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

XVIII.26 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 331 The numbers I have given in the scheme are practically what are found in the text, without emendation excepting three. In verse 25, I have emended captasteka into catvāryeka to get 146° the most plausible value. NP have made it ṣaṣṭāṣṭaika to get 186° which is too large. See discussion below, 150° is given by adhyardhaṃ ca śataṃ where tataḥ is emended into śatam. This is necessary to make up the total 410° motion in 780 days. Secondly, 43° motion for 60 days given from setting to conjunction is required to agree with the 17° usually given for heliacal rising. This is made up by emending viṃśatam into triṃśatam with the 13° given by daśatriyutam added. I shall now show that the motion of Mars is near 43° in 60 days, in the region of the conjunction. For its distance, nearly 1.53 that of the Sun, given by modern astronomy and also as computed from Hindu astronomy, the equation of conjunction at this region is 11' per day, (as can be verified) which, plus the daily mean motion of 31'.4 gives 42'.4 per day, making 42°.4 in 60 days, roughly 43°. This also agrees with the angle for heliacal rising of Mars, nearly 17°, given by Hindu astronomy. (In 60 days the Sun moves 59.1°. So, the elongation is 59.1 − 42.4 = 16.7°, nearly 17°). If viṃśatim is taken as it is, we get 20° + 13° = 33°, which is 9.4° short of the actual 42.4 and which also gives the angle for heliacal rising as great as 26°, so far from the 14°-17° given by all. In the mean, the motion from setting to conjunction must be equal to the motion from conj. to rising. That is why it is not given by the text separately. That the motion segments given in the two verses is mean is also clear, since no position of Mars from its apogee is taken into account. So the total motion must be equal to 409°. But the total got by adding the segments is 400°. This must be due to the defective method of the original or the empirical nature of the motions, and rounding off to whole degrees, as seen from 43° being given for 42.4°. The opposition must fall at the mid- point of the retrograde motion, − 18°, and divide it into −9, −9. The total motion from conj. to opposition must be equal to that from opposition to conj. But what we actually get is 43° + 146° + 18° − 9° = 198°, and −9° + 18° + 150° + 43° = 202°. It may be that the angle segments given are empirical and also there are errors in the apparently correct numbers giving the segments, needing emendation. It is only in the case of Mars, does VM give these eight types of motion. In II. 12-13 of the Later Sūrya Siddhānta, a set of 8 types of motion is given. But they cannot be equated to these each to each. So we have only to guess when in doubt. The days on the synodic cycles to pass each type of motion must be nearly equal to the average of the days given in verses 27-35 for that type of motion. This has been used to check the degrees of each type. But the synodic period, as also the mean motion of 1 + 18/133 revolution in that period are very nearly correct and they must have been got by analysis of the observed motions. So the Siddhānta must have known that the motions and times are half and half on both sides of the opposition. Beginning from rising type I is śīghra (quick) motion. II is manda (slow) motion. The distinction seems to be faster or slower than the mean motion. So, the dividing point must be where the tan- gent from the earth touches the synodic circle. Since the mean distance of Mars is 1.53 times that of earth from Sun, this point falls about 189.5° from conjunction. Subtracting 43.5° motion from                                                                                  d. A.B.C. द्यु (B. द्वा) नाषष्टितस्तोस्तमितः; 25a. A. षट्चप्तस्तेक॰; B. षट्वपप्तस्तेक॰;                            D. त्रिभ्रषष्टिं ततोऽस्तमितः       D. षट्कास्तैकं; C. पदसप्तकं                                 26a. A.B.C. त्रियुता; D. त्रिहतात्   b. A.B. ॰दशमस्तगस्ततो; C. ॰मष्टादशमासगस्ततो;             b. A.B.C. निरंशतो विशंति (B .विंशति)       D. ॰दश वक्रगस्ततो                                                D. [निरंशगस्त्रिंशतिं]       B. चक्रं; D. वक्रः                                                   c. B. उदयेमुपयाति   c. A.B.C. अत्यर्धं च ततः शीघ्रात्. D. गत्यर्थं च ततः शीघ्रात्      d. A.B.C. द्यु (B .द्वा) नाषष्टितस्तोस्तमितः;