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

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

346 PAÑCASIDDHĀNTIKĀ XVIII.48 46. In Leo, the gati-s are:

47. In Virgo, the gati-s are: | Degrees | Minutes | Textual (° ′) | Calculated (° ′) | | :--- | :--- | :--- | :--- | | 1. Rise to Retro. | 46 | 3³ × 2=54 | 46 54 | 44 52 | | 2. Retro. | 24 | 9 × 5=45 | 24 45 | 23 14 | | 3. Retro. to Set. | 20 | 3 × 8=24 | 20 24 | 19 23 | | 4. Set. to Rise | 35 | 50 + 9=59 | 35 59 | 35 59 | [तुला] ‘विंशतिरेकेन युता’ [हीना] ‘खा’-‘शा’-‘ष्ट’-‘खा’दिभिर्द्विसंगुणाश्च । अंशास्त्रि [युता] ‘वसु’विहीना ह्योक-त्रयोविंशद्युता चैव ॥ ४८ ॥ 46a. A.C.D. गुणेन्दुग्मार्णवदिग्ग्रहैः (D. र्णवैर्दिग्ग्रहैः) b. A.C.D. सार्णवर्तुयम. A. विषयाः c. A.C.D. तुल्यां (A.B. तुल्या) at the commencement of the line. A.C.D. सप्तविहीनां d. A.C.D. सदृशां० (A. सदृशां) 47a. A.C.D. कन्यायामृतुकृत्या b. A. ष्टत्रिंशत्तया तया न भूत:; C. ष्टत्रिंशता तया तयात्र भूयः; D. ष्ट[दशत्रि] त्रिंशं त्रिकृतैर्न भूयः c. B1.2.3. commerce again with सप्ताष्टकं शतार्धं, after the indicated gap. A.B. सप्ताष्टकदशशतार्धं च रवियुक्तम्, C.D. सप्ताष्टकं शतार्धं (D. ष्टकमष्टशतार्धं) च रवियुक्तम् | for ०कत्र्यष्टकं etc.

XVIII.50 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 347 48. In Libra, the gati-s are:

49. In Scorpio, the gati-s are: | Degrees | Minutes | Textual (° ') | Calculated (° ') | | :--- | :--- | :---: | :---: | | 1. Rise to Retro. | 10×3+ 6=36 | 36 + 2=38 | 36 38 | 35 39 | | 2. Retro. | 10×1+11=21 | 21 − 7=14 | 21 14 | 21 16 | | 3. Retro. to Set. | 10×3+ 4=34 | 34 + 3=37 | 34 37 | 33 38 | | 4. Set. to Rise | 10×4+ 2=42 | 42 + 26=68 | 43 8 | 43 6 | [धनु:] धन्वनि द्विदशावष्टौ, [विंशं], षट्सप्तकं, 'कृतोनं' च । ते ('इषु'युत) 'विषयोनाः' ('शैला' : त्रिंशा) न्विता भागाः ॥ ५० ॥ 48a. A.B. रेकेण b. A.B. व्यनखांसां तिथिद्विसंगुणैश्च; C. हीना खाशाग्रिभिर्द्विसंगुणाश्च; D. युता जूके सशून्यतिथिर्द्विसंगुणाश्च | d. A.B.C.D. ह्येक (A. ध्येक) त्रिंशद्युताश्चैव | 49a. A. दशघ्नी; B. दशघ्ना b. A.B.C.D. शशिकृत (B. om. त, D. शशिद्विकृत) for त्रिशशि. A.B. दहनाः षड्खरावर्णवाष्टयुताः; C. दहनयुगा वसु-शराणंवाष्टयुताः; D. दहनाः शरार्णवाष्टयुताः | c. A. तेशा; B1.3. तेषां. A.B.D. यममुनीशोना; C. यममुनीशेन d. A.B. समेना व (B. च)

348 PAÑCASIDDHĀNTIKĀ XVIII.52 50. In Sagittarius, the gati-s are:

51. In Capricorn, the gati-s are: | | Degrees | Minutes | Textual | Calculated | | :--- | :--- | :--- | :---: | :---: | | | | | ° ′ | ° ′ | | 1. Rise to Retro. | 20+ 3=23 | 23 + 4=27 | 23 27 | 23 28 | | 2. Retro. | 20+ 0=20 | 20 − 4=16 | 20 16 | 20 16 | | 3. Retro. to Set. | 20 + 7+18=45 | 45 + 7=52 | 45 52 | 46 54 | | 4. Set. to Rise | 20+12=32 | 32 +26=58 | 32 58 | 33 56 | [कुम्भः] कुम्भे (ऽह्नां) विंशत्या [रूप] युतया 'हुतभुग्वेद'-'द्विदिननाथैः । द्वाविंशतिरंशा पञ्च (दशा-ऽर्थार्थका) षष्टिः ॥ ५२ ॥ 50a. A. धन्वि; B. धन्वनि. A.B. दिच साधाष्टौ (B. याष्टौ); | 51a. A.B. द्युदशं. C. दिवसाधार्ष्टौ; D. दिवसानाष्ट्रि षट्कृति षट् | b. A.B.C. मुनिहीनं; D. [मुनियुक्तं] b. A.B.C.D. षोडश (A. षोडस) for विंशं | c. A.B.C.D. अंशा रूपेणोनाः A.B.C.D. दशोने. A. व for च | d. A.B.C.D. सैकैकाश्रोत्कृति c. A1. ते स्फुः; A2.B. ते स्युः. A.B.C.D. शशिविषयोनाः | (A.B. नौः) | d. A.B.C.D. सैकास्त्रिं (A. त्र्यं) शान्विता. |

XVIII.53 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 349 52. In Aquarius, the gati-s are:

53. In Pisces, the gati-s are: | | Degrees | Minutes | Textual (° ') | Calculated (° ') | | :--- | :---: | :---: | :---: | :---: | | 1. Rise to Retro. | 18 + 1=19 | 20 | 19 20 | 19 19 | | 2. Retro. | 18 + 5=23 | 13 | 23 13 | 23 14 | | 3. Retro. to Set. | 43=43 | 50 | 43 50 | 43 52 | | 4. Set. to Rise | 3 × 8=24 | 49 | 24 49 | 24 47 | [बुधगतीनां निर्णयः] (अस्तो)दयान्तरांशा बुधस्य दिवसाश्चतुर्थ [या] गत्या । उदयाद् वक्रं प्रथमा तृतीयगत्याऽऽनुवक्र(मस्तमयान्तम्) ॥ ५४ ॥ 52a. A.कुंभेह्ना. A1.त्रिंशत्या; D.त्रिकृत्या b. A.B.दगतभुग्विदेवदिननाथैः; C.D.हुतभुग् द्विवेद (D.दिनेश) दिननाथैः d. A.B.C.पञ्चवर्गमथाब्ध्रिका षष्टिः (C.र्गमर्थाब्ध्रिका)ः D.पञ्चवर्गं सुराधिपाः षष्टिः 53b. A.B.C.D.मीने त्र्यष्टकमह्नां b. for सागरका;, A1.संशरं; B1.शशीष्टं, B2.शासशिष्टं; B3.शशीरं; C.D.संयुक्तम् c. A.B.C.D.त्र्यष्टककृतिर्विंशत्या (D.विंशत्याः) d. B2.शनार्थ. A.B. मष्टां स्युः

350 PAÑCASIDDHĀNTIKĀ XVIII.56 Specifications of the gati-s of Mercury 54. From setting to rising the degrees and days are given by the fourth gati. From rising to vakra (beginning) is (given by) the first gati. The third gati is (from) anuvakra (i.e., end of retrogression) to setting. It will be seen that this verse explains what the four gati-s indicate a fact which has not been men- tioned earlier. Actually, there is no direct reference to the second gati. But it can be inferred that this gives the retrogression period and the degrees. TS have made some emendations but have not translated them but say that they are not able to comprehend the meaning of these verses. NP have adopted the emendations of TS and have just translated them as they are and that does not make any sense. They comment: "We cannot connect any rational procedure with the verses XVII, 54-56". गतिविश्लेषकृतिघ्नैरंशैर्गतिवर्गभाजितैर्लब्धम् | हित्वा राशिभ्यो भुक्तं प्रथमगतौ वक्रपश्चाच्च || ५५ || वक्रगतौ पूर्वार्धे तृतीयगत्यां च यत्कृति गुणितैः | भागैर्गतिकृतिभक्तैः फलमनुपाताच्चतुर्थगतौ || ५६ || 55. By the square of the difference in gati-s (days) multiply the degrees and divide by the square of the gati-s. The result is to be subtracted from the degrees and that gives the degrees gone in the first gati and in the second half of vakra-gati. 56. In the first half of vakra-gati and in the third gati multiply the square (of the days passed) by the degrees and divide by the square of the gati-s (days). For the fourth gati the result is obtained by (direct) proportion [since the motion in this section is practically uniform.] 54a. A. अष्टो; C. अर्कौ; D. अथो. A.B.C. न्तरांशान् 55a. B. ॰रंसैगत॰ b. A.B.C.D. दिवसाथतुर्थगत्या occurs as c. They c. B. भुक्तं have as b, बुधस्य कालांश (A.B. कालांश) d. A. गातौ. A. वक्रपश्वाद्वा; B. वक्रपश्चाच्च;. कांस्त्रिगत्यूनान् (A.B. गत्यूनात्, D. गतीनाम्) D. वक्रपश्चात् d. A.B.C.D. अनुवक्रमजमीनयोर्मन्दम् (A. योन्दम्, B. योर्मदम्). 56a. A. वर्गाक्रगतौ; B. चक्रगतौ b. A.C. गत्या च; D. गत्याश्च A. यात्कृतं; B. तक्षत. C. गुणितम्; D. [यात्कृति गुणितैः] c. A.B. गतिकृति (B. क्रति). B1. भत्यै; B2.3. भृत्यै d. D. ॰मनुपाञ्च च. A.B. ॰र्थभागगतौ (B2.3. गतौ)

XVIII.58 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 351 [दृकर्म—आक्षम्] ज्याविधिविक्षेपघ्ना (च्च) रकाला‘म्बराष्टवेदां’शम् | जह्यात् क्षिपेच्च याम्योत्त(रे) ग्रहे खं यथा(काष्ठम्) || ५७ || एवं कृते [ग्रहान्त]रांशकैरस्तदर्शनं तेषाम् | Correction for mean elongation in heliacal rising 57. Find the R sine of the latitude of the body. Multiply the (maximum) half- cara (i.e. the half difference between the half day-time or night-time from 15 (nāḍis.) in vināḍis, by this R sine, and divide by 480. Add this or subtract this (to or from the Moon or star-planet) if the latitude is north or south, according to the proper direction, (i.e. according as the phenomenon of setting or rising, takes place in the west or east, respectively). 58a-b. When this is done, their setting or rising happens according to the interval in degrees (between the Sun, and the planet given in XVII.12, or the Moon). Note 1. There is a lot of lacunae in verse 57. The half-cara-vināḍīs meant is the maximum for the place. yathākakṣam is meaningless here and is corrected into yathākāṣṭham, i.e. according to the direc- tion, but the direction is not mentioned. If north latitude, the addition is for the Moon or planet in the west. Also if north latitude, the subtraction from the Moon or star planet is to be done for the east. If south latitude, the subtraction is for the west, and the addition for the east. These things can be got by a little reflection. Note 2. The amount of degrees to be applied can simply be got by multiplying the degrees of latitude of the body by the tangent of the latitude of the place. (The equinoctial mid-day shadow of the 12" gnomon ÷ 12, is tan. latitude of a place). The amount got is very rough. The degrees wanted = Sin. half cara (i.e., tan latitude of place x tan. declination of the Sun) × sin (90° – angle for heliacal rising), nearly. The last term is neglected here, tan declination is roughly taken as 48', half-cara is converted into degrees by division by 10, and the conversion into sine-function is applied to the latitude of the planet instead of the half-cara, as roughly equal. Note 3. This application is what is technically called Ākṣa-dṛkkarma. The Āyana-dṛkkarma is neglected. Note 4. The heliacal rising of the Moon, and of Venus and Mercury when retrograde, takes place in the west. The heliacal setting of the Moon and retrograde Venus and retrograde Mercury takes place in the east. Otherwise, all star-planets set in the west and rise in the east. (This Siddhānta does not envisage the setting or rising of Venus and Mercury when retrograde, no separate degree for that being given). 57a. B1.3. ज्याविधिविधि d. A. ०्तरं; B. ०तंर०. C. स्वे. D. [कक्ष्यम्] b. A.B. च for च्च A. ०दंबराष्ट; B. चरकादि 58a-b. A.B.C.D. ग्रहार्कन्तरांशकैः (B2. कालादि) चराष्टवेदांशं B. ०तिष्ठतितिथ० c. A. जह्याक्षि. A. यान्मो 26

352 PAÑCASIDDHĀNTIKĀ XVIII.60 चन्द्रादीनां 'द्वादश मनुरवितिथ्यष्टतिथि'संज्ञैः ॥ ५८ ॥ 58c-d. The setting and rising (mentioned above in verse 58a) is by 12°, 14°, 12°, 15°, 8° and 15° for the Moon etc. Note 1. This has to be taken with verse 58a. The degrees given here separately are according to the Vāsiṣṭha-Pauliśa, which do not instruct the correction due to the latitude of the planet or for even the latitude of place (ākṣa-valana). The result will therefore be very rough. Note 2. These degrees are necessarily arbitrary as mentioned already, and the correctness of the numbers cannot be verified in the absence of the original siddhāntas which are now lost. But we can guess the probable values as we are sure of the relative luminosities of the planets. The numbers seem to have been misplaced. They should be dvādaśa, tithi, manu, ravi, aṣṭa, tithi (12°, 15°, 14°, 12°, 8°, 15° for Moon etc.) All siddhāntas give 17° for Mars instead of 15°. The rest are nearly correctly given, according to one siddhānta or other. [कालभागानां क्षेत्रभागकरणम्] (त्रि) शतविनाडीगुणितै (रू) द (य) [वि] नाडीप्रमाणहृतैः । लब्धांशकप्रमाणादुदयोऽस्तं वा स्फुटं वाच्यम् ॥ ५९ ॥ Conversion of time-degrees into distance-degrees 59. Multiply the degrees by 300 and divide by the vināḍīs of oblique ascen- sional difference of the sign, rising at that moment, (near sunset or sunrise, as the case may be), and get the respective degrees. When the distance bet- ween the sun and planet is that much, the respective setting or rising takes place. Note 1. This work is what is known as the conversion of time-degrees (kālabhāga) into degrees of distance on the ecliptic (kṣetrabhāga). Since the rule has to apply commonly to Saura on the one hand and the Vāsiṣṭha-Pauliśa on the other, it has been placed last. Note 2. Since the positions of the Sun, Moon and planets are given only on the ecliptic, this con- version is necessary to measure distances. ज्ञसिताऽऽरेज्या (र्व्यू) नाः शशिनः प्रत्युत्तरं खरां (शुश्च) । ज्ञात्वैवं विक्षेपादादेशमनागतं कुर्यात् ॥ ६० ॥ 60. (The rising takes place in the east when) Mercury, Venus, Mars, Jupiter and Saturn are less in longitude than the Sun, and the Sun is less than the Moon in the opposite direction, (i.e., west). Making the computation according to the instruction given above using the latitude etc, the phenomenon should be predicted. 60a. A.B.C. र्ज्यकोर्नाः 59a. A. त्रिंशत; B. त्रिशति. B. विनाडी b. A.B. खरांशोना; C. खगांशेन; D. [खंशाश्च] b. A. घदशनाडी; B. श्रदशनाडीं d. B. मनागमतत्

XVIII.63 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 353 Note. The verse is very corrupt. But knowing what it is about we can give the meaning, making possible corrections. The rising is mentioned here as it is more important for application to dharma- śāstra etc. But rising also envisages setting with the word 'less' taken for 'more', and 'more' for 'less'. Example 1. The latitude of the moon is 3° 45' N. The maximum half-cara of the place is 150 vināḍīs. The oblique ascensional difference of the rising sign is 280 vināḍīs near sunset. Find the ecliptic distance between the Sun and Moon, for the heliacal rising of the Moon. The time-degrees for the moon is 12°. The heliacal rising of the Moon takes place in the evening. R sin 3° 45′ × 150 ÷ 480 = 7 38/60 × 150 ÷ 480 = 2° 23′. This is additive since the Moon's latitude is north, and the phenomena pertains to the west. Therefore, the corrected time-degrees = 14°. 14° × 300 ÷ 280 = 15° is the distance on the ecliptic between the Sun and the Moon, required. Example 2. For the same place, (i.e., max. half-cara 150 vināḍis) find the ecliptic distance required for heliacal rising, given: the latitude of Mars 1° 15' N, and the oblique ascensional difference near sunrise at that time is 330 vināḍis. The latitude correction to the time degrees (17° for Mars) = R sin 1° 15′ × 150 ÷ 480 = 2′ 33 ″ × 150 ÷ 480 taken as degrees = 48′. As the latitude is north, and the phenomenon pertains to the east, (since it is the rising of Mars that is considered), it is subtractive. ∴ 17° − 48′ = 16° 12′ is the corrected time-degrees. 16° 12′ × 300 ÷ 330 = 14° 44′, is the distance on the ecliptic required. [पञ्चसिद्धान्तिकोपसंहारः] आवन्त्यकः समासा (च्छि) ष्यहितार्थं स्फुटाङ्कसमम् । चक्रे वराहमिहिरः ताराग्रहकारिकातंत्रम् ॥ ६१ ॥ प्रद्युम्नभूमितनये जी (वे) (सौरैऽथ वि) जयनन्दिकृते । बुधे (च भग्नो) [त्साहः] स्फुटमिदं करणं भजतात् ॥ ६२ ॥ दृष्टं वराहमिहिरेण सुखप्रबोधं .............................. .............................. .............................. ॥ ६३ ॥ 61. For the good of his disciples, Varāhamihira, belonging to the Avanti country (Ujjain region), wrote this section dealing with the star-planets, briefly but with the constants agreeing with the original (siddhāntas). 62. A learner, discouraged by the computation of Mars by the astronomer Pradyumna, the computation of Jupiter according to the Saura siddhānta, and

Here is the transcription of the page, formatted line by line in clean Markdown:

354 PAÑCASIDDHĀNTIKĀ XVIII.63 the computation of Mercury by Vijayanandi, can have recourse to this section of the manual. 63. By Varāhamihira has been seen, (i.e., written) (this karaṇa) easy to under- stand,...................... Note 1. Verses 61 and 62 clearly close the section dealing with the star-planets. Since VM says that he has improved on the earlier authors, he must be referring to Chapter XVI and XVII, dealing with the Saura. His reference to his improvement on the Saura itself in the case of Jupiter must refer to the bīja correction made by him in XVI. Indeed, his dissatisfaction with the Jupiter of the Saura is reflected in his formula for computing Jupiter to give the years of the sixty-year Jovian cycle, given in his Bṛhatsaṃhitā, in the chapter dealing with the motion of Bṛhaspati (Jupiter). As for chap. XVIII, he could not have meant the Vāsiṣṭha-Pauliśa star-planets there as an improve- ment, they being crude. Note 2. Verse 63 evidently closes the Pāñcasiddhāntikā, as indicated by the Vasantatilakā metre of the verse instead of the regular āryā metre. But unfortunately the last three feet are missing. Perhaps it is a purposely done ‘black-out’ by a later astronomer-scribe, to add his spurious verses 64-81 in continuation (see below) and, unfortunately, only his manuscript has survived as the archetype of the few extant manuscripts, 61a. B. आयंतकः समांसाः b. A. छिष्णहिं०; B. छिसंध्यं हिं०; B2.3. छिसंख्यं हिं० A.B. ०र्थं तमद्गस्फु०; C. र्थं [ततः] स्फु०; D. ०थं [वियद्गस्फुटांशम्] c. A.B. मिहरः 62a. A. प्रद्यम्र. B. भुमि b. A.B. जीवै (B3. जीवे) A. शौरयवावीजय०; B. सौरे यवविजयं D. सौरैऽथवा विजय० c-d. A. बुधे वनग्रास्फुट; B. छुधे च मग्रास्फुटं; D. बुधो भग्नः स्फुटमिदं करणं भजति दृष्टं वराहमिहिरेण || ६२ || d. C. प्रस्फुटमिदं, om. करणं. A.B. भजतां; D. drops the word. 63a. A.B.C. मिहरेण. B. प्रबोधां b-d. A.B.C. gap indicated for the three quarters of the verse. D. Ignores the expression सुखप्रबोधं in this verse and constitutes a new half verse for the previous verse. as: बुधो भग्नः स्फुटमिदं करणं भजति दृष्टं वराहमिहिरेण || In consequence, the numbering of verses than in A is one less in D, hereforward. [इति पञ्चसिद्धान्तिकायां वराहमिहिरविरचितायां ग्रहोदयास्तो नाम अष्टादशोऽध्यायः ] Thus ends Chapter Eighteen entitled ‘(Vāsiṣṭha-) Pauliśa-Siddhānta — Rising and Setting of Planets’, in the Pañcasiddhāntikā composed by Varāhamihira

Chapter Eighteen 64-81 (A Spurious Supplement) Computation of the Star-Planets in brief [पञ्चसिद्धान्तिकायां प्रक्षेपः — ताराग्रहाः] Spuriousness of this Section That verses 64-81 of Pāñcasiddhāntikā form only an appendage to a manuscript of the work and not a composition of Varāhamihira, is evident from its occurring after the work has closed in the customary way with a concluding colophonic verse, with its metre changed to Vasantatilakā from the āryā metre in which all the previous verses of the chapter had been couched, and with the author speaking about himself in this concluding verse. It is also to be noted that the set of verse 64 to 81 begin with a new salutation. Had these verses really belonged to the PS, the customary colophonic verse must have come at their end, and significantly there is no such colophonic verses at the end. Further, in verse 65 it is said that the author considers this as a superior set containing a previous method or matter and that he was giving it out, with a liberal mind, to the generality of astronomers without hiding it from them. But actually it is inferior stuff, and can give only very rough results since the equation of the centre is dispensed with, only the equation of conjunction being given, which makes it valueless. The author boasts here that he has made things easy, and takes credit for this which only a novice could have done. Fancy VM speaking thus, when in verse 62 he is so intent on accuracy that he says, "Let people who have been dissatisfied with the inaccuracy of astronomers like Pradyumna, Vijayanandi etc., have recourse to his treatment of the Saura." Further, there are mistakes in the computation of Venus and Mercury, unpardonable in any astronomer. (See below, Note 2 under verses 70-72). The above-mentioned aspects of verses 64-81 have escaped the notice both of TS and NP, who both take them as genuine compositions of VM. Moreover, NP obliterate verse 63, the concluding genuine verse of PS, by not including it in their text, though a few words thereof are present in all the manuscripts of the work and in some of the manuscripts it bears a serial number; thus, verses 64 to 81 are numbered in NP as 63 to 80. These spurious verses are dealt with below for the sake of completeness of the text as found in the parent manuscript of the PS from which all its manuscripts available now have been derived. [उपक्रमः] प्रस्तावेऽपि न दोषा [न्] जान (न्न) पि न वक्ति यः परोक्षस्य । प्रथयति गु(णां) श्च तस्मै सुजनाय न(मः) परहिताय ॥ ६४ ॥ अष्टादशभिर्बद्धान्त्या ताराग्रहतंत्रमेतदार्याभिः । (वरमिति) वराहमिहिरो ददाति निर्मत्सरः करणम् ॥ ६५ ॥ Salutation 64. Salutation to the good people, ever interested in the welfare of others, who even when knowing the faults of others, and even when there is an opportunity, do not mention their faults, but proclaim their good qualities.

356 PAÑCASIDDHĀNTIKĀ XVIII.66 65. In eighteen āryā verses, Varāhamihira, without feeling any jealousy, gives this manual to the world, ending with the treatment of the planets, thinking that it is good. Note 1. The emendations are TS's also. Note 2. Verse 64 is a paranomasia and means also, "Salutation to the good science of astronomy called technically parahita-gaṇita (prevalent in Kerala in South India), which at the beginning deals only with mean motions, though knowing its defective nature as not being true motions, and which furnishes tabular values of equations going by the means, mandajyā (R sine table of the equation of the centre), karkijyā (R sine table of the equation of conjunction for the anomaly 90° to 270°) and makarajyā (R sine table of the equation of conjunction for the anomaly 270° to 90°)." This meaning being not obvious to the ordinary reader, I give the phrase by phrase meaning: prastāve (granthārambhe), parokṣasya (asphuṭagrahasya) doṣān (asphuṭatvādi-doṣān) jānann api yaḥ na vakti (jānann api na vadati, madhyagater eva prakṛtatvāt) guṇān (mandajyā, karkijyā, makarajyā ityādi- guṇaśabda-vācyā jyāḥ) prathayati (prakaṭīkaroti, gaṇayitvā likhatīti yāvat), tasmai sujanāya (tasmai śobhanajanmane) parahitāya (parahitagaṇitāya) namaḥ (namo 'stu). Note 3. These two verses also form part of the 18 verses mentioned. So, actually there are only 16 verses (66 to 81), giving the computation. [सौरदिनम्] आकरणाद् रविभागा दिवसा (श्रा) रंशका रवौ कार्याः । अधिका (य) दा दि(ने) भ्यो भागा ज्ञेयास्तदा चक्रात् ॥ ६६ ॥ ‘Sun’s day’ (Sauradina) 66. From the epoch, to the time of computation of the planet, find the Sun’s degrees passed. These are to be technically called ‘days’, (and used in the com- putation). Find the remainder after dividing by the cycle number given for the respective star-planet. Take the ‘days’ of motion corresponding to the set of motions given to the respective planet. These are degrees of planetary motion. Add this to the Sun's longitude. The true planet is got. Note 1. The ‘days’ mentioned here is only what is called sauradina (‘Sun’s day’) as distinguished from the sāvana or civil day, and are actually degrees. (This is like the word ‘light-year’, which is used as a unit of distance). This instruction is given with respect to all planets. 64a. A.B. दोषाः c. A. वराहमिह वराहमिहिरो (A2. ०म्पितिहरो); b. A. जानन्नापि न; B. जानानापि (B. जुना०). B. मिहरवराहमिहरो; C. ०म्हिहरो A. पटोक्षस्य d. B. निमत्सरः c. B. प्रथयाति. A, गुणाश्च तस्मै; B. गुणास्तस्मै 66b. A. दिवमाश्ररांशका; B. दिवसाश्चंशका d. A. सुजनयानमपर; B. सुजनया तमः. B. परिहिताया B. कार्या 65a. A. ०र्वद्धा; B. ०र्वंधा c. A. ०कार्यदा दितेभ्यो; B. ०कार्यदा दिनेभ्यो b. B. दायाभिः d. A.B. वक्रात्

XVIII.69 XVIII. STAR-PLANETS 357 Note 2. The cycle given for each planet is only the period of the planet’s synodic revolution con- verted into the solar days, i.e., it is the synodic period × 360° ÷ 365-15-30, nearly. When so con- verted, we have: | | Mercury | Venus | Mars | Jup. | Saturn | | The regular synodic days: | 115-52-45 | 583-55 | 779-57 | 398-53 | 378-6 | | Converted into solar days: | 114 6/29 | 575½ | 768-45 | 393 1/7 | 372 2/3 | The second set is given for the respective planet, saying that the synodic period is so many ‘days’. Not knowing this TS have remarked that they do not understand why there is so much difference in the periods from the regular days generally known. Also, they say they cannot dismiss them as wrong, since the numbers given are checked in the computation itself. (See pages lxiii-lxiv of Intro- duction in TS’s edition). NP have understood that the cycles are in solar ‘days’. But, they have remarked that ‘VM’ has con- fused the days and degrees, not realising that there is a purpose in giving the cycles in the solar day units. These units have been used because, now, the ‘days’ and the ‘degrees’ will have the same meaning, and they can be combined without, at every point, instructing it. Thus, ultimately, the combined value is the degrees of the true planet. Example 1. Days from epoch 1,20,553. Find the ‘days’, and assuming the Sun at epoch as zero, find the Sun at the end of 1,20,553 days. 1,20,553 × 360 ÷ 365-15-30 = 1,18,187.5 ‘days’. This plus zero, and divided out by 360° = 17°.5, Sun’s longitude. [कुजस्फुट:] ‘नवयम (गुणर्तु’ हीने) ‘कृता’ (ह) ते ‘विषयसप्तखाग्नि’हृते । भूयो (हृ)ते चतुर्भिः [निरंश] दिवसा महीजस्य ॥ ६७ ॥ ‘षड् (विषयै)’ ‘स्ति (थ्यू)’नः दृष्टो ‘वसुधृति’ [भि]-रंशकाः (ष)ष्टिः अष्टशतेन(च)षष्टिः सप्तत्या(त्र्य)धिकया नवतिः ॥ ६८ ॥ षष्ट्याष्टयुक्तया (श) तदलं च ‘खाश्वि द्विकै’: ‘स्वराद्रि’ (घ्राः) । अस्तमितोऽतः सप्ताष्टकेन तिथयो’ निरंशग (गतिः) ॥ ६९ ॥ || कुजः || Motion of Mars 67. Subtract 6329 from the ‘days’. Multiply the remainder by 4 and divide out by 3075. Take the remainder and divide by 4. These are the ‘days’ after con- junction (i.e., the anomaly of conj.) for Mars. 68-69. After 56 ‘days’ it goes behind the Sun by 15°, and becomes observable, (i.e., the heliacal setting ends). In 188, 108, 73, 68, 220, ‘days’ Mars lags behind by 60°, 60°, 90°, 50°, 70°, respectively. Then it sets heliacally, and in 56 ‘days’ lags 15° behind and goes into conjunction.

358 PAÑCASIDDHĀNTIKĀ XVIII.69 Note 1. I generally agree with TS's emendations. But in verse 68, I give ṣaḍviṣayaiḥ for ṣaḍtriṁśat- savaiḥ, which latter is both meaningless and has one mātrā extra. TS's ṣaḍvargaiḥ does not agree with the last saptāṣṭakena, for the numbers should agree or at least nearly agree. saptatyā dvyadhikayā has been emended by me into saptatyā tradhikayā, and khābdhi into khāśvi. These will not only make the total correct, but also bring about agreement with the Siddhāntas, which all generally agree with the actual as given by modern astronomy.

XVIII.72 XVIII. STAR-PLANETS 359 (d) The rising and setting are given by observation at different regions and different conditions of the atmosphere, and therefore vary among the siddhāntas. (e) In the case of the inferior planets the degrees should add upto zero. When the degrees are positive and greater than the days, the planet is gaining upon the Sun, and the total gain is its elon- gation. When the degrees are less than the ‘days’, the planet is lagging behind. When the degrees are negative and numerically greater than the ‘days’, the planet is retrograde and comes at the middle of the cycle, if the cycle begins and ends at superior conjunction. Example 2. Compute Mars at 1,20,553 days from epoch. The solar days are, 1,20,553 × 360 ÷ 365-15-30 = 1,18,817.5, and the Sun is 17°.5, taking the sun at epoch as zero, which it nearly is as already shown. 1,18,817.5 − 6329 = 1,12,488.5 1,12,488.5 × 4 ÷ 3075 leaves the remainder 1004. 1004 ÷ 4 = 251, real remainder of ‘days’. During this period we get the movement: − 15° in 56 ‘days’, − 60° in 188 ‘days’, and − 4° for the 7 ‘days’ remaining, total − 79°. Adding − 79° to the Sun, 17°.5, True Mars = 298.5°. [बुधस्फुटः] वि‘शशिवसुरसे(न्द्रे)’ ‘नव(यम)’गुणितेऽर्करा[म]गुण'भक्ते । गुणकारहृते लब्धान्यहानि शीतांशपुत्रस्य ॥ ७० ॥ दशभिर्द्वादशही(नः) प्रागुदितो ‘म(नु)’भिरून'(नन्दां'शाः) । ‘धृति’भिः(स)नवोऽस्तमितः त्रिंशद्भिरुदेति स'(शराश्विः)' ॥ ७१ ॥ अष्टाद(श)भिः(स)नवः षोडशभिश्चा(र्क)वर्जितोऽस्तमितः । पश्चा‘द्वसू’भिर्नववर्जितो निरं(शं) बुधो याति ॥ ७२ ॥ ॥ बुधः ॥ Motion of Mercury 70. Subtract 14,681 from the ‘days’. Multiply the remainder by 29, and divide out by 3312. Take the remainder and divide by 29. The ‘days’ for Mercury in the cycle is got. 70a. A.विंशशि. A.B.रसेन्द्रा; D. [रसेन्दौ] 71a. A.दशभिद्वा०. A.B.हीनाः b. A.B.1.2.नवनवगुणिते. A.B.1.2.०रागुणभक्ते b. A. मनिभिरूनभश्वांशाः; B. र्मनाभीरूनत्तश्वांशाः; c. A.B.हृते C. मनु[भिरूनिताश्वांशाः]; D. मनु [भिर्विषयश्वांशाः] c-d. B1.2.०ब्यान्य-gap-तांशु०; c. A. शनवो; B. ०भिः-gap-नवो; D. [०भिर्मनवो] B3.०ब्युनाशि-gap-तांशु० d. A. ०रुदेत्ति. A.B. सरसाश्वः (B. श्वाः); C. [सरसांशः]; D. [स रसांशाः]

360 PAÑCASIDDHĀNTIKĀ XVIII.72 71. In 10 ‘days’ Mercury falls back by 12°, and rises in the east. In 14 ‘days’ more it lags by 9°. Then in 18 ‘days’ it gains 9°. Then it sets, and in 30 ‘days’ gains 25° and rises heliacally. 72. Then in 18 ‘days’ it gains 9°. In 16 ‘days’ it lags 12°, and sets in the west. Then in 8 ‘days’ it lags 9°, and gets into conjunction. Note 1. In verses 71 and 72 my corrections are based on the need to conform as nearly as possible to reality, and they are also, as far as possible, kept close to the text. śarāsviḥ, 25, may also be jalāśviḥ, 24. The values are:

XVIII.75 XVIII. STAR-PLANETS 361 [गुरुस्फुटः] रहिते 'द्वियमशरा[ष्ट्यां]' '(नगा)'हृते 'द्विविषय(स्व)राश्वि'हते । सप्तहृते देवगु(रोः) भवन्ति दिवसा [निरंशस्य] ॥ ७३ ॥ सर्वे(ऽर्का)त् संशोध्यः षोडशभिर्द्वादशोदितः प्रा(च्याम्) । 'कृतविषयैः' 'कृतवेदाः' सप्तत्या 'सार्णवाः षष्टिः' ॥ ७४ ॥ 'नवदिग्भिः' 'शून्यार्काः' '[सा]ष्टाशीत्या' 'रसस्वरा' [श्चैव] । 'शून्यकृ(तै)'र्द्वात्रिंशत् (ततोऽस्तगः) षोडशभि'र्काः)' ॥ ७५ ॥ ॥ जीवः ॥ Motion of Jupiter 73. Deduct 16,552 from the 'days'. Multiply the remainder by 7 and divide by 2752. Divide the remainder here by 7. The 'days' from conjunction are got. 74-75. All degrees given are to be subtracted from the sun. In 16 'days' it moves 12° and rises in the east. Then in 54, 70, 49, 88, 40 days it moves 44°, 64°, 120°, 76°, 32°. Then it sets in the west, moves 12° in 16 days and joins the Sun. Note 1. The first foot of verse 73 is faulty containing 3 mātrās extra, and corrupt. So it has been corrected. The rest of verses 73 and 74 are TS's emendations. In 75, all emendations are TS's, excepting those for grammar. Note 2. The cycle is 2752 ÷ 7 = 393 1/7 days. The days and degrees are:

362 PAÑCASIDDHĀNTIKĀ XVIII.78 [शुक्रस्फुट:] 'नयनार्क [धृतीन्दू]' ने द्विगुणे (रू) पेन्द्रि [येश्रु] रै' र्भक्ते | शे(षं) यत्त(द्द) लितं भृगुतनयनिरांशदिवसाः स्युः || ७६ || 'विषयै' र्नवकविहीनः प्रागुदित'स्तिथि' [भि] 'रेक (य) म' हीनः | 'वसुकृत्या' 'ति(थ्यूनः)' 'कृताष्टिभिः' स (पञ्चकास्त्रिंशत्) || ७७ || (पञ्चा) [ष्ट] केन सद(शः) निरं[शगो] ऽतो विलोमगः पश्चात् | उ(दे)ति (नि)रंशका(ले) (प्रया)ति (चा)स्तं वि(लोम)गतिः || ७८ || || शुक्रः || Motion of Venus 76. Deduct 1,18,122 from the 'days'. Multiply by 2 and divide by 1151. Take the remainder and divide by 2. We have the 'days' from the conjunction of Venus. 77-78. In 5 'days' Venus lags by 9°, and rises in the east. In 15 days it lags 21°. In 64 days it lags 15°. In 164 days it gains by 35°. Then it sets in the east. Then in 40 days it gains 10°, and joins the Sun. Then, moving in accordance with the reversed order of the days for cycles given, it rises, after the days given from setting to conjunction (i.e., 40 days), in the west, and moves till it reaches the setting in retrograde (and getting into the inferior conjunction) section. Note 1. I have corrected mitīndu into dhṛtīndu for agreement with the Sun in superior conjunction which alone fits. TS's correction (also NP's) mahīndu does not bring agreement with the Sun either at superior conj. or inferior conj. There can be another possible correction matīndu (mati is 8). In the 64 days, flanking the retrograde, the days may be a little more or less, since a small error of observation can produce a difference of a large number of days. The lacunae is filled by me with sapañcakāstriṃśat, meaning 35°, to fit the number of degrees wanted to make up the total zero, and fitting the number of days given. TS's emendation, kṛtāṣṭabhiḥ will be far from fitting the total. 76a. A.B. ॰र्कमितिदुने; C.D. ॰र्कमहीन्दूने 78a. A.B.C. ष (B. स) ष्टाष्टकेन सदश (B. सदृश); b. A.B. रूपेन्द्रियैः स्वरै र्भ (B2. भ) ते D. षष्टाष्टकेन स दश c. A1. शेषः. A1. यत्तदलितं; B. यकृदलितं b. A. निरंसतोतो; B. निरंशतातो d. B. ॰वसा स्युः c. A. उदयति तिथिनिरंशकालो; 77a. B3. नवका B. उदयतिथिनिरंशकालो b. A.B. तिथिरकपम (B. यम) हीनः c-d. C. उदयति निरंशकालेन, याति; c. A. तिथ्यून D. उदयति निरंशकालात्र याति d. A.B. ॰ष्टिभिः स, rest of verse missing: d. A.B. नयति (B. भवति) वास्तं D. नः कृत (ष्ट्रै) स्त्रिभिः स A.B. विनाथगतिः; D. [दिनानाथ] गतिः C. ॰भिः [सेषुरस्तगतः]; D. ॰भिः [सपञ्चास्तगः]

XVIII.79 XVIII. STAR-PLANETS 363 Moreover, their filling the lacuna by seṣuḥ, meaning 5° is quite inadequate to make up zero. I have emended saṣṭāṣṭakena into pañcāṣṭakena, meaning 5 × 8 = 40, which will fit the number of days. Also, 10° synodic motion there requires 40 days and it is also the period from setting to going into superior conjunction. ṣaṣṭa is patently wrong spelling, and ṣaṣṭāṣṭakena is meaningless. But TS and NP keep it, which is wrong. That this is the segment of heliacal setting to conj. can be inferred from udayati given for the next segment, and 10° for heliacal setting and rising at superior conj. is given by many siddhāntas. The other minor emendations are TS's. Note 2. 1,18,122 seems to be a very large subtractive constant, equal to more than 300 years, while all others are very near VM's time. But I cannot think of any other number to fit, Note 3. The maximum elongation is seen to be 45°, correctly. (Cf. Table).