be 3200 yojanas, and not Ujjain latitude circle. Why should the author use the yojana measure of the Āryabhaṭīya instead of that of the Saura, and in that why should he use the yojanas of the 14° latitude circle instead of the Ujjain (24°) latitude circle seems inexplicable. [रविशशिनोर्मध्यभुक्तिः] नव(तिः) सप्तशतीन्दोः सचतुस्त्रिंशद्विलिप्तिका भुक्तिः । षष्ट्यैका विकलाऽष्टकं च मध्या सहस्त्रांशोः ॥ ११ ॥ Mean motion of the Sun and the Moon 11. The mean daily motion of the Moon is 790′ 34″, and that of the Sun is 59′ 8″. These can be derived from the mean motions of the Sun and the Moon given in the first and second verses. In the former it is said that in 2,92,207 days there are 800 revolutions of the Sun. ∴ 800 revolutions ÷ 2,92,207 = 59′ 8″, the motion for one day. In the latter, we have that there are 9,00,000 revolutions of the Moon in 2,45,89,506 days. ∴ the motion per day = 9,00,000 revolu- tions ÷ 2,45,89,506 = 790′ 34″. The correction in verse 4 is too small per day to consider. 11a. A.B.नव (A.नच) सप्तसर्तींदोः b. B.त्रिंशद्विलिप्तिकासु भुक्तिः d. B.मध्याग्रहस्त्रांशोः