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

VI.13 VI. VĀS.-PAUL. SIDDHĀNTA – LUNAR ECLIPSE 169 13. The graphical representation of the lunar eclipse has here been described briefly, and can be understood properly only by explanation (followed by demonstration). From this, the total duration, the total obscuration, the magnitude, etc. can be found by inspection. The representation given by the author can do duty for all the figures used by us to explain verses 3, 5, 6 and 7, the centre of the concentric circles being the centre of the Shadow in each. An impor- tant difference is that in the previous illustrations, the orbs, of the Moon and the Shadow were shown separately, while here they are replaced by one circle for each of duration (radius = 38' + 17') and totality, (radius = 38' - 17'), the Moon being reduced to a point coinciding with its centre. As the points of contact etc. showing the direction cannot be marked on the point-Moon, another circle is drawn to represent the Moon, with the same centre. As the directions of the points on the two circles are diametrically opposite to the directions of the same points with reference to the Moon, the points can be marked on the Moon-circle by the intersection of the diameter on its oppo- site half. An examination of fig. 7 will show this, and an example will make everything clear. Example 3. (Note: This example is intended only as an illustration). The latitude of a place is 20°. The full moon occurs 4 nāḍīs after sunset. The Moon at that time is rā. 5-15-0, and the Sun, rā. 11-15-0. The uncorrected Rāhu (Head) at full moon is rā. 5-6-36, from which the latitude is 35'N. The full moon is 11 nāḍīs before mid-night. The daily motion of (Moon - Sun) = 780'. Find the times of first contact etc., and verify by a graphical representation. (i) The corrected Rāhu = rā. 5-6-36 - 1° 36' = rā. 5-5-0. Moon ~ Rāhu = rā. 5-15-0 - rā. 5-5-0 = 10°. This is less than 13°. ∴ there is a lunar eclipse. (ii) Minutes of duration = √(55² - lat²) = √(55² - 35²) = 42, minutes of arc. Now, 2 × 42 × 60 ÷ 780 = nā. 6-28 = Uncorrected duration. Difference between Moon and uncorrected Rāhu = rā. 5-15-0 ~ rā. 5-6-36 = 8° 24. Correction = 8° 24' × 5 = 42 vināḍīs. As Rāhu is less, deducting from uncorrected duration, the correct duration = nā. 5-46. Half this is nā. 2-53. Subtracting from the time of new moon, 4 nāḍīs, the first contact is at nā. 1-7 after sunset. Adding, the last contact is at nā. 6-53. (iii) Moon ~ cor. Rāhu = 10°. As this is greater than 5°, there is no total phase. (iv) The first contact is nā. 15-0 - nā. 1-7 = nā. 13-53 before midnight, i.e. the Moon is 83° east of the meridian, 11a. A.B. दशाष्टा 12a. A. प्रोक्तायां सकलङ्का; B. प्रोक्ता यो सवूलांका (B2. बू) B1.2. त्रिशतद्वय; B3. त्रिंशद्वय D. प्रोक्ताया [मं] शकलका [त्] b. A. मतेन सूत्रेण; B.C.D. मितेन सूत्रेण b. A.B.D. पूर्वापरयोश्च (A om र); C. पूर्वापरायाश्च c. A.B. शशिना बहुस्थिति (A2. नां) d. A. समात्ताराः; B. समां ताराः d. A. नि एक छेना निष्पालेख्य; B. नि एकछत्रो निवासलेख्य; 13a. A. छेदक; B. षेदक; C.D. छेद्यक D. न्येकस्थानि वा संलेख्य d. B1. मंस्थ्यानेनात्र (B2.3. सं०)