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

326 PAÑCASIDDHĀNTIKĀ XVIII.20 days are clear. Therefore, the days for the second segment must be 7. So I have emended manu into muni. The motion given there, 28', gives the rate 2', too absurd for that position, if the original 14 days are accepted, and it cannot be that the Siddhānta does not know the absurdity. Even for the emended 7 days, it is too low, being only 4' rate, while the rate on both sides is 5', and also consis- tent with facts. Therefore, ścaturguṇā is emended into śceṣuguṇā. Now, these three segments can be combined into 4° 55' for 59 days, without affecting the result. I do not know why the Siddhānta has broken it into such bits. Next, the total for the 378 days must be the mean motion for the period, i.e., 9 padas, equal to 12° 39'.4, roughly taken by the Siddhānta as 12° 39'. Therefore the motion for the fourth segment, 56 [

XVIII.20 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 327 I shall now give an example, to make the method clear. Example: Find true Saturn at 5000 days gone from epoch. i. Days 5000 To be subtracted 150-20

Divided by 378 4849-40 (12 = full cycles gone) 313-40 = (Remaining days) Days to be deducted 10/12 : 1-12

312-28 (corrected remainder) ii. Padas at 0 day of the 13th cycle: (89 + 12 × 9) / 256 = 197 remainder Mean longitude = 197 padas = 9ʳ 7° 2′ 197 = 30 + 127 + 40 (in the third sector) Eq. cent. corrected mean longitude:- = 1ʳ 15° 51′ + 5ʳ 27° 34′ + (2037 + 2 × 40) 40′ ÷ 27 = 1ʳ 15° 51′ + 5ʳ 27° 34′ + 1ʳ 22° 16′ = 9ʳ 5° 41′ Eq. cent. = 9ʳ 5° 41′ − 9ʳ 7° 2′ = −1° 21′ iii. Padas at 378 days gone in the cycle = 197 + 9 = 206 Mean longitude = 206 padas = 9ʳ 19° 41′ 206 padas = 30 + 127 + 49 (in the third sector) Eq. cent. corrected mean longitude = 1ʳ 15° 51′ + 5ʳ 27° 34′ + (2037 + 2 × 47) 47′/27 = 9ʳ 18° 0′ Eq. cent. = 9ʳ 18° 0′ − 9ʳ 19° 41′ = −1° 41′ Interpolated for days 312-28, the eq. cent = −1° 21′ − 0° 17′ = −1° 38′. iv. Correcting the remaining days 312-28 by this, 312-28 + 1-38 = 314-6 days, to be used to find anomaly of conjunction. v. 36 days +3° 7 ... + 0°.35′ Mean Sat. at 0 day 9ʳ 7° 2′ 16 ... + 1° 20′ Eq. cent − 1° 38′ 56 ... + 3° 42′ An. of conj. + 7° 40′ 55 ... − 3° --------------------------- 60 ... − 4° True Saturn = 9ʳ 13° 4′ Remaining 84-6 + 6° 1′ ---------------------------

314-6 + 7° 40′ As per Ephemeris: 9ʳ 11°.7 (sāyana)

Mars As indicated earlier, Mars, like Mercury, needed elaborate treatment owing to certain peculiarities about it, and so had been reserved by VM to the end of PS. The synodic period of

328 PAÑCASIDDHĀNTIKĀ XVIII.24 Mars, on which the equation of conjunction depends, is 780 days, during which there are more than two revolutions of the Sun, and one revolution of Mars, so that one full anomalistic period of Mars is contained within this period. This, with the large equation of the centre, and the large equation of conjunction causes large variations in its motion from sign to sign, and even in the same sign, according to the different types of motion governed by the anomaly of conjunction, like, fast, slow, retrograde etc. Hence is the need for detailed treatment. Further we have reason to think that the various motions given are all empirical, based on long observation, synodic period after synodic period. The separation into the equation of the centre, and the equation of conjunction is yet to come, it seems, unlike the cases of Jupiter and Saturn, where it is easy, and done. This would explain discrepancies found in the values given. Regarding the constants given, some can be verified by mutual comparison, and corrected where necessary, when there is a doubt about the reading itself. But some, like the epoch constants, which are peculiar to the Siddhānta itself, cannot be so verified and corrected when there is a doubt. Only in such cases, where we can argue that no Siddhānta is likely to give such wrong values, and when these values are so far from the real, that we can make some plausible corrections. TS and NP have not understood the nature of the motion of Mars, just as they have not under- stood Jupiter and Saturn. While TS have not even attempted translating some verses, wrongly interpreting those attempted, NP have attempted translating all, but many wrongly. I shall point out these after my own translation and discussion of the verses, step by step. [कुजचारः] द्युगणे ‘षट्(पञ्च)यमान्’ विहाय पञ्चाष्टकं च नाडीनाम् । ‘गगनाष्टमुनिभि’रुदया लभ्यन्ते प्राङ् महीजस्य ॥ २१ ॥ उदयगुणिता विनाड्यः ‘स्वरतिथयोऽ(ब्ध्य)’न्विता दिनक्षेपः । ‘धृतिगुणि(तांस्त्र्यग्रीन्दु)’भिरुदया(न्ह)त्वा स्थितो (तस्मिन्) ॥ २२ ॥ पञ्चाशीतिं कृत्वा प्रतिराश्य मध्यमः क्रमशः । राशिप्रमाणतोऽ(स्य) स्फुट(तश्च)रक्रमं कुर्यात् ॥ २३ ॥ स्फुटमध्यम(विश्लेषां)शान् क्षिपेत् मध्यमे[ऽधिके] द्युभ्यः । मध्यमहानौ जह्यात् गतितोऽथ चारा(न)भिधास्ये ॥ २४ ॥ Motion of Mars 21. Subtracting 256-40-0 days from the days from Epoch, and dividing by 780, the synodic risings of Mars in the East are got. 22-23. (157 plus 4) vināḍis, multiplied by the risings got, are to be added to the remaining days. Multiply the risings got by 18, and adding 85, divide by 133. The remainder, converted into rāśis is Mars at rising. According to the whole or portions of rāśis, the true motions are to be taken one after another, and pieced together.

XVIII.24 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 329 24. The difference between the mean and true degrees should be added (to the remaining days got in 21), if the mean is greater. If the mean is less, the difference should be subtracted from the remaining days. This done, I shall give the true motions, according to each type of motion: We learn from the verses the following: . 256-40-0 days from Epoch, Mars rises in the East, after which the counting of risings begin.

1. One synodic revolution takes 780 days — 161 viṇāḍis, (i.e. 779-57-19 days). The addition of viṇāḍis multiplied by revolutions, is for taking the synodic period as 780 days approximately. '. For this period of 779-57-19 days, we get 1 + 18/133 sidereal revolution of Mars, and 2 + 18/133 sidereal revolutions of the Sun. So, in one synodic period, Mars moves 408° 43′.3 ∴ In 133 syn. periods = 1,03,734-3-7 days, there are 151 sid. rev. of Mars, and 284 sid. rev. of the Sur. From this, the Sun's sid. period got is 365-15-38 days and Mars's 686-58-50 days. The Sun's period is 38 viṇāḍis more than that given for it by the Vāsiṣṭha, and near the 365-15-30 of the Pauliśa. Therefore, like the Moon, Venus, Jupiter and Saturn, Mars also is common to Pauliśa.
2. At the first rising when calculation commences, mean Mars = 85/133 rev. = 7ʳ 20° 4′.5
3. The addition or subtraction of the difference from the remaining days has been already explained with reference to Jupiter and Saturn. But, here, no method is given to find the equa- tion of the centre. Now the true motion is affected by both the eq. of the centre and eq. of con- junction. The segments of motion given in verses 25-26, below, are as affected by the eq. of con- junction alone. By making the days given for true motion in verses 27-35 conform to the seg- ments, we can get the degrees, and through that the days affected by the eq. centre alone. This can be of use only fōr the remainder of days. But the eq. of centre at the beginning of each cycle is necessary. It has not been given by any rule. Since its period is about 687 days and it has its own rise and fall of about 11° from perigee to apogee and back, it cannot be associated with the synodic period of 780 days. So this is an omission. I have corrected the corrupt tāstrayāmṛīdubhiḥ into tāms tryagnīndubhiḥ to mean 133. This is necessary for agreement with the actuals, and the effect of my emendation is seen in my discussion (3) above. TS have made it bāṇendubhiḥ. How can bāṇa, with such different lettering, come in here? Further, this will give 18/15 rev. = 432° as the mean motion of Mars in one syn. period, about 23° wrong per period. They have made pañcāśīti kṛtvā into pañcāmśonam kṛtvā and thus shut out the position constant of Mars on the first day where reckoning begins, viz. the point of time 256-40-0 days from epoch. (It will be remembered that in the cases of Moon, Venus, Jupiter and Saturn also, they have made this mistake). By this emendation they reduce the motion by 86° 24′, and make the 21a. C.D. द्युगणात् b. C.D. प्रतिराशिं; A.B. षट्कं व यमान् (B3. षट्कं). D. षट्कैकयमान् B. मध्यतः, A.B. क्रमश b. B. नाडित्वं c. A.B. प्रमाणतो स d. B. प्राक् d. A.B.C. स्फुटता चार०; D. स्फुटिता चार० 22b. A. योब्धान्विता; B. सोब्दान्विताः B. क्रकुर्यात्; D. क्रम[त्] कुर्यात् c. A.B. गुणितास्त्रयग्नी (B. त्री) दुभि; C.D. ०गुणितान् 24a. A.B. विक्षेपां बाणेन्दुभि b. A. ०शन् क्षिपेत्; B.C.D. शकान् क्षिपेत् d. A2. हत्वा; A.B. स्थितो तो समाः; c. A.B.C.D. मध्यमे द्युभ्यः C.D. स्थितोऽतोऽस्मात् d. A. गतितोथाचारमभि०; B. गतितोष्याचारमभि०; 23a. A.B. पञ्चशीति; C.D. [पञ्चांशोनं] C. गतितोऽथो चारमभि; D. गतितोऽप्याचारमभि०

330 PAÑCASIDDHĀNTIKĀ XVIII.26 mean motion of Mars 345° 36' per syn. period of 780 days! They have also wrongly emended pratirāśya to pratirāśyam. As for NP, they have made the correct emendation tryagnīndubhiḥ, giving correctly 151 revolu- tions of mean Mars in 133 syn. periods, and identified it with that given by the Babylonian astronomy of the Selucid period. But NP have not seen that pañcāśītim meaning 85, is correct as it is, and give the constant 7ʳ 20° 4'.5 at 256-40-0 days from epoch (see item 5 of discussion). They think it is the constant in degrees, though no word meaning degrees is found here. (This kind of mistake they have made in the case of Jupiter and Saturn also, as we have shown). But 85° would not do, so they have substituted satrirāśim for pratirāśya and made it 175°. But even this would not do, and therefore they have changed the days from Epoch itself into 216-40-0, by emending ṣaṭkam va yamān into ṣaṭkaikayamān. But this has led to other troubles, leading to their remark, “For Mars this would mean a longitude of 175° (instead of 194° derived on the basis of a₀ in table 32). This longitude would correspond to September 27, and a solar position at 186°, hence to an elongation of 11°’ (p.124, Part II). 11° for the first visibility of Mars is given by nobody. It is in the range of 14° to 17°. प्रागुदये षट्(चत्वार्येक)मष्टादश(ग)स्ततो वक्रम् | अध्यर्धं च शतं शीघ्रां [स्ततोऽस्तमितो द्यूनां षष्ट्या] || २५ || समतीत्य दशत्रियु(तं) निरंशगतो(ऽतस्त्रिंशतं) व्यतीत्य कुजः | उदयमुपयाति वक्ष्ये गतिचारदि(न)क्रमे चातः || २६ || 25-26. After rising in the East, Mars moves 146° (in quick motion) and then 18° each of (slow motion), retrograde and “follow up after” retrograde (anuvakra), and after that 150° of quick (śīghra) motion. Then setting, it reaches conjunction (niraṁśagataḥ) in 60 days moving 13 plus 30 (= 43) degrees. Then it rises, (moving the same degree in the same number of days). Beginning from here, I shall mention the series of motions with their days. The scheme is Rises East Moves 146°            I                      type of motion            (śīghragati)               18°           II                                                     (Mandagati)           −18°      III & IV                                                (Vakaragati)                                                                                    (Ativakragati)               18°          V                                                   (Anuvakragati)             150°          VI                                                  (Śīghragati) Sets in the West 43° VII in 60 days                                                     (Atiśīghragati) Conjunction                                                              (          ”          ) 43° VIII in 60 days Rises in the East Total 400°

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;

332 PAÑCASIDDHĀNTIKĀ XVIII.27 conjunction to rising (given as type VIII), 146° is left for type I. This segment extends upto the point where retrogression begins. As the planet is stationary, here a small error of observation can make this lesser or greater than the actuals. The text seems to give it as 18°. Types III and IV form the retrograde motion. III is called vakra (retrograde) and IV ativakra (faster retrograde). The text is defective here, and we cannot fix the exact extent of the two segments separately. But III and IV seem to be divided in the ratio 5:7 of the total. V is anuvakra (follow up after vakra). In the detailed motions given this is the sum of III and IV but direct motion. This anuvakra must be the counter- part of II. Type VI is śīghra and so the counterpart of I. Its extent is given as 150°. Type VII is the very quick motion from setting to conjunction and given as 43° in 60 days. Type VIII is the counter- part of VII from conjunction to rising. These divisions are mostly based on convention. But as these are given only in the case of Mars and classical astronomy does not give them, we have only to guess regarding them. To add to the difficulty the text is corrupt in the places giving the numbers. TS have expressed inability to understand verse 25. Still, they have made some emendations which do not give any cogent meaning. No translation is given. There is only a question mark. In verse 26, they give 20° motion from conjunction to rising. This can give only 26 days, as against the 60 days given by the text. By this the elongation for heliacal rising would be 7 ½°, so absurdly low. As for NP, in both verses, they have needlessly emended correct forms, wrongly emended the corrupt ones, some in faulty Sanskrit and given an untenable scheme. The following is their scheme: Rising east / 186° motion / 18° retrograde motion / 180° motion / setting / 30° motion / Conj. / 30° motion / rising east. They have made the emendations and substitutions with their eye on the total motion of 409° in the synodic period. They make the total 408°, nearly correct. But they do not identify the vestiges of the different types of motion found in these verses. Further, 30° motion from setting to conj. and then from conj. to rising, is short by 12 ½° from the actual 42 ½°. The time required to move 30° is 42.2 days and the Sun would move 41.5° during this time, giving an elongation of 11.5° for heliacal rising, far short of the actual, especially for such high latitudes as the Vāsiṣṭha-Pauliśa envisages. चत्वारिश (शच्छ)शि-न(ग)-[मु] (न्य)-ष्ट-यमान्विता वि‘पक्षा’ च । प्रथमगतौ (क्रमदि)वसा मीनाद्राशिद्वयसमानाः ॥ २७ ॥ 27. In the I type motion, there are 40 + 1 (= 41), 40 + 7 (= 47), 40 + 7 (= 47), 40 + 8 (= 48), 40 + 2 (= 42), 40 – 2 (= 38), days per motion of 30° each respectively in each month of the diad of rāśis beginning from Mīna, (i.e. Pisces). The above means, that for 30° of motion, the time taken is 41 days in the rāśis Mīna (Pisces) and Meṣa (Aries), 47 days in Ṛṣabha (Taurus) and Mithuna (Gemini), 47 days in Kaṭaka (Cancer) and Siṃha (Leo), 48 days in Kanyā (Virgo) and Tulā (Libra), 42 days in Vṛścika (Scorpio) and Dhanus (Saggittarius) and 38 days in Makara (Capricorn) and Kumbha (Aquarius). 27a-b. A.B.C.चत्वारिशशिन (B.नु) मध्य (B. om. ध्य) ष्ट० c. A.B. प्रथमगतौ कुर्याद्दिवसा D. चत्वारि श[शत द्वयमष्ट] ० D. यमान्वितं विपक्षांशं C.D. प्रथमगतौ कुर्याद् दिवसा; (D. दिवसान्) d. D. समान्

XVIII.28 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 333 An examination of the rate shows that the perigee is situated at the end of the Makara (Capricorn) and the apogee at the end of Kaṭaka (Cancer), which both fairly agree with the actual. TS say that they do not understand this verse, and no translation is given; its place being taken by a question mark. NP translate thus: “In the first gati 240 plus 28 minus 1/2 (= 267 1/2) (days). One should calculate days for every two signs from Pisces.” It is clear that they do not see that this verse gives the detailed rate of motion of the Type I gati in the diads of rāśis from Pisces, as affected by the equation of the centre. They think that the first motion given in verse 25, which 186° according to them, takes 267 1/2 days, as given by them here. If so, what use is the instruction to calculate for “every two signs from Pisces”? 'विषय-[रस-] खर-(रस-)र्तु-पञ्चका[न्] 'दशगुणान् द्वि[ती]यगतौ | सहितान् 'स्वरैकपक्षर्तु-चन्द्र-शीतांशुभिः' क्रमशः || २८ || 28. The II type motion, in the same order, (i.e. for each month of the diads, Pisces–Aries, etc.) for the 18° take 5 × 10 + 7, 6 × 10 + 1, 7 × 10 + 2, 6 × 10

• 6, 6 × 10 + 1, and 5 × 10 + 1 days. This gives 57 days each to move in the signs Pisces–Aries, 61 days for each of Taurus-Gemini, 75 days for each of Cancer-Leo, 66 days for each of Virgo-Libra, 61 days for each of Scorpio-Sagit- tarius, and 51 days for each of Capricorn-Aquarius. From the days given, it can be seen that there is a slight tilt in the apogee towards Leo, and in the perigee towards Aquarius. This small difference from the findings in verse 27 shows that the values are empirical. As for the readings, rasa has been inserted because we want six numbers for the six diads, and one is wanting. Symmetry requires that it must be rasa (= 6) there. Also two mātrās are wanting. sapta is emended into rasa because, 76 for Virgo-Libra, with 72 on one side, and 61 on the other side, will take the apogee to the end of Virgo, 60° off from its place. The average for II type motion is 18° for 81 days which is about the average of the mean rate and 0 (stationary). Thus I type motion is faster than the mean, and the II type slower, as we have sur- mised. TS have expressed inability to interpret this verse also, and not translated it. Yet they have made an emendation which need not be taken seriously, since it has been done without understanding. NP have interpreted the verse as giving 57, 71, 72, 66, 61 and 51 by inserting ṛtu as the fourth. But symmetry shows that the second number 71 is wrong, and it must be 61, to avoid the jump from 57 to 72. At any rate, read with their interpretation of verse 27, we can see that they do not under- stand the use of this series of numbers. They do not even say these are days. 28a. A.B.C.D.विषयस्वरसप्तर्तु (D.र्त्तु) b. A.B.पंचकदशगुणाद्विग्गतौ (B. ०द्विद्यगतौ) C. पञ्चैकदशगुणान् द्विगगतौ; D. पञ्चकम् दशगुणान् द्वि[वी] यगतौ c. A.B. सहिता; C.D. सहिताः;

334 PAÑCASIDDHĀNTIKĀ XVIII.32 झषवृश्चिकाज(चा)पेषु (वक्रं) षट्सप्तकेन (नव) भा(गान्) । ‘(द्वि)कृतेन’ (तैर्नवा)ऽतिवक्री दिनषष्ट्या षोडशानुगतिः ॥ २९ ॥ गोमिथुनतौलिकन्या(ख'त्रिसागरैः स्व)रा'नंशान् । ‘(त्रि)कृतैर्दश त्रिष(ष्ट्या)' सप्तदश यथाक्रमं वक्राशा[त्] ॥ ३० ॥ कर्कटसिंहयो'र्वेदसागरैः 'सप्त ‘(रसार्णवैः ‘शिवा'नंशान्' । षट्(ष)ष्ट्याष्टादश क्रमात्कुजो वक्रपूर्वासु ॥ ३१ ॥ घटमृगयो' (र्नग) दहनैः' षड्भागा' (नवहु)ताश(नं)'(च) । ‘मुनिविषयैः' पञ्चदशांशकांश्च तद्व(त् त्र)येऽप्यारः ॥ ३२ ॥ 29. In the signs, Pisces, Scorpio, Aries and Sagittarius, Mars moves 7° in 42 [L11

XVIII.33 XVIII. VĀSIṢṬHA-PAULIŚA — RISING AND SETTING 335 Types III, IV and V, called, respectively, retrograde (vakra), extra-retrograde (ativakra) and follow-up after retrograde (anuvakra) are given in these verses. The first two are actual retrograde motion, and the third is the slow direct motion following. They are shown hereunder in a tabular form.

336 PAÑCASIDDHĀNTIKĀ XVIII.34 Aquarius, there is a small excess of days for ativakra, but even this is far too small. The sum of vakra and ativakra is 18° and a maximum at Cancer-Leo, and minimum 15°, at Capricorn-Aquarius, and fairly evenly distributed in between. But actually, at Capricorn-Aquarius, the sum is near 9°, as a comparison with the motion of Mars given in the Vākyakaraṇa will show (vide App. III, Kujavakra, where retrograde occurs in the signs Capricorn-Aquarius). TS have translated verses 29-32, omitting verse 33 as obscure. But they think that all three types are retrograde motion, (while actually only III and IV are retrograde, and V is direct motion). This would make the range of the retrograde motion from 36° in Cancer-Leo to 30° in Capricorn- Aquarius, while the range given is 18° to 15°, actually the latter is even as small as 9°. Also, they do not see that the IV type should be greater than the III. So they give the numbers as they got from the words, instead of emending them appropriately. So, in verse 29, navabhāgam as emended by them should be navabhāgān. nagān vakrī should be navātivakrī. In verse 30, their emendation abdhisamudraiḥ should be agnisāgaraiḥ Khakṛtaiḥ should be trikṛtaiḥ. In verse 31, their khārṇavair divasaiḥ giving no degrees at all for the days, and defective in mātrās should have been emended into rasārṇavaiḥ śivānamśān. In verse 32, symmetry requires our emendation of yamadahanaiḥ into nagadahanaiḥ, while TS have kept it. As for NP, they have understood that type III gives retrograde and type IV, extreme retrograde, though the numbers they give for degrees and days are untenable in many cases. Seeing that the degrees of V are the sums of those of III and IV, they think that V is the total of the retrograde motions, while actually V is direct motion. They do not see that if the degrees of V are the total of III and IV, the days too must be the sum of the days, and therefore V is not the total retrograde. They have translated verse 33, but this does not give any sense. 'एकेन्द्रियवसुशिवमनु [मनु] भव त्रिवर्गतुं (पञ्च ) 'संयुक्तम् । शीघ्रगतौ पञ्चाष्टकमूनं च 'शशाङ्ककृतवेदैः' || ३४ || 34. In the quick motion following śīghragati (= type VI), there are the days, 40 + 1, 40 + 5, 40 + 8, 40 + 11, 40 + 14, 40 + 14, 40 + 11, 40 + 9, 40 + 5, 40 – 1, 40 – 4 and 40 – 4 for every 30 degrees. Obviously, these days are given for each one of the signs beginning from Pisces. The numbers are almost perfectly symmetrical on both sides of the inter-section of Cancer-Leo, and Capricorn- Aquarius, re-inforcing the conclusion that the former intersection in apogee, and the latter perigee. manu for Leo is a glaring omission and is inserted. Symmetry requires 45 for Scorpio, and so pakṣa is emended into pañca. The number-words forming a 'dvandva' compound, trivargam is wrong for trivarga, and so has been emended. — tu is removed being an extra mātrā and purposeless. This verse is of the same kind as verses 27, 28 combined, giving types I and II. TS have not understood what is given here, and its purpose, as they have not understood the corresponding verses 27-28. But they have translated this verse as the words go, and wrongly too, the numbers given by them forming a mere jumble, without any instruction, 2 + 1, 2 + 5, 2 + 8, 2

• 14, 2 + 11, 2 + 9, 40 – 1, 40 – 4, 40 – 4. No wonder, they append this with a question mark. 34a. A.B.C.D. Hapl om. of one मनु A.B.C. पक्षसंयुक्तम्; D. पञ्च संयुक्तं b. A.B.C.D. भवत्रिव (B. om व) र्गं (B2. ग्रं) c. D. पञ्च षष्टिं तु (A2.B1.2. नु: D. वर्गर्तु d. A. ०मूनं व B1.3. ततवेदैः; B2. ततवेदै

• का - र्क: it has ङ्क! Wait, what about D. ह्यनिलाङ्कार्क? ह्य - नि - ला - ङ् - का - र्क. It has नि and ला! Wait, in line 20: "TS have emended dvikālāhvārkā into dvyanalāṅkārka". And D is NP, they had hyanilāṅkārka? Wait, in line 43: C. ह्यनलङ्कार्क; D. ह्यनिलाङ्कार्क Wait, look at C in line 43: Is it ह्यनलङ्कार्क or ह्यनलइका्र्क? There is ह्य, न, ल, then ङ्क with ा? No, ह्यनलङ्कार्क has ङ्का! Wait, is there an ा on ल? Let's look at ल: no ा on ल. It's ह्यनलङ्कार्क. Wait, look at the ङ्क: is it इ with a dot? Look at line 8: ('ह्यनलाइ्‌कार्क) or ('ह्यनलाङ्कार्क)? Wait, look at line 8: ह्य न `ला

338 PAÑCASIDDHĀNTIKĀ XVIII.35 Example: Find true Mars at 800 days from Epoch. Days from Epoch 800 — 0 — 0 Subtract days at first rising 256 — 40 — 0 543 — 20 — 0 No. of revolutions gone (543-20) / 700 = 0 Remainder 543 — 20 — 0 Correction for revolutions gone 0 — 0 — 0 Days after rising 543 — 20 — 0 Mars at rising = (18 × 0 + 85) / 133 revolutions = 230°, i.e. 20° in Scorpio. Starting from this point, i.e. 20° in Scorpio at rising, true Mars moves in 543-20 days, as per the scheme given in verses 24-35, to 29° 47′ in Cancer as per details given below: Type I: 146° Total days = 543-20 Balance 10° in Scorpio 14 days (10/30 × 42) 30° in Sagittarius 42 ” 30° in Capricorn 38 ” 30° in Aquarius 38 ” 30° in Pisces 41 ” 16° in Aries 21 + 52 (16/30 × 41) Total 194 + 52 Balance No. of days .......... 348.28 II: 18° 14° in Aries 44-20 (14/18 × 57) 4° in Taurus 13-33 (4/18 × 61) 57-53 Balance No. of days .......... 290-35 III: 7° (Retrograde) — 4 in Taurus 24-34 (4/7 × 43) — 3 in Aries 18-00 (3/7 × 42) 42-34 Balance No. of days 248-1

XVIII.36 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 339 IV: 9° (Fast Retrograde) – 9 in Aries 42-00 Balance No. of days 206-1 V: 16° 12° in Aries 45-00 (12/16 × 60) 4° in Taurus 14-49 (4/17 × 63) —————— 59-49 VI: 85° 47' 26° in Taurus 41-36 (26/30 × 48) 30° in Gemini 51-00 29° 47' in Cancer 53-36 (53-36/54 × 30) —————— 146-12 Therefore, True motion in 543-20 days from 20° to 29° 47' Cancer = 249° 47 Mean motion in 543-20 days: 408 – 43 × 543 1/3 /780 = 284° 42' —————————— Therefore days to be added = 34-55 True motion for 34-55 to be added In Cancer 0-13' for 0-23, and for the balance 34-32 days, In Leo 30 × (34-32 / 54) = 19° 11' Therefore True Mars: 19° 11' in Leo. Motion of Mercury¹ As in the case of other planets, the epoch date is so selected that Mercury rises heliacally in the west on that date. Since, for Mercury, the elongation required for heliacal rising is given as twelve degrees, on the epoch day its longitude is 12 degrees ahead of the Sun. Then, the number of days elapsed from the epoch is obtained and divided by the sidereal period of Mercury, so that the resulting quotient represents the number of risings that had taken place since the epoch, and the remainder the number of days elapsed in the current sidereal cycle. The movement of Mercury in one synodic period being known, (given by the text), the total longitude moved during the elapsed number of risings is also known and adding to this the epoch constant, that is, the position of Mercury on the epoch day, its longitude on the day of the current rising is obtained. However, these figures are on the assumption that the motion of Mercury is uniform, which is not the case. So, what we have got is only the mean position of Mercury and not its true position. Here, as also in the text, 'mean position' does not mean the mean heliocentric position as we now understand, but the mean geocentric position on the assumption of uniform motion. The true position varies from the mean by quite a few degrees. The date of rising also is only a mean date and the true date may be several dates behind or ahead.

1. Mercury : Translation and Notes by S. Hariharan, Bangalore.

340 PAÑCASIDDHĀNTIKĀ XVIII.37 The text then gives a table from which for a given mean longitude the true position on the true date can be obtained. Since the Sun's position has to be 12 degrees behind the true position of Mercury, the same correction applied to Mercury has to be applied to the Sun. That means, keeping in mind that the Sun moves one degree in one day approximately, the true date is ahead of the mean date by as many days as the number of degrees in the correction, if the correction is positive, and vice versa. Consequently, the number of days elapsed since the (true) rising is also modified by the same number of days, reduced, if the correction is positive, and vice versa. Having got the true Mercury as on the true date of rising and the number of days elapsed since rising, we have now to get the degrees moved by Mercury during these remaining days in the synodic cycle. For this purpose the synodic period is divided into several sections just as in the case of other planets. In the case of Mercury the division is made into four sections or gati-s. The first is from rising to starting of retrogression, the second is the period of retrogression, the third is from end of retrogression or anuvakra to setting, while the fourth is from setting in the east to rising in the west. The number of days for each section and the movement are not constant but vary depending upon the position of Mercury in the zodiac. Accordingly, tables giving these values for each of the twelve signs are given in the text. With the help of these tables we can trace the move- ment of Mercury during the remaining days and finally arrive at its position. What is new in the case of Mercury is the method of interpolation within these tables. For other planets no specific method of interpolation is suggested, with the result we assume linear interpo- lation. But here a second degree interpolation is suggested for certain sections. TS and NP do not appear to have understood the procedure nor the rationale expounded by these verses, as could be gauged from the emendations they make and explanations they give to the verses. [बुधमध्यम्] [बुधचारः] (दद्यात् सप्तचतुष्कान्) द्युगणे त्र्यंशं च 'वसु'गुणो भागः | 'मुनियमनवके'रपि (रौहिणस्य) वेद्या, दिनाष्टांशाः || ३६ || [हत्वा] चतुर्भिरुदयान् नाड्यः शोध्या बुधस्य दिवसेभ्यः | 'त्रिरसयम'घ्नानुदयान् 'रामार्णव' वर्जितान् छिन्द्यात् || ३७ || 'नवयमवसु [भि] र्मध्यमथो सक्रमानुदयांशैः क्रमाद् | Mean Mercury 36-38a Add to the ahargaṇa seven times four, i.e., 28, and a third. Multiply by eight and divide by 927. The quotient is the risings of Mercury. Take the eighth part of the remainder and deduct therefrom, in nāḍikās, one fourth of the risings, and the result is the (remaining) days of Mercury. Multiply the ris- 36a. A. दद्या B. सप्तनुक्कान् D. दिनाष्टांशः b. B. द्यगणो A. त्र्यंशः; B. त्र्यंश 37a. A.B. कृत्वा B. गुणभागः D. भाव्यः b. A. दुधस्य; B. बुछस्या c. A. नवकै c. A.B. त्रिदशयमध्नान्; D. [अद्रिदशयम्] यमध्नान् d. A.B. रोचितस्यः C. रोहिणस्य; D. रोचिताः स्युः B. ॰नुदयां A. मेद्या; B. मेधा; D. शोध्यो d. B. रामणववर्जितान्; D. पाण्डववर्जिते श्छिन्द्यात्

XVIII.37 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 341 ings by 263, deduct 43 and divide by 829 and the result is the mean Mercury (in revolutions). These will lead to the following: i. 28 1/3 days before the epoch, Mercury rises in the west, after which the countings of the risings begin. ii. One synodic revolution takes (927/8 + 1/240) days. The deduction of 1/4th nāḍīs or 1/240th day per rising is for taking the synodic period as approximately 927/8 days. The balance remaining after division by 927 is the number of eighth parts of a day elapsed since the last rising. So, dividing this by eight, the number of full days are obtained. During a synodic period the motion of mean Mercury is equal to 263/829 revolutions (which is the same for Sun). Hence for one full revolution Sun will take, (927/8 + 1/240) × 829/263 days, or, 365.261708 days, i.e., 365-15-42. iii. At the epoch date, that is 28 1/3 days before 20-3-505 AD., Sun’s longitude is 357-37 minus 27-55 or 329-42. iv. On this date, Mercury’s longitude is given by: (No. of risings (zero) × 263 – 43)/829 or – 43/829 revolutions. This reduces to – (18-40), or 341- 20, which is ahead of Sun by 11-38 as against 12 needed, and therefore acceptable. In verse, 36c, we, also others, have emended the ms. reading muniva.nanaca as muniyamanava to get the correct figure 927. In 37a kṛtvā has been made as hṛtvā. The meaning and rationale of these verses is clear. But NP have made medhā in 36d as śodhyo and have translated it as “Subtract an eighth part of a day (for every synodic period)” etc. and comment, “We find in XVII, 36 a subtraction of 1/8 of a day and a division of the number of risings by 4. We cannot explain these steps which seem in excess of the normal procedure.” It is rather surprising that NP missed the elementary step of dividing the remainder by 8 to get the number of days, particularly when TS have correctly interpreted it. Without the correct number of days (elapsed since the last rising) the further processing does not make sense. Hence we feel that NP have not understood the process at all. In the next step of finding the longitude of Mercury at the time of the last rising, the figures in the verses have been badly corrupted. In 37b tridaśayama has been emended as tridivasapa by TS, and in 38a navavasuyama as navavasurāma, so as to give them a multiplier of 123 and divisor of 389. But this would give the Sun’s period as 366.479641 days which cannot be. NP have made tridaśayama as adridaśayama; rāmārṇava as pāṇḍava and navavasuyama as navavasurasa. They have also changed the meaning so as to subtract pāṇḍava (5) from the divisor 689 rather than to make the deduction from the product. All these they have done just to make these constants agree with those of Babylonian and then claim that “Table 24 reveals exact numeri- cal agreement for the outer planets and Mercury” (!). They forgot that in this process they have obliterated the initial epoch constant of the longitude of Mercury and comment “For Mercury we have no epoch constant giving us directly a longitude.” We have emended tridaśayama as trirasayama, and navavasuyama as navayamavasu. As shown above, these numbers give the sidereal period of Sun as 365-15-42, which is within limits. Of

342 PAÑCASIDDHĀNTIKĀ XVIII.40 course, the constants as emended by NP also will give the correct sidereal period, namely, 365-15- 35, as it should be, but the emendments made are too violent. [बुधस्फुटः] पञ्चयुतैस्त्रिंशद्भिस्त्रिंशद् [भुङ्क्ते] स्फुटानंशान् ॥ ३८ ॥ ‘नव(षष्ट्या)षष्टिः [स्यात्] ‘वसु’युताशीत्या शतं (वितीक्ष्णांशुः) । सर्वैस्त्रिभिरभ्यधिकैस्त्रिंशद्भिस्त्रिं(शद्युताश्वांशाः) ॥ ३९ ॥ चतुरधिकेन शतेना[र्कयुतं] शत, मतोऽर्थ’संयुतया । षड्‌विंशत्या त्र्यधिका त्रिंशतिरेवं स्फुटः सौम्यः ॥ ४० ॥ True Mercury 38c-40. For the rising degrees in order, we have for 30 + 5 35 degrees 30 degrees 9 + 60 69 60 8 + 80 88 100 - 12 88 3 + 30 33 30 + 7 37 4 + 100 104 100 + 12 112 5 + 26 31 3 + 30 33 Total 360 360 Thus true Mercury. We have made some minor emendations like navakṛtyā ṣaṣṭim to navasaṣṭyā ṣaṣṭiḥ, ca tīkṣṇāṁśum to vitīkṣṇāṁśuḥ, triṁśadbhuṅkte for triṁśadbhakta, to get the total as 360 for both sides as they should be. With this table corresponding to the mean mercury obtained as per the previous verse the true mercury can be got. This is for the true date of rising. Now, the true date has to be obtained or, what is the same as getting the true remaining days passed after the true rising date. This is dealt with in the next verse. 38a. A.B. नववसुयममध्य (B. rep. यममध्य) मध्योः C.D. नववसु रामै मध्यं D. [मध्यमो] b. A. सा क्रमांनुदशैशः B. शक्रमाह दर्शैश D. [बुधोऽष्टांशान् क्रमादहर्दसैश्च] 38c. B3. Hapl. om. युतै [स्त्रिंशद्भि] त्रिं० d. A.B. त्रिंशद्भक्तस्फुटानंशान् 39a. A.B. नवकृत्यात् षष्टिः; C.D. नवकृत्यात् षष्टिं b. A.B. युतयावशीत्या. A.B. शतं सतीक्ष्णांशोः; C.D. शतं सतीक्ष्णांगुम् c. C.D. शर्वे. A. रभ्युधिकै d. A.B. त्रिंशदेवाकांन्; C.D. त्रिंशदेवांशान् 40a. A1. चतुरधिकेन्. A.B.C.D. शतेन त्रिभिरूनं c. A.B.C.D. त्र्यधिकां d. A.B.C.D. विंशतिमेवं

XVIII.40 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 343 These verses actually give the true longitudes at the time of rising corresponding to mean lon- gitudes. The mean longitude is obtained as per the previous verse. TS and NP think that, in verses 38b-40, the true motion of Mercury is given, for certain days cer- tain degrees, and so on. They have made some emendments of their own and both of them get the total degrees moved as 360 but as for the number of days TS get 389 while NP get 388. The 389 of TS is the same as the divisor of the previous verse and so they think that corresponding to the remaining days which will be upto 389 these verses give the true śīghra-sphuṭa. But their idea is vague and they are not able to expand it properly. NP think that what is given is an eightfold division of the ecliptic but they are not able to explain anything further. They comment, "The text calls n1 'days' which, in any case, is meaningless". In fact there seems to be no reference to days at all in these verses. अनयोर्विश्लेषांशान् दिवसेभ्यः शोधयेत् स्फुटाभ्यधिके । अधिके.तु (मध्यमेऽंशान्) दद्याच्चारः स्फुटबुधाच्च ॥ ४१ ॥ 41. Deduct from the days the degrees of difference of these two, (i.e., of the mean and true places of Mercury), in case the true place is in excess of the mean place, and add if the mean is in excess of the true. Then the course of true Mercury is as follows. TS and NP have not been able to appreciate the rationale for this operation. TS have not given any rationale. NP think that the correction applied to the days is a mistake and it should be applied to the longitude; and the correction to the days should be applied by dividing the correction (in degrees) by the synodic motion per day. This however is not the correct position. Since this relates to the rising position of Mercury on the true date the Sun will be 12 degrees less than the true Mercury. So the Sun also will have to be corrected by the difference between the true and mean positions of Mercury. Since the motion of the Sun can be taken as one degree per day for small durations, to that extent of the difference the rising date will shift. If the true Sun is in excess, the date will get advanced, and, consequently, the remaining days will get reduced, and vice versa. Obviously the number of days will be equal to the number of degrees. Note on Verses 42-53 These verses give the gati-s of Mercury relating to the twelve signs, Aries to Pisces. In each verse, the first quarter gives the degrees (days) of motion from the rising of the planet to the commence- ment of retrogression, the second quarter for the period of retrogression, the third for the period from the end of retrogression to the setting of the planet and the fourth from setting to its rising. In order to check the accuracy of the figures, they have been calculated by modern methods. The variants, as: चतुरधिके पञ्चशतेन तिरूनं and 41a. A.B. ॰पांशा धिशातिरवं. b. A. शोधये स्फु. C. धिके च. c. A.B. मध्यमे स्या c. A.B. repeat after b, verse 40, with a few d. A.B. दद्याच्चार (B1.2. चारः)

344 PAÑCASIDDHĀNTIKĀ XVIII.43 textual figures might be seen to agree with the calculated figures in several cases with minor differ- ences, of course on account of the constants used in Pauliśa and Vāsiṣṭha, and due to observational errors. Where they differed widely, it has been examined whether there could be due to defective readings and suitable emendations have been suggested in consonance with the reading of the manus- cripts, as far as possible. Neither TS nor NP appear to have understood the purport of these verses and have suggested all sorts of emendations. TS do not translated at all verse 54. [मेषः] मेषे 'दिन'षट्कृत्या' 'शिव'-'भव'-'ख'-'द्विसप्त' हीन्या (भागाः) । 'पञ्चविंशत्'-'त्रिः''कृत'-'षट्सप्तक'-'त्रिवर्गौरिषु'गुणितम् ॥ ४२ ॥ Mercury’s gatis for Aries 42. The gati-s in Aries are:

43. In Taurus, the gati-s are: | | Degrees | Minutes | Textual | Calculated | | :--- | :--- | :--- | :--- | :--- | | | | | ° ′ | ° ′ | | 1. Rise to Retro. | 4 × 8 + 0 = 32 | 44 − 11 = 33 | 32 33 | 31 34 | | 2. Retro. | 2 × 8 + 8 = 24 | 44 − 33 = 11 | 24 11 | 24 9 | | 3. Retro. to Set. | 4 × 8 + 3 = 35 | 44 − 7 = 37 | 35 37 | 33 36 | | 4. Set. to Rise | 2 × 8 + 3 = 19 | 44 − 1 = 43 | 19 43 | 20 43 | | | | | :--- | :--- | | 42a. A.B.2.3. कृत्यां; B1. षट्कसा | 43a. A. गाव; B. माव. A1. वेदे; A2- दे. | | b. A.B. शंमव; C.D. समुवा (D. समव) सप्त. | A. कृतो; B. ततो; | | A.B. भागः; C.D. भागान् | C.D. वेदयमद्विकृतैः | | c. A.B. विकृति; C. त्रिकृति; | b. A.B. द्विम्रैः; C.D. दिग्घ्नैः. | | D. द्विकृति | A.B.C.D. विषयाग्रिगणनवाभ्यधिकैः; | | d. A.B.C.D. त्रिसप्तकं. A.B. षड्वगौव (B. षट्दव) | c. A.B. शतार्धममलो; C.D. शतार्धममरैः | | गणितं (B. गणित); C. षट्कमिरिषुगुणितम्; | d. A.B. रुद्रावथ; C. रुद्रैरथ; D. रुद्रूनं च. | | D. षडङ्गगुणितम्. | C. सप्तभिर्हीनम्; D. सप्तर्ति व्येकाम् । |

XVIII.46 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 345 [मिथुनम्] द्विदशं सपञ्चवर्गं [त्रि-रस-गुणा] न्वितं च मिथु(ने) च | भागार्धशत (द्व्यूनं) 'मुनय' - 'स्त्रिघनं च [पञ्चवेदाश्च] || ४४ || 44. In Gemini, the gati-s are: | Degrees | Minutes | Textual ° ' | Calculated ° ' | | 1. Rise to Retro. | 20 + 25=45 | 50 - 7=43 | 45 43 | 38 42 | | 2. Retro. | 20 + 3=23 | 3 | 23 3 | 23 8 | | 3. Retro. to Set. | 20 + 6=26 | 3³ =27 | 26 27 | 27 29 | | 4. Set. to Rise | 20 + 3=23 | 45 | 23 45 | 21 45 | [कर्कः] (कर्किकणि 'दिग्घ्नै:') ['कृता'-'श्वि'-'गुण'-'पक्षै:'] स ('दि'-'ग्')-'ष्ट'-'शून्य'-'रसैः' | ('सेभान्') 'दलितान्' ('सेन्दून्') 'पञ्चकवर्गान्विता' नंशान् || ४५ || 45. In Cancer, the gati-s are: | Degrees | Minutes | Textual ° ' | Calculated ° ' | | 1. Rise to Retro. | 8 × 4+8=40 | 40 + 7=47 | 40 47 | 42 48 | | 2. Retro. | 8 × 2+8=24 | 24 × 1/2=12 | 24 12 | 24 10 | | 3. Retro. to Set. | 8 × 3+0=24 | 24 + 1=25 | 24 25 | 22 24 | | 4. Set. to Rise | 8 × 2+6=22 | 22 + 25=47 | 22 47 | 23 47 | [सिंहः] सिंहे ('बाण'-'गुणा'-'क्षि'-'रामै:' 'दिग्'घ्नैः 'सार्णवे'-'न्दु'-'यम'-'विषयै:' | (सप्ताधिकां) दलितां स('कृता')मधिकां 'विषय'कृत्या || ४६ || 44b. A.B.C.D. स्वरसघनान्वितं A.B. मिथुनं च c. B. शत; C.D. शतं. A.B. द्यून; C.D. द्व्यूनं d. A. पवसुतश्च; B. त्रिघनपवसु and indicated omission upto सप्ताष्ट of verse 47c below; C. पञ्चवस्; D. पञ्चसप्त 45a. A. कर्किनि. A.B. दिग्घैः b. A.C.D. कृतशशिगुणवेदैः सद्द्रिकाष्टशून्यरसैः c. A.C.D. सैकान्. A. सेन्दु d. A.C.D. पञ्चकवर्गान्वितांश्चांशान्