XIV.38 XIV. ASTRONOMICAL INSTRUMENTS 277 दक्षिणतारा हस्ते सार्पस्यांशे तथोत्तरा तारा । पित्र्यस्य स्वक्षेत्रे षष्ठे चांशे समायॊगः ॥ ३६ ॥ चित्रार्धाष्टमभागे दक्षिणतः संस्थिते त्रिभिर्हस्तैः । विक्षेपकलान्तादङ्गुलानि मध्याच्छशाङ्कस्य ॥ ३७ ॥ Positions of Certain Junction-Stars 34. (The junction-star of) Kṛttikā is at the end of the sixth degree (from the initial point of that nakṣatra) and 3 1/2 cubits to the north of the ecliptic. (The junction-star of) Rohiṇī is at the end of the eighth degree (of that nakṣatra) and 5 1/2 (cubits) to the south. 35. The southern and northern (junction-) stars of Punarvasu are at the end of the eighth degree (of the nakṣatra) and 8 (cubits) south and north (respectively). The (junction-)star of Puṣya is at the end of the fourth degree (of that nakṣatra) and 3 1/2 cubits to the north. 36. The southern (junction-) star of Āśleṣā is at the end of the first degree (of that nakṣatra) and one cubit (to the south); so also is the northern (junction- star). The conjunction (of the Moon) (with the junction-star of) Maghā occurs in its own field at the end of the sixth degree (of that nakṣatra). 37. (The junction-star of) Citrā is at the end of 7 1/2 degrees (of that nakṣatra) and 3 cubits to the south. The digits are counted from the centre of the Moon where the minutes of the latitude end. [शशितारयोरङ्गुलमानम् योगकालश्च] विक्षेपात्सप्तदशापनीय तिथिसङ्गुणात् कृताग्न्यंशः । विद्यादङ्गुलमानं कालं दिनभोगविवरेण ॥ ३८ ॥ Digits between the Moon and a Star in Conjunction And Time of Conjunction 38. Having subtracted 17 from the latitude (of the star with respect to the Moon) multiply by 15 and take a thirty-fourth of that; this is to be known as the number of digits (between the Moon and the star). 34a. B. चन्द्रा; D. बहुलाः 35a. B. ॰मेऽष्टमेशे d. A.B. षष्ठे A. वांशे; B. वाशे A. षष्ठांशात्ते; B. षष्ठाशाति; B2. हातं b. A.B.D. पुनर्वसौ दक्षि 37a. A. चित्रार्थाश्रमभागे b. A. भगणोदक; B. भगणोदकः c. A2. तरे for तारे B. हस्तेषु पुष्य b. B. त्रिहस्तैः c. A. दलात्ते d. A. ॰स्पोदक् A. चतुर्थेशे c. A. कलातादंगु; B. कलातादृगु d. A.B. दक्षिणस्तश्च A. स्वार्ध; B. स्वार्द्धे; 36a. A. सार्पस्यांसेत्तथोत्तरात्तारा d. A. मध्याछशां; B. मध्याछः शकस्य A. षष्टेषु c. A. पित्र्यस्य स्वछेत्रे; B. स्वष्टे च त्रे

278 PAÑCASIDDHĀNTIKĀ XIV.41 The time (of conjunction) is to be known from the distance between the star and the Moon and the daily motion of the Moon. According to Varāhamihira, the measure of the Moon's diameter is 34 in terms of minutes and 15 in terms of digits. Hence the above rule.

Polar longitudes and latitudes of the Junction-stars

39. Multiply the square of 5 (i.e. 25) by half the equinoctial midday shadow; (treating it as the Rsine of an arc) find the corresponding arc (in terms of degrees) and add 15 (degrees) to that. Multiply that by 10 and add 21 times the equinoctial midday shadow. These are vināḍīs. 39-40 Quoted by Utpala on BS 12.21 38a. B. ॰दशापनीय 39a. A. विषुवच्छाया B. द्विगुणा b. A. संगुणाकृता b. A.B. पंचकृतेस्तत्कलास्ततः; D. पञ्चकृतिस्तत्कला ततः c. A. ॰माणं c. A. छायानृसप्तक॰; B. छायात्तृप्तक A1. युत A.B. भोगोविरेण (B. ॰चिरेण); d. A.B. गुणिता

XIV.41 XIV. ASTRONOMICAL INSTRUMENTS 279 40-41. Assuming these vināḍīs as the time elapsed since sunrise and taking the Sun at the first point of Cancer, calculate the longitude of the rising point of the ecliptic. When (the longitude of) the Sun happens to be equal to that, then, by virtue of the graphical methods and instruments available to the science of mathematical astronomy, the sage Agastya (i.e. the star Canopus) that looks like the special red tilaka-mark on the forehead of the lady-like southern direction shines forth and delights the minds of men. Such is the divine knowledge based on time. Fig. XIV. 4 Consider Fig. 4. It represents the celestial sphere for a place in latitude Ø. SEN is the horizon and Z the zenith; ♈RET is the equator and P and Q are its north and south poles; ♈GSD is the ecliptic. 40a. A1.B. काद्यायगग्रं (B3. काझाप) D. याम्यतातो वनिता 41a-b. B. ०पलब्धः छेध्यकं (B2. क) b. B1. तदशे; B2. तदंशो; B3. तदृशो B. सहस्तांशो d. A. सुख; B. स्तुख B. विषतिल्को b. B. प्रकाशना पातम् | B. यातं c. A.B. याम्यास्ता (B. त्ता) वनिता; A. मुनिणस्त्यः c. B. खसुखपति

280 PAÑCASIDDHĀNTIKĀ XIV.41 A is Canopus at the time of its heliacal rising and S the Sun at that time. PGAQ is the hour circle of Canopus, and G the point where it intersects the ecliptic. Assuming that the celestial longitude of Canopus is 90° and the celestial latitude 75° 20' S¹, we have ♈G = 90°, AG = 75° 20' and AA' = 75° 20' − 24° = 51° 20'. Therefore Rsin A' E = Rsin (asc. diff. of Canopus A) = Rtan δ tan θ, vide formula (2), where δ is the declination AA' of Canopus and θ the latitude of the place, = (sin δ . sin θ / cos θ) × (R / cos δ) = (sin 51°20' . palabhā / 12) × (120 / cos 51°20') because, according to Varāhamihira, R = 120' = 25 × (palabhā / 2), approx. ∴ A'E = arc (in terms of degrees) corresponding to Rsine equal to 25 × (palabhā / 2), approx. EG" = asc. diff. of G, approx. = 21 × palabhā, vināḍīs, approx. because for unit palabhā, the ascensional difference for G (the first point of Cancer) is 21 vināḍīs. Also, assuming 15 to be the time-degrees for the visibility of Canopus, G'S = G"S' approx. = 15 degrees, approx. ∴ A'S' = A'E + EG" + G"S' degrees = [10 (A'E + 15) + 21 palabhā] vināḍīs, where A'E + 15 is in degrees and palabhā in digits. Degrees multiplied by 10 are vināḍīs. Now GS is the arc of the ecliptic which rises above the horizon (of Laṅkā) in the time given by the arc A'S' of the equator. Hence it is obvious that Canopus A will rise heliacally when the Sun is at S, i.e., when Sun’s longitude = longitude of G + arc GS = longitude of G (i.e., 90°) + arc of the ecliptic which rises (at Laṅkā) in the time given by the arc A'S' of the equator.

1. Actually, the longitude of Canopus is 85°4' and the latitude of Canopus is 75°50'S.

XIV.41 XIV. ASTRONOMICAL INSTRUMENTS 281 Hence the rule. Obviously, the rule is very crude. It was discarded by the later astronomers who replaced it by better rules. [इति पञ्चसिद्धान्तिकायां वराहमिहिरविरचितायां छेद्यकयन्त्राणि नाम चतुर्दशोऽध्यायः ||]¹ Thus ends Chapter Fourteen entitled ‘Graphical Methods and Astronomical Instruments’ in the Pañcasiddhāntikā composed by Varāhamihira

1. A. छेदकयंत्राणि चतुर्दशोऽध्यायः | B.D. इति छेदके यंत्राणि चतुर्दशोऽध्यायः | C. इति छेद्यकयंत्राणि नाम चतुर्दशोऽध्यायः |

Chapter Fifteen

SECRETS OF ASTRONOMY

पञ्चदशोऽध्यायः

ज्यौतिषोपनिषत्

[ग्रहणम्] सूर्येन्दुभगणधात्रीसंस्थानविदोऽधिकृत्य कथयामि । ग्रह(णं) सदैव भानोः स्थानविशेषात् क्वचिद्दृश्यम् ॥ १ ॥ अविदितसंस्थानानां बोधोऽपि हि जायते यथाऽऽधान्याम् । क्षीरं शंखोपहितं द(श)नविनाशक्षमं भवति ॥ २ ॥

Eclipses

1. I declare the following to those who possess pre-knowledge of the relative positions of the Sun, the Moon, the zodiac with the principal stars, and the earth. There is always an eclipse of the Sun visible somewhere in space, according to the position of the place. This is what is meant: If a solar eclipse is defined as being caused by the Moon hiding the Sun, it is obvious that at any moment some place in space will have the Sun hidden behind the Moon.
2. For those who do not know the relative positions of the above mentioned, even knowledge will become similar to the milk in the container with conch in it becoming capable of destroying the teeth. This is the meaning:- Milk and Conch are by themselves beneficial things, especially conch which can strengthen the teeth on account of its calcium content. But milk with conch soaked in it becomes positively harmful to the teeth on account of their incompatibility. So also, even know- ledge can become harmful unless the knowledge as to when, where and how to use it is also known. TS have amended the correct dhānyām into dhānyam, not realising that the word intended in the context is ādhānī, meaning the vessel for holding the milk, and also not understanding what is meant by the verse. For similar reasons, NP have emended the word as dhyānāt, and gives a meaning opposite to what is intended by VM. 1a. A. भगणा B. धात्रीं c. A. ग्रहाणां d. B. विशेषात A. क्वचिदृश्यं; B. क्वचिदृश्यम् (B3. कवि) 2a. B1.3. आअविदित A. सस्थानानां; B. सस्तानानां b. B. वेद्योपि B3. तायते B. ध्यान्याम्; C. यथा ध्यानम्; D. यथा ध्यानात् c. A. दशान; B1.3. दशानन; B2. दशा विना

XV.4 XV. SECRETS OF ASTRONOMY 283 संक्षेपसू(त्रवशतः) शशिना(ऽऽश्रि)यते दिवाकरो येषाम् । तेषां सूर्यग्रहणं स(च) देशः प्रतिदिनं क्वापि ॥ ३ ॥ सकृदेव रविं ग्रस्तं पक्षं पश्यन्ति शशिगताः पितरः । अग्रस्तमपि च पक्षं ग्रहमध्यं पौर्णमास्यां तु ॥ ४ ॥ 3. For these to whom the Sun is hidden by the Moon, according to the straight line from them through the Moon touching the Sun, for them there is a solar eclipse. And every moment (lit. every day) there is such a place somewhere. 4. The pitṛs (Manes) on the Moon see the Sun eclipsed for one whole fortnight, and not eclipsed during the other fortnight. The mid-eclipse is at full moon. [चित्र विवरण: Fig. XV. 1] S Light from the Sun Fig. XV.1. (diagrammatic, not to scale) P: The Pitṛs on the moon M₁: Position of moon at middle of dark fortnight. M₂: New moon position M₃: Position at middle light fortnight M₄: Position at full moon On the side facing the sun, the Moon has sunlight. On the other side it is darkness. E: Earth Fig. XV. 1 3a. A2. संक्षेपा A.B. सूत्रावशशिना (B. सूत्रावं); 4a. B. रविग्रस्तं D. सूत्राविशेषेण b. B3. पितराः b. A.B. त्रियते; C. ध्रियते; D. तीर्यते c. A. अग्रस्य B. ०मवि च c. B. Hapl. om of तेषां d. B. ग्रस्तं मध्या A. मध्य d. A. स व देशः

284 PAÑCASIDDHĀNTIKĀ XV.7 At $M_1$ position P (Pitṛs) just begin to get sunlight. It is sunrise to them. At $M_2$ it is midday, with Sun abovehead. At $M_3$ daylight ends and darkness begins. At $M_4$, it is midnight for the Pitṛs. On the earth, $M_2$ is new moon, $M_3$ mid-light fortnight, $M_4$ is full moon, and $M_1$ mid-dark fortnight. Thus, full moon on earth is midnight for the Pitṛs, the whole night being the eclipsed time. Note that the Pitṛs are supposed to dwell in the region opposite, along the line of sight of the Moon. Note also that the synodic month forms the whole day for the Pitṛs, full moon being mid- night and new moon being mid-day. Note again that the explanation above can hold good only if the Moon shows the same face to the Sun, as it really does. The Hindu astronomers held the same view, without any conception of it, for they held this view in the case of every planet. TS are [L1

XV.9 XV. SECRETS OF ASTRONOMY 285 7. Though the Sun is low near the horizon, near sunrise or sunset, the Moon, being higher up, can hide the Sun like a cloud. VM here answers an objector to his stand (5-6). He is unaware that the case in (7) is similar to that (5-6). TS’s emendations paramocca, which means ‘standing high up in the sky’, will make an eclipse itself impossible. NP’s emendation candroparasamavastha does not give the sense of ‘being under the Moon’ given by them for the expression. अस्माकमुदयसमये येषामल्पास्तगो दिवसनाथः । मध्याह्नो वा येषां तेषामपि न युगपद्ग्रहणम् ॥ ८ ॥ तदतीतमुदयगानां क्षणद्वये (नैष्य)दस्त(देशा)नाम् । मध्याह्नदे(श)गानामनवरतं वर्तमानेन ॥ ९ ॥ 8. For people who have sunset and for people who have mid-day, when we have sunrise, for all of us, the solar eclipse does not occur at the same time. 9. Throughout the time when there is eclipse for the mid-day people, it is past for the sunrise people by four nāḍikās, and will be yet to occur for the sun- set people by four nāḍikās. The context is the solar eclipse and the Moon is near the Sun, So for the sunrise people the apparent longitude of the Moon has increased by parallax, and the circumstances of the eclipse are advanced by more than four nāḍīs. The opposite happens for the sunset people, and the circumstances are delayed by four nāḍīs. The duration itself is shortened by a slow rate of change of parallax for both. Therefore when the mid-day people’s eclipse begins, the morning people’s eclipse has ended, and when it ends, the evening people’s eclipse has not begun. So there is no overlapping of them. The explanation given by me is general, and several other circumstances will have to be taken into account. But VM’s statement is correct in a general way. Hindu astronomers give the maximum parallax converted into time as four nāḍīs. We must contrast this with the lunar eclipse, which begins and ends at the same moments, wherever the Moon is visible on the earth. 7a. A.B. यद्यं (B. द्य) द्युदये; C. ग्रासे ह्युदये 8a. B. Hapl. om of one ये b. A.B. निञ्चस्थो A. ॰मंशुमा भवति b. B. दिवनाथः c. A.B. चन्द्रोपरमवस्थो; C. चन्द्रः परमोच्चस्थो; d. B. तेषां मेयिनमुग्रापत ग्रहणम् । D. चन्द्रो पर[स]मवस्थो 9a. B. तदानीतमु—यश्रंमानां d. A1. ध्नन्द्वानोः; A2. द्यनद्धानोः; b. A.B. नेषदस्तदोषानाम् (B3. सेष्य) B. ग्रनह्रा (B3. द्रा) तो c. A. देशे In B2, there is transposition of folios here. d. B. मनपरत वर्तमान; B. gap for, न ॥ उ (of next verse)

286 PAÑCASIDDHĀNTIKĀ XV.16 (उक्तश्च) संहितायां मया प्रपञ्चोऽ(स्य) राहुचारादौ । ग्रहणस्य यन्निमित्तं विनै[व] राहुं रविहिमांश्वोः ॥ १० ॥ 10. This matter of eclipses has been expatiated upon by me at the beginning of the chapter on Rāhu’s (the Node’s) motion (in the Bṛhatsaṁhitā, 5. 8-11). Also the causes for the eclipse of the Sun and the Moon without the consider- ation of Rāhu has been dilated upon. VM indicates both the nodes as Rāhu (the dragon of mythology), one as the ‘head’ and the other as the ‘tail’. Here, VM takes the correct astronomical position in the matter of the eclipses. In this chapter as also as in his Bṛhajjātaka, VM refers to without inhibition, the incorrect views of the authors of the early astronomical saṁhitās. [ध्रुवस्य स्थानम्] मेरोर्न दिग्विभागो यस्मात् प्राची न भास्करात्तस्मिन् । उदय(ते) याव(द्धि)वं पर्येतीव सुन्दरी तावत् ॥ ११ ॥ अणुमात्रदर्शनात् प्राग्विभाग इति चेत् समार्धमि(त्वा तु) । तस्मिन्नेवाऽस्तमये किं वा प्राची भवेत् त्वपरा ॥ १२ ॥ तेषामपक्रमवशाद्दिवसो न खलु भ्रमाद्यथास्माकम् । षष्टिर्नाड्योऽस्माकं वर्षमहोरात्रममराणाम् ॥ १३ ॥ वर्षे वर्षे द्युनिशं सुरासुराणां विपर्ययेणाह्नः । मासं तु तत् पितॄणां मनुजानां नाडिकाषष्टिः ॥ १४ ॥ यन्मात्रं भूवृत्तात् क्षण[मात्रेणो]न्नतिं व्रजत्यर्कः । तन्मात्रान्तर(चा)रिणममराः पश्यन्ति नो(र्ध्व)म(तः) ॥ १५ ॥ होराधिपतिदिनेश्वरपरम्परा न [घ]टते यथास्माकम् । षष्टिर्नाड्यस्तस्मि[न्] नाहोरात्रो भवति यस्मात् ॥ १६ ॥ Situation at the Poles 11. There is no distinction of direction at the North pole, because East cannot be determined there using the Sun (rising and setting and culminating), for, as long as the Sun stays risen, it goes round and round the sky like a beautiful damsel. The idea is that there is no daily rising and setting of the Sun to determine east and west. In fact, at the North pole all directions are south. 10a. A1. उक्तं च; A2. उक्तं व; B. —क्तं च      11a. B1.2. दिविभागो b. B. संतायामवाप्रपंचोस्य              b. B. भास्करामस्मिन् c. A1. यन्निमितं; B. यनिमितं             c. B. नदयति d. A.B. विनैराहुं (B. हु)              d. A1. यावद्विवं; A2. यावर्द्विवं; B. हुपरपि हिमांश्च                 B. यावद्विपर्येतीव C.D. यावद्दिनपः पर्येति वसुन्धरीं तावत्

XV.16 XV. SECRETS OF ASTRONOMY 287 12. If it is argued that from the point where the Sun just appears above the horizon east is determined, as the Sun sets at the same point after half a year, can this east become west also? What VM says in these two verses is essentially true. But his statement that it sets at the same point after half a year is not correct. It is not exactly half a year, and the Sun will disappear at any point proportionate to the fraction remaining over the full sidereal days gone between rising and setting. 13. For the gods at the North Pole, the day is determined by the Sun's decli- nation, (north declination being day-time, and south declination night), not like ours, depending on the daily rotation. It is 60 nāḍikās for us, and one year for the gods. 14. Every year the day and the night of the gods and of the asuras (demons, at the South Pole) is opposite, (i.e. when it is day-time for the gods it is night- time for the asuras, and vice versa); for the pitṛs (on the Moon), the day-night is one synodic month; and for men, it is sixty nāḍikās. 15. To the extent the Sun rises above the horizontal by two muhūrtas, (i.e. 24° above the horizon) to that extent the gods at the pole see the Sun rising above the horizon, and not more than that. The Sun spirals round and round after rising, with its altitude increasing with its north declina- tion. As the maximum declination is 24° (according to Hindu astronomy, and fairly correct at VM's time), the altitude never exceeds 24°. After that is spirals down. 16. The series of the Lords of the Horās and Lords of the days do not fit there as it does for us, because the sixty-nāḍikā-day-night does not obtain there. This statement fits not only the pole, but also all places in the arctic zone, when the Sun seen above the horizon exceeds 24 hours. The horā is one hour's time, and the Lords of the horās are successively Saturn, Jupiter, Mars, Sun, Venus, Mercury and Moon, and again Saturn etc. The lord of the first horā after sunrise is the lord of the day. It can be seen that the lord of the 25th horā is the lord of the day next in the day series. So, if the day is more than 24 hours, the two series cannot fit. 12a. A.B. अनुमात्र b. A.B. समार्धमिवा नु ( A2. ॰मिचा नु; B. ॰मित्वात्) c. B. तस्मिन्वास्तमये d. B. प्राचि भवेत् परा 13a. A. तेषामपक्रम; B. तेवाम ( B1.2. om म) पक्रमवशादिवसो ( B2. दि) c. B. षष्टिनोर्द्धोस्माकं d. B3. gap after णाम्; ( B1.2. no gap) 14a. B. वर्षे वर्षेन्दुर्निशं c. B. मास तु A.B. पितॄणां d. B. मनुज्ञानां B. नाडिकषष्टिः 15. Quoted by Utpala on BS 17.4-5. 15a. B1. भ्रमक्ता; B2. भ्रमवत्ता; B3. भ्रमवता for भूवृत्तात् b. A.C.D.U. क्षणद्वयेनोन्नतिं; B. क्षणवृयेणोन्नति ब्र ( B3. ०ण्णदाये) c. A.B.वारिण ( B. om ण) d. B. पश्यन्ति A. नोर्धमधः; B. नोर्धमंधः 16a. A. नटते ( A. नद्यते) यथास्माकं a-b. C. परम्परा तत्र नो यथास्माकम् | D. परम्परा न स्यात्तु यथास्माकत् c. A. तस्मिन्नाहो; B. षष्ठिनाड्यस्तस्मिन्नहो 38

288 PAÑCASIDDHĀNTIKĀ XV.21 [वारज्ञानम्] दिनवारप्रतिपत्तिर्न समा सर्वत्र कारणं कथितम् । (नहोऽपि) भवति यस्मात् विप्रवदन्तेऽत्र दैवज्ञाः ॥ १७ ॥ द्युगणाद्दिनवाराप्ति (र्धु) गणोऽपि हि देशकालसम्ब (न्धात्) । ला(टा)चार्येणोक्तो यवनपुरे (ऽर्धा) स्तगे सूर्ये ॥ १८ ॥ Weekday 17. The determination of the weekday is not the same everywhere. As no reason is given in this matter too, even astrologers disagree among there- selves. The commencement of the day is fixed arbitrarily, as a matter of convention, like midnight, sun- rise, sunset, etc, following the custom of different peoples. 18. The weekday is obtained from the total days commencing from a stated point of time, of a particular day at a particular place. Ācārya Lāṭadeva has said that the day begins at the exact (mean) sunset at Yavanapura. This convention is that of the Romaka and the Pauliśa Siddhāntas, mentioned by VM in PS I 8-10, Lāṭadeva is said to have redacted these two siddhāntas. Yavanapura is Alexandria in Egypt, as can be fixed from the longitude correction for Ujjain in PS III. 13. see also I. 8 and note on p. 10 above. [दिनगणना] रव्युदये लङ्कायां सिंहाचार्येण दिनगणोऽभिहितः । यवनानां निशि दशभिर्मुहूर्तैश्च तद्गुरुणा ॥ १९ ॥ लङ्कार्धरात्रसमये दिनप्रवृत्तिं जगाद चार्यभटः । भूयः स एव सूर्योदयात्प्रभृत्याह लङ्कायाम् ॥२० ॥ देशान्तरसंशुद्धिं कृत्वा चेन्न घटते तथा तस्मिन् । कालस्याऽस्मिन् साम्यं (तै)रेवोक्तं यथाशास्त्रम् ॥ २१ ॥ 17-20. Quoted by Makkibhaṭṭa on 18-29. Quoted by Utpala on BS 2, pp. Si. Śekhara, 2.10. 31-32 17a. A. वारप्रतिपत्ति न ; B. वारप्रति पति न 18a. B. द्युगणांदिन b. M. कारणे कथिता B1.2. ०प्तिद्विगुणोपि; (B3. ०प्तिर्द्वि०) c. A.B.C.D.M. नेहापि b. A1. संवधा; A2. संबन्धा; B.D. M.U. सम्बन्ध: c. A.B1.2. लाजाचार्ये d. A.B. पुरेवा (B. या) स्तगे; M. चास्तगे

XV.27 XV. SECRETS OF ASTRONOMY 289 मध्याह्नं भ(द्राश्वेऽ)स्तमयं कुरुष्व्[त्तरेषु] केतुमालानाम् । कुरुतेऽर्धरात्रमुद्य(न् भा)रतवर्षे युगपदर्कः ॥२२॥ उदयो यो लङ्कायां सोऽस्तमयः सवितुरेव सिद्धपुरे । मध्याह्नो यमकोट्यां रोमकविषयेऽर्धरात्रः सः ॥ २३ ॥ अधिमासकोनरात्रग्रहदिनतिथिविसमेषचन्द्रार्काः । अयन(र्त्वा)र्क्षगतिनिशाः समं प्रवृत्ता युगस्यादौ ॥ २४ ॥ अन्यद् रोमकविषयाद् देशान्तरमन्यदेव यवनपुरात् । लङ्कार्धरात्रसमयादन्यत् सूर्योदयाच्चैव ॥ २५ ॥ सूर्यस्यार्धास्तमयात् प्रतिदिवसं यदि दिनाधिपं ब्रूमः । तत्राऽपि नाऽऽप्तवाक्यं न (वा) युक्तिः काचिदन्याऽस्ति ॥ २६ ॥ सन्ध्या क्वचित् क्वचिदहः क्वचिन्निंशा [दिवसपतेः] क्वचित् क्वचित् । स्वल्पे स्वल्पे स्था(ने) व्याकुलमेवं दिनपतित्वम् ॥ २७ ॥ Day-reckoning 19. Siṃhācārya has declared that reckoning day-total commences at a sun- rise in Laṅkā. The preceptor of the Yavanas has said that the day commences for the Yavanas ten muhūrtas, or twenty nāḍikās, in the night, (i.e. after sun- set). Hindu siddhāntas suppose Laṅkā to be on the equator, at the junction of the Ujjain meridian. Siṃhācārya's view is that of many later siddhāntas. The preceptor of the Yavanas mentioned is probably the Yavanācārya of the Yāvanajātaka, the well-known astrological work. There is a section devoted to astronomy also in that work. If the people in Greece are meant by Yavanas here, Yavanācārya perhaps tries to fit a Greek astronomical work into serviceability in Ujjain, for 20 nāḍīs after sun-set in Greece is the moment of sun-rise at Ujjain, assuming a rough longitude correction 10 nāḍīs. 20. Āryabhaṭa has said that the day commences at mid-night at Laṅkā. He himself again has said, the day commences from sunrise at Laṅkā. Āryabhaṭa has written two works. One is the wellknown Āryabhaṭīya. He has written another work, not extant now. It is referred to by others as the Midnight School and commences the day at midnight. Bhāskara I has given its system in chap VII of his Karmanibandha, better known as Mahābhāskarīya. The system given in this is the same as that of the Saurasiddhānta of the PS. Brahmagupta professes to follow this in his Khaṇḍakhāyaka. 20a. Jy, N. समयात् 19c. B. यवनानांशिनिशिभिर्गतैर्मु॰ 20. Quoted by Nīlakaṇṭha in his b. B1.3. प्रवृत्तिञ्-गाद; B2. प्रवृत्तिः जगाद A.D.U. ॰द्शभिर्गतैर्मु॰; Jyotirmīmāṃsā, p.8, as also on A. चार्यमट्टः; B1.3. चार्यभटः M. यवना निशीह दश॰ ABh. Kāla. 16. c. M, N, U. चार्कोदयात्

290 PAÑCASIDDHĀNTIKĀ XV.27 21. If it is argued that the different times for commencing the day can be accounted for by correction for longitude, it does not agree with what they themselves have said in this matter, according to the śāstras, (which is as follows). 22. 'The sun rising in Bhārata-varṣa, makes at that very moment, mid-day in Bhadrāśva-varṣa, sun-set in Uttara-kuru-varṣa, and mid-night in the Ketumāla-varṣa. 23. What is sun-rise at Laṅkā, that same moment is sun-set at Siddhapura, noon at Yamakoṭi, and mid-night in the Romaka-pura. In the above two verses the early siddhāntic conception of a world geography is given briefly. The equator is the Jambūdvīpa, with the North Pole at its centre. Laṅkā is the point where the Ujjain meridian cuts the equator. The point 90° east of Laṅkā is Yamakoṭi, also called Yavakoṭi. Here seems to be a vague concept of Java, called Yavadvīpa, whose exact distance was not realised. Ninety degrees west of Laṅkā is Romaka-pura, answering to Rome, whose exact position was not realised. The antipode point of Laṅka is called Siddhapura. A vague notion of the Mayan and Aztec civilisa- tion brought in by early exporters sailing the seas might have given rise to the idea. The astronomical idea of sun-rise, moon etc. is correct according to the conception. The four varṣas mentioned, Bhārata, Bhadrāśva, Kuru, and Ketumāla are supposed to be situated round the North Pole, at its south, east, beyond the pole and west, from our stand point, in Bhāratavarṣa. The Purāṇas give seven divisions of the Jambūdvīpa, and these are the principal four. The purāṇic concept is that of an earlier period of a flat earth, with the mountain Meru at the centre with Jambūdvīpa arranged all round, transmitted by tradition. The Siddhāntas tried to fit whatever is possible of the Purāṇic geography, into the conception of the spherical earth, refuting the rest outright or explaining them away. 24. At the beginning of the yuga, the intercalary months, the omitted days, the planetary days, the lunar days, the first point of Meṣa, the Moon, the Sun, half-years, ṛtus, and the sidereal days, begin together (and can be reckoned anew). 25. The longitude correction reckoned from the Romaka region is different from that from Yavanapura. Reckoning time from mid-night at Laṅkā is different from that from sun-rise. 21a-b. B. द्धिंत्तचन्न (B3. ०न०) | 23a. A. Hap. om of one यो; c. B. ०स्मात् साम्यं (B3. साम्यां) | B. दनम्रो यो लङ्कायां d. A. नैर्वोक्तं | c. A.B1. यमकोद्यां U. यवकोट्यां मध्याह्नं B1.2.3. gap indicated for यथाशास्त्रं | d. B. रोमवियेर्द्ध U. रात्रं च and part of the next line up to कुरुषू | 24a. B. 'अ' lost. B. रात्रिग्रह 22a. A. भद्रेभ्रस्त; C.D.U. भद्राश्वेष्वस्तमयं | b. B. दिवसमयूष A. मेषं b. A.C.D.U. om उत्तरेषु and read | c. A. अयन-र्क्ष; B. अयनत्वर्क्ष; D. अयनत्वृक्षगति कुरुषु केतुमालानाम; | A1. युगस्पादौ B. .....तरेषु कालेंतुलानानाम् c. A. ०मृद्यद्धरात | 25b. B. विषयादेशा d. B2. युगपदर्कः | d. A. दन्यसूर्यो; B. दन्यः सूर्यो

XV.29 XV. SECRETS OF ASTRONOMY 291

26. If we determine the Day-lord from the half-setting of the Sun every day, there is neither traditional authority nor reasoning to support this.

27. Even in quite adjacent places, in one place there is sun-rise or sun-set, and not in the other, day-time in one place and night in the other, and vice versa. Thus, there is confusion among people in the matter of the Lord of the day.

होरावार्ता(प्ये)वं यस्माद् होरा दिनाधिपस्याद्या | तस्याऽपरिनि(ष्ठा)ने होराधिपतिः कथं भवति || २८ ||

अविचार्यैवं प्रायो दिनवा(रे) जनपदः प्रवृत्तोऽयम् | स्फुटतिथिवि(च्छे)दसमं युक्तमिदं प्राहुराचार्याः || २९ ||

28. The matter of determining the Horā-lord also is in the same mess. When the Day-lord is not determined, how can the Horā-lord be determined?

29. Without giving a thought to all these difficulties, people generally use the name of the Day-lord in their daily routine, (and get on with their work). Learned authorities say that the best thing would be to use the true tithi, (lunar day) and its parts for daily intercourse (as for fixing a definite point of time etc.)

What is meant is as follows:- Sun-rise etc. may vary from place to place, according to the local time. But the lunar day is the same for every place on the earth. So this can fix a point of time without any ambiguity. We learn that the ancient Babylonians used the lunar day as the unit of time, just as we use the solar day.

In the above verses VM indulges in a lot of discussion about Horā-lord, Day-lord, etc. But these are only matters of convention, and astrologers and governments can agree upon some convention to avoid difficulties, e.g. do we not have the standard mean time for our daily dealings.

26a. B. ॰र्धस्तमयात् 27b. A.B. निशा दिनपतिः 28a. A. वार्त्ताध्येवं; B. वत्ताप्येवं (B3. ॰र्त्ता॰) b. B. ॰दिवस यदि B. दिनाधिपत्यं A2. ब्रूमः A2. क्वचिक्वचित् b. B. ॰धिपश्वाद्याः c. B. नाप्तं वाक्यं c. A.B. स्थानं c. A. निष्ठाने; B. निष्ठाने d. A. नवयुक्तिः; B.C.D. न च युक्तिः d. D. व्याकुलमेव 29a. U. अविदित्वैवं B. ॰दन्यास्तः; U. ॰दप्यस्ति b. A. वारौ; B1.2. वारै; B3. वारैः c. B. स्फुरतिथि A.B1.3. विच्छेद d. B1. राचार्योः

[इति पञ्चसिद्धान्तिकायां वराहमिहिरविरचितायां ज्योतिषोपनिषन्नाम पञ्चदशोऽध्यायः ||]¹ Thus ends Chapter Fifteen on ‘Secrets of Astronomy’ in the Pañcasiddhāntikā composed by Varāhamihira

1. Col.: A.B.D. ज्यो (A1. ज्यौ) तिषोपनिषत् पञ्चदशो (B. दशमो) ध्यायः | C. इति ज्योतिषोपनिषन्नाम पञ्चदशोऽध्यायः ||

Chapter Sixteen

SAURA SIDDHĀNTA : MEAN PLANETS

१६. षोडशोऽध्यायः

सौरसिद्धान्तः — ग्रहमध्यमानयनम्

Introductory Chapter XVI of the Pañcasiddhāntikā deals with the computation of the mean star-planets, Mars etc., according to the Saura Siddhānta, and chapter XVII of their true motions, with their heliacal risings and latitudes. The mean planets are made true by employing the method of epicycles, as in the case of the Sun and the Moon, in chapters XI and X. Of the five siddhāntas condensed by Varāhamihira the Saura alone uses epicycles, and there is no evidence of its use in any other. So, in the originals also, only the Saura must have used epicycles, since VM follows the originals as far as necessary. Thus the Saura is the most mature, and may be considered to begin the highest developed stage of Hindu astronomy, represented by the Āryabhaṭīya, the Brāhma-sphuṭa-siddhānta, the Later Sūrya Siddhānta etc. Though VM's Saura, being a karaṇa, does not use yuga-cycles for the planets, the original must have had them and they can be reconstructed from the epoch-constants given, as we have done in the case of the Sun, Moon, Moon's apogee and nodes. These can be seen to agree with the corres- ponding parameters of the Pauliśa quoted by Bhaṭṭotpala in his commentary on the Bṛhatsaṁhitā, and with the Ārdharātrika-pakṣa of Āryabhaṭa, a work now lost, but reconstructible from its descrip- tion given in the Mahābhāskarīya, chapt. VII, 21-35, and from the Khaṇḍakhādyaka of Brahmagupta, which latter expressly follows the Ārdharātrika-pakṣa. Not only the yuga-cycles, but also the yuga days, and epicycles and apogee positions and nodes agree in these. Strangely enough, the 'New' Sūrya Siddhānta does not agree with the 'Old' in many things. In the matter of computing the latitudes of the star-planets, the Saura gives the same method as the Ārdharātrika-pakṣa combining two types of latitudes, but the Khaṇḍakhādyaka follows the Āryabhaṭīya itself exactly as propounded in the Mahābhāskarīya, VI. 52-55. As for agreement of VM's Saura with the other siddhāntas of the period, a perusal of the table given under XVII. 11 will show this. But it must be noted that the agreement in mere number of cycles is not real agreement, because, the yuga days being different, there will be difference in the calculated mean values. But at the period we are considering, viz. c. 500 A.D., the mean positions fairly agree with one another, and also with what would be got by modern astronomy, showing thereby the accuracy of their observations. For example, for PS's epoch, all except the later Sūrya Siddhānta give nearly 236° for Rāhu, including the moderns. This is seen only in the Rāhu of the Later Sūrya Siddhānta. (Evidently, there is error of reading here. In I.33 of the Later Sur. Sid., the original should have been vasvaśviyamāśviśikhidasrakāḥ instead of vasvagni etc. This mis-reading must have occurred before the commentator Raṅganātha, for he gives aṣṭarāmākṛtirāmadvimitāḥ. If what I suggest is correct, 3° will be added to the 232° 29' got according to the wrong reading making Rāhu = 235° 29', giving fair agreement). There is agreement in the degrees for heliacal rising and setting and the method of computing the star-planets between the Saura of the PS and the Later Sūrya Siddhānta, though the epicycles differ in many ways.

XVI. 1 XVI. SAURA : MEAN PLANETS 293 Another important matter should be mentioned. In XVI. 10-11, and XVII. 10-11a, VM gives corrections, which are his own, to secure agreement with observation to make the Saura fit for correct almanac-making, which naturally will be demanded by the literate. Thus, in XVI.10-11, certain bījas are given to correct the means of Mars, Jupiter and Saturn and the śīghra of Mercury and Venus. The corrections amount, in terms of yuga-cycles, to: Mars, + 57; Mercury, + 400; Jupiter, – 33¹/₂; Venus, – 150; and Saturn, + 25. These corrections are similar and approximately equal to the famous Vāgbhāvona correction on the Āryabhaṭīya, propounded by his successors in his school, to correct his cycles to agree with their observation. I do not suggest that VM was aware of the Vāgbhāva correction in that form, but the tendency to correct the earlier results with bījas based on observations is found everywhere, whether north or south, a healthy sign of the growth of the science. One might refer also to XVII.10-11a, where VM attempts to correct Mercury and Venus to secure agreement with observation. Another thing is to be noted. In (1) the Āryabhaṭīya, in (2) the Ārdharātrika-pakṣa (which means ipso facto the Khaṇḍakhādyaka), VM's Saura and Bhaṭṭotpala-quoted Paulisa, and in (3) the Later Sūryasiddhānta, the yuga cycles are such that the mean planets are all zero at the beginning of Kali, the Moon's apogee is 90°, and the Moon's node 180°. Now the Āryabhaṭīya had equal yuga-pādas, Kṛta, Tretā, Dvāpara and Kali, i.e., they are equal in length. The other siddhāntas have unequal yuga divisions, Kṛta being 4 parts, Tretā 3 parts, Dvāpara 2 parts and Kali 1 part. If the other siddhāntas also postulate, like the Āryabhaṭīya, that the planets were created and began to move from the beginning of the Kalpa from a zero position, then the cycles should be divisible by 20. But they are not so divisible in all. This necessity is avoided by postulating a time later than the beginning of the Kalpa called 'the time of creation of planets' by the Later Sūrya-Siddhānta, as started in the verse, graharkṣadevadaityādi sṛjato'sya carācaram kṛtābdhivedā divyābdāḥ śataghnā vedhaso gatāḥ || I.24 || and by having both the number of cycles and yuga-cycles divisible by four. In the case of the Moon's apogee, the cycles should be odd, and in the case of Rāhu the cycles should be even, but not divisible by 4. These necessary conditions are indeed found in the Later Sūrya Siddhānta and its kind. Thus, if there is any observed difference in the mean planets, Moon's apogee and nodes, they must be due to the 3600 years elapsed after Kali, for the period *c.*499 A.D. But the observed differences should be only small, and due to error of observation. The cycles must have been, and have been, constructed with an eye to this also. In fact, the number of cycles have been determined by observa- tion, and by using the Diophantine equation (kuṭṭaka). The difference of just 300 days in the length of the yuga, (it does not matter much if it is 328 days, as in the Later Sūrya Siddhānta) to secure equal- ity at *c.*499 A.D., between the Ārdharātrika-pakṣa and the Āryabhaṭīya, which is called, for the sake of distinction, the Audayika-pakṣa, meaning the type beginning the day from mean sunrise at Ujjain, provided the number of cycles are the same. (See tables under XVII.11). There is a difference of just a quarter of a day accumulated from zero Kali to *c.*499 A.D. and the difference is made zero at this point of time. [ताराग्रहाणां मध्यमानयनम्] एष निशार्धेऽवन्त्यां ताराग्रहनि(र्णयोऽ)र्कसिद्धान्ते । तत्रेन्दुपूत्रशुकौ तुल्यगतौ म(ध्य)मार्केण ॥ १ ॥

294 PAÑCASIDDHĀNTIKĀ XVI.11 Mean positions of the star-planets

1. The following is the determined position of the star-planets at midnight at Ujjain according to the Saura Siddhānta. For their computation, the mean Sun should be taken as the mean Mercury and Venus. Note: I follow TS's emendations. Example: Find the mean Venus at 1,20,553 days after Epoch for the star-planets, viz. 427 śaka elapsed midnight at Ujjain. This is the mean Sun at 1,20,553.5 days from midday of the Saura epoch, (vide expl. under IX. 1). Therefore the mean Venus = the mean Sun = 1,20,553.5 × 800 - 442) ÷ 2,92,207 = 17° 18′ 27″. जीवस्य 'शता'भ्यस्तं 'द्वित्रियमाग्नित्रिसागरै' (र्वि) भजेत् । द्युगणं कुजस्य चन्द्राऽऽहतं तु 'सप्ताष्टषड्' भक्तम् ॥ २ ॥ सौरस्य 'सहस्र' गुणा (द्) 'ऋतुरस (श्) न्यर्तुषट्कमुनिखैकैः' ॥ यल्लब्धं ते भगणाः शेषा म(ध्य) ग्रहाः क्रमेणैव ॥ ३ ॥ दश दश भगणे भगणे संशोध्यास्तत्पराः सुरेज्यस्य | 'मनवः' कुजस्य देयाः शनेश्च 'बाणा' विशोध्या (स्तु) ॥ ४ ॥ राशिचतुष्टयमंशद्वयं कलाविंशतिर्वसु'समेताः | 'नववेदा'श्च विलिप्ताः शनेर्ध(नं) मध्य (मस्यै) व ॥ ५ ॥ अष्टौ भा (गा) लि(प्ता) '(ऋत)वः' 'ख(पक्षौ)' गुरौ विलिप्ताश्च | क्षेपः कुजस्य '(य)मतिथि-पञ्चत्रिंश'च्च राश्याद्याः ॥ ६ ॥ शतगुणिते बुधशीघ्रं 'स्वरनवसप्ताष्ट'भाजिते क्रमशः | अत्रार्धपञ्चमास्तत्पराश्च भगणाह(ताः) क्षेपः ॥ ७ ॥ सितशीघ्रं दशगुणिते द्युगुणे भक्ते 'स्वरार्णवाश्विव्यमैः' | अर्धैकादश देया विलिप्तिका भगणसंगुणिताः ॥ ८ ॥ सिंहस्य 'वसुयमां'शाः 'स्व(रेन्दु)वो' लिप्तिका ज्ञशीघ्रधनम् | शो [ध्याः] सितस्य विकलाः 'शशिरसनवप [क्ष] गुणदहनाः' ॥ ९ ॥ [वराहमिहिरकृतः शोधः ] क्षेप्याः 'स्वरेन्दु'विकलाः प्रतिव (र्षं) मध्यमक्षिति (जे) | दश दश गुरोर्विशोध्याः शनैश्चरे सार्धसप्तयुताः ॥ १० ॥ 'पञ्चा (ब्ध) यो' विशोध्याः सिते बुधे 'खाश्विचन्द्र'युताः | 'खखवेदेन्दु' विकलिकाः शोध्याः [स्युः ] सुरपूजितस्य मध्याः स्युः ॥ ११ ॥

XVI.11 XVI. SAURA : MEAN PLANETS 295

2-9 To get mean Jupiter, multiply the days from epoch by 100, and divide by 4,33,232. Revolutions etc. are got. Deduct 10‴ per revolution. Add 8ʳ 6° 20″, the mean at epoch (This is called kṣepa.) (A bīja correction is given by VM, to this, for which see verses 10-11, below.) To get Mean Mars, divide the days by 687. Revolutions etc. are got. Add 14‴ per revolution. Add 2ʳ 15° 35′ 0″, the mean at epoch. (See verses 10-11, below, for bīja correction.) To get mean Saturn, multiply the days by 1000 and divide by 1,07,66,066. Revolutions etc. are got. Deduct 5‴ per revolution. Add 4ʳ 2° 28′ 49″, the mean at epoch. (See verses 10-11, below, for bīja correction). To get the Śīghra of Mercury, multiply the days by 100 and divide by 8797. Revolutions etc. are got. Add 4½‴ per revolution. Add 4ʳ 28° 17′ 0″, the Śīghra at epoch. (See verses 10-11, below, for bīja correction.) To get the Śīghra of Venus, multiply the days by 10 and divide by 2247. Revolu- tions etc. are got. Add 10½″ per revolution. Add 8ʳ 27° 30′ 39″, the śīghra at epoch. (See verses, 10-11, below, for bīja correction).

[Apparatus Criticus — Column 1]

1a A. ॰र्धेवत्पां; B. धैवत्यां b. A. निर्णेर्किसिधांते; B. गणकसिद्धान्ते c. A. महमार्केण; B. मध्यमाकेसा 2a. B. जिवस्य B2. शताभ्यासं b. A1.C. ॰यमाग्निचिसागरैर्विभजेत्; B. ॰विभजेन d. A1. हतं A1. ॰ष्ट्र्द्धक्तं 3a. B. repeats words from previous verse: सौम्यस्य सप्ताभ्यस्तं द्वित्रियमाग्निसामरैः सहस्रगुणा a-b. D. गुणमृत् b. A. दतुरससून्युर्तु; B. रुतु॰ B. खैकः d. B1.2.D. शेषा मध्या 4a. B1.3. दशांश भगणे and one भगणे om by haplography b. B. ॰ध्यास्तसराः c. B. नमवः कुकुक्षु देया d. B1.3. शनैश्च B3. विशोध्य A. ॰ख्रु; B. स्युः 5a. B. ॰मंशं b. B3. ॰शतिवसु C.D. समेता c. B. ॰वेदाक्षलिप्ताः d. A. ॰धनेर्मध्यमास्येव; B. शने मध्यमस्त्वेयम् 6a. A. भामा लिप्त; B. मागाः लिप्त b. A.C.D. र्तवः; B. तवः; A. खमक्षोगरौ (A2. ॰क्षौ॰); B. तवः शेषसौ गरु विः

[Apparatus Criticus — Column 2]

C. खमक्षो गुरौ; D. खपछो गुरोः c. B. क्षेवः A. जमतिथि; B. यमतितिथि d. B. त्रिशद्य 7a. B. गुणितं c. B. ॰र्धपंचमौस्त॰ (B3. ॰स्तस. d. A. हतः; B. हतक्षिपा; C.D. क्षेप्याः 8a. B. गुणीते b. A. ॰वाश्वियमैः c. A1. अर्कैका॰; A2. 'अर्कैका d. A. विलिप्ता 9a. A. सिंहस्य; B. सिंहेस्य b. A. खरेन्वो; B. खरे देवो विलिप्तिका c. A. शोसितस्य; B3. शोषितस्य B. विकला d. A.B. पक्षा गुणा दहनाः (A. ताः) 10a. A.B. क्षेप्या B. विकला b. A.B. वर्षमाध्यम A.B. क्षितिजो 11a. A.B 1.2 पञ्चद्वयो; B3. ॰द्वयोः b. A.B. ॰स्ताश्वि B. चन्द्रयुक्ताः c. A.B. विकालिकाः d. A.B.C.D. om स्युः B. सुर —— प्जतिस्य (B3. पू). A.B.C.D. मध्यात् In D. ch. XVII of the Mss. and of C is continued as part of ch. XVII. with verse numbers duly altered.

296 PAÑCASIDDHĀNTIKĀ XVI. 11 Note 1. I follow TS's emendations, except in verse 6, where I have read khamakṣau as khapakṣau instead of their khamakṣo, makṣo being meaningless. But their meaning, 20, is all right. In 7, the word kṣepa can stand, and need not be emended as done by them. Note 2. The word madhya with reference to Mars, Jupiter and Saturn is mean planet in modern parlance, and śīghra with reference to Mercury and Venus, is mean planet according to modern terminology. Note 3. How to get the days from epoch has already been explained, and it should only to be brought to the mid-night following to be used here. Example 1. Find the mean Mars at 1,20,553 days from the midnight following the Romaka epoch, which is the epoch given for star-planets. 1,20,553 ÷ 687 = 175 revolutions and = 5ʳ 21° 52' 40" The revolution correction = 175 × 14" = + 41" Kṣepa or mean at epoch = 2ʳ 15° 35' 0"

Mean Mars at required date = 8ʳ 7° 28' 21" Example 2. Find the Śīghra Venus at 1,20,553 days for epoch. 1,20,553 × 10 ÷ 2247 = 536 revolutions and 6ʳ 2° 19' 23" Revolution Correction: 536 × 10½" = + 1° 33' 48" Śīghra at epoch = 8ʳ 27° 30' 39"

Śīghra of Venus at 1,20,553 days = 3ʳ 1° 23' 50" Note 4. The rules give to find the mean planets etc. depend on the fact that there are approxi- mately 100 revolutions of Jupiter in 4,33,232 days, one revolution of Mars in 687 days, 1000 revolutions of Saturn in 1,07,66,066 days, 100 śīghra (truly mean) revolutions of Mercury in 8,797 days and 10 of Venus in 2247 days. The revolution corrections make these exact. The epoch constants are the means at epoch. Note 5. From the rules given we can reconstruct the yuga cycles of the original Saura-siddhānta of which the Saura of the PS is a Karaṇa, and from these the epoch constants. These we shall do now. The yuga days of the original Saura are 1,57,79,17,800, as computed from the short Saura yuga given in I.14, from which it can be computed that in 1,80,000 years there are 6,57,46,575 days, since the yuga is 43,20,000 years, being 24 times the short yuga. We might now verify by calculation, the yuga revolutions (yuga-paryaya) and epoch constants (kṣepa) of the several planets. Jupiter: Yuga revolutions 1,57,79,17,800 × 100 ÷ 4,33,232 = 3,64,220, rev. 0ʳ 17° 25' 1" Revolution correction = 3,64,220 × 10''' = – 16° 51' 43"

∴ The number of rev. etc. in the yuga = 3,64,220 rev., 0ʳ 0° 31' 18"