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

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.

262 PAÑCASIDDHĀNTIKĀ XIV.4 ised to give a method for other places in a subsequent chapter devoted to chedyaka. The following rule is in fulfilment of that promise.

1. Construct on the ground a level circle with diameter equal to 180 digits. On its circumference put down, at equal distances, marks showing signs and degrees (etc.). Also put down marks showing the declinations (of the end- points of the signs Aries, Taurus and Gemini). (Through the centre of the circle draw the north-south line and at right angles to it draw three chords through the marks showing the declinations for the ends-points of the signs Aries, Taurus and Gemini).
2. From the centre, draw three circles with diameters equal to the three chords which have been drawn through the declination marks at right angles to the north-south line, and graduate them with marks (of signs and degrees) like the first circle.
3. Then (from the same centre) draw a line towards the latitude (i.e. towards that point of the first circle which marks the latitude of the place) and extend it upto the mark (indicating the latitude of the place) on the circumference of the first circle. (This is the latitude-line). On the chord corresponding to the desired declination (i.e. declination of the end-point of the desired sign), mea- sure the portion lying between the latitude-line and the north line (i.e. the line drawn from the centre to the north point).
4. Lay off the double of that (like a chord) on the corresponding circle. Ten multiplied by one-half of the degrees in the arc subtended by that chord are to be known as the vināḍīs of ascensional difference in the case of the first sign. In the case of the other two signs, they are the vināḍīs of the mixed ascen- sional difference (i.e., the mixed ascensional difference of Aries and Taurus and the mixed ascensional difference of Aries, Taurus and Gemini). Consider Fig. 1. ENWS is the level circle of diameter 180 digits drawn on the ground, E, W, N and S being the east, west, north and south cardinal points, respectively. EW is the east-west line and NS the north-south line. The arcs Ed₁, Ed₂ and Ed₃ are equal to the declinations δ₁, δ₂ and δ₃ of the end-points, of the signs Aries, Taurus and Gemini respectively. Wd' = Ed₁. Wd" = Ed² and Wd"' = Ed₃. d₁d', d₂d" and d₃d"' are the three chords corresponding to the declinations δ₁, δ₂ and δ₃, respectively. These are at right angles to the north-south line. 1c. A. राश्यंकचिह्नं C. राश्यंकू चिह्नं c. B. अक्शेतरे d. A. मापक्रमं; B. मायक्रमः d. A.B. ॰शोच्छमादाय (B2. शोछ) 2b. B. पद for दप B2.3. क्रमाशा c. AB. ॰वदंकाक्षिप्रं; (B. gap for वं) 4a. B. द्विगुण B1.3. प्रसार्य; B2. प्रस्तार्य B. वृशौ d. A2. वृत्तं; B. वृत्तनुत्रय b. A.B. om दिक् B. नवापांशकादलाभ्य (B1. भ) स्ताः 3b. A. om प्र A. कुर्याक्व भगणपर्यन्तां; c. A. विनाड्ये; B. विनाप्रे B. कुर्यार्कलंगणपर्यन्तात् (B1.2. ॰कर्यार्क॰) d. B2. त्तेथाः B3. मिश्रा

XIV.4 XIV. ASTRONOMICAL INSTRUMENTS 263 Fig. XIV.1 The arc NL is equal to the latitude Ø of the place, L being the point marking the latitude of the place. OL is the latitude-line drawn from 0 to meet the point L. ON is the north line. enws is the circle drawn with centre 0 and diameter d₁ d’. (The other two circles drawn with diameters d₂ d” and d₃ d’’’ are not shown in the figure). dl is the portion of the chord d₁ d’ lying bet- ween OL and ON. In the triangle Odl, Od = Rsin δ₁ dl = Od. tan Ø = Rsin δ₁.tan Ø, (1) R denoting the radius of the circle ENWS.

264 PAÑCASIDDHĀNTIKĀ XIV.6 The chord DMD' of the circle enws, with its middle point at M, is equal to 2dl. Let 2c₁ be the angle subtended by DD' at 0 (or, wdhat is the same thing, the arc DWD' subtended by DD'). Then ½ DD' = DM = OD sin c₁ = Rcos δ₁ . sin c₁. ½ DD' = dl = Rsin δ₁ . tan Ø, from (1). ∴ Rcos δ₁ sin c₁ = Rsin ε₁ . tan Ø. ∴ sin c₁ = tan δ₁ . tan Ø (2). This c₁ is the ascensional difference of the end point of the sign Aries, or the ascensional differ- ence for the sign Aries. See supra, IV. 26. See also IV. 34. Since c₁ is equal to the number of degrees lying in half the arc DwD', therefore the degrees in half the arc DwD' give the ascensional difference of the sign Aries. These degrees multiplied by 10 give the corresponding vinâḍîs. Similarly, in the case of Taurus and Gemini. But in these cases if c₂ and c₃ be the ascensional differences for the end-points of Taurus and Gemini respectively, then ascensional difference for Taurus = c₂ - c₁ and ascensional difference for Gemini = c₃ - c₂. [नाडीतः छाया छायातः नाडी च] नाड्यः (षड्घ्न्यो) भागास्तज्ज्या व्यासार्धशोधिता छाया । माध्यन्दिनीसमेता नाड्यर्थे सा तया हीना ॥५॥ छायाहरिजाभ्यन्तरजीवाचापांशषष्ठभागो यः । ता नाड्यः (प्राग् याताः) पश्चाच्छेषास्तथा (प्राप्ताः) ॥६॥ Rsine of the Sun's zenith distance for the given time, (and vice versa). 5. The nâḍîs (elapsed since sunrise in the forenoon or to elapse before sunset in the afternoon) multiplied by 6 are degrees; the (versed) Rsine of that sub- tracted from the radius (R) and then increased by the Rsine of the Sun's zenith distance for midday gives the Rsine of the Sun's zenith distance (for that time). In order to find the nâḍîs (from the given Rsine of the Sun's zenith dis- tance) the (given) Rsine of the Sun's zenith distance should be diminished by the Rsine of the Sun's zenith distance for midday. 6. Whatever is the sixth part of the degrees of the arc corresponding to the (versed) Rsine equal to the difference between the given Rsine of the Sun's zenith distance (as diminished by the Rsine of the Sun's zenith distance for midday) and the radius (chāyāharijābhyantara), gives the nāḍīs elapsed since sunrise in the forenoon or to elapse before sunset in the afternoon. Let n be the nāḍīs elapsed since sunrise in the forenoon or to elapse before sunset in the after- noon, and zₒ the Sun's zenith distance at midday. Then, according to the rule stated in verse 5 above, the Rsine of the Sun's zenith distance for that time (which we shall denote by Rsin z) is given by Rsinz = R - Rvers (6n) + Rsin zₒ, (3) where R stands for the radius.

XIV.6 XIV. ASTRONOMICAL INSTRUMENTS 265 This relation is approximately correct for a place on the equator, and is accurate at an equinox. For any other place it is incorrect, for Rsin z really depends upon Ø, the latitude of the place, and the Sun's declination on the day in question, besides the time of the day elapsed since sunrise in the forenoon or to elapse before sunset in the afternoon. Any such formula must therefore involve these elements. Formula (3) stated above does not occur in any other work on Indian astronomy. But analogous formulae do occur. Of these mention may be made of the following. (i) Vasiṣṭha's formula. Let s₀ denote the gnomonic shadow at midday and s the gnomonic shadow at any other time. Then, in the forenoon: s = 64800 / [(lagna − Sun) in mins.] − 12 + s₀ and in the afternoon s = 64800 / [10800 − (lagna − Sun) in mins.] − 12 + s₀ (see above II.12-13) (ii) Paulīśa's formula s = (6 × day-length) / (day elapsed) − 12 + s₀ (gnomon = 12. See IV. 49. This formula was later restated by Mahāvīra in the form: s = gnomon / (2 day elapsed / day-length) − 12 + s₀ (gnomon = 12. See Gaṇita-sāra-saṅgraha, IX. 18). (iii) Śrīdhara's formula s = (½ gnomon) / d − gnomon, where d = (day elapsed or to elapse) / (day-length) See Triśatikā (ed. Sudhākara Dvivedi), Rule 65. This may be derived from Paulīśa formula by assuming s₀ = 0. Śrīdhara's formula was restated by Nārāyaṇa Paṇḍita in the form: s = { (½ day-length) / (day elapsed or to elpase) − 1 } × gnomon See Gaṇita-kaumudī, Rule 13, p. 207. 5a. A. षड्या भागा; B. ष (B2. श्र) मध्याभागा 6a. B2. छया d. A. B. पश्चाल्लेषा० A. स्तथा C. ॰स्तुया (B2. °सागा) ab. B. ॰भ्यन्तरजा जीवा A. प्राप्नो; B. प्राप; C. [प्राची] b. A. तज्या b. A. षष्ट; B1.2. षष्टं; B3. षष्ठं c. A माध्यंदिनी B समेत्ता c. A. प्राग्यतः; B. प्राग्युता

266 PAÑCASIDDHĀNTIKĀ Formula (3) may also be stated in the form: Rvers (6n) = R − (Rsin z − Rsin z₀), so that n = one-sixth of the degrees in the arc corresponding to the versed Rsine equal to R − (Rsin z − Rsin z₀). Hence the rule stated in vs. 6. [राश्युदयः] तिर्यग्रेखा समदक्षिणोत्तरापक्रमांशरेखायाम् | तच्चापांशा दिग्घ्नाः राश्युदयविनाडिकाः क्रमशः || ७ || Right ascensions of the signs (defined by means of the armillary sphere) 7. The degrees in the arcs of the equator which lies orthogonally (tiryak) bet- ween the north-south declination arcs for the ends of the signs, multiplied by 10, are the vināḍīs of the right ascensions of the signs (Aries, Taurus and Gemini) in their respective order. Fig. XIV.2 In Fig. 2, ♈'R is the equator and ♈'C the ecliptic. AP, BQ and CR are the declinations for the end- points of the signs Aries, Taurus and Gemini, respectively. Then ♈P is the right ascension of Aries, PQ is the right ascension of Taurus, and QR is the right ascension of Gemini. 7a. C. रेखासम० c. A. दिघ्नाः; B. दि—राश्युं b. A. ०रावक्रमांश; B. ०राचक्रमांशा A.B. रेखायाः d. A. विनाडिकां क्र० A. क्रमशं; B. क्रमश i. Chāyāharijābhyantara literally means the distance between the chāyā (i.e. Rsine of the Sun's zenith distance) and the hori- zon. This is equal to the difference between the Rsine of the Sun's zenith distance and the radius, for the former being diminished by the Rsine of the Sun's zenith distance for midday as instructed in verse 5.

XIV.10 XIV. ASTRONOMICAL INSTRUMENTS 267 The degrees of the equator multiplied by 10 are obviously vinâḍîs. The vināḍīs of the right ascensions of the signs could also have been defined with the help of Fig.

1. Let the arc WP (in Fig. 1) be equal to 30° (i.e., the tropical longitude of the end-point of the final sign Aries), OQ, the perpendicular dropped from P on OW intersecting the circle drawn with radious Rcos δ₁, at R, and ORT, the line drawn from O through R. Then the number of degrees in the arc WT, multiplied by 10, are the vināḍīs of the right ascension of the first sign Aries. The vināḍī-s of the right ascensions of the second and third signs may also be defined similarly. यन्त्राणि शङ्कुः [रविक्रान्तिः] माध्यन्दिनीसमेता नाड्यर्थे सा तया हीना ॥ ५ ॥ (शङ्कग्रयातसूत्राद् विषुवान्तरे या क्रान्तिरुक्ता सा) ॥ ८ ॥ ASTRONOMICAL INSTRUMENTS Gnomon The Sun’s declination defined by means of the moving gnomon and the armillary sphere.
2. Whatever be the position of the (moving) gnomon in the path described by it (lit. in the shadow), whether at midday, or when towards the east or elsewhere, the angular distance between the equator (viṣuvat) and the thread that proceeds from the centre and passes through the vertex of the gnomon is called the (Sun’s) declination. [मध्याह्नच्छायातः अक्षांशः] विन्यस्योदक् छायां छायाग्राच्छङ्कुरपरतः (पात्यः) | तत्कर्णसमं मध्यात् प्रसारयेत् सूत्रमापरिधेः ॥९ || तद्विषुवान्तरमक्षोऽतोऽक्षाच्चैवं प्रकल्पयेच्छायाम् | 8a. A. मध्यानां प्रांतथा; B. मध्यान्त्यां धातपा; c. A. यातंत्सूत्रा; B. यातत्सूत्राः C. [खग्रान्तं सूत्रं] C. [मध्ये विन्यस्य] तथा d. A.B. विषुवान्तरयाश्च्व; C. विषुवान्तरभांशका उदिताः b. A.B. छायायामन्य (B. ख) तो; C. छायाऽभावे A. कांद्गदिता:; B. कान्दिः दिताः (B2. ॰कान्द्रिदिनाः) स्वतो गते D. विषुवान्तरं यश्च कांक्षितम् A.B. गते ततः शं B. शकौ; D. शङ्कौ

268 PAÑCASIDDHĀNTIKĀ XIV.11 Local latitude (from the equinoctial midday shadow and vice versa) 9-10 (a-b). Lay off the (equinoctial midday) shadow towards the north, and let a gnomon be caused to fall to the west (or east) from the tip of the shadow. Then stretch a thread from the centre along the hypotenuse (of the gnomon triangle) up to the circumference (of the circle drawn on the ground). The (angular) distance between the point thus reached and the equinoctial point (i.e. the west or east point, whichever is nearer) is the latitude of the place. Similarly, from the latitude one may find the (equinoctial midday) shadow. In Fig. 3, let ENWS be the circle drawn on level ground, E, N, W, and S being the east, north, west and south cardinal points. OA is the equinoctial midday shadow of the gnomon, AB the gnomon which is caused to fall to the west from the tip of A of the equinoctial midday shadow. OBP is the thread stretched along the hypotenuse OB up the point P on the circumference of the circle. Then, the angle PON or the arc PN is equal to the altitude of the equinoctial midday Sun, i.e., the colatitude of the place, and the complementary angle POW or arc PW is equal to the zenith dis- tance of the equinoctial midday Sun, i.e., the latitude of the place. Fig. XIV.3 [रेखांशः] इष्टेऽहनि बुद्ध्वाऽपममक्षादधिकं यदूनं वा ॥ १० ॥ तज्ज्या तिर्यग्रेखा विषुवद्रेखा स्थिता स्पृशति यस्मिन् । तच्चापांशसमानो ज्ञेयोऽर्को गोलभागेन ॥ ११ ॥ Sun’s longitude 10 (c-d)-11. On the desired day find the Sun’s declination, no matter whether it is greater or less than the latitude. Find the Rsine of that and insert it bet- ween the ecliptic and the equator (at right angles to the latter, in its own quadrant). The arc of the ecliptic measured eastwards from the first point of Aries up to the point where the Rsine touches the ecliptic, should be known as (the longitude of) the Sun. 9a. A.विन्यस्यो; B.विष्टभ्यस्यो (B2.विन्यं) B.दृक् for दृक् B. छाया and hapl. om of one छाया b. A.पात्पः; B.पाताः d. A.सूत्रं मा B2.परिधो; B1.3.एरिधो 10a. A.तद्विष्टंतरं; B.तद्विष्टंतरं b. A.कल्पये. B. छाया 10c. A.बुध्यायन्; B.बुद्ध्ययनक्षा०; D.बुध्धायन d. A1.०महाधिकं 11a. A1.तज्या; A2.तज्पा a-b. B. Hapl om. ग्रे-खादिषु c. B1.2.चापाश d. B.०मान ज्ञेयोको B.भागेना

XIV.14 XIV. ASTRONOMICAL INSTRUMENTS 269 यष्टिः [स्फुटतिथिः] छेद्यार्धयष्टिवेधादर्कैनूद्धोरन्तरांशकार्काशः । स्फुटनष्टतिथिज्ज्ञेया तस्मात्कार्या तथा चान्या ॥ १२ ॥ V-Shaped Yaṣṭi True tithi 12. One-twelfth of the degrees intervening between the Sun and Moon observed by means of a (V-shaped) Yaṣṭi of length equal to the semi-diameter of the level circle (with one arm pointed towards the Sun and the other towards the Moon) is to be known as the true tithi which being destroyed is to be known. From that (true tithi) one may derive another. Similar rules are found to occur in Lalla's Gola (VIII 42-43) and Śrīpati's Siddhānta-śekhara (XIX 26). [चन्द्रांशः] दत्त्वांशकेषु तेष्वेव भास्करं छेद्यकेन विज्ञातम् । स भवति तस्मिन् काले निशाकरश्छेद्यकेनैव ॥ १३ ॥ Moons longitude 13. When the Sun's longitude, obtained graphically, (vide above. vv, 10 c-d-11) is added to those degrees (intervening between the Moon and the Sun), the result is the Moon's longitude for that time. This is how the Moon's longitude is obtained graphically. [शङ्कुच्छायातः दिगानयनम्] नाभ्याः शङ्कुच्छायाग्रमङ्कयेत् त्रिस्ततो लिखेन्मत्स्यौ । तन्मत्स्यवदननिःसृतसूत्रद्वयपातमध्येन ॥ १४ ॥ 12a. A. छेद्यर्ध; B. छेद्यद्य; C. केन्द्रार्ध 13a. A. ॰केषु; B1.2. read: द चंशकेषु (B2. अंशकेषु) b B. दकेद्वोरंत्वशशवतकाशिः । B3. दचंशकेषु c. A. तिथिशेया b. B. भास्करछेद्यकेन d. A2. चान्पा c. A.B1. भवति हि तस्मिन् d. A. ॰करात् छिद्यं; B. ॰कर—य (B2.3. ध) केनैव