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

242 PAÑCASIDDHĀNTIKĀ XII.2 The period after which the Sun, Moon, and the planets all meet again at the first point of the zodiac is commonly called the yuga, meaning "the period of union." Here this is meant for the Sun and Moon alone, and this Siddhānta takes it to be five years, approximately, with a view to convenience. In the same way, the statements that there is an intercalary month after every thirty months, and an omitted day for every 62 lunar days, are approximate, and rounded off for convenience. The first tithi of the light fortnight of Māgha begins the yuga, and the year and the day begins with sun- rise. The author has not mentioned the number of intercalary months or days in the yuga, nor has he given how to get the 'days from epoch', expecting the readers to be experienced enough, by now, to know it for themselves. He has indicated it in I.16, and we have explained it under I.14-17. The only thing that is necessary is to know the years of the beginnings of the yuga, and this has been given here as two years after the śaka epoch, and every five years thereafter. We shall first compute the number of the intercalary months etc in the Yuga. The number of years in the yuga is 5, given. The solar months are 5 × 12 = 60. The intercalary months are, 60/30 = 2. The lunar or synodic months are, 60 + 2 = 62. The lunar days or tithis are 62 × 30 = 1860. The omitted lunar days are, 1860 ÷ 62 = 30. The (civil) days are, 1860 - 30 = 1830. The Moon's revolutions are, the Sun's revolutions + the synodic months = 5 + 62 = 67. The Vyatīpātas are, solar revolutions + lunar revolutions = 5 + 67 = 72. The number of days in the solar year is, 1830 ÷ 5 = 366. The days per ayana are 366 ÷ 2 = 183. This is enough for our purpose. To get the 'days':- (i) (Elapsed śaka years — 2) ÷ 5. Take the remainder alone. (ii) The solar months gone = (i) × 12 + elapsed months from Māgha. (iii) The intercalary months = (ii) ÷ 30. Take the quotient alone. (iv) The lunar months gone = (ii) + (iii). (v) The lunar days gone = (iv) × 30 + tithis gone in current month. (vi) Omitted days = (v) ÷ 62. Take the quotient alone. (vii) The days from epoch are, (v) - (vi). The tithis gone, used in (v) are actual elapsed tithis, and not those increased by one (according to verse 4. of this chapter,) for calendrical purposes. If the latter is used, subtract the calendrical elapsed tithi from the remainder got in (vi). If this is greater than 46, lessen the days from epoch by one to get the correct days. The reason for this will be explained while dealing with verse 4, following. Further, since there can be no fraction of intercalary month or avama at the beginning of a yuga carried over from a previous yuga, there is no kṣepa for these, in the computation rules. As for the explanation of these rules it has already been given in chap. I, when dealing with the rules for days from epoch according to the Romaka. The names of the five years, (not given in the text,) are: Saṁvatsara, Parivatsara, Idāvatsara, Anuvatsara, and Idvatsara. In certain Vedic śākhās, there is a slight variation in some names. As for the reading of the text, we have corrected dyūnam, into dvyūnam, since the former is meaningless in the context.

XII.3 XII. PAITĀMAHA SIDDHĀNTA 243 Example 1. Compute the ‘days from epoch’ according in the Paitāmaha, for the sunrise of calendrical date eleventh of the light fortnight of Kārttika, in the elapsed Śaka year 426. (i) (426 − 2) ÷ 5 = 424 ÷ 5. Here the remainder is 4, the years gone, in the current yuga. The fifth, Idvatsara is current. (ii) Counting from Māgha, 9 months have elapsed before (Kārttika), in the current year. ∴ the solar months gone = 4 × 12 + 9 = 57. (iii) Intercalary months = 57/30, = 1 27/30 (quotient = 1) (iv) Lunar months gone = 57 + 1 = 58. (v) The calendrical tithis gone in the month are 10. ∴ the total tithis gone = 58 × 30 + 10 = 1750. (vi) Omitted tithis = 1750 ÷ 62 = 28 14/62. (The quotient, 28 are the omitted tithis). Since the remainder, 14, minus 10, leaves 4, which is not greater than 46, the calendrical tithi itself is the tithi. (vii) Days from epoch = 1750 − 28 = 1722. [तिथिनक्षत्रादिः] सैक (त्वं) शे द्युगुणे तिथिर्भमार्कं नवाहते 'ऽक्ष्यर्कैः' । ‘दिग्रस’भागैः सप्तभिरूनं शशिभं धनिष्ठाद्यम् ॥ ३ ॥ Tithi, Nakṣatra etc. 3. Add to the ‘days’ a sixty-first part of itself. The total tithis are got, (which, divided out by thirty, leaves the tithis in the month). Multiply the ‘days’ by 9, and divide by 122. The total nakṣatras are got, (which, divided out by 27, gives its actual nakṣatra, reckoned from Śraviṣṭhā). Multiply the ‘days’ by 7 and divide by 610. Subtract this from the ‘days’. The remainder are the total nakṣatras of the Moon, (which, divided out by 27 and the remainder counted from Śraviṣṭhā, is the Moon's nakṣatra). The following is to be done:– (i) Tithi = ‘days’ + ‘days’ ÷ 61. (This, divided out by 30, and the remainder counted from śukla-pratipad, is the tithi proper). (ii) Sun’s nakṣatra = ‘days’ × 9 ÷ 122. (This, divided out by 27 and the remainder counted from Śraviṣṭhā, is the Sun’s nakṣatra). (iii) Moon’s nakṣatra = ‘days’ − ‘days’ × 7 ÷ 610. (This, divided out by 27 and the remainder counted from Śraviṣṭhā, is the Moon’s nakṣatra). Example 2. For the date of Ex. 1, find the tithi etc. The ‘days’ got there are 1722. (i) Tithi = 1722 + 1722 ÷ 61 = 1722 + 28 14/61 = 1750 14/61. Divided out by 30, the remainder is 10 14/61. ∴ the 10th Tithi of the light fortnight is gone, and 14/61 of Ekādaśī has gone at sunrise. 3. Quoted by Utpala on BS 8.22. 3a. A.B. सैकत्र्यंशत्वं (B.न्वं) चेद्युगणे; C. सैकषष्ट्यंशे द्युगुणे; D. सैकषडंशे द्युगणे; U. सैकत्रिशे b. A.B. भमार्कनचा (B. वा) हस्तेऽर्कैः (B. हस्तेष्टकैः); U. ॰नवाहतो॰ c. A.B. दिग्रह; D. भक्तैः d. A. नूनं A. धनिष्ठाद्यं; B2. धनीष्ठाधं

244 PAÑCASIDDHĀNTIKĀ XII.4 (ii) Sun’s nakṣatra = 1722 × 9 ÷ 122 = 127 4/122. Dividing out by 27, the remainder is 194/122. Counting from Dhaniṣṭhā, Citrā is gone, and the Sun is at 4/122 of Svāti. (iii) Moon’s nakṣatra = 1722 - 1722 × 7 ÷ 610 = 1722 - 19464/610 = 1702 146/610. Divided out by 27, the remainder is 1 146/610. Śraviṣṭhā is gone, and the Moon is at 146/610 of Śatabhiṣaj. It is to be noted, that two of these being known, the third can be counted from them. The following is the explanation of the rules: Under verses 1–2, the number of days in the yuga etc. have been got. Using them, the total tithis are got by the proportion, 1830: ‘days’ :: 1860: Tithis. ∴ Tithis = 1860 × ‘days’ ÷ 1830 = ‘days’ × 62 ÷ 61 = ‘days’ (1 + 1/61) = ‘days’ + ‘days’ ÷ 61. Next, since there are five solar years in the yuga, there are 5 × 27 = 135 solar nakṣatras. We have the proportion, 1830: ‘days’ :: 135: total Sun’s nakṣatra. ∴ Sun’s nakṣatra = 135 × ‘days’ ÷ 1830 =‘days’ × 9 ÷ 122. Next, since there are 67 revolutions of the Moon in the yuga, there are 67 × 27 = 1809 nakṣatras. So, we have the proportion, 1830: ‘days’ :: 1809: Moon’s nakṣatras. ∴ Total Moon’s nakṣatras. = 1809 × ‘days’ ÷ 1830 = ‘days’ × 603 ÷ 610 = days (1 - 7/610) = ‘days’ - ‘days’ × 7 ÷ 610. While the mss. readings tryaṁśatvaṁce etc. are corrupt, Bhaṭṭotpala’s reading saikatrīṁśe itself is wrong, since it contradicts facts, and we have emended it into saikartvaṁśe. TS have corrected is as saikaṣaṣṭyaṁśe gaṇe which is not proper since the correction does not follow the letters of the text. NP emends it as saikaṣaḍaṁśe for the number 61 that is required, but generally the said number is not found to be formed thus. [तिथि: व्यतिपातश्च] प्रागर्धे पर्व यदा तदो(त्त)राऽतोऽन्यथा तिथि: पूर्वा । ‘अर्क’घ्ने (व्यति)पाता द्युगणे ‘पञ्चाम्बरहुताशै’: ॥४ ॥ Vyatīpāta 4. If the moment of full or new moon falls before noon, the second of the two tithis connected with the day is the (civil) tithi for the day, otherwise the first. Multiply the ‘days’ by 12 and divide by 305. The Vyatīpātas are got. The tithi of this Siddhānta is mean tithi. Since this is less than the day, each day has parts of two tithis connected with it, and we have to fix one of them as the date of the particular day. It is this that is done by the first half of the stanza, it seems. If others like the Śrāddha-tithi are meant to be fixed here, they would be mentioned by name. The mere word tithi without an attribute must mean only the date. Agreeing that the date is meant to be fixed here, is it the date of the full or new Moon alone that is fixed here, or that of any day? From the word parva used, one may think it is only the former that is sought to be fixed. But this cannot be, since fixing the date of one particular day among so many is practically useless. If it is argued that the fixing of the day as parva or pratipad is useful to 4b. A. तदोत्तस्तोन्त्यथा; B1.3. तदा तए सोन्यथा; B2. तदा तएं तोन्यथा c. AB. व्यापिपाता; D. व्यतिपातो d. A. द्यगणे A. पंचावरहु..ाशैः; B. पञ्चाम्बरं हूताशैः (B2. दूतां शैः)

XII.4 XII. PAITĀMAHA SIDDHĀNTA 245 determine whether the anvādhāna or the iṣṭi is to be performed on that day, then the general term, tithi, need not have been used, and it would have been easier to mention the thing. Further this is a matter for the Dharmaśāstras to deal with, not for an astronomical work. Therefore, by fixing the date of the parva, the author means to fix all the subsequent dates following, upto the next parva, and make them convenient for civil use. If the dates are consecutive, one for each day, it will be con- venient for civil reckoning. If there is a jump, omitting one date in the middle (tithikṣaya), it is plainly inconvenient. The instruction in the verse secures that the dates follow without omission in the middle of the fortnight. For, if the moment of full or new moon is after noon, there will be no omitted tithi in the fortnight following, and the corresponding dates will follow one after another each day, beginning from prathamā, next day. But, if the moment of full or new moon is before noon, then there will be an omitted tithi in the fortnight following, since the remainder in getting the omitted days will be greater than 46, increasing by one each day. Therefore, if now the day of full or new moon itself is reckoned as the first date of the fortnight, then the reckoning can be continued to the end of the fortnight without omission. It is bearing in mind this idea implied by the text, that we made a distinction between the astronomical and the civil date, in giving the computation of the 'days from epoch'. The Siddhānta is only repeating here the idea of the Vedāṅga Jyotiṣa in: dyu heyaṃ parva cet pāde pādas triṃśattu saikikā | the term pāde (meaning 'quarter day') corresponding to the term ardhe in our text. The thirty-one parts mentioned form the measure of the pāda, in units of 1/124 parts of a day. We have explained the vyatīpāta in detail, in our commentary on III.20. We must remember here two things that we said there: (1) Vyatīpāta occurs when the Sun and the Moon have the same declination, (both north or both south), and when one is moving northward while the other is moving southward. (2) If the Sun, Moon, and declination are all mean, as here, and if the first point is at the solstice, as here, mid-vyatīpāta-yoga must fall when the Sun + Moon equals 12 rāśis. In the yuga, (of 1830 days) there are 5 + 67 = 72 such yogas, i.e., vyatīpātas. Therefore, for given 'days', there are, 72 × 'days' ÷ 1830 = 12 × 'days' ÷ 305, vyatīpātas, as given here. The quotient obtained are the vyatīpātas gone. But this knowledge is practically useless, and we must take it that the Siddhānta intends here to give when the vyatīpāta occurs, a time extremely propitious for gifts, japa, homa, etc. This can be found easily from the remainder. Divide this by 12. The result is days etc. gone from the last vyatīpāta. Subtracting the remainder from 305 and dividing by 12, we get the days to the middle of the next vyatīpāta. If the remainder is zero or nearly so, it is clear that the vyatīpāta is on. Example 3(a). Given the 'days' 1697, what is the tithi for that day, and the subsequent days, upto the end of the fortnight? The tithis gone = 1697 + 1697 ÷ 61 = 1697 + 27 50/61 = 1724 50/61. Dividing out by 30, the remainder is 14 50/61, i.e. 50/61 part of pūrṇimā has gone, and 11/61 part remains. Since the tithi is equal to 61/62 day, 11/61 tithi equals, 11/61 × 61/62 = 11/62 day. The full Moon ends at 11/62 day, i.e. before noon. Therefore that day itself is Prathamā, (not Pūrṇimā). (The same conclusion follows from the remainder of the omitted day, 51, in this case, (minus zero, for the civil day gone,) being greater than 46. After this, for ten days, the tithis are from the second to the eleventh, for civil purposes, though at sunrise the tithis are from the first to the tenth, the eleventh being the omitted tithi. On the next day the tithi at sunrise is the twelfth, as also the civil tithi, and so on.

246 PAÑCASIDDHĀNTIKĀ XII.5 Example 3(b). Given the 'days' 1722, find when the vyatīpāta falls. 1722 × 12 ÷ 305 = 67 229/305, i.e. 67 vyatīpātas have gone, from the beginning of the yuga. The remainder is 229. Dividing by 12, we get 19-5, days etc. gone from last vyatīpāta. Subtracting from 305, and dividing by 12, we get days etc. 6-20, to go for the middle of the next vyatīpāta, i.e, it will be falling at 20 nāḍīs on Kārttika Kṛṣṇa-dvitīyā. The correction of the reading here is easy to understand. Of TS, the latter says some farfetched thing as the meaning of the first part of this verse, which seems meaningless to me, and the former without saying anything himself, refers us to the Sanskrit commentary, evidently not understanding it himself. In explaining the Vyatīpāta, their use of the one forming the seventeenth of the series Viṣkambha etc., can serve no purpose in the present case. The same confusion is seen also in NP (see Pt II.p.82). We have already shown that the series itself did not exist at the period of Varāhamihira. [अहर्मानम्] (गतमयनादुत्तरतो) (द्यूनां) (गन्तव्य)मपि च याम्यस्य । (द्विघ्नं) 'शशिरस'भक्तं द्वादश(सहितं) दिवसमानम् ॥ ५ ॥ Duration of a day 5. Take the days gone in the Uttarāyaṇa, i.e. the northward course of the Sun, and the days to go in the Dakṣiṇāyana, i.e. the southward course. Multiply by two, divide by 61, and add 12. The duration of the day time (in muhūrtas) is got. Though the text is very corrupt here, since we know that the duration of daytime is given here, and that as mentioned in the Vedāṅga Jyotiṣa, many words occurring in that work being recognisable here, we have succeeded in reconstructing the verse using the letters found in the text, though not to our entire satisfaction. But there is no doubt about the idea intended to be conveyed, viz. that of VJ (verse 22 of the Ṛgveda version and verse 40 of the Yajurveda version). But TS and NP, in order to retain the expression dvādaśāhinam, read into the text many impossible things and make several emendations not caring even for the metre. The rule given is thus explained: According to this Siddhānta the shortest day is 12 muhūrtas, at the end of the southward course and the beginning of the northward at Winter solstice, and the longest is 18 muhūrtas at the end of the northward course and the beginning of the southward, at Summer solstice. Each course has 183 days, and the increase or decrease of daytime is considered uniform. Therefore, since there is an increase of 6 muhūrtas from 12 in the 183 days of the north- ward course, the increase for a desired number of days (counted from the beginning) is: days gone × 6 ÷ 183 = days gone × 2 ÷ 61. So, the duration is 12 + days gone × 2 ÷ 61. Taking the south- ward course, it is 12 muhūrtas at the end, proportionately greater, the earlier is the day, the increase being 6 in 183 days, at the beginning of the course. Therefore, during the southward course, the duration is 12 + the days to go in the course × 2 ÷ 61. It is to be noted that the author has not said 5a. A.B. धृतिरनयाद्युत्तरयो (B1.3. ॰त्तरयो); C. खमितमेष्य दिनमपि याम्यायनस्य C. द्व्यग्निगोष्ट्ररतः; D. [सत्रि] धृति [च] रणध्यु [मु] त्तरगे D. त्वगतद्युमपि च याम्यस्थे b. A. खमृणं तद्यमपि च याम्यस्य; c. A. द्विग्नं; B. द्विग्रं B. भक्तं B. सू (B3. ख) मृणं गतद्यमपि च याम्यास्य; d. A.B.C.D. द्वादशहीनं

XII.5 XII. PAITĀMAHA SIDDHĀNTA 247 when the northward course begins, and when the southward one. (Perhaps he has said that in this verse, and the corruption of the text has masked it.) When the Sun enters Śraviṣṭhā its northward course begins, and when it is at the middle of Āśleṣā, its southward course begins, or the first half of the year is the northward course, and the second half, the southward one. It can also be inferred from the rule for vyatīpāta. Example 4. Given the 'days' 1722, find the daytime for the day following. 1722 ÷ 366 = 4 258/366. Four years have gone, and 258 days in the fifth. The 183 days of the northward course have gone, and 75 days have elapsed in the southward course. The days to go = 183 − 75 = 108. The duration of daytime in muhūrtas = 12 + 108 × 2 ÷ 61 = 12 + 3 33/61 = 15 33/61. To conclude, it has been said in the introduction to this chapter that the Sun, Moon etc. of this Siddhānta are only mean, not true. Some think it is even worse than this, which we must investigate now. We have seen that, according to this Siddhānta, there are 366 days in the year, 5 years or 1830 days constitute the yuga, and there are 62 synodic months in it. But actually there are about 365 ¹/⁴ days in the year, and also 62 synodic months take 1830.8965 days. Therefore, instead of being at the zero point of Śraviṣṭhā at the beginning of each yuga, the Sun will be advancing by about three degrees per yuga. The synodic month being not completed, it will be really only Caturdaśī then, and at the end of every yuga, the tithi will be preceding by about one per yuga. This is common to both this Siddhānta and the Vedāṅga Jyotiṣa. But accumulation of this error is prevented by tying the Yuga to the correct Śaka year, by the instruction to use the Śaka year for finding the year of the yuga. (This is of the same nature as tying the lunar year to the solar.) It may be said, in passing, that at the period when the VJ was followed, actual observation was used to find out when a correction was wanted and the same made by simply omitting an intercalation, for which, it is possible, they could even have discovered a formula in the long run. We have made this clear in our Notes to the VJ, (Indian National Sc. Ae., New Delhi, 1985) and the during the Seminar on Indian Calendar held by the Institute of Traditional Cultures, University of Madras. (Bulletin of the Institute of Traditional Cultures, Madras, 1968, Part I, page 60.) When thus the accumulation of error is taken care of, giving 366 days to the year is extremely convenient for civil, calendrical, and even religious purposes, since it makes calculations easy in the same way as we, even now, take the year to have 365 days, and the months 31 etc. days. We get 183 days for each ayana, 122 days for each cātarmāsya, and 61 days for each ṛtu, all in whole numbers. There are 61 sāvana months in the yuga. Even the saura month has 30 days and a half, a fraction easy to work with. Further, the fortnight or pakṣa was the unit used then in the place of the modern week. We have shown, in our Notes on verses 2 and 4 above, how it was secured that the dates follow consecutively in the pakṣa, a factor so essential for a civil calendar. The approximateness of the tithis etc. being mean, is of course there, but this is only an advantage in civil reckoning. As for religious purposes, the true tithis etc. required for rites like darśa-pūrṇa-māsa were guessed from earlier observations, as we have said, and there are several indications in the Vedas that such was the case. The abhyudayeṣṭi, enjoined to be performed if the Moon is observable in the east between the anvādhāna on the previous day and the iṣṭi on the next day, is one such indication, for, if the visibility had been properly calculated from the true Sun and Moon, using dṛkkarma etc. there would be no need for abhyudayeṣṭi at all. [इति पञ्चसिद्धान्तिकायां वराहमिहिरविरचितायां पैतामहसिद्धान्तो नाम द्वादशोऽध्यायः ] Thus ends Chapter Twelve entitled 'Paitāmaha Siddhānta' in the Pañcasiddhāntikā composed by Varāhamihira Col. A.D. इति (A om इति) पैतामहसिद्धान्ते द्वादशोध्यायः B. इति पितामहसिद्धान्ते द्वादशोऽध्यायः C. इति पैतामहसिद्धान्तो नाम द्वादशोऽध्यायः

)? Wait, look at the top: there is an i-matra! Wait, look at the top of that conjunct: there is an i-kar (ि)! Wait, and the consonant: it has 'श्' on the left, and below it/connected to it: Is it 'च'? Yes, 'श्च'! And after it: 'त'? Wait, does it have 'ि' over 'श्च'? Yes, 'श्चि'! And after it: 'त'? With an anusvara or visarga? Wait, look at: "भिश्चिनुतः"? No, look at the glyph: It is: श् + च + ि = श्चि, then त + ः = तः! Wait, that is "भिश्चितः"! Wait, in line 8: "तरुनगनगरारामसरित्समुद्रादिभिश्चितः सर्वः |" WAIT! Look at line 8 again! Is that "भिश्चितः" in the main text?! Let's look at line 8: दि - भि - श्चि - तः ! Wait, where is 'श्रितः'? Look at the footnote 2b: b. B2. ०भिश्रितः ! WAIT! Look at footnote 2b: Is it ०भिश्रितः?! LET'S LOOK AT FOOTNOTE 2b: b. B2. ० then `भिश्र

XIII.6 XIII. SITUATION OF THE EARTH 249 3. Just as the reflection of the objects on the bund of a water course is upside-down, so the Asuras are, (with respect to the Devas). The Asuras too consider the Devas to be upside-down. 4. Just as the flame of the fire, observed by men here, flares upwards, and anything thrown up falls down towards the earth, the same upward flaring of the flame, and the down-ward falling of a heavy object is experienced by the Asuras, (at the anti-podal region). [भूभ्रमणम्] मेरोः सममुपरि वियत्यक्षो व्योमस्थितो ध्रुवो (ऽधोऽ)न्यः । तत्र निबद्धो मरुता प्रवहेन भ्राम्यते भगणः ॥ ५ ॥ भ्रमति भ्रमिस्थितेव क्षितिरित्यपरे वदन्ति नोडुगणः । यद्येवं श्येनाद्याः न खात्पुनः स्वनिलयमुपेयुः ॥ ६ ॥ Rotation of the earth 5. The axis of the earth extends right up and right down to the stellar sphere. The stellar sphere, bound by the axis to the earth, rotates by the wind system called Pravaha. Note: Seven wind systems are spoken of by Hindu astronomers. The uppermost, blowing permanently westward in the region of the planets and stars, is the cause of their westward rotation once a day. 6. Others say that the earth rotates on its axis, like an object placed at the hub of a wheel, and not the stars. If so, birds like the eagle flying up into the sky, cannot reach their nests back. Note. This is what is meant: During the time they are away from the nest, they would have been carried far away by the rotating earth, from the spot of origin of their flight and the birds cannot reach the nest. But they do reach, and so this theory is false. 3a. A.B. तजासंताना (B3. सेताना); C. तटसङ्गताना Utpala on BS 2,pp.56-57, and 6 c-d quoted by b. B1.3. दृशाते Pṛthūdaka on BrSS 21.4. c. A1. तद्वगत्ति; A2. तद्वंक्षति; B. तद्वक्षगति. B. पंन्यन्ते A. Hapl. om. रसुराणां [... मसुराणां] त 5a. B. समुपवियत्पक्षो; U. समोपरि. A. वियत्पक्षो (in verse 4) b. U. व्योम्नि स्थितो A.B. ध्रुवो धन्यः d. B1.2. विबुधानाम् c. A. निबधो A. मतुला; B1.3. महता; B2. मरुता 4a-b. B. शिखाक्षितिमुपैति; D. शिखा [क्षिप्तमपि] क्षिति d. B. द्राहवेन; C.D.U. प्रवहेण c. B. तद्वदिह 6a. A. भ्रम B. स्थिते च; U. स्थितिरिव 5. Quoted by Utpala on BS 2,p.56 b. A. त्पपरे B1. नोद्रुगणः and by Pṛthūdaka on BrSS 21.4: 6-8 quoted by c. B. पद्येवं A. शेनाद्या; B. शेनाधा

250 PAÑCASIDDHĀNTIKĀ XIII.13 अन्यच्च भवेद्भूमरह्रहा भ्रमरंहसा ध्वजादीनाम् । नित्यं पश्चात्रेरणमथाल्पगा स्यात् कथं भ्रमति ॥ ७ ॥ अर्हत्प्रोक्तेऽर्केन्दू द्वौ द्वावेकान्तरौ किल तौ । यद्येवमर्कसूत्रात् किं ध्रुवचिह्नं भ्रमत्यह्ना ॥ ८ ॥ 7. Further, on account of the great speed of the rotation of the earth, banners, flags, etc. will always be flown westwards, (just as the cloth of a man running eastwards in still air, is blown westwards). If, to obviate this objection, a very slow rotation is postulated, how does the rotation (once a day), take place at all (i.e. one rotation cannot be completed in one day). 8. Arhat, (the propounder of the Jain religion) has written that there are two Suns and two Moons, each rising alternately. If so, how does the line join- ing the Sun and the celestial pole goes round exactly once in a day round the pole? Note. This observation shows that the celestial sphere movers once round in a day and carries with it all heavenly bodies. So the same Sun appears each day after one rotation. Therefore, the postulation of a second Sun is purposeless. The same for the Moon. [देवासुराणां स्थितिः] प्रोद्यद्रविरमराणां भ्रमत्यजादौ कुवृत्तः सव्यम् । उपरिष्टाल्लङ्कायां प्रतिलोमञ्चामरारीणाम् ॥ ९ ॥ मिथुनन्ते च कुवृत्तादंशचतुर्विंशतिं विहायोच्चैः । भ्रमति हि रविरमराणां समोपरिष्टात्तदाऽवन्त्याम् ॥ १० ॥ नष्टच्छायाप्येवं छायोदक् तत्प्रभृत्युदक्स्थानाम् । तद्दक्षिणगानां मध्याह्ने दक्षिणा छाया ॥ ११ ॥ मेषवृषमिथुनसंस्थे दिवसोऽर्के कर्कटादिगे रात्रिः । यैरु (क्तो) विबुधानां मेरुस्थानां नमस्तेभ्यः ॥ १२ ॥ येष्वेवोदङ् मेषादिस्थानेषु संनिवृत्तोऽपि । तेष्वेव कथं दृश्यः पुनर्न दृश्यश्च तत्रस्थः ॥ १३ ॥ 7a. A. रहाद्; B. रन्यद् 8a. A. केंन्दु; B. केंन्द्रौ b. A.B. भ्रमणोद्भ्रमा; D. भ्रमरंहस b. A.B.C.D.U. वेकान्तरोदयौ किल तौ (A -तै) c. B. पश्चाध्वेरण c. B. मर्कस्तत्र किं d. B. मथाज्यगा स्यान्कथं d. B. ध्रुवविन्दुह्नां; U. ध्रुवसूत्रं A. भवत्पह्ना; B. भवत्यह्याम्बुह्ना

XIII.13 XIII. SITUATION OF THE EARTH 251 Situation of the Gods and Asuras 9. The Sun, situated at the beginning of the sign Meṣa, moves along the horizon in the clockwise direction, as seen by the Devas, at the North pole. As seen at the equator, it moves upwards (along the prime vertical). For the Asuras at the South pole it moves along the horizon, in the anti-clockwise direction. 10. The Sun at the end of the sign Gemini is seen moving (by the Devas) round at an altitude of 24°. On that day, it is seen crossing the zenith at Ujjain. (Note. VM considers that the maximum declination of the Sun is 24°, and the latitude of Ujjain is 24°, which is only approximately correct.) 11. Thus, on that day, at mid-day, there is no shadow cast by the gnomon at Ujjain. North of Ujjain the mid-day shadow is directed north, and for people south of Ujjain the shadow is directed south. 12. Some say, “when the Sun is situated in the three signs Meṣa, Ṛṣabha and Mithuna, it is day-time for the Devas, but when in the signs Karkaṭaka, Siṃha and Kanyā, it is night-time. I salute them, (and wish to be rid of them since they are quite wrong.) Note. The authors of the Dharmaśāstras, followed by the generality of people, consider that the uttarāyaṇa, i.e. the northward course of the Sun from the beginning of Makara to the end of Mithuna is day-time for Devas. Its southward course from the beginning of Karkaṭa to the end of Dhanus is considered their night-time. It is their ignorance that is referred to here. 13. Moving in the same north latitudes when in Karkaṭa, Siṃha and Kanyā, as when in Mithuna, Ṛṣabha and Meṣa, how can the Sun be seen and not seen by the Devas, so that it is day-time (in the first three months,) and night-time (in the next three months). Note. The mistake of these people lies in thinking that uttarāyaṇa is the day-time of the Devas, and dakṣiṇāyana is night-time. It is only when the Sun is north of the equator while in the 6 signs Meṣa to Kanyā, it can be seen by the Devas, forming their day-time, and in the 6 other signs, it can- not be seen, and it is night-time. 9-13 Quoted by Utpala on BS 2. pp. 57-58, 9 quoted by Pṛthūdaka on BrSS 21.6; 12 quoted by Parameśvara on Abh. Gola 14. 9a. U. प्रोद्यतरवि b. A. भ्रमत्यजागो कृवृत्तगः; B. भ्रमत्यजागो वूभूतूगतः (B3. नृतगः) c. B. ०ष्ठाध्यङ्गायां (B3. ०श्पा०) d. B. चामराराणाम् 10a. B. ०न्ते तेच A.B. कृवृता b. A1. दशचतुर्थिंशतिहायोच्वैः; A2. दंश—र्भि—ति; B. दशचतुर्विंशतिहापोच्चैः; d. A. समोपह्ञातादवांत्यां; B. ०न्तदावल्यम् 11a-b. A. छायोदक् च भृत्युस्थाना; B. छायोदक्य भृत्युदस्थानां c. A. तद्दक्षिणादेनां; C.D. तद्दक्षिणदे [शा] नां B. Hapl. om.: स्थानाम् (11b) [........ स्थानाम्, 12d] नम. Scribe oblivious of the omission and numbers the extant verses consecutively and breaks the lines to suit the metre. 12a. A. मिथुन संस्थे U. संस्थे दिनं खौ कर्क; Pa. दिन मर्के; Pr. कर्कटादिके c. A.C.D. U. यैरुक्ता c-d. Pa. मेरुस्थितदेवतानामिति यैरुक्तं नमस्तेभ्यः | 13a. A.C.D.U. मेवद्यादि; B. येषेवो दङ्-मेषाद्यादि b. A. संनिवृत्तोऽपि (A2. तेपि व तैष्वेव); B. स्थानेषु सन्निवृवृशेपि c. B1.2. तेष्केव B. दृश्य पुनर्नदस्यश्च

232 PAÑCASIDDHĀNTIKĀ X.6 tioned only for the first contact, the two common statements anayā sthitir bhavati and sthityaviśeṣaḥ kṛto yāvat, indicate this. [इष्टकालग्रासः] अर्केन्दुभुक्तिविवरं वाञ्छितनाडीहतं तु षष्टिहृतम् | स्थितिलिप्तास्ताभ्यस्त(त्त)कालेन्दोश्च वि(क्षे)पात् ॥ ५ ॥ कृतियोगपदं शोध्यं शशिराहुकला(प्र)माणयोगदलात् | यच्छेषं तद् ग्रस्तं ज्ञेयं तत्कालमर्केन्द्वोः ॥ ६ ॥ Obscuration at any desired moment 5-6 Take the nāḍīs before or after full or new moon upto the times for which the amount eclipsed is wanted. Multiply this by the difference of the Sun's and Moon's daily motions, (mentioned above), and divide by 60. The 'corres- ponding minutes of arc' are got. Square this, square the Moon's latitude for the moment, add them, and get the square root. Subtract this from the half- sum of the diameters of the eclipsing and the eclipsed bodies. The remainder is the minutes of arc eclipsed, at the moment taken, of the Moon in the case of the lunar eclipse, and of the Sun in the case of the solar eclipse. It is clear that by 'corresponding minutes of arc' is meant here, the distance in minutes between the Moon and the shadow, measured along the ecliptic. From the instruction it is clear that the nāḍīs taken is the interval between full or new moon and the moment for which the amount of eclipse is wanted. It is clear from the context that the Shadow is meant by the word Rāhu. Though from the mention of the Shadow, and the Moon's latitude without any mention of parallax, this seems to be given for the lunar eclipse only, the expression arkendvoḥ at the end shows that this is meant for the solar eclipse also. The author thinks that the reader has acquired sufficient knowledge, by now, to make the necessary changes when applying the rule to the solar eclipse. Therefore, in the case of the solar eclipse, the amount eclipsed is got by using in the rule, the parallax-corrected latitude for latitude, the Sun's and the Moon's angular diameters for those of the Moon and the Shadow, and the parallax-corrected difference of daily motions for the mere difference of daily motions. Thus, the following is instructed to be done: A. To find the amount eclipsed in the case of the Moon (i) "Corresponding minutes of arc" = difference of instantaneous daily motions of Sun and Moon × interval in nāḍīs from full moon ÷ 60. b. B.शशिशङ्ग (B2.B.ब्ज) कलां. A.C.D.कलाद्यमान; 5c. C.तत्स्थितिलिप्ताविवरत्, A.B.ताभ्यस्ता; D.ताभ्यस्तु B.कलाद्यमाण d. A.तान्तकालेन्दोश्च (A2.तात्तत्का). AB.विशेषात् c. A1.यछेपं; A2.यछेषं 6a. B.ततियोग० d. B1.3.मर्केन्दोः

X.6 X. SAURA-SIDDHĀNTA — LUNAR ECLIPSE 233 (ii) Distance in minutes between the centres of the Moon and Shadow = √((i)² + (the Moon’s latitude at the given time)²). (iii) The amount eclipsed in minutes = half-sum of angular diameters of the Moon and Shadow - (ii) B. To find the amount eclipsed in the case of the Sun. (i) “Corresponding minutes of arc” = The minutes obtained as by A (i) × the half duration not corrected for parallax ÷ the half duration corrected for parallax. (This will be a little approximate, but has been given for case of computation, since the two times are known.) (ii) Distance in minutes between the centres of the Sun and the Moon = √((i)² + (Parallax-corrected lat. of time)²). (iii) The amount eclipsed in minutes = half sum of angular diameters of the Sun and the Moon

• (ii). Example 3. Continuing Ex. 2, find the amount of the moon eclipsed 3 nāḍīs after T. A. (i) Corresponding minutes of arc = (780' - 60') × 3/60 = 36' (ii) Distance between centres = √(36² + 26.6²) = 44'.76 (having found that the Moon’s lat. at the moment is 26'.6). (iii) Amount eclipsed = 54'.34 - 44.76 = 9'.6. Example 4. At a certain solar eclipse the difference of Sun and Moon’s motions is found to be 720', the parallax-corrected latitude, 2 nāḍīs before the parallax-corrected new moon, is found to be 15', the sum of the semi-diameters is 31'.9, the un-corrected half duration is nā. 2-30, and the corrected half duration is nā. 3. Find the amount of the Sun eclipsed, at 2 nāḍīs before the parallax corrected new moon. (i) Corresponding minutes of arc = (720 × 2 ÷ 60) × nā.2 1/2 ÷ nā.3 = 24 × 5 ÷ 6 = 20' (nearly). (ii) Distance between centres = √(20² + 15²) = 25'. (iii) The amount eclipsed = 31'.9 - 25' = 6'.9. The following is the explanation of the method: Let us first take the case of the lunar eclipse. At full moon, the Moon and the Shadow are in conjunction, i.e. they have the same true longitude. Since the Shadow has the same motion as the Sun, the interval between them for any interval of time before or after full moon is the same as the interval in tithi proportionate to the time interval. Therefore there is the proportion, if for 60 nāḍīs there is the difference of the daily motion, how much for the interval in time. So the difference in motion is multiplied by the given time and divided by 60. Since the motions are measured along the ecliptic, the interval in minutes along the ecliptic is got, corresponding to the time interval. The distance between the centres is got thus: In fig.2, S is the centre of the Shadow and M is that of the Moon. SM' is the ‘corresponding minutes’ got for the interval in time. MM' is the Moon’s latitude at the given moment. Since MM' is directed towards the pole of the ecliptic, the triangle SM'M is right-angled at M'. Since the triangle, being small, can be treated as a plane triangle, we have, by the Pythagoras Theorem, the distance between the centres, SM = √(SM'² + MM'²) = √(corres. minutes² + latitude²), as given. The amount eclipsed in minutes = Rr = SR - Sr = SR - (SM - Mr) = SR + Mr - SM = sum of semi- diameters of the Shadow and the Moon, minus the distance between their centres.

254 PAÑCASIDDHĀNTIKĀ XIII.23 Visibility of the Sun 20. At any latitude, the equatorial Sun is bent so many degrees south at mid- day, as the north pole is raised up from the north point of the horizon. 21. Going north from Ujjain, 373 1/3 yojanas, the stellar sphere, (marked by the 27 asterisms of the ecliptic rising in an order) becomes discontinuous, (i.e. the order in the rising is disrupted). Note. At 66° North latitude, which is 42°, (i.e. 66° – 24°), north of Ujjain, peculiarities occur in the rising of the signs of the ecliptic, duration of day-time etc. 42° = 373 1/3 yojanas. (षष्टिर्नाड्य)स्तस्मिन् सकृदुदितो दृश्यते दिवसनाथः | परतः परतो बहुतरमा षण्मासादिति सुमेरौ || २२ || योजनपञ्चनवांशां स्त्र्यधिकांश्च चतुःशतीमुदगवन्त्याः | गत्वा न धनुर्मकरौ कदाचिदपि दर्शनं व्रजतः ||२३ || 22. At that latitude, the Sun can be visible even throughout a day. North and north of this place, the Sun may not set more and more than one day, until at the north-pole it will not set for six months at a stretch. 23. At a distance greater than 403 5/9 yojanas north of Ujjain, the signs Dhanus and Makara can never be visible. Note. The Dhanus and Makara segments of the ecliptic have a south declination greater than 20° 36'. In the north latitudes 90° – 20° 36' (= 69° 24') and beyond, the zenith distance of these signs becomes greater than 90°, and so they are not visible in those latitudes. 69° 24' is 45° 24' north of Ujjain, i.e. 45° 24' × 8 8/9 = 403 8/9 yojanas north. 20-29. Quoted by Utpala on BS 2, p.58-59. 20a. B. विषमुद्दक्तंगो b. A. हरियाद्याद्या ध्रुवः; B. हिरिया छान्वा ध्रुवः B2. खमध्या तु c. B. दिनक्तदपि ममति A1. विषुवविदक्षिक; B. रिपुवति (B2. रिष्रुवति) d. A. दक्षिणतस्त्राव 21a. A1. त्रिशति; A2. त्रिशर्ति; B. त्रिशति. A2. सप्तर्ति युतां b. A.C.D. गत्वोदक्; B. गचोदक् A2. योजनं न. A. विभागं च c. A.B.C.D. विरमति d. A.B1.2. C.D. पर्यस्तोऽयं. B. भगणं गोलः 22a. A. षष्टी नाडी; B. र्षष्टिं नार्डी (B3. नाडी) C.D. षष्टिं नाडीः b. B1.3. सदुदितो; B2. मदुदितो c. A.B1. ॰वहुतर॰ 23a. B. योनपञ्च॰ A. नवांशाः; U. नवांशान् b. A.C. स्त्र्याधिक्यं; B. स्त्र्यधिका; D. स्त्र्यधिकां च A.B.D. सचतुः (A1. सवतुः; A2. सवन्ः) C. शत. B3. मुदगवल्याः c. B. गचान A. धनुर्मकरं; B2. धनुर्मकरा d. B1. दर्शन व्रजतः

XIII.28 XIII. SITUATION OF THE EARTH 255 तस्मादेव स्थानाद् द्व्यशीतियुक्तां चतुश्शतीं साग्राम् । (नोदयमुपयान्त्यलिमृघटचापधराः) कदाचिदपि ॥ २४ ॥ षडशीतिं पञ्चशतीं त्र्यंशोनं योजनं च तत एव । गत्वान्त्यं चक्रार्धं नोदेत्याद्यं न यात्यस्तम् ॥ २५ ॥ लङ्कास्था भूलग्नां नभसो मध्यस्थितां च मेरुगताः । ध्रुवतारामीक्षन्ते तदन्तरालेऽन्तरोपगताः ॥ २६ ॥ 24. At latitudes north of Ujjain greater than 482 yojanas and a fraction Vṛścika, Dhanus, Makara and Kumbha signs will never be visible. Note. These four signs have a declination greater than 11° 44' south. Therefore latitudes 90° – 11° 44' = 78° 16' North and more cannot see these signs, since their zenith distance is greater than 90°. 78° 16' is 54° 16' north or Ujjain = 54° 16' × 8 8/9 = 482 10/27 yojanas. 25. 586 2/3 yojanas north of Ujjain, i.e. at the North pole, the second half of the ecliptic, i.e. the signs Tulā to Mīna, cannot be seen. Note. Being situated south of the celestial equator, the zenith distance of these signs from the North pole is greater than 90°, and therefore they are not visible at the North pole. The distance of the North pole from Ujjain is 90° – 24° = 66° = 586 2/3 yojanas. 26. People on the equator see the North polar star on the horizon. At the North pole, people observe it at the zenith. In between, people observe it at attitudes 0° to 90°. Note. As the north latitude increases, so the latitude of the Pole star increases equally. This fact is mentioned elsewhere also. सकृदुदितः षण्मासान् दृश्योऽर्को मेरुपृष्ठसंस्थानाम् । मेषादिषु षट्सु चरन् परतो दृश्यः स दैत्यानाम् ॥ २७ ॥ मेषस्तेषां नित्यं लग्नं त्र्यंशश्च भूमिपुत्रस्य । त्रिंशद्भागनवांशद्वादशभागाश्च तस्यैव ॥ २८ ॥ 24a. A. स्थाना B. ०द्यशीति c. A1. गत्वाच्य; B1.3. गत्वात्यं; B2. गवान्त्यं b. A. ०शतीं सांग्रं; B1.3. शतीत्यागाम्; B3. ०शतीसागां; B. चक्रार्त्तं D. ०शतीं त्याग्य d. A. नोत्पादं न यातस्तं; B. नोसाधं (B2. त्यार्धं) न c. A. नोदयमदयांत्यलि०; B. नोदयसु (B2. मु) यात्यस्तं दयां सलि०; 26a. A.B. भूलग्ना C.D. नोदयमिह यान्त्यलि; U. दृष्टिपथं नो यान्त्यलि b. B. नमसो A. मध्यां स्थि; B. मध्या ये (B2. य) मे० d. B1.3. घर्टचाप U. om अपि A.B. मेरुगता 25a. A. षडशीतां; B1.3. षडशीतीं and d. B1. तदन्तले; B3. तदन्त-ले A.B1.2. रेपगताः; B2. षडशतीं in place of पञ्चशतीं B3. रेपगता

256 PAÑCASIDDHĀNTIKĀ XIII.32 विषुवल्लेखाऽधस्ताल्लङ्का तस्यां समो भगणगोलः । त्रिंशन्नाड्यो दिवसः त्रिंशच्च तस्यां सदा च निशा ॥ २९ ॥ 27. For the people on Meru, i.e. at the North Pole, the Sun is visible at a stretch, when it is in the six signs Meṣa to Kanyā. When it is in the next six signs, it is visible to the demons at the South pole, at a stretch. Note. Moving in the first six signs, the Sun’s zenith distance is less than 90° at the North pole and it is visible to the Devas there. Being greater than 90° at the South pole it is invisible to the Asuras at the South pole. It is vice versa in the next six signs. Thus the Devas and the Asuras have their day and night alternately, each for six months at a stretch. 28. For them, the first point of Meṣa is the Lagna or Orient ecliptic point, permanently, Mars is the Lord of the Drekkāṇa, Navāṁśa, Dvadaśāṁśa and Triṁśāṁśa lagnas permanently. Note. The first point of Meṣa moves round and round there on the horizon, and no other point rises or sets. The lordships are as prescribed in the Horāśāstra. There the Lord of Meṣa is not only the master the Rāśi-lagna, but also of Drekkāṇa, Navāṁśa etc. lagnas. 29. Laṅkā is beneath the celestial equator, i.e. the celestial equator itself is the prime vertical at Laṅkā. There the stellar sphere is equally divided (into the northern half with the N.P. at its centre, and the southern half with the S.P. at its centre). There the day and night are always 30 nāḍīs each. Note. This is because all diurnal circles of the Sun are divided into two equal halves by the equatorial horizon. Note also that what is said of Laṅkā applies to all places on the equator. [वेधप्रकारः] सलिलेन समं कृत्वा तुङ्गं फलकं यथादिशं दृष्ट्वा । दक्षिणकोट्यां शङ्कुं फलकप्रमितं व्यवस्थाप्य ॥ ३० ॥ ऋजुशङ्कुबुध्नविन्यस्तलोचनो नमयेत्तथा शङ्कुम् । भवति यथा शङ्कग्रं ध्रुवता दृष्टिमध्यस्थम् ॥ ३१ ॥ पतितेन भवति वेधो लङ्कायां ऊर्ध्वगेन तु सुमेरौ । विनतेन च तथान्तराले फलके (चाक्षोर्ध्व) सूत्रसमम् ॥ ३२ ॥ 27a. B1.3.सक्तदुदितः; B2.सतदुदितः 29a. B.विषुवध्रे (B2.ल्ले) खाधस्ताल्छत्रे (B2.ल्ल) ङ्का b. B.भेकपृष्ट c. B.त्रिंश नाड्यो A.B.द्विवस c-d. B.षन्दुवरन्यस्तो (B2.वन्त्यस्तो) दृश्यः d. A.B.C.D.U.त्रिंशत्तस्यां च सदा (A.सहा) 28a. A.लग्ने; B.लगोत्यंशश्च (B1.2.शदा; U.निशा) b. B.पुत्रः स्यात् d. B.तस्मैव

XIII.33 XIII. SITUATION OF THE EARTH 257 Astronomical observation 30-32 Place a plank in a raised position, with its surface plane, as examined by dropping water on it. Set it so as to have its surface horizontal and level with the eye, and its parallel sides north-south and east-west. At the southern edge, in the middle, hinge a sighting tube (śaṅku) equal in length to the north-south length of the plank. With the eye at the hole of the rigid sighting instrument, at the hinge, lower the instrument so much, that the North-pole-star is sighted through the hole of the instrument. When lowered completely, (the observation) will be towards Laṅkā: when vertical it will be towards Meru; and lowered appropriately, it will be equal to the (local) latitude (as read) from the plank. Note. From the next verse we can understand that V.M. implies here that the north-south length of the plank is 120 units, so that the length of the sighting instrument also is 120 units = R. So taken, the perpendicular dropped on to the plank from the end of the instrument will be equal to R sine raised angle, and the base from the foot of the perpendicular to the hinge will be R cos. raised angle. तत्राऽवलम्बको यः सोऽक्षज्या तस्य शङ्कुविवरं यत् । विषुवदवलम्बकोऽसौ याम्योत्तरदिक्प्रसिद्धिकरः ॥ ३३ ॥ 33. When so sighting the pole-star, the perpendicular, dropped on to the plank from the end of the sight is the R.sine of the latitude of the place. The base so formed is the R cosine of the latitude of the place. The R cosine line, i.e. the base, coincides with the north south-direction line. Note. VM uses a table of R sines, taking R = 120 units. Hence the rule. Fig. XIII.1 [Diagram: A right-angled triangle representing a sighting instrument on a plank.

• The hypotenuse is labeled "Sight" and "R = 120 Units".
• The angle at the left vertex is labeled "θ".
• The left vertex is labeled "Hinge".
• The horizontal adjacent side is labeled "R Cos θ" and "Plank".
• The vertical opposite side is labeled "R Sin θ".] 30-34. Quoted by Utpala on BS 2.p.59. 30a. B. सभक्तता तुगं; b. B. फलर्क. C.D.U. दृष्ट्या c. A. कोद्यां; B. कोधां. A. शङ्कु; B1.2. शंशंकु d. A1.प्रंतिम; A2.प्रंतम; B.प्रतिम B. व्ययं व्यवस्थाप्य 31a. B.रुजुशंकु (B3.omकु) A.वुम्रथ; B. बुध्र्य b. B.नामये; A.C.D.नामयेत्. A2.शङ्कु c. B.शष्कुवम्रे d. A.B.C.D.ध्रुवतारादृष्टि 32a. A2.चेधो b. B.लम्बतया A.B.मूर्ध (B.र्द्धं) गेन (B.नं) तु c. A.चान्तराल; B.चान्तराला; C.D.चान्तराले d. A.छेधार्धसूत्रसमे; B.छेधृद्धं सूत्रसमाः (B2.समोः); C.फलकच्छांदार्धसूत्रसमे |; D.फलके भासार्थसूत्रसमे |; U.फलकच्छेदार्धसूत्रसमे | 33a. A.लंवोको य; B.लवको य b. A.B.सोरज्या; B.शकुविवरं यतं (B3.तं) c. A1.०लंकोसौ; B.लंडकोसौ

258 PAÑCASIDDHĀNTIKĀ XIII.37 स्वप्रत्ययेन सन्तो विज्ञायैवं वदन्ति भूमध्यम् । सकलमहिमानं वा रसमिव लवणाम्भसाऽल्पेन ॥ ३४ ॥ 34. Learned men, observing things for themselves thus, determine the North pole, the dimensions of the whole earth, etc. as one would determine the salty taste of the whole quantity of the solution by tasting a small quantity of it. Note. What is meant here is that observation made at a small place on the earth can give us know- ledge of the whole earth, by suitable reasoning. [चन्द्रशौक्ल्यम्] नित्यमधःस्थस्येन्दो (र्भाभि) र्भानोः सितं भवत्यर्धम् । स्वच्छाययाऽन्यदसितं कुम्भस्येवातपस्थस्य ॥३५ ॥ सलिलमये शशिनि रवेर्दी(धित)यो मूर्च्छितास्तमो नैशम् । क्षपयति दर्पणोदरनिहिता इव मन्दिरस्यान्तः ॥ ३६ ॥ प्रतिदिवसमेवमर्वाक् स्थानविशेषेण शौक्ल्यपरिवृ(द्धिः) । भवति शशिनोपरा(ह्ने) पश्चाद्भागे घटस्येव ॥ ३७ ॥ Moon’s luminosity 35. The Sun lights up one half of the Moon situated below it always, (at any position round the earth), and the other half is dark by its own shadow, (i.e. the Moon obstructing the sun-light by its own body) just like a pot placed in sun-light. Note. This is because the Moon gets its light from the Sun, and is not self-luminous. 36. The Sun’s rays, reflected in the watery Moon dispels the darkness on the earth, just as the rays of the sun falling on a mirror in the interior of a house, does. Note. It is the belief of the ancients that the Sun is fiery, the Moon watery and the earth mainly earthy. 37. According to the position of the Moon underneath the Sun, every day, the lighted up part increases (from the time of new moon, as seen from the earth), as the lighted portion increases on the pot, on the western side, in the afternoon. Note. Instead of the expression, after-noon a better one would be, ‘as the day-time elapses, beginning from sunrise.’ 34c. B1.3. सकलं d. A.B.D. रसमि—लवणाम्भसोऽल्पेन; (B. रसमितं; D. रसमिव)

XIII.41 XIII. SITUATION OF THE EARTH 259 असितात् सिताच्च पक्षाद् असितं पक्षार्धमर्कमीक्षन्ते । राशित्रयादुभयतो नभो यतः शीतकरसंस्थाः ॥ ३८ ॥ 38. Anywhere on the Moon, its denizens, (the Pitṛs, in this case) see the Sun for half the time during each fortnight, (on the whole, not seeing the Sun for a fortnight's time, and seeing it for a fortnight's time), because the visible part of the sky extends only upto 90° from the zenith. [ग्रहाणां स्थानम्] चन्द्रादूर्ध्वं बुधसितरविकुजजीवाऽर्कजास्ततो भानि । प्राग्गतयस्तुल्यजवा ग्रहास्तु सर्वे स्वमण्डलगाः ॥ ३९ ॥ तैलिकचक्रस्य यथा विवरमराणां घनं भवति नाभ्याम् । नेम्यां स्यान्महदेवं स्थितानि राश्यन्तराण्यूर्ध्वम् ॥ ४० ॥ पर्यति शशी शीघ्रं स्वल्पं नक्षत्रमण्डलमधःस्थः । ऊर्ध्वस्थस्तुल्यजवो विचरति तथा न महदर्कसुतः ॥ ४१ ॥ The Planets and their situation 39. Beyond the moon are orbiting higher and higher, Mercury, Venus, the Sun, Mars, Jupiter and Saturn, and beyond that there are fixed stars. All the planets (from Mercury to Saturn) move in their own individual orbits at a con- stant speed. Note. All this is Hindu theory. 40. Just as the spokes of the oil-press wheel are thick, (close to one another), near the navel, and the space between one another increases as the rim is approached, so the linear extension of the rāśi increases as the orbits are situated higher and higher. 35a. Quoted by Pṛthūdaka on BrSS d. B. इमं वयं हरिस्यान्तः 21.8 end, 36 quoted by Sūryadeva on 37a. A.C.D. ॰मर्कात् Abh. Gola. 5, and Makkibhaṭṭa on b. B. विदोषेण शौक्य A. परिवृधिः Sid. Śekhara 1.1. d. B. घटस्येवा 35a. A2. भित्यमथ A. स्पेंदोः; D. ॰स्येद्रोः A.B. भवति भानोः 38a. B. अप्रसिता सिताश्च c. A. स्वछायान्द्वसितं b. B. ॰मीक्तन्ते 36a. B. सलिलमपे. A. ये च शशिनि. A. दिंधयो (A2. दी); c. A. ॰त्रयादूभ; D. ॰क्षयादुभ B. - धत्तयो d. A. मभोयतः; B.C. नभो यत (C. ॰तः); c. A.B. क्षपयन्ति D. न भान्य [था] तु. B. गेतीतकर

260 PAÑCASIDDHĀNTIKĀ XIII.42 41. Situated near-most, the Moon goes round in the shortest time, its orbit being the shortest. But Saturn situated farther-most, in its longest orbit, cannot move so fast, i.e. moves slowest. [मास-दिन-वर्षाधिपाः] मासाऽधिपा यथो (र्ध्वं) चन्द्रात् सौरादधश्च होरेशाः । ऊर्ध्वक्रमेण दिनपाश्च पञ्चमा वर्षपाः (षष्ठा) ॥ ४२ ॥ Lords of the Months, Days and Year 42. The successive Lords of the Month are the successive farther planets, beginning from the Moon. The Lords of the Horās are the successive nearer and nearer planets, beginning from Saturn. The successive fifth in the ascending order of its distance is the successive Lord of the Day. The sixth in its ascending distance order is successively the Lord of the year. Note. The month meant here is the sāvana month of 30 days, and the year, the sāvana year of 360 days. We get the lords of the horās; Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon, Saturn etc. the lords of the day, Sunday, Monday, etc., the lords of the months, Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, Moon etc., and the lords of the year, Moon, Jupiter, Sun, Mercury, Saturn, Mars, Venus, Moon etc. [इति पञ्चसिद्धान्तिकायाम् वराहमिहिरविरचितायां त्रैलोक्यसंस्थानं नाम त्रयोदशोऽध्यायः ॥]¹ Thus ends Chapter Thirteen entitled ‘Situation of the Earth: Cosmogony’ in the Pañcasiddhāntikā composed by Varāhamihira 39-41. Quoted by Utpala on BS, 2, 41a. B. राशिशीघ्रनक्षत्रं (B2.3.शीघ्रं न) pp. 42-43 b. B.मध्यस्थः 39a. A. चन्द्रादूर्ध्ववुधसितं (A2. बुध) ; c. A.ऊर्ध्वस्तस्तुलजवो B1.2. चन्द्राधुधखित; B3. चन्द्राद्बुधस्वीत d. B.विवरति c. B. प्रागातरा (B3. प्राणां) A.B. om तथा; C.D. om न; A. स्तुल्यजवा; B.-ल्पजवा U.°जवोऽपि संस्थितस्तथा० d. A. ग्रहाः स्तु. B1.3. मण्डलर्गाः 40a. B1.3. तैलक 42a. A.B. मासाधिपो यथोर्ध्वां (B. द्धर्वाः) b. B. विपर. B. ना धुभ्या b. चन्द्रा c. B. मेम्यं स्या c. A.ऊर्ध्व; C.D. ऊर्ध्वं. A.दिनपा च; B. ष्पिपा च c-d. U.नेम्यां महदेवं संस्थितानि d. A.B. पंचमास्याः A.B.C.D. स्पष्टाः d. B.देवस्तिष्ठानि. A.°यूर्ध्व; B.°यूर्द्धम् 1.col. A. त्रैलोक्यसंस्थानं त्रयोदशोध्यायः B.C.D. इति (B.om इति) त्रै (B1.2. सै) लोक्यसंस्थानं नाम त्रयोदशोऽध्यायः

Chapter Fourteen GRAPHICAL METHODS AND ASTRONOMICAL INSTRUMENTS* १४. चतुर्दशोऽध्यायः छेद्यक-यन्त्राणि Introductory In chapter I, vss. 5-7, Varāhamihira enumerated yantra and chedyaka among the topics to be dealt with in the present work. The present chapter deals with these two topics. The compound word chedyakayantrāṇi is equivalent to the compound word yantracchedyāni of I. 7. The word chedyaka means graphics or graphical methods and the word yantra, in the present con- text, means astronomical instruments. Dvivedi interpreted the word chedyakayantrāṇi as follows: “That which cuts or removes doubts is chedyaka; the instruments which serve as chedyaka are chedyakayantrāṇi.” If it were so, there would be no difference between yantra and chedyakayantra. Chedyaka and Yantra, in fact, are two distinct topics of Indian astronomical works called Gola or Spherics. Lalla, Vaṭeśvara and Bhāskara II, for example, have earmarked two separate chapters for their treatment in their works on spherics. Pingree, on the other hand, translates chedyakayantrāṇi as “the Magical Diagrams of the (Graphical) Construc- tions.” But the diagrams or astronomical instruments discussed in the present chapter bear no magical significance. [चरः] साशीतिकाङ्गुलशतं विस्तीर्णवृत्तमविषमं धरित्र्याम् । समराश्यंशकचिह्नं परिधौ सापक्रमं कुर्यात् ॥ १ ॥ याम्योदक्समसूत्रादपक्रमांशावगाहिभिः सूत्रैः । प्रथमवदङ्कक्षिप्तं वृत्तत्रयमालिखेन्मध्यात् ॥ २ ॥ अक्षे क्षिप्तां लेखां [प्र]कुर्याच्च भगणचिह्नपर्यन्ताम् । अक्षोत्तरलेखान्तरमपक्रमांशोत्थमादाय ॥ ३ ॥ द्विगुणं प्रसार्य वृत्ते स्वे [दिक्] तच्चापांशदलाभ्यस्ताः । प्रथमर्शचरविनाड्यो ज्ञेयाः परिशेषयोर्मिश्राः ॥ ४ ॥ GRAPHICAL METHODS Ascensional differences of the zodiacal signs. In III, 10-12, Varāhamihira stated an approximate practical method for finding the ascensional differences of the signs for places living between the Indian Ocean and the Himalayas and prom-

• This chapter was left untranslated by T.S. Kuppanna Sastri. The translation given here was supplied by K.S. Shukla.