स्फुटचन्द्राप्तिः

by माधवः

स्फुटचन्द्राप्तिः माधवः १९७३

स्फुटचन्द्राप्त • • • The Sphutacandrapti of Madhava, edited here for the first time from its only known manuscript, enun- ciates an easy and ingeni- ous method which would enable the accurate com- putation of the the Moon at intervals of about 40 minutes each throughout the day. The Chart pre- pared for the above pur- pose is so designed that, with minor changes, it could be used for several days in succession. The author, MSdhava of Sahgamagrama, is an astute astronomer of medi- aeval Kerala (c. 1340-1425), who has several works to his credit. He is widely quoted by later astonomers of Kerala and is also reputed for his enunciation of formulae for the accu- rate determination of the circumference of a circle and the nature of 7T by the method of .indetermin ate series, a method which was re-discovered in Europe about three centu- ries later by James Gregory (1638-75) and Wiihelm Leibnitz (1646-1716). Price ; Rs„ 6-00 Gen. Editor — VISHVA BANDHU VISHVESH VARAN AND INDOLOGICAL SERIES— 62 VTSriVESHVARANAND INSTITUTE PUBLICATION — 619 STTfejim ^f^^rf g^r^t spst^* n Printed and published by DEVA DATTA, Shastri at the V. V. R. I. PRESS, Hoshiarpur (Pb., India) वि. भाभा. ग्रन्थमाला-६२ सङ्गमप्रामज्ज-माधव-कृता स्फुटचन्द्राप्तिः BY Critically Edited with Translation and By Introduction, Notes Reader in Sanskrit, vishweshwaranand Institute of Sanskrit and Indological Studies होशियारपुरम् विश्वेश्वरानन्दसंस्थानम् H ० s H I A R P U R v 1 s + v = ऽ + w A R A N A N D० । । | 9 7 3 V. 1. Series- ऽ । । T U T 62 =

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सवर्वाधिकार सुरक्षित प्रथम संस्करण, २०३० वि . प्रकाशक-विश्वेश्वरानन्द-संस्कृत-भारतभारती-अनुशीलन-संस्थान _ पंजाब-विश्वविद्यालय (पत्रगृह) साधु-आश्रम, होशिश्रारपुर, (पं०, भारत) नः 1|| 0F /* FIRST EDITION, 1973 SANSKRIT AND INDOLOGICAL STUDIES, PANJAB UNIVERSITY, C (0) INTRODUCTION N T F Introductory-Thc present edition1-Moon-Sentences, Appendix 1-Verification of the Sentences-Manus cript material-Appendices I and III-Splutaca11drapti and Vervar0/167- 1xaाrolla method for the Moon N T S Madhava's Candravakyas Cr. Edition, with Translation and Notes Object of the work-Principle of the Method-Method of Numbers--Zero-correction to longitudes-Longitudimal Table—C01'rections for the True M1001-Correction for the Eduation of time- Correction for Terrestrial longitude-Correction for Declinational ascensional difference 17-23 APPENDIX II Zero-Corrections for the Aeon APPENDIX III Some Lump-days and their Zero-Corrections Pages 7-15 24-45 46-59 60-61 62-63 64-66 The Sp/114f4c41drdpti of the remownced mediaeva1 astronomer of Kerala, Madhava of Saigamagrama (c. A.D. 1340-1425), critically edited here for the first t111e , enunciates an ingenious method for the computation of the True Moon. Besides being the fastest graha, the Moon has also the maximum changes in its motion, with the result that its p0sition if calculated on the basis of its position at sumrise and/or at Sunset and its average motion for the day would give only rough results. Madhava describes in the present work the construction of a Chart from which the True M001 could be read out at intervals of about 40 minutes each throughout the day. The Chart is also so designed that, with minor changes, it could be used for the succeeding days as well The critical edition of Spl11410c07drapti, presented in the following pages , is based on its only available manuscript. For facilitating the comprehension of this technical treatise, an English rendering has been added on pages facing the text. In the foot 10tes to the edition, an endeavour has been made to derive the several formulae enunciated by the author for the computation . The principles underlying the method have been set out in detail in the Introduction that follows this Preface. A concrete example has also For ensuring accuracy in the above, it is essential that the daily motion of the Moon used for the calculations is very accurate. The Moon-sentences of Vararuci, which are ordinarily used in Kerala astronomical practice, 1 are correct only to the minute and so can give only rough results Madhava has, therefore, computed in place of the above, more s0plhisticated M001-sentences, correct to the second, for nine anomalistic cycles of the Moon (248 days) and set them out and 1. For a critical edition of these Moon-sentences called Gr१८}} &re yतdi (Cr. ed. by T. S. K. Sastri K. V. Sarma, K. S. Res. Inst , Madras-4, 1962), App. [1, pp. 125-34 in the form of a Table. A critical edition of this Table, which begins ith the sentence silam1 ।rdjॉ07 5riye, has been added to the present edition as Appendix 1. ८d l0c mnemonic expressions independent of each other and having no contextual sequence. Quite often, they do not have any logical sense either. This nature of these sentences, apart from creating conditions for errors to crep in, also debars the correction of such errors with reference to the context or grammar. The same holds good rutatis 1714tardis in the verification of doubtful readings. Two methods have been enunciated in the Imanuscripts of these Sentences for the correction of errors and for the clarification of doubts. These methods have been duly 10ticed at the close of the edition of the Sentences and have been demonstrated by concrete examples Manuscript Material Text : The present edition of Spl1410c01d/apti is based on its only available manuscript which originally belonged to the collection of the Namputiri brahman house of Kuta11ur Mana in S. Malabar (Kcrala) and is now deposited in the Kerala University (Oriental Research Institute and Mss. Library, Trivandrum, as its Ms. No. 1055 A. The work is inscribed in Malayalam script on the first two folios of this palm-leaf codex of Jyotisa works, 10'x2}", with 11 1ines a page and about 45 letters per line. The mamsucript is old and slightly damaged and the edges are all frayed. The writing is small, clear and inked. It has passed through the hands of a revisor whose corrections can be identified by their not being inked. The text presented is generally correct and free from errors . Besides the Splurac८॥1drapti, which is catalogued as A, the codex contains the C. M4/1॥rtara tr1d by Govinda Parame5vara ; E. $04015ak/riyayidhi ; F. D. Acard.50ाigral८ by Mult2rt(0p47casika ; (G. (Willip1altli-Carldrawakya11i) is based on four independent manuscripts called here A, B, C, D, all in palm-leaf , inscribed in Malayalam Script on account of its textual purity, and C belong to the (Oriental Research Institute and Manuscripts Library, Kerala University , Trivandrum, being Mss. Nos. MC. 595-A (catalogued as 7ilipad; walkyaigal) and C. 2297-C, an । uncatalogued stray leaf at the end. Ms. B belongs to H. H. The Maharaja's. Palace Collection Trivandrum, and is inscribed on a few stray uncatalogued leaves at the end of Ms. No. 4116, Drggapitakram10. Ms. D occurs as the third work in a codex of astronomical works beginning with the P८ictab0d/ld preserved in the private collection of Elamprakkotatu Mana, Eravor (mear Tripunithura, Cochin) and carries the inscription

• Kutallur Meletatu Paॉcab0dll:1di' indicating that it originally be

longed to the Namputiri house of Kuitallur Meletatu in S. Malabar Mss. A, B and D are complete, while C breaks of in the middle of the 31st walk)ya, the rest of the leaves being lost. All the manus cripts exhibit minor differences from one another and sometimes present entirely different vdly/0s, but to the same import. Possibly these variants go back to the author himself In continuation of the Spl॥tac01drapti, the text manuscript contains two short tracts. The first depicts the Yugd-bloga-diruwas (Zero-corrections per aeon) of the planets correct to 1/60th of a of Haridata1 and seem to have been extracted here for some practical use an account of their forming an independent unit The second tract, which is more interesting, sets out large chunks of full days, ranging from 16,45,705 to 248 with their ८ll।'uwd for the Moon correct to the second. These are obviously intended for the subtraction of days in chunks and correction of the results by the application of the corresponding dlhruwas in the computation of the Moon. The dhr'uwa of the last of these chunks, viz. 248 (dewal prajों0 1010171), is given as 0r–27०-43'-29', the mnemonic sentence therefor being d/li।'0'lant bl८.stur० iोंari . This mnemonic resembles closely the corresponding mnemonic of Madhava's Moon sentences, which reads as d/hiragir blastura, indicating the possibility of common authorship Both these tracts have been included in the present volume as Appendices [ and III, in the form of Tables, with the numerical figures of the sentences duly set out against then 1. 2. Cr. ed. by K.V. Sarma, (K. 8. Res. Inst., Madras-4, 1954), pp.-3-4 ; See Appendir 1, below 10 The well-known Verwar0ha of the author1 deals with the same subject as the present work, but in a better organised manner. It incorporates most of the verses of the an present work, often in improved form. It seems very likely that the author wrote the present work first and recast it later as ye५१॥varolla. This (deduction is substantiated from another source. Now, in the present manuscript after the natural closing of the work with the verse sila17 ।rajia! Sriye etc , are found, in continuation, the following lines : ‘कान्तं कर्म'विहीनं सत् प्राक्फलं ‘सदना'हतम् । प्रहतान्मूलहीनात्] स्वात् ‘संसारा'प्तसमन्वितम् । हित्वा लिप्तात्मक राशिषट्काच्छिष्टं विधुन्तुद: । वाक्यसंख्यावशाद् वाक्यकालेष्वेष तबर्कवत् । अत्राप्यौत्पत्तिकोऽस्त्येव वेण्वारोह इव क्रमः । द्युनिशोरविशेषेण द्वयोस्तत्पाश्र्वयोरिव ।। उपर्युपरि पूर्वस्माद् ध्रुवाः स्युः क्रमशः स्थिताः । वाक्यसंख्यास्तथाधोऽधो व्यत्ययो व्यत्ययाद् द्वयम् ।। वोच्चतुल्यतनोस्तस्य पुनः शिशुतमा गतिः । निजनीचसमस्यात : परिपूर्ति व्रजत्यसौ । ‘शाश'हीना स्फुटः सा स्यादल्पाऽस्माल्लुब्धकाधिका । 'तीर्थकाङ्गा'न्मृगानीक'भक्तं भागादि तद् ध्रुवे । प्र'गुणात् ‘स'गुणं स्वर्ण क्रमात् तद्वाक्यसंख्ययो: । नाडीषष्ठयन्तरे सैका व्येका चैकमुपर्यधः । प्रणम्य प्रणयाम्येनां साधवो माधवोऽस्म्यदः ।। (corrected to माघवोऽस्मि वः ) seen that some It may be of these lines are earlier repetitions of 1ines revised in the form in which they occur in the Vervaroha ; some of the lines depict new ideas not found in the present work , but pertinent to it and also find a place in the confirming Verwarolt, thus the suggestion that the Verwarold in 75 verses is a revised version of the present work in 51 verses 1, cः. ed. by K.v. sura, (Tripunithura, 1956), wit to ******** The facile method enunciated by Mādhava for the corinputation of Moon seems to have caught the fancy of later astronomers who have pursued it further. They used fresh dates and revised figures for calculations and extended the method by introducing immo vations with a view to securing greater accuracy. It has been possible for the present writer to identify the undermentioned texts of this genre, which are mostly anonymous. 1. Drg-721arollakriya, in 14 verses, beginning with verydrolha kriya seyaा71 43arita'tra likhyate, an uncatalogued anonymous tract found inscribed on f. 163-65 of Ms. 5867 of the Kerala University Orienta1 Res. Institute, Trivandrum 2. 3. 4. PREFACE Verwaroha:stakd by Putumana Somayāji, in 8 verses beginning 5. Sk:$710-21dr(spluta10]/07107, in 15 verses, beginning in some of the miscellaneous leaves at the end of a manuscript of /ervarold in the private collection of the Elamprakkotatu Mana, Eravoor (Tripunithura, Kerala), with an incomplete commentary in Malayalam The two tracts noticed below, found in the same codex in said miscellaneous leaves, are also related to the We१1ydroll40 : A short tract in Another short tract with 10 verses, beginning with sाk71eta diruva in 8 the verses, beginning with dhiputir It is proposed to bring out a critical edition of these tracts also, 11 due course, along with the awarolla of Mādhava 1. The ider:1 ification of such works is a problem for the reason that these short tracts are, more often than not, found inscribed in stray leaves at the ends of manuscripts and are left uncatalogued as insignificant sets of verses which do not mak2 up full-fledged texts. (Quite the ends of manuscripts are clubbed together in catalogues under innocuous 12 COMPUTATION OF TRUE MOON Madhava, the Author Among the several astute astronomers of Kerala of the middle ages, Madhava of Sangamagrama holds a position of eminence. Till recently, he was unknown to the scholarly world, especially outside his native land. He hailed from the village of Sangamagrama, the modern Irinjalakkuda, near Cochin, in Central Kerala, the name of his house being IraHni ninna palli to be identified with one of the two still existing houses in the village, named Irinnanavalli and IrinnSrappalii. This information the author gives in his Venvdroha and is corroborated by his commentator Acyuta. 1 Madhava was the teacher of Paramesvara, (AD 1360-1455), the promulgator of the Drgganita school of Kerala astronomy and is frequently quoted in the mediaeval astronomical literature of Kerala with the appellation of Golavid ( 'Adept in Spherics' ). Thus Nilakantha Somayaji (I444.I545 A.D.), while referring to Paramesvara in his Aryabhapya- Bhusya says : Paramesvaras tu ... Madhavadibhyo 'Golavidbhyo' Ganita-gola-yuktir api bnlya eva samyag grhitxci ... . 2 Acyuta Pisarati uses the same appellation for Madhava in the introductory verse to his Sphutanirnaya : vande 'golavidaf ca Madhavamukhan etc Works of Madhava , The Venvaroha? depicting a facile method for the computation of the Moon and the Moon-sentences, 4 commencing with silam iT^TTJTfa hW Smfasramfr TW: U (verse 13) Com. in Malayalam . *Rto f^TT SffSlfafec^ ^ On this, see K.V. Sarma, Introduction to his edn. of Venvdroha., op. cit., pp.fc-7. 2. Edn., Trivandrum Sanskrit Series, No. 185, p. 154. For other similar statements, see tfe., p. 75 ; tac ca Sangamagramajena 'Golatattvavi da Madhavena pradartitam; p. 108 : ata eva 'Golavid? Madhavena kgepavatam sphufapakramana- yane ganitavidepah pradarhtah 3. Cr. ei. by K. V. Sarma, (Tripunithura. 1956), with the Malayalam commentary of Acyuta. 4. Ed. as Appendix I, below, has been shown lately1 that he is the author also of 1.0g10praka7012 in six chapters, 4ganita, an extensive work on the computation of planets , using novel methodologies and two short tracts entitled Madhyaा71a7aya70prakara and Mahajyam10)"0710prakara. Still. another work possibly composed by him is the Gollavadu , which seems to have helped to stabilise his appellation as 'Goldwid'. Sp/lt/[0c07drapti, edited here, is the latest addition to this works .* Besides the said full-fledged works, a number of stray verses of Madhava are quoted by later astronomers like Nilakantha Somayaji Nārāyana, commentator of the Llavat, Saikara, commentator of 7antrasaiोgraha etc. One of his significant contributions to mathe Imatics, known from these quotations , is his e nunciation of formulae value of 7 by the method of indeferf ate series, a method which was re-discovered in Europe mearly three hundred years later by James (Gregory ( 1638-75 A. D.) and (Gottfried Wilhelm Leibmit7 (1646-1716 A. D.).* His iye por८ऽpura-1ya]yur contains the emun ciation, probably for the first time in India, of the formula for the Sime of the sum of two angles, sine (A+B)=sin A. Cos B + Cos A. Sime B. The study and interpretation , in terms of modern mathe of the enunciations of Madhava in his stray verses and in his full-fledged works is bound to yield valuable results in the history of Hindu astronomy Certain directions given in the Sphutac८ndrapti give a general indication of its date of composition. Thus, for the calculation of the Mean Sun we are asked to subtract from the current Kaliday the the editon of 1e११varoha, pp. 8-9: History of ८1str071०71y, (Hoshiarpur, 1972), pp. 51-52, 151 pp. 32-33, 117, with a view to 3. Pp. 20-26 On the this 13 Kerala school of Hindu। I had mentioned this text am anony mous work related However, editing it established its being an earlier work of M1adh1va 709) 14 COMPUTATION ata 15,02,008 and 5180 anomalistic cycles of the Moon . If there be further days, the number of such days has to be multiplied by the mean daily motion and added (verses 20-21). This would show that the work was composed about this time. This date would be 15,02,008 days (Kali 4112, A.D. 1010) plus 5180 anomalistic cycles of the Moon (390 years), i.e., about 1400 A.ID) Madhava's recently identified work, 4garita, also gives a clue to his date . Indicating the sodhyabda -ऽ ('deductive years') for the computation of the planets, the author states : C. 1360 to 1318 1320 शाकाब्दात् ‘नरलोको'नाद् राघवैधत्सुना कुजः । 1340 “दिव्यलोको'ननीलाप्रैस OF TRUE MOON 1158 ‘हेमपुण्यो'नशाकाब्दात् ‘नवलोको'नसारङ्गर्गजैराप्ते गुरुर्भवेत् । तत्वभजिते वधः ।। सारवैगवरैर्भगुः ।

• यज्ञलोको'ननीतांशैर्धर्मेराप्ते

शानिर्भवेत । The 'deductive years' for the different planets Mars etc. are Saka 1320, 1318, 1340, 1158, 1301 and 1276, corresponding to A. Do 1398, 1396, 1418, 1236, 1379 and 1354 . In consonance with the principle of 50d}}]yabda-s, these figures represent the largest number of years possible to be cut of for the different planets at the time when the work was written. The date of composition of the work would thus, be just ahead of the largest 'deductive year' mentioned, which in the present case, is A.D. 1418. 1276 ‘तीर्थप्रियो'नशाकाब्दाद गन्धमििजते तम: ।। A clue to the date of birth of Madhava is provided by that of his younger contemporary and pupil, Parame5vara who was borm From the above considerations Madhava have lived between A. D. 1340 and 1425 could be supposed In the preparation and presentation of this volume, I had had the benefit of the valuable c00peration and advice of Prof. T.S. Kuppamma Sastri, lately of the Presidency College, Madras, for which I am particularly thankful to him . I am indebted also to the authorities of the Kerala University Oriental Research Institute and Manuscripts Library, Trivandrum, and Shri Trātan Namputirippād of the Elamprakkotatu Mana, Eravoor, for permitting me kindly to utilise the 1manuscripts in their possession, for this edition. The credit for the meat printing and get-up of this volume goes to the W.W.R.1. Press, Hoshiarpur. 15 Vishweshvaranand Institute, Hoshiarpur, Independence Day, August 15, 1973 I N T R 0 0 U C T I 0 N (OBJECT OF THE WORK 1method which would enable one to compute True Moon at in tervals of about 40 minutes cach, throughout the day. Now, amongst the celestial bodies, the Moon has not only the fastest motion, of about 13० per day, but also the greatest variation in motion. On account of this, True Moon for any specific moment if calculated by the rule of three using its true position and motion, at sunrise, as is generally done in the case of the other planets, cannot be expected to give correct results, the possibility of error being as large as 10 windikas. Even if the calculation is done using its true position and m10tions at sum rise and Sunset, the results obtained would still be far from acc:1rate. Accurate results can be obtained only by the Second or third differences, which, however, would entail inordinate labour. The method described in the present work obviates this labour and makes it possible to read out from a chart the True longitude of the Moon accurately at nine times a day, at intervals of a little over six and a half 74lka.s (2 hrs. 40 min.). From the True Moon at the quarter (40 min.) of these intervals, the True Moon at any moment falling within any such 40-minute-interval can be calculated by the rule of three, to get remarkably accurate results The fact that calculations are made correct t0 seconds adds to the accuracy of the results Certain peculiarities of the popular Moon-sentences (C011dra wakyas) of the Kerala astronomer Vararuci have provided the clue to our author for devising the meth0d described here. The said sentences comprise of 248 expressions couched in the Kat0payindi motation and give the longitudinal positions of the Moon for cor। secutive days contained in 9 ful11umar anomalistic cycles of 27 days, 33 7alikas and 16-24/55 winadikas each. These Ca11dra1akyas can be used from the moment when the amormally is zero, '.e., from the com junction of the Moon and its Higher Apsis (Candra-Turig८-yoga), which occurs at the end of every anomalistic cycle, which may be at any time of the day and not necessarily at sunrise At sunrise, say, on the current day, suppose a full days and b part-day have gone by since when the anomaly was last Zero. This ould mear that we can commence using the Caा7dra)valk)'05, one per day, from the moment which is exactly (a+b) days before the current day. Now, let us consider a moment which is b day before the current day. Since b is only a fraction of a day, this Moment will fall in the previous day, its /141-wi7a4f being the s071e as the moment of the end of the cycle a days ago. So, if we add to the Moon's Dl।ruva (Zero correction) at the end of the cycle, the Moon-sentence equal to ८, the result will be the True Moon (Ca11dro-Spluta) for that Momment on the previous day Now, the above argument will apply not only for the end moment of the last cycle, but also for the end-moment of any cycle before that , the corresponding Momments being exactly (1 +b) days+1 cycle, (0-+b) days-+2 cycles, (a +b) days-+-3 cycles etc. before ७१॥rise on the current day, (i.e., the end of the final Kal:#dird, for the current day). Only, for every additional cycle by which the moment is pushed backwards , a zero-correction of 30-4'-72#', which is the D}}॥१५॥४0 for one cycle, will have to be deducted For mine such previous Zero anomalies (by the reckoming of which one full series of 248 days and 248 Ca71dravakya.s would be exhausted), True Moons can be obtained at nine Momments on the day previous to the current day, i.e., the last day of the Kalidind. The intervals between consecutive Monents will be a little more than 6 1alkds, and a quarter thereof, for which the longitudes could be calculated by the rule of three, would be about 40 minutes. If the true Moons at the nine Momments are required for the current day and the succeeding days, they could be had by adding the succeeding relevant Caा71drovakya in place of the vaky0 first used. For this reason, when the Momments, Vakya.s and True Moons for any day, during a 248 day period, have been calculated and duly entered in a Table, the Tables for the further days could be prepared with ease therefrom It is to be m७ted here that this method depends on the accident that an anomalistic cycle does not consist of a whole number of days, INTRODUCTION in which case, one would, again and again, be getting the same long It is again to be noted that, in order to secure a high degree of accuracy, the author has devised a new set of Moon-sentences, correct to the second, for use in the calculation of the Moon by the method set out in the present work, in place of the commonly used (C271drayakyas of Vararuci which are correct only to minutes. In actual working, the author has introduced several ingenious innovations with a view to lighten the labour involved and to arrive at quick results. Thus, by calculating backwards, he has arrived at an Epoch (Kha१140-di10), wi2., Kalidi10 15,02,008 (dinta707 715as y0) (verse 5). ८t 1e (21d (१/ whill a conjunction of the 140on and its Higher Apsis (C07dra-7ig0-Yoga) had occurred . Thus, am ano Imalistic cycle of the Moon commenced at sumrise, at the expiry of the said Kha110-di10, thereby removing the part-day, wi८., b of (a+b) days (vide supra), and enabling calculations with full days For computing the True Moon on any particular day, subtract the above K7011adli10 from the Kalidi70 for that day and find out the number of completed anormalistic cycles which have gone by subseuent to the epoch. For this, the remaining days (Khaा70-5es०) is asked to be multiplied by 6845 (ऽivadlnta) and divided by 188,611 (paryaptalrday), the underlying reason being that the period of a cycle is given by the fraction 138,611/6845 days which works out to 27 days, 33 7adlikds, 16-24/5 winadikas (verse 5). The quotient is called the 'First result' (4grimraphala). The further eight results are also noted by reducing the quotient progressively by 1, 2 etc 1. Of course this could be obviated by using. instead ['dyas, new 17akyas constructed for fractions of days and appropriately 2. 19 For a cri•ical edition of these Moon-sentences, whic 3. For an edition of Vararuci's Can:lreauwakyas by T. S. K. Sastri and K. V. saruna, (K. S. R. Institute, 135-34 of the current applying them commence with ed Madras-4, 1962), pp 20 These nine figures , which are termed Dhrunw०-8ddharm10-s, form basis for the calculation of the Dhruvas etc. (verse (6) Example : No. of completed cycles or 'First result' Remainder Example (contd.) 7aky0-17bers : 6845 5638 2589 6385 3336 0 The nine Dhruwa-saldha71as will be 12,502; 12,501 ; 12,500;... 12494 M00n-sentence-Numbers (Wakya-satikhya-s) Next is to be ascertained the serial number of the Yakya, in the current a normalistic cycle of the day taken, and those of the further eight Momments in the preceding eight cycles. Since the remainder left in the division for getting the full cycles gone by (verse 5) is really the number of days in the current cycle multiplied by 6845 ($iyadata), the said number can be retrieved by dividing the remainder by 6845. Again , since the preceding eight Momments will precede the first Momment successively by one full cycle each, their vaky4-numbers can be ascertained by adding 1,88,611 to the respective remainders and dividing by 6845 and adding the quotient got to the immediately preceding valy0-number 28 days =18,46,496 55 =15,02,008 83 = 3,44,488 .. 3,44,488X6845 1,88,61] 12.502 =5,638 = 287 111 4083 1034 4830 1781 138 the days 166 Zer0-Montents (Dhruwakala-s) Now, the first Moment (Dl।'11akala) falls at Re71ailder / Sivadra days before sumrise of the current day, or, in other words 193 12 1369 221 ०fter sumrise on the previous day . The preceding eight Momments will fall, similarly , at (6845- relevant Remainder) 138, 7adika७ verse 8) Example (contd.) 1. 2. 3. 4. 5. 6. 7. 8. 9. 5638 2589 6385 3336 287 4083 1034 4830 1781 Example (contd) The corrections would be : (i) (ii) 6 6 2८er0-C0rrection to 10ngitudes (Dhruva-s) 13० 10 (6845- in 12 8 Rel71airder) the 1207 4256 460 3509 37 30 658 2762 5811 2015 5064 Momments (Dhruvakald-s). The two items which go to make up these corrections are : (1) the M001's longitude at epoch, and (2) the additional longitude due to the cycles which have gone by For facilitating calculation, the author has isolated two lumps (Kha11a.s) of cycles and indicated the corrections due to them : (i) 5105 (71a71a kārata) cycles, the longitude due to which added to the Zero-correction at the epoch, wiट., Kaliday 15,02,008 (d17010717anu5asy0), gives a result ending in complete minutes, being 57-24०-47' (ऽ0trwa141 ।ram1al), and (ii) 69 (lt) cycles, the longitude due to which, again ending in complete minutes, is 77-1०-44” (wiऽvaikarta11;al). For each additional cycle, the longitude is given as 3०-4-6 3' (verse 10), which is 1/69 of 77-1०-44” In actual practice, however , it is sufficient to calculate the correction for the First result (4grim10plhala, verses 5-6); Since the further cight results are successively 1 less than the First their corrections can be had by diminishing the previous corrections by 3०-4'-6 22 23 2 example taken 71 10 35 37 18 4 2 30 45 57 24 50 17 44 calculated 29 as 13 56 40 23 21 ab0ve (iii) 6 (iv) 6 (v) 6 (vi) 5 (vii) 5 (viii) 5 (ix) 5 Table of Longitudes 10 17 24 30 37 44 50 57 The above results have now to be adapted for nine Momments in the Kaliday taken, in order to enable the corresponding longitudes to be read out with ease. For this the nine Momments are rearranged in the ascending order and posted in a table with the corresponding Walyas, Yalky0ऽ0ikhyas and Dlruwas against each. The sum of the Yakyas and the Dhruvas will give the Sphuta (True longitude) of the 35 40 13 45 18 23 56 29 Walkya Momment ! saikhya 7० 4 ’ 23 ” 4 0 17 0 56 10 27 52 3 24 47 56 21 43 49 18 39 42 55 193 138 83 28 221 166 111 Vakya Table 0 4 49 26 6 7 4 23 0 0 0 0 6 13 12 37 | (0 22 54 2 | 5 21 43 49 0 18 4 36 5 27 52 3 0 13 15 11 6 4 0 17 (0 8 25 46 6 10 8 30 1 11 19 52 | 5 18 39 42 | 0 26 30 30 | 5 24 47 56 | (0 21 41 9 6 0 56 10 True ]M1001 6 11 53 49 6 13 12 37 6 14 37 51 6 15 56 39 6 17 15 28 6 18 34 16 6 19 59 34 6 21 18 26 6 22 37 19 As instructed earlier, the above Chart can be re-adjusted to give the True M001 for the nine Momments on any other day if the }/ak yo for the reguired day is used in place of the vakya used here Corrections for the Tru10 M1001 The True Moon read out from the Chart would be correct only as reckoned from the Zero meridian at Ujjain. It has, therefore, to be reduced to the local place, by the application of corrections for the Equation of time, Terrestrial longitude and Declensional Ascensional Difference, before the Chart becomes ready for use These corrections are derived in the manner generally prescribed in astronomical manuals, (correction for the B0uati01 0f Time (Bhujantara-sariskara) In the calculation of the Mean Sun (Surya-71adhya71a ) required for this correction, the labour is lightened, again, by the use of a For the further completed cycles , it is 27०-9'-283 " each . That for the days etc . elapsed in the current cycle is to be found by multiplying the same by the Mean Daily Motion of the Sun, viz., 59-8-ः . The sum of these three would give the Mean Su1 , which has to be calculated for the mine Momments (verses 22-23) Exumple (contd.) First result 12502 Less 5180 (adikया710) cycles Dh।"10 for 7322 cycles at 27°-9'-28" per cycle [00. at. ॐ " per cycle //akyass(aik/lyd of the day=0 Sun's motion for 0०== 0)x 59'-8-8, Mearn motion for the relevant Mean Sun for First result 4 7 7 0 0 /10 11-11०-5'-11" 23 9 - 19 - 14-56 9 0 35-26 0 0 - 0- 55-- 33 10- 26 9 - 1 - 5= 59 1he Mean Sun 71irus its Higher Apsis (Mar1docca), viz., 2-18 " (llust stri) wil1give its Kerala. This Kerala is converted into arc and its sine read off from the of Table of sines. This divided by 160 will give the correction for the Equation of Time (Bhujart८rd stailskara) in viradikas (verse 24) Correction for Terrestrial L0ngitude The Correction for Terrestrial Longitude (De.5antara-sariskara) depends upon the east-west distance of the place in question from the Ujjain meridian which is to be known from tradition (verses 25-26) 24 The R Sine of Sun-plus-precession in the sine table gurodya71a (153) etc. gives the Declensional Ascensional Difference (cara) in terms of gurytalkऽ07as for places where the equinoctial shadow Imeasures two (algulass. For the place in question it will have to be derived from the above by the rule of three. The algebraic sum of these three corrections is now to be applied to the Dhrutiv0-kalaऽ (Zero-Momments) to get the Walky4-kalass (True Zero-Momments). The sum of the Waky0.s and the corresponding Diruvaऽ will give the True Moon at these Waky८-kalaऽ (True Zero-Momments) (verse 35). The True Moons now recorded in the Chart are for inter vals of just over six and a half radikas (about 2 hrs. 40 min). The True Moons at one fourth these intervals might now be calculated by the rule of three posted in the chart so that the Moon at 40-minute intervals could be read out directly therefrom. स्फुटचन्द्राप्तिः स्फुटचन्द्राप्ति 2. [ मङ्गलाचरणम् ] 'शिरश्शरणशीतांशुशिखानिष्यन्दिचन्द्रिकम् । अनकारहरं दिव्यं सिन्धुभूषं भजे महः ॥१॥ [ ग्रन्थोद्देश: ] अधोऽधः क्रमशोऽतीतचन्द्रतत्तुङ्गसङ्गमात् । प्रत्यहं वाक्यनवकात् ‘स्फुटचन्द्रप्तिरुच्यते ॥२॥ श्रुतमात्रे प्रकारेऽस्मिन् न स्याद् यस्यातिविस्मयः । स्वस्यैवानधिकारेण स न गृह्णात्विमां गतिम् ॥३॥ प्रणम्य प्रणये युष्मान् साधवो माधवोऽस्म्यदः । भवद्भ्यः प्रणतोन्नत्यै भवद्भ्यः किं न लभ्यते ॥४॥ 1. The Ms, Ker. Uni. 1055-A, begins श्रीगणपतये नमः । [ ध्रुवसाधनानि ] 1502008 ‘दीननम्रानुशास्यो'नं दिनराशि कलेर्गतम् । 6845 188611 'शिवदूता'हतं हत्वा ‘पर्याप्तहृदयेन यत् ॥५॥ with the प्रणम्य प्रणयाम्येनां साधवो माधवोऽस्म्यदः ।। words : This line occurs among the extra verses after the work as : The last two letters have, later, been struck of and revise d हरि: tि वः । By) (Inw0cation) 1. 1 adore that divine efulgence (God Siva), which removes the root cause of worldly extistence (10), is adormed by the river (.viz., Ganges), and is shedding cool moonlight on account of the rays emanating from the 1001 e1sconced in its crown (0bject 0f the work) 2. (Herein below) is expounded the Computation of True Moon by means of , daily, the placingone below other, mine numeri cal expressions (vakya-s) as calculated from (the time of ) the (previous) conjuction of Moon its Higher Apsis the and 3. (Ifever there be) one who is not delighted on hearing about this method, let 1im not accept it. To be sure, he will not have the ability (to practise it) 4. Oh ! ye good souls ! I, Mādhava, bow before you and beseech you. For, what does not one obtain from you who are bent upon elevating those who bend before you. (Dhuruva-sadhana-s) 5-6. From the elapsed Kalidays (for any desired date) deduct (a kha१140, 1ump number of days , e१ual to) 15,02,008 (dinar107 ra116८sy८). Multiply the remainder (kha१14a5ed) by 6845 (5ivadlta) and divide by 1,68,611 (p0aryaptalrday0). The quotient (got is Rational८ : (15,02.08) is a (Lump of days) D1१८१८amaranu6asya Kha१nda 188611 surprise at Ujjain. This Lump can, therefore be discarded and calculations need be based only on the remaining days (Kha११da6es८). Now, 6845 (5ivadछt८) anomalistic cycles of the Moon are contained in 1886.1 (paryaptahrd०y८) days. anomalistic cycles completed during the Kha१14akest is given by the expression : Hence the लभ्यते तेन कर्तव्या वक्ष्यमाणविधेध्रवाः । तेनैवाद्यस्तथैकैकरहितेन तदष्टकम् ॥६॥ [ : वाक्यसंख्या: ] शिष्टात् तु ‘शिवदूता'प्ता वाक्यसङ्ख्याऽग्रिमा, ततः । 6845 1359 मुहुःप्रक्षिप्त पर्याप्तहृदया'त् क्रमशः परा: ॥७॥ 1886 11 [ ध्रवकाला: । 6845 पृथक् तच्छेषरहित'शिवदूता'त् ‘प्रिया'हतात् । ‘धृतालय'हृता नाड्यो ध्रुवकाला इमे स्मृताः ॥८॥ [ ध्रुवा: । 12 5-24०-47' 5105 लिप्तादि ‘सत्त्ववान रामो' 'मौनकामे'ऽग्रिमे फले । 69 7-1*-44 स च ‘विश्वैकनाथ'श्च तस्मिन् ‘धृतियुते ध्रुवः ॥९॥ called Dhr'uw0-ऽddhara and) is to be used for deriving the several 2Zero-corrections (Dhru।va.s) to be used for calculations which will be emunciated below . The first Dlrt14 (is to be calculated) using this quotient itself (4grim10plhald) , while the further cight (Dltruvaऽ) are to be derived from this Dhruva reduced increasingly by 1 (M100n-Sentence-Numbers) 29 7. Divide the remainder (in the division in 5) by 6845 (5iwordnta ) The quotient obtained will be the first Moon-Sentence-Number (Yakyasaikhya).1 The further (eight Sentence-numbers can be obtained) in the same mammer from the division by 6842 (5ivadura) of the successive remainders to which 1,88,611 (paryaptalrday0) has been added . (Zero-M0ments) 8. Subtract (each of the mine) remainders (obtained in 7) from 6845 (5iy0dt0). Multiply the (mine) balances by 12 (priya) and divide by 1369 (d}}rtalaya). The ( Imine) results obtained will be in 14liks and are (to be called) Zero-Morments (Dhruvakald-s)." (Zer0-Corrections) 9. At the end of 5105 (71am10/ka710) (cycles) of the first (D/hiruva ऽadlu710, wi८., the Agrim10plala of 5-6), the Zero-correction, beginning with minutes, is 5-249-27' (softworyan rai710}}). For each increase of 1. Rationale : "Thc remainder (of the division in 5) is, in fact, the number of days in the current anormalistic cycle multiplied by 6845 (४iwadata) ; hence the division of this remainder by 6845 to get days. It may be noted here that since 188611 the further 17ak५८s०१ill yds will successively 68-45 increase by 27 or 28. 6845 - 1तduka. 30 ततोऽधिकं तु तत्रांशा ‘गो'गुणा, ‘वि'गुणाः कलाः । ‘सुगुणा विकलास्तासु तद्गौरां'शं विशोधयेत् ।। १०॥ [ परितालिका ] साधयित्वा धुवांश्चैव ध्रुवकालांस्तथानयेत् । प्राद्यमल्पतमं कृत्वा यथाऽधिकतमोऽन्तिमः ॥११॥ त: साघ तत्र तत्र स्युः सह तद्वाक्यसख्यया । तद्धुवा स्वार्कमध्याय स्वसाधकफलान्विताः ॥१२॥ 'अत्राप्यौत्पत्तिकोऽस्त्येव वेण्वारोह इव क्रमः । द्युनिशोरविशेषेण द्वयोस्तत्पाश्र्वयोरिव ॥१३॥ उपर्युपरि पूर्वस्माद् ध्रुवाः स्युः क्रमशः स्थिताः । वाक्यसंख्यास्तथाधोऽधो, व्यत्यये व्यत्ययाद् द्वयम् ॥१४॥ 1. Verses 13-14 occur among the extra verses after the close of the work . They are editorially inserted here in consonance with their sense and similar ७ccurrence in this context in the Yervarolha, the revised version of the present work. 69 (d}}!ti) (cycles, thereaffer), 1he increase in 7r.-10-44' (wi5vaikar८arld). 10. (To get the Dhruva for) the remaining cycles, multiply the same by 3 (g०), getting thereby degrees, by 4 (wi), getting thereby in the case of minutes, and by 7 (51), getting thereby seconds ; seconds, however, reduce them by 1( /23 of the number of the said cycles) (The 11 . when a11 the Diruv८s have been calculated (as instructed in 9-10) and so also the Diruva-kalas (as instructed in 8), arrange them In (the ascending) order , so that the smallest (Dhruwakola) comes as the first and the largest as the last It 12. Alongside each (of the Diruwakala.s), chart the corres ponding Dl॥ruvas with their respective Walkyasaiklyds. Chart also the Phala.s which enabled the calculation (of the above), for use (later) in the computation. of the Mean Sun rom 13-14. Here (in the chart of verses 11-12, above), there will be apparent a natural order, irrespective of (the two) sides of the day, wi2., day and might, as in climbing a bamboo tree (wherein the branches will be found edually distributed on its two sides). Thus, the has to be a manner that their Dhruy८ added to the D:121)८ of the Kh८१८ 15,02,008, and not be carried forward to seconds. 69 (dht) is the least number of anomalistic cycles for which, too, the which Chart) (69) + wis.waikarmatha (7r.10-4'). remembered, the 22 in 2ero-correction this also. Therefore 5105 (१101१८lana) cycles sbuld be reduced from the Agrim८phala only once, even if it is possible to reduce it by 5105 more than once. For further reductions, 69 (d;ti) and its Dr५८ alone should be made use of completed 1 circle could Diruva for 1 cycle 31 connection, be is 69 dropped. that the [0714y a प्रमुष्टसम्प्रदायस्य प्रक्रियेयमुदीरिता । तत एवाञ्जसाऽमीषां भवत्यवगमोऽन्यथा ॥१५॥ एकस्मिन् ध्रुवकाले या वाक्यसङ्ख्याऽवकल्पते । 3. 55 'शश'हीना पुनः सा स्यात्, न चेत् स'गुळिको'नयोः ॥१६॥ 3176 1035 'तीर्थकाङ्गात् ‘मृगानीकै ’ ‘प्र'गुणात् ‘सुगुणाच्च यत् । विभज्य लब्धं भागादि धनर्ण तद् ध्रुवेऽस्तु तत् ॥१७॥ ध्रुवकालोऽपि येनैकः साध्यते तदनन्तरम् । 747 193 808 ततः ‘सर्वार्थ'युक्तेन ‘दीनदान'युतेन च ॥१८॥ अस्मिन्ननन्तरातीते समस्तं तद्विपर्ययात् । एकद्वित्र्यन्तरे काय कर्तव्यस्तत्समुच्चयः ॥१९॥ नाडीषष्ट्यन्तरेऽप्येवं सैका व्येकाऽथवा भवेत् । वाक्यसंख्या, धुवो नान्यः, सा गतिः सार्वलौकिकी ॥२०॥ 1. This and the next two lines occur in a form a mong the extra verses after the work, as : 1035 ‘शश'हीना स्फुट: सा स्यादल्पास्मात् 'लुब्धका'धिका । 3176 ‘तीथिकाङ्गात्’ ‘मृगानीक'भक्तं भागादि तद्ध्रुवे । slightly ‘प्र'गुणात् ‘स'गुणं स्वर्ण क्रमात् तद्वाक्यसंख्ययोः ।। different 2. For युक्तेन the ms. reads हीनेन, which is wrong . The emendation is based on the parallel verse in the author's We१॥varolha. This line occurs among the extra verses after the work, as : नाडीषष्टयन्तरे सैका व्येका चैवमुपर्यधः । Dru10:s will be, in order, successively. greater than the one before , the 7ak]'(strik/yds being so in the descending order. If otherwise, the order will be reversed (in both) 15. This method of work has been spelt out for (the benefit) of one who has forgotten the tradition. (Otherwise, 010e would have an easy understanding thereof from tradition itself 16-17. When the /al.jy1ऽ८rikhya for a (particular) Dhr1५vakala is considered, the /alkyasailk)'d next to it will be less tha1 it by 55 (545a) or greater than it by 193 (8ulika). The (Dirty८s) for these two (via 5 and 193 days) will be given by 3176 (i।rt/htalkaliga) divided by 1035 (71garika) multiplied, respectively, by 2 (pra) and 7 (ऽ1). The results, which will be in degrees, are to be added to or subtracted from the previous Dlr1)05. 18. When a )})'t॥y0/kal( has been calculated from a number (viz., 6845 71i711ऽ the remain der, wide verse 8), the subsequent (D/1711alkal(-s) would have been derived from numbers increased by 747 (s0।'yartl८) or 808 (fm.ada10).* 19. In the case of a succeeding (Dlhr10kal८), all (the above said) corrections should be applied, inversely. In the case of those removed by one, two or threc (intervening D/hruwakalu-s), the s14॥ of the (relevant) corrections (should be similarly applied ) 20. Again, at 60 71ddikas (after or before) a Dlruwakala, the corresponding Wakyasaik/]ya will increase or decrease by 1. But the Dl। 1५0 will not change. Indeed, this is a universal rule 38 above, p. 21, No; where the which is the 0;"uw2 for one anomalistic cycle (wide 10). Since one cycle e५ual to 27 days, roughly, (vide verse 7), Dhruva for 2 cycles or 55 days 3176 2X 1035 3176 3176 1035 22 is figures are : 460, 1207, 2015, 2762, 3509, 4256, 5064, 5811 [ ध्रुवकालसंस्कार : ] इत्थं तथैव वाप्तेषु तत्तद्वाक्यधुवैः सह । ध्रुवकालेषु कार्योऽन्यः संस्कारः, सोऽभिधीयते ॥२१॥ 27०-9-28" 5180 11-11०-5-11 ‘आदिकूर्मेऽग्रिमफले ‘कर्कशानेककार्यकृत् । अर्कमध्यं विलिप्तादि विद्यात्, प्रतिफलं पुनः ॥२२॥ [ रविमध्यम् ] ‘दाराधीनसुख' तद्वत् तत्तद्धी'घ्न'युगां'शयुक् । वाक्यसंख्यावशाद् भूयः तत्काले तद्दिनेऽपि तत् ॥२३॥ [ भुजान्तरसंस्कारः ] तत्कालमध्यमार्कस्य स्वोच्चहीनस्य दोर्गुणात् । 160 प्रधऊध्वर्धजात् स्वर्ण ‘प्रातपा'प्ता विनाडिकाः ॥२४॥ 4 (0f opp. page). Rational८ : The Druvakald-s have been reckoned as from mean sunrise at Ujjain . They should be reckoned from true sumrise of place, which depends on : (i) the Sun's e५uation of the centre (ii) the reduction to the euator, (iii) the longitude of place, and (iv) the declinational ascensional difference (c८ rardha) at place for that day. Of these, item (ii) is neglected by earlier astronomers like Aryabhata, and not given by our author in this work, following Aryabhata, though he must have known its need. Item (1) is given here. The eguation of the centre is taken as 129' X R. Sin Ma11d८-५erndra / 3438 (Arvabhata) and the True Sun rises earlier or later, as this is negative or positive, at the rate of 1 produ८ of time per minute of arc. Thereforeit is equal to R. Sin Manda-Rerndr८ X 129/ (3438 X 6) == R. Sin 1441d८-kendra | 160 in windias, and is additive for the first six sig subtractive for the next si It may be noted that item (iii) is given in verses 27-32, below verses 25-26 and , item (iv) in (Correction to the Dhruwakala-s) 21. To the Dhr१ryakalas derived in this manner , along with their Wakyasaikhyas and Dhrunwas (verses 16-20), or calculated in the mammer enunciated before (verses 7-9), another correction has to be applied. That is stated hereinbelow 2-23. At the end of 5180 (adikarm10) (anomalistic cyles) con tained in the first result (4gri710plhala, being the first Dhruwaऽadhan10, vide verses 5-6), the Mean Sun, correct to the seconds, is 11-110-5-11' (karka5amekakaryakt). For each remaining (cycle) the Mean Sum is (to be calculated at the rate of) 270-9-28” (daradhinasuklar) plus 9/31” (dlhilyuga)* (and added). Again, (is to be calculated and added, the Mean Sun) for ( the number of days equal to ) the yakyasafीkhya and for that portion of the day under consideration upto the time (of each Dhr11akal). 2. 24. The sime of arc of the difference between the Mean Sun and (the Sun's) Higher viz., 2-18', dusta str ) divided by 160 Apsis ( (atop0) would give windlkas. * These should be added (to the Dhruwakalas) if Sun minus Apsis (Ker1dra) is less than a half-circle (6) and subtracted if greater author's (the C0rrection for the Euation of Time due to the Eguation of the Centre) ) is number of armormalistic cycles, the Mean Sun for which period when added to the Mear sum of the Khatra 15,02,008 (drarrarrarru5asya) gives a result in full seconds, wi2ट 4. (Mean Sun) 270.9'-28 Rationale : The Mean Motion of the Sun in one anomalistic cycle is 31 (See opposite page) 35 the Mean Motion of the Sun e१avaroka, (verse 38), is 59-8 for this calculation. as given in the प्राक् पश्चात् समरेखायास्तथा देशान्तरोद्भवाः । तद्विदां सम्प्रदायाद्धि तदियत्तावधार्यते ॥२५॥ इयत्यो लिप्तिकाः स्वर्णमिन्दुमध्य इति स्थितौ । 158 व्यत्यस्यर्णधने तास्ताः शिशिर'घ्ना‘स्तमो'हृताः ॥२६॥ 153 [ देशान्तरसंस्कार : ] स्फुटीकृत्य पुनर्भार्नु सायनस्यास्य दोर्गुणात् । गुणोद्यानं 756 गुणोद्याना'दयो ग्राह्या गुणाश्चरदलाप्तये ॥२७॥ तृणासनं 1840 255 [ चरसंस्कार! । 305 मनोलीनं 903 [ णोद्यानादिचरज्याः ] लूनधनु 457 समभिज्ञः 1048 56 र्देवानीक 2544 607 सनातनः । 1329 1464 1595 धरालयो वीतभयो मधुमान्यं परार्थकृत् । 1953 2059 2156 नवोदयं गुणाधिक्यं धर्मनिष्ठा क्षमापरः ॥२९॥ 2245 2323 2391 2448 शिवरात्रि गरुिगिरः काळागरु दिवाध्वरः । 2493 2525 2551 बन्धुवैरं शिखिशिखा भवः शूरः कृशः स्मरः ॥३०॥ 1190 निधिव्ययः ॥२८।। 1721 (Correction for Terrestrial L0ngitude) 25. Then again, the corrective (viradik८s), on account of the place (in question) being situated to the east or west of the central (Ujjain) meridian, (has to be calculated). Its measure (for the place) is to be known from the traditional knowledge of the learned 26. Therefore, when the correction in minutes to the Mean Moon (for the place, as got by tradition) has been found to be additive or subtractive, the minutes are to be multiplied by 255 (Siऽira) and divided by 56 (ta710) and applied inversely as viradikas. (Correction for Declinational Ascensi0mal Difference) 27. The True Sun is them computed and the precession added Its R Sime in the Sine Table (below) beginning with 153 (gu70dya10) is then noted in order to compute the Declinational Difference (Card-dala) (1-4) (5-8) (9-12) (13-16) (17-20) (21-24) Gurval:Staraऽ (2|5 second) 153 756 1329 1840 2245 2493 305 903 1464 1953 2323 2525 457 1048 1595 2059 2391 2544 607 1190 1721 37 2156 2448 2551 1. Rationale : The sum rises at the rate of 10 wind(likतs earlier or later. as the place is 1० east or west of the standard meridian and this is additive or subtractive, respectively. to get the true [0];ru१७८k८l८. Expert astronomers find this time by various means, and usually express it in terms of correction to the Mean Moon, which, obviously, is negative for the east, and positive for the west . This is transmitted through tradition to succeeding astronomers This can be re-converted into windika s by multiplying the Moon's correction by 25 and dividing by 56. since the mean motion in 255 witadikas is 56 Since the correction-viradikals and the Moon's correct1०n are opposite in sign, the sign is asked to be reversed. 38 1. छाया वैषुवती यत्र द्व्यङ्गुला तत्र केवलम् । गुर्वक्षरात्मकमिदं विद्याच् ततो न्यूनाधिकायां तु तत् स्यात् तदनुपाततः । सायनेऽर्केऽजजूकादौ ज्ञेया तस्य धनर्णता ।। ३२॥ चरदलं तेषामेकविधत्वे स्यादेकीभूतानि तानि सः । भेद एकस्य' चेत्तस्य चापरैक्यस्य चान्तरम् ।।३३॥ चरार्धमात्रसंस्काराद् दिनार्ध त एते धुवकालाः स्युवाक्यकालाः सुसस्कृताः । [ चन्द्रस्फुट: ] कृतम् ॥३१॥ 15 दिनमानाल्लधीयांसस्तेऽहन्येव, निशीतरे । is i eads ‘शुकनाडिकाः ॥३४॥ तेषु स्वभ्रवयुक्तानि वाक्यानि स्फुटशीतगुः ॥३५॥ ततस्तदन्तरालेषु स भवत्यनुपाततः । चापरं, both of which are तस्य तत्कालगमनं यतस्तद्भद्वितयान्तरम् ।। ३६।। For एकस्य the ms. reads ऐक्यस्य and for चान्तरं at the end of the wrong. The emendation is in consonance with the parallel lines in the author's Wepyrol4a. 31. It is to be moted that the above (table) gives the half-ascen and pertain to a place where the cquinoctial shadow is two fingers 39 32. (When the equin0ctial shadow of the place in question is) 1ess or more than (2 aigult.s), (the half-ascensional difference) will be proportional (to the shadow). Its positive or negative nature is to be underst00d from the Sayana-Sum being in (the six signs) from aries (ajadi) or from libra (inlkadi) 33-34a. When the sign of all the three is the same, (the total correction) is their su11 ; when one is different, (thc total correction) is the difference between it and the sum of the other two . The Walk y0 kalा-ऽ duly corrected (as above) will be the ( correct) Dhruwakala 34b-35a. Fifteen (81८८) 141ikas corrected merely by the half ascentional difference will give (the length of) the half-day. Those (Yaky07/kala-s) which are less than the length of the (full) day (i.e., twice the half-day as found above) will fal during daytime and the other (Wakyak८ld-s) will fa11 during might-1ime (True M001) 35b-36. The sum of the (relevant) Valk y'01ऽ (Moo1-sentences) and the (relevant) D/truva.s will give the True Moon-s (at those Walkyakala-s). The True Moon (for times) in between (two Waky८ kala-s) will have be calculated by interpolation. The Moon's motion during a11 interva1 is the difference between the two (relevant) True Moons (and hence the said interpolation) 1. This would correspond to a region having a latitude of 9}°, like Central Kerala, from where the author of this work hailed 221 [ इष्टकालस्फुटानयने मागन्तिरम् । 220 ‘कठोरं’ ‘निष्ठुरं' चैके क्षिपन्त्यूध्वं त्यजन्त्यधः । यथोक्तवाक्यसंख्यायां ‘सुखं' 'दुःख'मतोऽन्यथा ॥३७॥ 27 विदधीतैवमेवार्के स्वर्ण 28 तदन्तरं निहत्येष्टनाङया ‘नत'हृतं ततः । धनर्ण विदधन्त्यूध्र्वमधश्चादावथोदिते ।।३८।। 60 1550 [ इष्टकालरविस्फुटम् ] तथा तन्मध्यमे कृत्वा कुर्याद्वा तत्स्फुटक्रियाम् ॥३९॥ विदित्वास्य गतिं स्फुटाम् । स्वोच्चोनमध्यार्कककिनक्रादिषटकजा । कोटिज्या'त्माशय'हृता गतिर्मध्याऽस्य तत्स्फुटा ॥४०॥ (Am10ther meth0d for True M100n at any time during the interwal) 37. (Another method to derive the True Moon at any desired time is now stated. If the desired time is ) later ( than the Yakyakdla mearest to it), some add 221 (:01/hora) to the Walkyasaiोklya and (if the desired time is) earlier, subtract from it 220 (1ist/hura) (Or perform the operation with 27 (ऽ॥klla) and 28 (dulkha), applied 38. Multiply the diffcrence, i.e., the rate of the daily motion of the Valkya got, by the desired time , in 1तdika.s, and divide the product by 60 (16ti). The result should be added to the Moon's longitude (of the relevant !/akyalk८l() if (the desired time) is later and subtractad if earlier 41 (True Sun at desired time) 39. In the case of the Sun, too, (its True position at any desired time) can be computed using its True Motion. Computation of the True Sun can be done also by finding the Mean Sun (at the time) using its Mean Motion 40. R (Cosine of the Mean Surn-71i115-Higher Apsis is to be divided by 1550 (1710:50]'t) and the result applied to the Sun's Mean Motion, positively (when it is) in the six signs beginning with Cancer (Karki) and negatively in the six signs beginning with Capricorm (Wokra). The True (Daily) Motion of the Sun is got 1. Ratio१८le : Subtraction of 27 from above or addition below gives the mid-wtly0, whose rate is taken as the average for Spbuta-6 of 28 from the interval of 221 is the same as subtraction of 27, and subtraction of 220 is the same adding: 28, the total being 248. Either can be chosen according to convenience. as 2. Rati01१८le : Since the Sun's eu:ation of Centre is proportional to the Sun's Sin M८१nd(a-१८१droः, the variation in it causing true daily motion is proportionate to the Cosine , and, therefo४०, 2ero at 90° and 270° of K८१dr८ः 42 तत्फलं वा ‘जनेनादिं गृहीत्वा स्वयुगां'शयुक् । विदधीत विलिप्तासु तद्वदेव धनक्षयौ ॥४१॥ 10-27१०-3'-10" इष्टाङ्गनासखो नित्यम्’ ‘निःशेषमदनार्तिनुत्' । भागमात्रगतेभर्भानोः स्फुटद्वयमिदं विदुः ॥४२॥ 10'-25०-4'-25" 6-8०-56'-50" ‘शौरीव नश्शिरोनम्यः’ ‘शूली शुष्मिनिकेतनः'। इमौ तन्मध्यमौ ज्ञेयौ श्रीमदार्यभटोदितौ ॥४३॥ 'स्वोच्चतुल्यतनोस्तस्य पुनः शिशुतमा गतिः । निजनीचसमस्यातः पूरिपूर्ति व्रजत्यसौ ॥४४॥ ध्रुवकालोक्तसंस्कारः सधुवेषु तथेष्यते । सूर्यसंक्रमवाक्येषु सूक्ष्मद्युगतसिद्धये ॥४५॥ प्रहर्णणेऽप्ययं शक्यः कर्तुमुक्तविपर्ययात् । स हि तत्संस्कृतो नित्यं भवत्यकर्कोदयाद् गतः ॥४६॥ 1. This verse occurs among the ex'ra has been inserted here in consonance with author's Yepwarolha. verses after the work and itऊ parallel verse in the 41. Alternatively, take the reading for Sun-7iruऽ-Higher Apsis in the Sine Table beginning with j८7erाd. Add to it 1/31 (yag८is०) of itself and apply the result, taken as seconds, to the Mean Motion of the Sun, its being positive or negative being the same as before, (i.e., as stated previous verse). (The Sun's True Motion is got) 42. The two positions of the True Sun (in its course) correct to seconds, when its daily motion is exactly 1 ", are 10-270-3'-10 ' (istaiga71asakho miryam), and 6-8०-56-50” (ris5esaा71adamarinut) 43. The Mean Sun-s at these positions are , according to Aryabhata, 10-25-4-25” (5auriva 705 5ir07071yah) and 6-100-55-35” 4. When the (true) position (Split41a) (of the Sun) is equal to its Higher Apsis, it will have the slowest motion. And, when it is equal to its Lower Apsis, it will have its fastest motion 45. The corrections prescribed for the Dhr't८yakal45 are to be (computed and) applied also to the mnemonics for the Sun's transits (from one sign to another) so that correct results might be obtained 46. This correction can be applied inversely also to the 4harga10 (Total number of Kalidays up to the current day). When corrected in this manner, it will give the True 4largapor which elapsed at sumrise (on that day) 1. This is the table of the Mandajys of the Sun enunciated in the Gralacaranibandh८॥८ of Harridata (ed. K.V. Sama, K.S.R. Institute, Madras, 1954, p. 19) : (1-8) (9-16) (17-24) 8 116 17 41 49 57 64 जनेन सत्येन मुखेन लिङ्गिना यवेन धावेन समेन वर्तनम् । 72 78 85 91 97 102 107 112 रसेन हासेन मदेन योधनं सुधेनु रत्नस्य सुनीप रूपकः । 119 25 121 43 33 124 126 128 129 129 तटस्य धान्यस्य परस्य भद्रक रुचरस्य हारस्य धराप घारकः । These are the Sun's equation of the centre for every 3० of K८rdra beginning from 0० to 90". These are proportionate to Sin Kendra. When shifted by 90", so as to begin from 90° onwards, these will be eual to the Cosines, and proportionate to the variations in the equation of the centre causing the true motion. 8i:ce the constant variation is 1/60 x (1+1/31) of 129', the 44 35 [ राहुः ] 'कान्तं कर्म'विहीनं सत् प्राक्फलं ‘सदना'हतम् । 277 87 प्रहता'न्मूल'हीनात् स्वात् ‘संसारा'प्तसमन्वितम् ॥४७॥ हित्बा लिप्तात्मकं राशिषट्काच्छिष्टं विधुन्तुदः । वाक्यसंख्यावशाद् वाक्यकालेष्वेष तदर्कवत् ॥४८॥ [ ग्रन्थसमाप्तिः ] वदतैतावदैवेत्थं यन्मया नोक्तमन्तरा । सिद्धं कृत्वा समक्षेपि समक्षेऽपि तदस्तु वः ।।४९॥ इति संक्षिप्य सन्देहान् हन्तुं हन्त सतः सताम् । केनचित् सुधिया ख्याता सन्मार्गे शशिनो गतिः ॥५०॥ 12-2-35" 'शीलं राज्ञः श्रिये' कृत्वा प्राक् पुनर्येन निर्मितम् । विलिप्तादिकं वाक्यजातं तेनेयमारचि ॥५१॥ येन [ इति सङ्गमग्रामज-माधव-कृता स्फुटचन्द्राप्तिः समाप्ता । ] 1. Verses 47-48 0ccur among the extra verses at the close of the work and are inserted here as required by their sense and propriety. 2. For यन्मया नोक्तमन्तररा, the ms. reads, यन्मयेनान्तरान्तरा । The correction follows its parallel verse in the author's Veruvarolha. 3. After this occur 7} verses, obviously written by Mādhava himself, (see Preface, p. 10), 2} of them being revised versions of verses in the text. The rest have been fitted into this edition on the basis of the parallel verses in the author's Yeएाvarold. (Node) 47-48. The first result (4gri70plalld of verses 5-6) is reduced by 5161 (karta71 karm10) and multiplied by 87 (sodar10). From the result subtract 35 (71210) and add to the remainder its 277th (staliasara) part. (The result obtained is in ) minutes and * is to be subtracted from 6 to get (the position of) the Node. Its position for the (different) Wakyakala.s is to be computed proportiomately using the /alk yers८ik/hya-s in the same manner as that prescribed for the Sun.1 (Conclusion) 49. Stating but this much and that in a succinct manner, possibly certain details might have been left out by me, at places, under the presumption that those (details) are (generally) known May all those (details) be before your (mind's eye) 50. With a view to dispel the doubts of good men, the motion of the Moon has been set out in a proper manumer, concisely, by a Iman of intellect (which I consider myself to be) . 45 51. By the very same person who composed the set of Moon sentences, beginning with ऽfla71 rajोंal7 6riye (12-2-35"), correct to the seconds, has this work, t00, been composed (Thus ends THE COMPUTATION OF TRUE M00N by Mādhava of Saigamagrāma) minutes per Moon's anormalistic cycle. At 5161 Moon's anomalistic cycles after the Khapda-di१८, the Kep८ for the Node is (35-+-3527) minutes, negative. Hence the subtraction of 35. Since the Node's motion is retrograde, the total result is to be subtracted from the position of the Node at the beginning of Kali, which is 6 r06is. The use of proportion for the days gone during the current cycle is obvious, the motion of the N०e being uniform, 7akya W०. 1. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10 . 11. सङ्गमग्रामज-माधवकृतानेि विलिप्तादि-चन्द्रवाक्यानि Val.ya as Big० शील राज्ञ: श्रिये धिगिदं नश्वरम लोलः पुरुषो नार्याम्' तपस्वी वैदिक: स्यात सेव्याळका किन्नरैः दीप्रो दिने भास्कर धर्मरम्यं सुराष्ट्रम् स्तनौ लीलानुकूली पुत्रादौ न विरागः शौरिः समर्थ एव दुष्टैर्देशोपद्रव : * 0 1 46 1 2 4 12 24 6 18 14 27 10 24 7 21 na' wa' 2 8 21 44 19 8 12 33 8 57 58 35 39 33 16 17 28 59 2) 25 This critical edition of the Walkyas is based on the following four independent mss . : A. Kerala Univ., Ms. No. MC 595-4A ; B. Trivandrum Palace, No. 4116-B ; C. Ker. Univ., No. (C. 2297-C ; D. KItallur Meletatu Mana Ms . 18 2. A. यै ; B. या : ; D शूली त्रिनेत्रोऽव्यात् । Some of the 7akyas in B and D are entirely different and represent different versions. 3. A. र्या: ; B. 4. A. for पद्रवः, A reads बभूव, a scribal error on account of similarity in the Malayalam script. 1. 3. 5. 12. 13. 14 . 15. 16. 17. 18. 19. 20. 21. 22 . 23 . 24 . 25 . 26. 27 . 28 . 29. 30. 31. 32 . 33 . 34 . व्यग्रो जनः क्षुन्नाशे योगीश्वरो निराशा शिाखण्डी भवनेष1 नागो यानाधिपति : परिणयेऽङ्गनेच्छा कविकण्ठस्था कथा शीलसम्पद्यानन्दः श्रीर्विना न मुकुन्दात् निराधारोऽहिराज कुबेरो विकटधीः स्तेनानां इवा विरोद्धा दीर्घरिरंसुन नाके वानरो मधुपानाढ्य : घननिकरो निर्ययौ रीगे' धैर्यविपर्ययः स्थूलो गिरिश्चित्रकूट: स्तम्भमात्रो हि धीरधीस्त्रिनेत्रः प्रपदौ गुरोर्नम्यौ छन्नो' माणवकः किम् गानगोष्ठी सुखाय काकुध्वनिर्नकारात् तनुर्न नगरे श्री: D. स्मरगभ वनिता A. रावणो, corrupt. B. मात्रोऽहिः 2. 5 4. 9 9 10 6. 11 10 11 11 0 1 1 Bhaga 20 19 4 17 3 28 11 24 7 19 14 26 200 8 14 A. रोगो 27 10 23 24 43 15 21 17 29 42 40 22 52 10 19 23 25 29 38 55 23 B. निोद्धा, corrupt. ' 21 31 25 30 21 41 35 42 20 31 6 48 4 32 37 46 29 12 7 C Breaks of with this word. 47) 43 35 . 36 . 37 . 38. 39 . 40 . 41. 42 . 43 . 44 . 45 . 1. 47 . 46. 48 . 49. 50. 51. 52 . 53 . 7. 54 . 55 . 56. 57 . शैलाः पुष्पितनगा लोलो जलधि: किल धनी नरोऽङ्गनावान्’ सर्वविद व्यास: कवि: स्तेनेन द्रव्शानाशा: सूर्यो बलमाकाशे मनुष्यो मधुरात्मा गान नेष्ट विपत्तौ पर्वचन्द्रोऽग्रिस्त: भोगेच्छालं प्रियेऽर्थे मागधी गीतरसः लीनो नागो5 निकुञ्जे गामुक्षा न विरेजे" रवौ हरे: ’ सन्निधिः वर्णान् वागनुरुन्धे भावे स्मरोऽङ्गनानां स्यात् गायत्री नास्तिकैनिन्द्या धनं चोरो हरेन्नित्यम् धर्म धिगनपायस्य धीगतिर्भद्ररूपेयम् क्षीराब्धौ विभूः यमोऽयमन्तिके गौरी स्थाणोदररा: A. नला: A. सूर्य A. लोनोऽनङ्गो B. हारः 4 5 6 7 7 8 9 10 10 10 11 0 2. 4. 6. 8. 19 3 17 15 29 1 4 28 12 26 10 24 7 20 3 16 28 10 22 4 16 28 38 A. वागनिरुन्धे 20 14 20 33 10 26 37 39 30 28 34 25 2 26 39 46 49 A. -ङ्गना वा D. मधुराशः B. D. विरुजेत् 51 57 35 33 9 47 17 41 34 35 53 42 54 44 13 9 59 39 26 51 23 58 59. 60. 61. 62 . 63 . 64 . 65. 66. 67 68. 69. 70 . 71. 72 . 73 . 74 75 . 76 . 77 . 78 . 79. 80 . 81. 82 . गरळं नोपयञ्ज्यात गोमानलं गरीयान सुग्रीवोऽनन्तनिष्ठ :1 प्राज्ञो रामो दैत्यारि : प्रशाभाशया नागा: चपलः कामपाल: वाग्मी तु वादरागी गङ्गा भागीरथ्यभूत् तपस्वीगतिरूध्र्वम जरद्भवोऽनुद्यम सूनुर्धामाभरणम् गुणोऽसूया धनिषु विकृता गौडरीति: लघुर्न मैथुनेच्छा' प्रानन्दमयो रस: कल्यः शिशुर्मनुज : वढधीलब्धपद लीना प्रापोऽम्बुनिधौ। क्षामवारिस्तोयधि भाग्यविरोधः क्रोधात् धरा हीनाश्रया नित्यम् जनोऽन्धो गत्वरो नश्येत् मुकुन्दान्मोक्ष उपेयः श्रा गोहीनोऽधिकः पटुः ज्ञानी गाग्यय 1. D. सुखी वनितानिष्ठ 3. D. [बालरीतिः 5. B. गागोंऽयम् Sphuta-7 3 4 5 5 6 8 9 9 10 10 11 11 Bhaga 23 18 28 12 26 10 24 9 23 21 19 16 29 12 24 6 19 30 52 54 13 46 34 34 43 59 17 36 50 58 55 39 10 24 24 8 39 58 8 13 2. D. राज्ञां 4. D. गावोऽनुशासनस्थाः 23 53 27 50 54 33 16 28 53 14 43 11 48 56 14 29 15 30 49 83. 84. 85 . 86 . 87. 88 . 89 . 90. 91. 92 . 93 . 94 . 95 . 96. 97 . 98 . 99 . 100 . 101. 102. 103 . 104. 105 . कृपणः कौण्डिन्यः लोला दीपशिाखा स्वर्गस्तु प्रार्थनीयः सौम्रात्रं वाधिक स्यात् लीनोऽळीनो* त्रिनेत्र: धिगाहवविकारः शिशिरा वासरश्री : अमिरामा नकली धमर्मोऽर्थः पूर्वरङ्गः मानुजो मिथुनेऽभूत् रौद्रो यमस्यारम्भ धिगाशामशानेऽस्मिन् जनार्दनो नरेशा : मृगाः शूरा वनान्ते चण्डो वै भोजपतिः धीगम्योऽनङ्ग एव धैर्यालय: सन्न्यासी" चन्द्रात्’ तापापनोदः सेव्यो जनैर्मुकुन्दः अभिषवोऽहरहः कायऽनायै*रुपधि:7 मानदेयं मरळी ज्वलनो यजने " नम्यः R 1 2 } * 6 8 10 Bhaga 25 7 19 14 27 10 24 21 5 20 4 18 15 28 12 25 15 18 26 42 48 42 52 17 58 51 55 25 44 1. B. सु (wrong 2. D. लीनोधीनो B. लीनोळिनोश्र नेत्र 4. B.D. सन्न्यासः 3. 5. B.D. चन्द्रः 6. B. नान्यै 7. B. –रधिपतिः (corrupt) ; D. कार्या नार्या रूपधीः 8. D. ज्वलनोऽयं जनैः 1 13 16 46 10 18 10 33 34 27 39 55 40 59 22 39 35 36 39 19 26 17 40 11 34 106. 107 . 108. 109 . 110. 11. 112. 113. 114. 115. 116. 117. 118. 119. 120 . 121. 122. 123 . 124 . 125. 126. 127 . 128. 129. क्रीडा दृढा नरनार्यो : विश्वं गोपाल एकाकी ' फलाहारो मूख्यकल्प : धन्वी झाली सुरैः पूज्य : गोमदो गळी धनुज्य विपाठा आढच्य: षड्भागैर्तृपः धन्यः* स्थाणुमुपेयात् धिगसौख्यं हिरण्यात् देवो धावन्नैकत्र तन्वी शीलगरिष्ठा लक्ष्मीस्तुङ्गस्तनाङ्गी चला लक्ष्मीर्धन्यगा धिगशीघ्रगा नाव : पूर्णः पयसा कुम्भः कठिनोऽयं कीनाशा: धिगहंयुमकस्मात् षड्भागबन्धुरोश कठोरो मृगपतिः क्षीणो न व्याहरति धर्मशास्त्रं श्रेयसे लोकोऽभिलाषी रसे6 सागरो गोर्न पदम् रविजुष्टं वारिजे' 1. D. विभुगपालनायकः 3. B. विपरी 5. B. धीमान् मुरारिव्यास 7. B. रविजो युवराज R 10 11 11 11 1 1 2 3 5 6 8 20 15 27 21 3 15 28 10 23 19 17 3 29 13 28 12 26 4. 10 24 6. 48 13 28 35 38 41 46 57 17 49 35 36 53 25 18 33 52 10 25 34 32 18 B. धन्या B. लाषिरसौ 32 44 32 49 53 10 19 39 48 46 53 36 39 51 21 39 46 21 56 59 13 37 42 5 1 52 1. 3. 130 . 131. 132 . 133. 134 . 135. 136. 137 . 138. 139. 140. 141. 142 . 143. 144 . 145. 146 . 147. 148. 149 . 150. 151 . 152. 153. 154. साम्बोऽनिशां सन्नद्धः A. रोगः प्रत्यासन्नः पुरोधा इष्टिदनं विना नेष्टा नानाभिमतं कनकम् श्रीनतः श्रीधरो नित्यम1 सुकृति: स्वयं पाककृत् काष्ठसमा गात्रयष्टि : प्ररिरनाप्तः चण्डभानुर्जयी व्यवच्छिन्नोऽनुनयः* कीनाशो व्याघ्रप्रकल्पः वाङ्माधुरी वरेण्या श्रीकृष्णो मोक्षनिष्ठ हृष्टो लीलाधिकारी स्वामी शरीरेऽनिलः स्थाणुर्गङ्गाशयालुः तैलाथ भन्दरोगी3 स्धानाच्चला रिपवः विनोदरुचिः प्रभुः साध्यो योगो नियमात्' पत्नी गभभरणा स्तेनो न निर्धनैषी सेनाधिकाङ्गरक्षा श्रीगतिालसा नासीत् धर्माज्जीवेत् परासुः B. रत्नचक्रधरा नार्यः 10 10 10 11 11 1 1 2 3 3 4 5 7 7 2. 4. 7 21 4 16 29 11 23 18 0 12 24 19 2 15 28 12 26 10 24 23 7 21 50 8 54 26 46 57 7 15 29 55 33 25 33 57 36 28 31 43 36 48 B. छिन्नेऽन्ननयः D. योगनियमः 37 12 10 2 17 21 20 36 41 54 12 18 54 57 36 17 32 59 Valk]ya 1. 3. 5. 7. 9. Wo. 155 . 156. 157. 158. 1 59. 1660. 161. 162. 163. 164 . 165 . 166 . 167. 168 . 169. 170. 171. 172. 173. 174. 175. 176 . धनी गुणी मनुजः परिषत्स्वधिकेहा दिव्य: क्षीराम्बनिधि: धीरः कर्णस्तु योद्धा तनयो ज्ञानिनां नम्यः! गोकर्णमित्रं पिनाकी प्रभवो गुणरत्नाढया: प्रकृत्याऽऽनन्द उत्पाद्य: अनसूया निरपाया जिष्ण*र्वरिष्ठः दिश्यादिन्द्रो भाग्यम् नगो न गोचरत्’ गानशीलो जनोऽयम पुराणो भानुरीडय: बालोऽभून्नीलनेत्रः जटी शूली शाङ्करः प्रवद्धोऽयं जाठर:6 सन्निधौ स्यात कपाली7 दीनेष्वीडा विफला बाल्येऽवज्ञो जनो वै सौम्यधीः स्वयं प्रभुः बालास्तु वाग्मिनोऽमी” RS 8 9 9 10 10 10 11 11 0 1 2 3 3 5

Bhaga 19 16 0 12 25 20 2 14 26 20 28 11 24 21 5 K ala 53 46 26 51 55 34 17 24 28 30 35 45 35 19 19 34 49 46 21 18 29 13 42 12 58 18 30 21 33 18 42 13 17 33 A. नेयो ज्ञानिना नम्यः (corrupt) 2. D. नूनं सत्येन श्रेय(:)स्या(त्) D. विष्णु 4. D. गोचरः B. पुराण 6. D. प्रवृद्धः कुञ्जरेन्द्र D. सन्नद्धोऽयं कपिलः 8. B. खाण्डवघ्नो B, दाशाह्मिनोनै (corrupt) ; D. स्वामीनोऽमी 54 177 . 3. 178 . 179 . 180. 181 182 . 183 184. 185. 186 . 187. 188. 189. 190. 191. 192. 193 . 194 . 195 . 196. 197. शाशलक्ष्माधिकाँशुः सुखदं नवनीतम् घन्वन्तरिर्जयति वागीशो वारनाथ : फलज्ञानेच्छा " कथम् धान्ये न कस्यानन्दः दगयमनिन्द्या प्राज्ञौ विष्णरुद्रौ10 चारार्थी महाराजः 8 सोमोऽनङ्गारिव्याधः' 9 मत्यर्थो धन्वा शारधी: शशी कुमुदिनीनम्यः 10 रुद्रो धीगम्यः प्राज्ञेः स्यात6 10 पद्माक्षी शोभनास्या ईशप्रियो7 विनायकः 11 विद्योज्ज्वला तार्किकस्य ' 11 धनाप्ताभूदद्रिकन्या 11 मगों" गोनाथः पूज्यः हरिः सेव्यो धरया * पौलस्त्यो भयङ्करः 1. B. D. सत्राजिन्न विनीतः R B. धान्यै: ; D. घन्यै: S 5. D. मुकुळाभा मुरळी 7. B. रङ्गप्रियो 9. D. धनुषा भेदो रिपोः स्यात् 11. B. स्वगों 6 7 0 1 19 18 17 15 28 12 2:5 21 4 16 28 10 22 17 29 53 26 45 0 57 30 49 51 39 12 34 46 51 54 56 17 2. D. पयस्यनिच्छा 41 55 8. B. ज्वलस्तु 10. D. प्रज्ञावान् मुरारिः 12. B. धरायाम् 27 49 34 32 19 55 26 57 15 22 50 14 38 51 34 28 4. B. -रिव्यधि: ; D. सुमनोङ्गरू *** 6. D. प्रारब्धं लङ्केन्द्रनाट्यम् 31 198 . 7. 9. 199 : 200. 2011. 202. 203. 204. 205. 206. 207. 2008 . 209, 210. 211. 212. 213. 214. 215 . 216. 217 . 218. 219. स्थाने जयो वरिष्ठ:1 मानघनः सानुग * तरुण: को न रागी गौरी सलीला न वा करीभव्योऽसौ युवा तमस्विनीयं निशा रत्नासनमुपेमः हेम सम्पद्धारिणाम् ' जडी विडम्बयति सलिलाशा सम्प्रति गुरुकाय' प्रयास पाण्डवा: प्राप्तरथा: शिवधीरनापदे6 चापी वीरो द्विरदे ’ शाश्वन्मौनीजनोऽन्ध : मूल फलाढयश्राद्ध. तमालामो घनो नित्यम् प्रभोधिगच्छकनकम् ' वैश्वानरं नानुयायात् रागादिवैराग्यं पथ्यम् श्रीरामनाम रम्याग्रयम10 प्रज्ञावान पार्थः 1. D. पवेन्दुः पर्वरात्रि 3. D. करभः पाथेयवान् 5. D. काव्ये D. तपस्वी प्रवरो हि D. प्रवाळऽल्पासिकनकम् RS 5 10 1 0 11 11 2. 4. 8 11 6. Bhaga 24 20 17 15 - 29 13 27 12 26 10 24 21 4 17 0 12 25 B.D. धारिण: 18 15 37 B. घीरा नापदी 14 17 34 53 24 29 24 32 43 39 20 48 D. मानाधिनाथो नागः 14 8. B. शृङ्गीरङ्गोपरुद्धम् 10. D. श्रीरामो नामरकल्प: 26 23 21 56 58 38 37 23 31 45 16 45 35 56 42 44 32 22 56 220. 221. 222 . 223 . 224, 225 . 226. 227 . 228 . 229 . 230. 231. 232 . 233 . 234 . 235 . 236. 237 . 238 . 239 . 240 . 241. 242 . बीभत्सुर्योधोऽयम् ग्रामाधिपः* कनकी धम्मिल्ले फुल्लपुष्पम् कालो बली शारण्य तुङ्गयशसो नराः धर्मज्ञा: प्राड:नरेन्द्राः दीघङ्गो नीलनाग : फलाढयो ऋतकाल केशवो योद्धा रङ्ग सौबलो वरयवा पद्मेषु रन्ता रविः भ्रमरश्रीनिकामम तपोधराः स्वैरिण श्राद्यो गोविन्द एषः षट्'काव्यज्ञोऽम्बरीष उद्यानं स्त्रीसनाथम दीपतैलं पात्रस्थम सूर्योऽस्तु वो मानदः भानुः सर्वाधिको हि पीनोत्तुङ्गाङ्गो नळ: हीनपापः सुयोद्धा सूनुः कुलीनोऽनुनेथः तरुणो बलीयानाढय : 1. D. वि(व)ासाः काळ्यि : 3. D. श्रीमान् धृष्टद्युम्नो 5. D. सत्कृ(तो) वा मनो हि 1 1 2 3 4 4 5 6 7 10 10 2. 6. 4. 13 25 20 16 29 2 12 26 24 10 23 7 1 19 17 13 B. ग्रामाधिक 19 D. धरणो 23 33 51 20 1 4 43 26 22 29 43 20 4 6 47 36 31 35 B. सत for षट 52 59 31 36 59 48 32 51 37 51 52 16 10 10 18 26 243 . 244 . 245 . 246 . 247 . 248. बालेऽभिरुचिरनल्पा ' 2. स्थिरधीर्महीनायकः स्वनरीि रम्यरूपाढया । भीमो वलल: शशी नभोमध्ये धीरगीर्मासुरा 10 D. धरालाभे सुखम् 11 11 225 248 0 0 26 8 21 3 15 1. B. बालोऽभिरुचिरं नित्यम् ; D. बलभद्रस्तु प्राश्रिक : 27 विलिप्तादि-चन्द्रवाक्यानि । ]* . इष्टसंख्योन-‘देवेन्द्र-वाक्यं तत्प्रतियोगिकम् । तस्याधऊध्र्वविवराद् द्विगुणाद्यविवर्जितात् ।। 24 [ इति सङ्गमग्राम्ज-माधव-विरचितानि 59 22 34 40 43 33 'शिखरा'प्तकलाहीनं प्रतियोग्यं ततस् त्यजेत् । इष्टवाक्यं भवेच्छिष्टम् एवं स्याद् वाक्यशोधनम् । 27 3. Ms. B carries the following two verificatory verses which set out a method for checking, in case of doubt, the correctness of any Sentence in the above Table : 54 95 29 Tra115. : 248 (de1yermudra) 171inus the number of the desired (i.e ., the doubtful) Sentence is (to be termed) the former's Complementary Sentence (pratiy08ik८). Take the (two) Sentences above and below it and find their differ ence. Subtract from this difference twics the Initial Sentence of the Table Divide this difference by 225 (8ill apra) and subtract the quotient from the Complementary Sentence. Subtract the Remainder from the Final Sentence (of the Table, viz., d ragr blaऽ१५ra). The result will be the correct figures of the Checking of the S Example : It Complementary Sentence, (248-50) ==198 Difference Sentence above Do, wi८, 199 Do. below D0., yiट., 197 Difference Twice the Initial Sentence, 2X(0-12-2-35) = Do. divided by 225, i.e ., correction Complementary Sentence (1993) Final Sentence (248) Difference (i.e., Corrected Compl. Sent.) = Final minus Cor. Compl. Sent. may be दुष्टैः facilitating recollection : (71) 'eti1f d (i ४. In ms. D, in continuation of the according to this ms . of woky ya numbers (131) (191) noted that that the result धनुषा कुबेर ८c ul tful) Ser ter ce. (81) अ गो (141) (201) गौरी च्छन्नो प्रत्यासन्नः वाङ्माधुरी स्तेन (151) (21) तपस्वी मनुष्यो (101) सेव्यो (161)

1. #

= प्रभवः (221) श्रीमान् = = गायत्री प्रवृद्ध (171) 3 (231) 2 (12) भ्रमर is the value of 2 2 10 T b।'s is (stated) the 7 11 24 25 1 24 24 27 3 the (181) 9 41 27 पयसि 22 18 vakyas, the initial letters (proatk८-s), 11, 21, 31 etc. are given, obviously for 17 43 25 कठिनो (241) राज्ञाम्. 5 31 34 10 24 7 22 45 29 desired 50tb 44 M. Do then continue doubtful sentence :

• y

with a verse

,

इष्टसंख्योन-‘देवेन्द्र'-वाक्योनान्त्यमिहे(ष्ट)कम् । स्वोध्र्वाघोविवरार्धाद्यविवरात् प्रियका ‘'प्तयुक् । इतु वाक्य वरुत्वान् । 248 7rans. : (Sentence number) 248 (d८५४१॥dra) mi१u the number of the desired (i.e., doubtful) Sentence (owill give the number of the complementary Sentence) : this (Sentence) when subtracted from the Final Sentence will give the (Rougb) desired Sentence, (which needs the following correction). Find the 248 (de1"611drd) १mi१us 5 b८low it, balve his difference and divide by 112 (priyaka). Add the quotient to (Rough) desired Sentence (as found above. The result will be the correct desired Sentence). This is (the method) to derive the (doubtful) Sentence) . (Correction The Final Sentence (248) Rough desired Sentence for checking Half of difference Sentence just above (199) D०. just below (197) 198 Difference Divided by 112i.e., Correction Correct desired Serate nce Correction added to the Rough sentence the correctness of It may be noted that this is 1e 5[1] = =ः (1 ।। 1 (e, (12) 2 10 3 10 10 {। 21८ 27 43 24 3 25 7 11 25 18 12 9 41 27 12 43 2 41 3 25 3 25 29 7 22 5 31 34 47 35 12 59 22 any 44 अनुबन्धः २ युगभोगध्रुवा: 5-100-7'-40'. 48"' 2-279-33'.7"-12"' दिवि नव सानु निकामं, प्रापुः सेना बली सुरा राज्ञः । 7-69-57'-31".0' 6-220-45-7"-12" अनु किल सम्मतिनाथं, प्राप्य स्थानं शिवारितम् ।। १ ।। 3-249-37-26"-24" 6-150-4'-19"-12"' वरतरसालभराङ्ग, राज्यं धन्यं भुनज्मि पूतान्नम् । 1-49-30'-43'-12 11-16०-50'-52"-48 प्रियगभों नगवनकृत् , देवरमौनं मतं कृपया ।। २ ।। पादे पादे ज्ञेया युगभोगाः शीतरश्मिमुख्यानाम् । पातान्तानामष्टौ यथाक्रमं तत्परादीनि ।। ३ ।। 1. These three versॐs give the Zero-corrections, correct to t41 para-s (1/60th of a second) for Moon etc. per yuga (aeon, of 2,10,389 days). The verses occur in the Graliacara1ib011dlharma (1.17-19) of Haridata (A.D. 683) the basic manual of the Parahita school of Kerala astronomy (Ed. by K.V. Sarma, K.S. Res. Inst., Madras-4, 1954), preceded by the following verses : अहरात्मकमत्र स्यात् ‘धीजगन्नूपुरं' (2,10,389) युगम् ॥१२॥ युगभोग ध्रुवं कुर्याद् युगमानविवर्धितम् । राशिषट्कत्रिकाबिन्दुपातोच्च ध्रुवयोर्धनम् ॥१६॥ 2. सदा कृपया (corrupt), for मतं restored from the Gralhacaratribarldllar1. 60 कृपया, which latter has been Moon Mars Mercury Jupiter Saturn Moon's Higher Apsis Mo0n's Node Foot by foot, (the 5 7 6 3 2 27 33 6 1 0 10 above ।। 7 6 57 22 45 15 24 37 4 4 30 11 16 50 verses ) 40 7 31 7 26 19 43 52 are (giving) the Zero-corrections, correct to the ta1p007 48 12 0 12 24 12 12 48 to be the planets from Moon to Node, in order, per aeon. understood. as (1/60th second), to अनुबन्धः ३ कतिचन खण्डाः तदीय-स्फुटचन्द्रध्रुवाश्च ‘मनसा शम्भुः स्तुत्य ’ ‘स्वगथीं लोक ईशानात्' । लोलो गङ्गाम्बुचयो' ‘भद्रा धीभगिनाथानाम्' ।। २ ।। पाताळेन श्रुतयो' “भाग्यं ध्यानार्चनाधीनम्' । ‘धीजो मदनश्चापी’ ‘भानुगपो जनैः पूज्यः' ।। २ ।। ‘मोहाधिक्यं प्रणयात्’ ‘क्षोणीशोऽलं गुरोध्यनिी' । ‘स्त्रीसङ्गः प्रीत्यै नो' 'नित्यं दैवं स्थिरं धेनौ' ।। ३ ।। ‘भद्राकारा श्येना’ ‘कविवरग् ज्ञानी नळो नूनम्' । ‘गोळो नद्धोऽनेन’ ‘व्यालोलाङ्गः खराधीनः ।। ४ ।।

• प्रीतोऽनन्तः ज्ञानी’ ‘काष्ठा रत्नांशुकानां का' ।

‘योगी नो गानज्ञो’ “नित्यं पिण्डाथिनः काकाः' ।। ५ ।। ‘तीर्थ धारा नूनम्’ ‘भवेत् पवित्रं न पापानाम्' । 'होरासारः ज्ञानी' 'शोच्यो हिमवाननुद्यानः' ।। ६ ।। ‘इन्दुर्भद्रो नूनम्’ ‘सर्वे विद्यार्थिनो धनिनः' । ‘रङ्गे रुद्रो नग्नो' ‘दिव्यो योगी धनैहनः' ।। ७ ।। ‘वैदग्धी यज्ञेरज्ञा’ ‘धन्वी सेवापटुः सूनुः' ।

• चण्डः सम्पन्नो ना’ ‘पुरभिन्नैवाच्र्यतेऽज्ञेन' ।। ८ ।।

‘देही विद्या नूनम्’ ‘श्रीमानिन्द्रस्तपोमानी' । ‘नीवी रम्या नूनम्’ ‘गौरी साम्बा जपाभा नु' ।। ९ ।।

• श्रद्धाधीनं ज्ञानम्’ ‘जीर्णा गीर्मेऽनुरागोना' ।

विष्वक्सेनो ज्ञानी' ‘क्षेत्रज्ञोऽयं गुरुः प्राज्ञः' ।। १० ।। ‘स्तब्धा वाङ् नो ज्ञानं’ ‘सोमस्तरुणप्रियो नूनम्' । ‘देवः प्राज्ञो नूनं’ ‘धीरोऽलं भासुरो ज्ञानी' ।। ११ । । श्लोकदलाद्ये पादे त्यक्तव्यो दिनगणः समुद्दिष्टः । विकलाद्यः स्फुटचन्द्रस्तदीयभाजो ध्रुवा द्वितीयेऽस्मिन् ।। १२ ।। 62 SOME LUMP DAYS AND THEIR TRUE-M00N 16,45,705 16.33.333 16,20,961 16.08,589 15,21,985 12,372 12,124 9093 6062 303 11 2976 2728 2481 2232 1984 1736 1488 1240 992 744 496 248 11 9 10 11 11 23 63 27 22 14 20 23 25 37 49 13 35 48 33 31 41 58 14 47 20 37 53 10 26 34 24 14 56 10 31 21 11 44 47 18 49 21 52 23 58 26 27 43 29 In the first part of each half, the number -verseof days to be deducted are indicated. And, in the second part, the True Moon , being (also) the corresponding Zero-correction, to c0rrect the second (vikala), has been indicated. 57 अत्राप्यौत्पत्तिको 13 a अधोध: क्रमशो 2 a अनकारहरं 1 b अनु किल सम्मतिनाथं App. II. 1 b अर्कमध्यं विलिप्तादि 22 b अस्मिन्ननन्तरातीते 19 a अहर्गणेऽप्ययं शक्य: 46 a आदिकर्मेग्रिमफले 22 a प्राद्यमल्पतमं कृत्वा 11 b सङ्गमग्रामज-माधव-कृता। स्फुटचन्द्राप्तिः श्लोकाधनुक्रमणिका इति संक्षिप्य सन्देहान् 50 a इत्थं तथैव वाप्तेषु 21 a इन्दुर्भद्रो नूनम् App. App. III. 7 a इमौ तन्मध्यमौ 43 b इयत्यो लिप्तिका: 26 a इष्टाङ्गनासखो नित्यं 42 a उपर्युपरि पूर्वस्मात् 14 a एकद्वित्र्यन्तरे कायें 19 b एकस्मिन् ध्रुवकाले 16 a कठोरं निष्ठुरं चैके 37 a कान्त कर्मविहीनं सत् 47 a केनचित् सुधिया 50 b कोटिज्यात्माशयत्रता 40 b गुणोद्यानं मनोलीनं 28 a | 64 गुणोद्यानादयो ग्राह्या 27 b गुर्वक्षरात्मकमिदं 31 b गोळो नद्धोऽनेन App. III. 4 b चण्डः सम्पन्नोना App. IIII. 8 b चरार्धमात्रसंस्कारात 34 b छाया वैषुवती 31 a त एते ध्रुवकालाः स्युः 34 a तत एवाञ्जसामीषां 15b ततः सर्वार्थयुक्तेन 18 b ततस्तदन्तरालेषु 36 a ततोऽधिक तु तत्रांशा 10 a ततो न्यूनाधिकायां तु 32 a तत्कालमध्यमार्कस्य 24 a तत्फल वा जनेनादिं 41 a तथा तन्मध्यमे 39 b तदन्तरं निहत्येष्ट 38 a तद्ध्रुवा स्वार्कमध्याय 12 b तद्विदां सम्प्रदायाद्धि 25 b तस्य तत्कालगमनं 36 b तीर्थकाङ्गात् मृगानीकैः 17 a तीर्थ धारा नूनम् App. II. 6a तृणासनं लूनधनु 28 b तेनैवाद्यस्तथैकैक 6 b तेषामेकविधत्वे 33 a तेषु स्वध्रुवयुक्तानि 35 b तैः सार्ध तत्र तत्र स्यू: 12 a दाराधीनसख 23 a दिनमानाल्लघीयांस: 35 a दिवि नव सानु App. II. 1 a दीननम्रानूशास्योनं 5 a देवः प्राज्ञो नूनम् App. III. 11 b देही विद्या नूनम् App. II. 9 a द्युनिशोरविशेषेण 13 b धनर्ण विदधन्त्यूध्र्व 38 b घरालयो वीतभयो 29 a धीजो मदनश्चापी App. III. 2 b घृतालयहृता 8 b ध्रुवकालेऽपि येनैक: 18 a श्रवकालेष कार्योऽन्य: 21 b भ्रवकालोक्तसंस्कारः 45 a नवोदयं गुणाधिक्यं 29 b नाडीषष्टयन्तरेऽप्येवं 20 a निजनीचसमस्यात: 44 b नीवी रम्या नूनम् App. III. 9 b पातान्तानामष्टौ App. II. 3 b पाताळेन श्रुतयो App. III. 2 a पादे पादे ज्ञेया App. II. 3 a पृथक् तच्छेषरहित 8 a प्रणम्य प्रणये 4 a प्रत्यहं वाक्यनवकात् 2b प्रमुष्टसम्प्रदायस्य 15 a प्रहतान्मूलहीनात् 47 b प्राक् पश्चात् समरेखाया 25 a प्रियगर्भों नगवनकृत् App. . 2b 11 प्रीतोऽनन्त: ज्ञानी App. I1. 5 a बान्धवैरं शिखिशिखा 30 b भद्राकारा श्येना App. III. 4 a भवद्भ्यः प्रणतोन्नत्यै 4 b भागमात्रगतेभनो: 42b भेद एकस्य चेत्तस्य 33 b मनसा शम्भुः स्तुत्य: App. II. 1 a मुहुःप्रक्षिप्तपर्याप्त 7 b मोहाधिक्यं प्रणयात App. II. 3 a यथोक्तवाक्यसंख्यायां 37 b योगी नो गानज्ञो App. II. 5 b रङ्गे रुद्रो नग्नो App. II. 7 b लभ्यते तेन कर्तव्या 6 a लिप्तादि सत्ववान 9 a लोलो गङ्गाम्बुचयो App. III. 1 b वदतैतावदैवेत्थं 49 a वरतरसालभराङ्ग App. II. 2 a वाक्यसंख्या ध्रुवो नान्यः 20 b वाक्यसंख्यावशाद् भूयः 23 b वाक्यसंख्यावशाद् वाक्य 48 b वाक्यसंख्यास्तथाधोऽधो 14 b विकलाद्यः स्फटचन्द्र: App. III. 12 t विदधीत विलिप्तासु 41 b विदधीतैवमेवार्के 39 a विभज्य लब्धं भागादि 17 b विलिप्तादिक वाक्य 51 b विष्वक्सेनो ज्ञानी App. III. 10 b वैदग्धी यज्ञेरज्ञा App. III. 8 a [C) COMPUTATION OF TRUE M1030N व्यत्यस्यर्णधने 26 b शशहीना पुन: 16 b शिरश्शरणशीतांशु 1 a शिवदूताहतं 5 b शिवरात्रिर्गुरुगिर: 30 a शिष्टात्तु शिवदूताप्ता 7 a शील राज्ञ: श्रिये 51 a ; App. I. 1 शौरीव नश्शिरोनम्य: 43 a श्रद्धाधीनं ज्ञानम् App. 11. 10 a श्रुतमात्रे प्रकारेऽस्मिन 3 a श्लोकदलाद्ये पादे App. III. 12 a स च विश्वैकनाथश्च 9 b स हि तत्संस्कृतो नित्यं 46b साधयित्वा ध्रुवांश्चैव 11 a सायनेऽर्केऽजजूकादौ 32b सिद्धं कृत्वा समक्षेपि 49 b सुगुणा विकलास्तासु 10 b सूर्यसंक्रमवाक्येषु 45 b स्तब्धा वाङ् नो App. III. 11 a स्त्रीसङ्गः प्रीत्यै नो App. III. 3 b स्फुटीकृत्य पुनभर्नुि 27 a स्वर्ण स्वोच्चोन 40 a स्वस्यैवानधिकारेण 3 b स्वोच्चतुल्यतनोः 44 a हित्वा लिप्तात्मक 48 a होरासारः ज्ञानी App. II. 6 b