Vedanga Jyotisha

पञ्चसम्वत्सरमयम्युगाध्यक्षम्प्रजापतिम्। दिनर्त्वयनमासाङ्गम्प्रणम्यशिरसाशुचिः ॥ १ ॥

pañcasamvatsaramayamyugādhyakṣamprajāpatim| dinartvayanamāsāṅgampraṇamyaśirasāśuciḥ || 1 ||

Having bowed my head in purity to Prajapati, lord of the yuga that consists of five years, whose limbs are the days, the seasons, the ayanas and the months —

प्रणम्यशिरसाकालमभिवाद्यसरस्वतीम्। कालज्ञानम्प्रवक्ष्यामिलगधस्यमहात्मनः ॥ २ ॥

praṇamyaśirasākālamabhivādyasarasvatīm| kālajñānampravakṣyāmilagadhasyamahātmanaḥ || 2 ||

and having bowed my head to Time and saluted Sarasvati, I shall declare the knowledge of time of the great-souled Lagadha.

ज्योतिषामयनम्कृत्सनम्प्रवक्ष्यामनुपूर्वशः। विप्राणाम्सम्मतम्लोकेयज्ञकालार्थसिद्धये ॥ ३ ॥

jyotiṣāmayanamkṛtsanampravakṣyāmanupūrvaśaḥ| viprāṇāmsammatamlokeyajñakālārthasiddhaye || 3 ||

I shall set out in due order the whole course of the heavenly lights, as it is agreed among the learned of this world, for establishing the times appointed for sacrifice.

निरेकम्द्वादशार्धाब्दम्द्विगुणम्गतसञ्ज्ञिकम्। षष्ट्याषष्ट्यायुतम्द्वाभ्याम्पर्वणाम्राशिरुच्यते ॥ ४ ॥

nirekamdvādaśārdhābdamdviguṇamgatasañjñikam| ṣaṣṭyāṣaṣṭyāyutamdvābhyāmparvaṇāmrāśirucyate || 4 ||

The half-years, less one, multiplied by twelve and then doubled, joined with the number already elapsed, and increased by sixty for each of the two — this is called the sum of the parvans.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Sarma and Kuppanna Sastry differ on whether the sixty is added once or to each of the two terms; the rendering keeps the text’s literal "sixty and sixty". Read the numbers as the text's own, not as a settled interpretation.

स्वरार्कमेकेसोमार्कौयदासाकम्सवासवौ। स्यात्तदादियुगम्माघस्तपःशुक्लोदिनम्त्यजः ॥ ५ ॥

svarārkamekesomārkauyadāsākamsavāsavau| syāttadādiyugammāghastapaḥśuklodinamtyajaḥ || 5 ||

When sun and moon stand together in the asterism of the Vasus, then the yuga begins: the month Magha, the season Tapas, the bright fortnight, the first day.

प्रपद्येतेश्रविष्ठादौसूर्याचान्द्रमसावुदक्। सार्पार्धेदक्षिणार्कस्तुमाघश्रावणयोःसदा ॥ ६ ॥

prapadyeteśraviṣṭhādausūryācāndramasāvudak| sārpārdhedakṣiṇārkastumāghaśrāvaṇayoḥsadā || 6 ||

Sun and moon begin their northward course at the start of Sravistha; the sun turns southward at the midpoint of Aslesha — always in the months of Magha and Sravana.

धर्मवृद्धिरपाम्प्रस्थःक्षपाहासउदग्गतौ। दक्षिणेतौविपर्यस्तौषण्मुहूर्त्ययनेनतु ॥ ७ ॥

dharmavṛddhirapāmprasthaḥkṣapāhāsaudaggatau| dakṣiṇetauviparyastauṣaṇmuhūrtyayanenatu || 7 ||

In the northern course the day increases by one prastha of water and the night wanes by as much; in the southern course the two are reversed. Over an ayana the change is six muhurtas.

द्विगुणम्सप्तमम्चाहुरयनाद्यम्त्रयोदश। चतुर्थम्दशमम्चैवद्विर्युग्माद्यम्बहुलेप्यृतौ ॥ ८ ॥

dviguṇamsaptamamcāhurayanādyamtrayodaśa| caturthamdaśamamcaivadviryugmādyambahulepyṛtau || 8 ||

The seventh doubled, they say, and the thirteenth, begin an ayana; likewise the fourth and the tenth, and twice the second, in the dark fortnight of the season as well.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Which parvans open an ayana depends on where the count is taken to start, and "the seventh doubled" is read by some as "the first and the seventh", as the Yajusa parallel at yajusa.10 in fact has it. Read the numbers as the text's own, not as a settled interpretation.

वसुस्त्वष्टाभगोजश्चमित्रःसर्पाश्विनौजलम्। धाताकश्चायनाद्याश्चार्धपञ्चनभस्त्वृतुः ॥ ९ ॥

vasustvaṣṭābhagojaścamitraḥsarpāśvinaujalam| dhātākaścāyanādyāścārdhapañcanabhastvṛtuḥ || 9 ||

Vasu, Tvastr, Bhaga, Aja, Mitra, Sarpa, the Asvins, Jala, Dhatr and Ka — these stand at the beginnings of the ayanas; and a season is four and a half asterisms.

Note: The names are the deity-regents of asterisms, standing for the asterisms themselves: Vasu for Dhanistha, Tvastr for Chitra, Sarpa for Aslesha, and so on. Rendered as the list of names the text gives rather than silently substituting the star names.

भाम्शाःस्युरष्टकाःकार्याःपक्षाद्वादशचोद्गताः। एकादशगुणस्योनःशुक्लेर्धम्चैन्दवायदि ॥ १० ॥

bhāmśāḥsyuraṣṭakāḥkāryāḥpakṣādvādaśacodgatāḥ| ekādaśaguṇasyonaḥśuklerdhamcaindavāyadi || 10 ||

The parts of the asterism are to be taken in eights, twelve of them raised from the fortnight; lessened by eleven times, and halved in the bright fortnight if they are lunar.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. The referent of "twelve raised from the fortnight" is not agreed. Read the numbers as the text's own, not as a settled interpretation.

कार्याभाम्शाष्टकास्थानेकलाएकान्नविम्शतिः। ऊनस्थानेद्विसप्ततीरुद्वपेदूनसम्मिताः ॥ ११ ॥

kāryābhāmśāṣṭakāsthānekalāekānnavimśatiḥ| ūnasthānedvisaptatīrudvapedūnasammitāḥ || 11 ||

In the place of the eights of asterism-parts to be taken, the kalas are nineteen; in the deficient place one should set down seventy-two, reckoned as deficient.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. The figures nineteen and seventy-two are secure in the manuscript; what they are counting is not. Read the numbers as the text's own, not as a settled interpretation.

त्र्यहम्शीभशेषोदिवसाम्शभागश्चतुर्दशस्याप्युपनीतभिन्नम्। भार्धेधिकेचाधिगतेपरेम्शेद्वावुत्तमैकम्नवकैरवेद्यम् ॥ १२ ॥

tryahamśībhaśeṣodivasāmśabhāgaścaturdaśasyāpyupanītabhinnam| bhārdhedhikecādhigateparemśedvāvuttamaikamnavakairavedyam || 12 ||

The remainder of the asterism is a third; the fractional part of the day is fourteen, and what is brought over is separate. When more than half an asterism has passed, the further part is two, and the highest is to be known by nines.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. One of the most contested verses in the text; the syntax admits several groupings of the fractions. Read the numbers as the text's own, not as a settled interpretation.

पक्षात्पञ्चदशाच्चोर्ध्वम्तद्भुक्तमितिनिर्दिशेत्। नवभिस्तूद्गतोम्शःस्यादूनाम्शद्व्यधिकेनतु ॥ १३ ॥

pakṣātpañcadaśāccordhvamtadbhuktamitinirdiśet| navabhistūdgatomśaḥsyādūnāmśadvyadhikenatu || 13 ||

Beyond the fifteenth of the fortnight, one should declare that much as elapsed. The part raised is by nines, and the deficient part by two more.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Reads as a continuation of arca.12 and inherits its uncertainty. Read the numbers as the text's own, not as a settled interpretation.

जौद्राघःखेश्वेहीरोषाचिन्मूषण्यःसोमाधानः। रेमृघ्राश्वाओजस्तृष्वोहर्येष्टाइत्यृक्षालिङ्गैः ॥ १४ ॥

jaudrāghaḥkheśvehīroṣācinmūṣaṇyaḥsomādhānaḥ| remṛghrāśvāojastṛṣvoharyeṣṭāityṛkṣāliṅgaiḥ || 14 ||

Jau, dra, gha, khe, sve, hi, ro, sha, cin, mu, sha, nyah, so, ma, dha, nah, re, mri, ghra, sva, ojah, stri, svo, har, yeshta — thus are the asterisms denoted by their tokens.

Note: Not a sentence. A mnemonic in which each asterism is compressed to a syllable or two, so that the list can be held in memory. Rendered as the sequence of tokens it is; any smooth English would be an invention. Compare the Yajusa parallel at yajusa.19, whose tokens differ.

जावाद्यम्शैःसमम्विद्यात्पूर्वार्धेपार्वसूत्तरे। भादानाम्शाच्चतुर्दशीकाष्ठानाम्देविनाकलाः ॥ १५ ॥

jāvādyamśaiḥsamamvidyātpūrvārdhepārvasūttare| bhādānāmśāccaturdaśīkāṣṭhānāmdevinākalāḥ || 15 ||

One should know it as equal to the parts beginning with ja and va in the first half, and in the parvans of the latter half. From the parts of the asterism taken comes the fourteenth; of the kasthas, the kalas are as stated.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. The "parts beginning with ja and va" refer back to the mnemonic at arca.14, so the reading depends on how that verse is resolved. Read the numbers as the text's own, not as a settled interpretation.

कलादशचविम्शास्याद्द्विमुहूर्तस्तुनाडिके। द्वित्रिम्शस्तत्कलानाम्तुषट्शतीत्र्यधिकम्भवेत् ॥ १६ ॥

kalādaśacavimśāsyāddvimuhūrtastunāḍike| dvitrimśastatkalānāmtuṣaṭśatītryadhikambhavet || 16 ||

A nadika is ten kalas and a twentieth; two nadikas make a muhurta; and of those kalas there are six hundred and three.

Note: The figure of 603 kalas is secure: sixty nadikas of ten and one-twentieth kalas each give exactly 603 in a day and night. The "thirty-two" in the received text sits awkwardly with that and is generally treated as a corruption; it has been left untranslated rather than silently emended.

नाडिकेद्वेमुहूर्तस्तुपञ्चाशत्पलमाषकम्। माषकात्कुम्भकोद्रोणःकुटपैर्वर्धतेत्रिभिः ॥ १७ ॥

nāḍikedvemuhūrtastupañcāśatpalamāṣakam| māṣakātkumbhakodroṇaḥkuṭapairvardhatetribhiḥ || 17 ||

Two nadikas make a muhurta. Fifty palas make the masaka measure; from the masaka come the kumbha and the drona, which increases by three kutapas.

Note: The received text does not parse cleanly. The Yajusa parallel at yajusa.25 gives the water-clock rule intelligibly — a drona of water less three kudavas is the measure of a nadika — and should be read alongside this verse.

ससप्तकुम्भयुक्स्योनःसूर्याद्योनिम्त्रयोदश। नवमानिचपञ्चाह्नःकाष्ठापञ्चाक्षराःस्मृताः ॥ १८ ॥

sasaptakumbhayuksyonaḥsūryādyonimtrayodaśa| navamānicapañcāhnaḥkāṣṭhāpañcākṣarāḥsmṛtāḥ || 18 ||

Joined with seven kumbhas ... thirteen from the sun ... and the five of the day; a kastha is held to be five syllable-lengths.

Note: Corrupt. Only the final quarter is secure: a kastha is five syllable-lengths. The ellipses mark where the text does not yield a construable sense.

श्रविष्ठाभ्याम्गुणाभ्यस्तान्प्राग्विलग्नान्विनिर्दिशेत्। सूर्यान्मासान्षळभ्यस्तान्विद्याच्चान्द्रमसान्ऋतून् ॥ १९ ॥

śraviṣṭhābhyāmguṇābhyastānprāgvilagnānvinirdiśet| sūryānmāsānṣaḷabhyastānvidyāccāndramasānṛtūn || 19 ||

Counting from Sravistha, multiplied by the factor, one should declare those that stand before. The solar months multiplied by six give the lunar seasons.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Which factor multiplies the count from Sravistha is not stated in the verse and has to be supplied. Read the numbers as the text's own, not as a settled interpretation.

अतीतपर्वभागेषुशोधयेद्द्विगुणाम्तिथिम्। तेषुमण्डलभागेषुतिथिनिष्ठाम्गतोरविः ॥ २० ॥

atītaparvabhāgeṣuśodhayeddviguṇāmtithim| teṣumaṇḍalabhāgeṣutithiniṣṭhāmgatoraviḥ || 20 ||

From the parts of the parvans elapsed one should subtract twice the tithi. In those parts of the circle the sun has reached the end of the tithi.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Part of the procedure for locating the sun; the "parts of the circle" are variously taken as degrees or as asterism-divisions. Read the numbers as the text's own, not as a settled interpretation.

याःपर्वभादानकलास्तासुसप्तगुणाम्तिथिम्। प्रक्षिपेत्कलासमूहस्तुविद्यादादानकीःकलाः ॥ २१ ॥

yāḥparvabhādānakalāstāsusaptaguṇāmtithim| prakṣipetkalāsamūhastuvidyādādānakīḥkalāḥ || 21 ||

Whatever kalas are taken from the asterism of the parvan, into those one should cast the tithi multiplied by seven; the aggregate of kalas is to be known as the kalas so taken.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Continues arca.20. Read the numbers as the text's own, not as a settled interpretation.

यदुत्तरस्यायनतोयनम्स्याच्छेषम्तुयद्दक्षिणतोयनस्य। तदेवषष्ट्याद्विगुणम्द्विभक्तम्सद्वादशम्स्याद्दिवसप्रमाणम् ॥ २२ ॥

yaduttarasyāyanatoyanamsyāccheṣamtuyaddakṣiṇatoyanasya| tadevaṣaṣṭyādviguṇamdvibhaktamsadvādaśamsyāddivasapramāṇam || 22 ||

Whatever has passed of the northern ayana, or whatever remains of the southern: that, doubled and divided by sixty and by two, and increased by twelve, gives the measure of the day.

Note: The rule gives day length across the year, running between twelve and eighteen muhurtas — the six-muhurta swing stated at arca.7. How the divisors sixty and two combine is read differently by the editors, so the arithmetic here follows the text literally rather than reconciling it to the known result.

तदर्धम्दिनभागानाम्सदापर्वणिपर्वणि। ऋतुशेषम्तुतद्विद्यात्सङ्ख्यायसहपर्वणाम् ॥ २३ ॥

tadardhamdinabhāgānāmsadāparvaṇiparvaṇi| ṛtuśeṣamtutadvidyātsaṅkhyāyasahaparvaṇām || 23 ||

Half of that is the measure of the parts of the day, at every single parvan; and one should know the remainder of the season by reckoning it together with the parvans.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Continues arca.22. Read the numbers as the text's own, not as a settled interpretation.

इत्युपायसमुद्देशोभूयोप्येनम्प्रकल्पयेत्। ज्ञेयराशिम्गताभ्यस्तान्विभजेज्ज्ञानराशिषु ॥ २४ ॥

ityupāyasamuddeśobhūyopyenamprakalpayet| jñeyarāśimgatābhyastānvibhajejjñānarāśiṣu || 24 ||

Such is the statement of the method; one should apply it further still. Multiply the quantity sought by the elapsed quantity and divide by the known quantities.

Note: States the rule of three in general terms, as a closing remark on method rather than a specific computation. The rendering is literal.

अग्निःप्रजापतिःसोमोरुद्रोदितिर्बृहस्पतिः। सर्पाश्चपितरश्चैवभगश्चैवार्यमापिच ॥ २५ ॥

agniḥprajāpatiḥsomorudroditirbṛhaspatiḥ| sarpāścapitaraścaivabhagaścaivāryamāpica || 25 ||

Agni, Prajapati, Soma, Rudra, Aditi, Brihaspati, the Serpents, the Fathers, Bhaga and Aryaman;

सवितात्वष्टाथवायुश्चेन्द्राग्नीमित्रएवच। इन्द्रोनिर्ऋतिरापोवैविश्वेदेवास्तथैवच ॥ २६ ॥

savitātvaṣṭāthavāyuścendrāgnīmitraevaca| indronirṛtirāpovaiviśvedevāstathaivaca || 26 ||

Savitr, Tvastr, Vayu, Indragni, Mitra, Indra, Nirriti, the Waters, and likewise the All-Gods;

विष्णुर्वसवोवरुणोजएकपात्तथैवच। अहिर्बुध्न्यस्तथापूषाश्विनौयमएवच ॥ २७ ॥

viṣṇurvasavovaruṇojaekapāttathaivaca| ahirbudhnyastathāpūṣāśvinauyamaevaca || 27 ||

Vishnu, the Vasus, Varuna, Aja Ekapad likewise, Ahirbudhnya, Pushan, the two Asvins, and Yama.

नक्षत्रदेवताएताएताभिर्यज्ञकर्मणि। यजमानस्यशास्त्रज्ञैर्नामनक्षत्रजम्स्मृतम् ॥ २८ ॥

nakṣatradevatāetāetābhiryajñakarmaṇi| yajamānasyaśāstrajñairnāmanakṣatrajamsmṛtam || 28 ||

These are the deities of the asterisms. By these, in the rites of sacrifice, those who know the science hold that the sacrificer’s name is formed from his birth-star.

इत्येतन्मासवर्षाणाम्मुहूर्तोदयपर्वणाम्। दिनर्त्वयनमासाङ्गम्व्याख्यातम्लगधोऽब्रवीत् ॥ २९ ॥

ityetanmāsavarṣāṇāmmuhūrtodayaparvaṇām| dinartvayanamāsāṅgamvyākhyātamlagadho'bravīt || 29 ||

Thus has the reckoning of months and years, of muhurtas, risings and parvans, with its limbs of days, seasons, ayanas and months, been expounded. So Lagadha declared.

सोमसूर्यस्रिचरितोलोकाँल्लोकेचसम्मितम्। सोमसूर्यस्रिचरितोविद्वान्वेदविदस्नुते ॥ ३० ॥

somasūryasricaritolokām̐llokecasammitam| somasūryasricaritovidvānvedavidasnute || 30 ||

The threefold course of moon and sun is measured out through the worlds; he who knows the threefold course of moon and sun, knowing the Veda, attains it.

Note: The received text is repetitive and partly corrupt, apparently a displaced version of the closing verse that the Yajusa recension gives more fully at yajusa.45.

विषुवम्तद्गुणम्द्वाभ्याम्रूपहीनम्तुषड्गुणम्। यल्लब्धम्तानिपर्वाणितथोर्ध्वम्सातिथिर्भवेत् ॥ ३१ ॥

viṣuvamtadguṇamdvābhyāmrūpahīnamtuṣaḍguṇam| yallabdhamtāniparvāṇitathordhvamsātithirbhavet || 31 ||

The equinox, multiplied by that factor and by two, less one and multiplied by six: what is obtained is the parvans, and above that is the tithi.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. The equinox computation; the multiplier is not named in the verse. Read the numbers as the text's own, not as a settled interpretation.

माघशुक्लप्रवृत्तस्तुपौषकृष्णसमापिनः। युगस्यपञ्चवर्षाणिकालज्ञानम्प्रचक्षते ॥ ३२ ॥

māghaśuklapravṛttastupauṣakṛṣṇasamāpinaḥ| yugasyapañcavarṣāṇikālajñānampracakṣate || 32 ||

The five years of the yuga, beginning with the bright fortnight of Magha and ending with the dark fortnight of Pausha — this, they declare, is the knowledge of time.

तृतीयाम्नवमीम्चैवपौर्णमासीम्त्रयोदशीम्। षष्ठीम्चविषुवाम्प्रोक्तोद्वादश्याम्चसमम्भवेत् ॥ ३३ ॥

tṛtīyāmnavamīmcaivapaurṇamāsīmtrayodaśīm| ṣaṣṭhīmcaviṣuvāmproktodvādaśyāmcasamambhavet || 33 ||

The third, the ninth, the full-moon day, the thirteenth and the sixth are declared equinoctial; and on the twelfth too it falls even.

Note: A list of the tithis on which the equinox falls across the years of the yuga. The sequence differs between the recensions, and the twelfth is an addition whose place in the series is unclear.

चतुर्दशीमुपवसथस्तथाभवेद्यथोदितोदिनमुपैतिचन्द्रमाः। माघशुक्लाह्निकोयुङ्क्तेश्रविष्ठायाम्वार्षिकीम् ॥ ३४ ॥

caturdaśīmupavasathastathābhavedyathoditodinamupaiticandramāḥ| māghaśuklāhnikoyuṅkteśraviṣṭhāyāmvārṣikīm || 34 ||

The fourteenth is the fast-day, and so it comes about that the moon reaches the day as stated; the daily reckoning from the bright fortnight of Magha joins the yearly asterism at Sravistha.

Note: Corrupt, and metrically irregular in the source. The sense of the first half is reasonably clear; the second half is reconstructed from the parallel at arca.5.

यथाशिखामयूराणाम्नागानाम्मणयोयथा। तद्वद्वेदाङ्गशास्त्राणाम्ज्योतिषम्मूर्धनिस्थितम् ॥ ३५ ॥

yathāśikhāmayūrāṇāmnāgānāmmaṇayoyathā| tadvadvedāṅgaśāstrāṇāmjyotiṣammūrdhanisthitam || 35 ||

As are the crests upon the heads of peacocks, as are the gems upon the hoods of serpents, so does Jyotisha stand at the head of the sciences that are the limbs of the Veda.

वेदाहियज्ञार्थमभिप्रवृत्ताःकालानुपूर्वाविहिताश्चयज्ञाः। तस्मादिदम्कालविधानशास्त्रम्योज्योतिषम्वेदसवेदयज्ञान्योज्योतिषम्वेदसवेदयज्ञानिति ॥ ३६ ॥

vedāhiyajñārthamabhipravṛttāḥkālānupūrvāvihitāścayajñāḥ| tasmādidamkālavidhānaśāstramyojyotiṣamvedasavedayajñānyojyotiṣamvedasavedayajñāniti || 36 ||

The Vedas arose for the sake of sacrifice, and the sacrifices are ordained according to the sequence of time. Therefore he who knows Jyotisha, this science of the ordering of time, knows the sacrifices.

अथयाजुषज्योतिषंप्रारभ्यते। पञ्चसंवत्सरमयंयुगाध्यक्षंप्रजापतिम्। दिनर्त्वयनमासाङ्गंप्रणम्यशिरसाशुचिः ॥ १ ॥

athayājuṣajyotiṣaṃprārabhyate| pañcasaṃvatsaramayaṃyugādhyakṣaṃprajāpatim| dinartvayanamāsāṅgaṃpraṇamyaśirasāśuciḥ || 1 ||

Now begins the Yajusa Jyotisha. Having bowed my head in purity to Prajapati, lord of the yuga that consists of five years, whose limbs are the days, the seasons, the ayanas and the months —

ज्योतिषामयनंपुण्यंप्रवक्ष्याम्यनुपूर्वशः। संमतंब्राह्मणेन्द्राणांयज्ञकालार्थसिद्धये ॥ २ ॥

jyotiṣāmayanaṃpuṇyaṃpravakṣyāmyanupūrvaśaḥ| saṃmataṃbrāhmaṇendrāṇāṃyajñakālārthasiddhaye || 2 ||

I shall declare in due order the holy course of the heavenly lights, as it is agreed among the foremost of brahmins, for establishing the times appointed for sacrifice.

वेदाहियज्ञार्थमभिप्रवृत्ताःकालानुपूर्ण्याविहिताश्चयज्ञाः। तस्मादिदंकालविधानशास्त्रंयोज्योतिषंवेदसवेदयज्ञम् ॥ ३ ॥

vedāhiyajñārthamabhipravṛttāḥkālānupūrṇyāvihitāścayajñāḥ| tasmādidaṃkālavidhānaśāstraṃyojyotiṣaṃvedasavedayajñam || 3 ||

The Vedas arose for the sake of sacrifice, and the sacrifices are ordained according to the sequence of time. Therefore he who knows Jyotisha, this science of the ordering of time, knows the sacrifice.

यथाशिखामयूराणांनागानांमणयोयथा। तद्वद्वेदाङ्गशास्त्राणांगणितंमूर्धनिस्थितम् ॥ ४ ॥

yathāśikhāmayūrāṇāṃnāgānāṃmaṇayoyathā| tadvadvedāṅgaśāstrāṇāṃgaṇitaṃmūrdhanisthitam || 4 ||

As are the crests upon the heads of peacocks, as are the gems upon the hoods of serpents, so does computation stand at the head of the sciences that are the limbs of the Veda.

येबृहस्पतिनाभुक्तामीनान्प्रभृतिराशयः। त्रिवृताःपञ्चभिर्ऋतायःशेषःसपरिग्रहः ॥ ४ ॥

yebṛhaspatinābhuktāmīnānprabhṛtirāśayaḥ| trivṛtāḥpañcabhirṛtāyaḥśeṣaḥsaparigrahaḥ || 4 ||

Those signs, beginning with Pisces, that have been traversed by Brihaspati, are threefold; by fives they are made even, and the remainder is taken with them.

Note: The only verse in either recension to mention Brihaspati and the twelve-sign zodiac, which is otherwise absent from the text and belongs to a later stratum of Indian astronomy. Widely regarded as an interpolation. Rendered literally; the arithmetic is obscure.

माघशुक्लप्रपन्नस्यपौषकृष्णसमापिनः। युगस्यपञ्चवर्षस्यकालज्ञानंप्रचक्षते ॥ ५ ॥

māghaśuklaprapannasyapauṣakṛṣṇasamāpinaḥ| yugasyapañcavarṣasyakālajñānaṃpracakṣate || 5 ||

The five years of the yuga, beginning with the bright fortnight of Magha and ending with the dark fortnight of Pausha — this, they declare, is the knowledge of time.

स्वराक्रमेतेसोमार्कौयदासाकंसवासवौ। स्यात्तदादियुगंमाघस्तपःशुक्लोऽयनंह्युदक् ॥ ६ ॥

svarākrametesomārkauyadāsākaṃsavāsavau| syāttadādiyugaṃmāghastapaḥśuklo'yanaṃhyudak || 6 ||

When sun and moon stand together in the asterism of the Vasus, then the yuga begins: the month Magha, the season Tapas, the bright fortnight, and the northward course.

प्रपद्येतेश्रविष्ठादौसूर्याचन्द्रमसावुदक्। सार्पार्धेदक्षिणार्कस्तुमाघश्रावणयोःसदा ॥ ७ ॥

prapadyeteśraviṣṭhādausūryācandramasāvudak| sārpārdhedakṣiṇārkastumāghaśrāvaṇayoḥsadā || 7 ||

Sun and moon begin their northward course at the start of Sravistha; the sun turns southward at the midpoint of Aslesha — always in the months of Magha and Sravana.

धर्मवृद्धिरपांप्रस्थःक्षपाह्लासउदग्गतौ। दक्षिणेतौविपर्यस्तौषण्मुहूर्त्ययनेनतु ॥ ८ ॥

dharmavṛddhirapāṃprasthaḥkṣapāhlāsaudaggatau| dakṣiṇetauviparyastauṣaṇmuhūrtyayanenatu || 8 ||

In the northern course the day increases by one prastha of water and the night wanes; in the southern course the two are reversed. Over an ayana the change is six muhurtas.

प्रथमंसप्तमंचाहुरयनाद्यंत्रयोदशम्। चतुर्थंदशमंचैवद्विर्युग्माद्यंबहुलेऽप्यृतौ ॥ ९ ॥

prathamaṃsaptamaṃcāhurayanādyaṃtrayodaśam| caturthaṃdaśamaṃcaivadviryugmādyaṃbahule'pyṛtau || 9 ||

The first and the seventh, they say, and the thirteenth, begin an ayana; likewise the fourth and the tenth, and twice the second, in the dark fortnight of the season as well.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Compare arca.8, which reads "the seventh doubled" where this has "the first and the seventh". Read the numbers as the text's own, not as a settled interpretation.

वसुत्वष्टाभवोऽजश्चमित्रःसर्पोऽश्विनौजलम्। धाताकश्चायनाद्याःस्युरर्धपञ्चमभस्त्वृतुः ॥ १० ॥

vasutvaṣṭābhavo'jaścamitraḥsarpo'śvinaujalam| dhātākaścāyanādyāḥsyurardhapañcamabhastvṛtuḥ || 10 ||

Vasu, Tvastr, Bhava, Aja, Mitra, Sarpa, the Asvins, Jala, Dhatr and Ka stand at the beginnings of the ayanas; and a season is four and a half asterisms.

एकान्तरेऽह्निमासेचपूर्वान्कृत्वादिरुत्तरः। अर्धयोःपञ्चपर्वाणांमृदूपञ्चदशाष्टमौ ॥ ११ ॥

ekāntare'hnimāsecapūrvānkṛtvādiruttaraḥ| ardhayoḥpañcaparvāṇāṃmṛdūpañcadaśāṣṭamau || 11 ||

On every alternate day and in the month, having placed the earlier ones first, the latter follows. In the halves of the five parvans, the fifteenth and the eighth are the mild ones.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. The sense of "mild" applied to the fifteenth and eighth is not explained anywhere in the text. Read the numbers as the text's own, not as a settled interpretation.

दुहेयंपर्वचेत्पादेपादस्त्रिंशत्तुसैकिका। भागात्मनापवृज्यांशांनिर्दिशेंशोऽधिकोयदि ॥ १२ ॥

duheyaṃparvacetpādepādastriṃśattusaikikā| bhāgātmanāpavṛjyāṃśāṃnirdiśeṃśo'dhikoyadi || 12 ||

If the parvan is to be milked at the quarter, the quarter is thirty with one added. Having cast off the parts by their own measure, one should declare the part, if it is in excess.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. "Milked" is the text’s own metaphor for extracting a quantity; the referent of the quarter is unclear. Read the numbers as the text's own, not as a settled interpretation.

निरेकंद्वादशाभ्यस्तंद्विगुणंगतसंयुतम्। षष्ट्याषष्ट्यायुतंद्वाभ्यांपर्वणांराशिरुच्यते ॥ १३ ॥

nirekaṃdvādaśābhyastaṃdviguṇaṃgatasaṃyutam| ṣaṣṭyāṣaṣṭyāyutaṃdvābhyāṃparvaṇāṃrāśirucyate || 13 ||

Less one, multiplied by twelve and doubled, joined with what has elapsed, and increased by sixty for each of the two — this is called the sum of the parvans.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Parallel to arca.4 and subject to the same dispute over the sixty. Read the numbers as the text's own, not as a settled interpretation.

स्युःपदोऽर्धंत्रिपाद्यायात्रिदव्यैकेऽह्नःकृतेस्थितिम्। साम्येनेन्दोःस्तृणोऽन्येषुपर्वकाःपञ्चसंमिताः ॥ १४ ॥

syuḥpado'rdhaṃtripādyāyātridavyaike'hnaḥkṛtesthitim| sāmyenendoḥstṛṇo'nyeṣuparvakāḥpañcasaṃmitāḥ || 14 ||

They are a quarter, a half, three quarters, when the position is made for one, two or three days. By equality with the moon, in the others the parvans are reckoned as five.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Has no parallel in the Arca recension and is among the least clear verses in the text. Read the numbers as the text's own, not as a settled interpretation.

भांशाःस्युरष्टकाःकार्याःपक्षाद्वादशकोद्गताः। एकादशगुणश्चोनःशुक्लेऽर्धंचैन्दवायदि ॥ १५ ॥

bhāṃśāḥsyuraṣṭakāḥkāryāḥpakṣādvādaśakodgatāḥ| ekādaśaguṇaśconaḥśukle'rdhaṃcaindavāyadi || 15 ||

The parts of the asterism are to be taken in eights, twelve of them raised from the fortnight; lessened by eleven times, and halved in the bright fortnight if they are lunar.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Parallel to arca.10. Read the numbers as the text's own, not as a settled interpretation.

नवकैरुद्गतोंऽशःस्यादूनःसप्तगुणोभवेत्। आवापस्त्वयुजेऽर्धंस्यात्पौलस्त्येऽस्तंगतेऽपरम् ॥ १६ ॥

navakairudgatoṃ'śaḥsyādūnaḥsaptaguṇobhavet| āvāpastvayuje'rdhaṃsyātpaulastye'staṃgate'param || 16 ||

The part raised is by nines; when deficient it becomes multiplied by seven. The addition in an odd [fortnight] is a half, and in the set Paulastya it is otherwise.

Note: Paulastya is the asterism Rohini, named for its regent. The condition "when it is set" is a visibility rule whose application is not spelled out.

जावाद्यंशैःसमंविद्यात्पूर्वार्धेपर्वसूत्तराः। भादानंस्याच्चतुर्दश्यांद्विभागेभ्योऽधिकोयदि ॥ १७ ॥

jāvādyaṃśaiḥsamaṃvidyātpūrvārdheparvasūttarāḥ| bhādānaṃsyāccaturdaśyāṃdvibhāgebhyo'dhikoyadi || 17 ||

One should know it as equal to the parts beginning with ja and va in the first half, and the latter ones in the parvans. The taking of the asterism falls on the fourteenth, if it is more than two parts.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Refers back to the mnemonic at yajusa.19 and inherits its uncertainty. Read the numbers as the text's own, not as a settled interpretation.

जौद्रागःखेश्वेऽहीरोशाचिन्मूषण्यःसूमाधानः। रेमृघास्वाऽपोऽजःकृष्यहज्येष्ठाइत्यृक्षालिङ्गैः ॥ १८ ॥

jaudrāgaḥkheśve'hīrośācinmūṣaṇyaḥsūmādhānaḥ| remṛghāsvā'po'jaḥkṛṣyahajyeṣṭhāityṛkṣāliṅgaiḥ || 18 ||

Jau, dra, ga, khe, sve, hi, ro, sha, cin, mu, sha, nyah, su, ma, dha, nah, re, mri, gha, sva, apah, ajah, kri, shya, ha, jyeshtha — thus are the asterisms denoted by their tokens.

Note: Not a sentence. The mnemonic list of asterism-tokens, parallel to arca.14 but with several tokens differing, which is itself evidence of how unstable this verse was in transmission.

कार्याभांशाष्टकस्थानेकलाएकान्नविंशतिः। ऊनस्थानेद्विसप्ततिमुद्वपेद्युक्तसंभवे ॥ १९ ॥

kāryābhāṃśāṣṭakasthānekalāekānnaviṃśatiḥ| ūnasthānedvisaptatimudvapedyuktasaṃbhave || 19 ||

In the place of the eights of asterism-parts to be taken, the kalas are nineteen; in the deficient place one should set down seventy-two, where the conjunction is fitting.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Parallel to arca.11. Read the numbers as the text's own, not as a settled interpretation.

तिथिमेकादशाभ्यस्तांपर्वभांशसमन्विताम्। विभज्यभसमूहेनतिथिनक्षत्रमादिशेत् ॥ २० ॥

tithimekādaśābhyastāṃparvabhāṃśasamanvitām| vibhajyabhasamūhenatithinakṣatramādiśet || 20 ||

The tithi multiplied by eleven, together with the parts of the asterism of the parvan, divided by the aggregate of asterisms — thus one should declare the asterism of the tithi.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. The rule for finding the asterism of a given tithi; the divisor is read variously. Read the numbers as the text's own, not as a settled interpretation.

याःपर्वभादानकलास्तासुसप्तगुणांतिथिम्। उक्तास्तासांविजानीयात्तिथिभादानिकाःकलाः ॥ २१ ॥

yāḥparvabhādānakalāstāsusaptaguṇāṃtithim| uktāstāsāṃvijānīyāttithibhādānikāḥkalāḥ || 21 ||

Whatever kalas are taken from the asterism of the parvan, into those the tithi multiplied by seven is stated; of those one should know the kalas so taken for the tithi and the asterism.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Parallel to arca.21. Read the numbers as the text's own, not as a settled interpretation.

अतीतपर्वभागेभ्यःशोधयेद्द्विगुणांतिथिम्। तेषुमण्डलभागेषुतिथिनिष्ठांगतोरविः ॥ २२ ॥

atītaparvabhāgebhyaḥśodhayeddviguṇāṃtithim| teṣumaṇḍalabhāgeṣutithiniṣṭhāṃgatoraviḥ || 22 ||

From the parts of the parvans elapsed one should subtract twice the tithi. In those parts of the circle the sun has reached the end of the tithi.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Parallel to arca.20. Read the numbers as the text's own, not as a settled interpretation.

विषुवन्तंद्विरभ्यस्तंरूपोनंषड्गुणीकृतम्। पक्षायदर्धंपक्षाणांतिथिःसविषुवान्स्मृतः ॥ २३ ॥

viṣuvantaṃdvirabhyastaṃrūponaṃṣaḍguṇīkṛtam| pakṣāyadardhaṃpakṣāṇāṃtithiḥsaviṣuvānsmṛtaḥ || 23 ||

The equinox doubled, less one, and multiplied by six: whatever half of the fortnights results, that tithi is held to be the equinoctial one.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Parallel to arca.31. Read the numbers as the text's own, not as a settled interpretation.

पलानिपञ्चाशदपांधृतानितदाढकंद्रोणमतःप्रमेयम्। त्रिभिर्विहीनंकुडवैस्तुकार्यंतन्नाडिकायास्तुभवेत्प्रमाणम् ॥ २४ ॥

palānipañcāśadapāṃdhṛtānitadāḍhakaṃdroṇamataḥprameyam| tribhirvihīnaṃkuḍavaistukāryaṃtannāḍikāyāstubhavetpramāṇam || 24 ||

Fifty palas of water held make an adhaka; from this the drona is to be measured; reduced by three kudavas, that becomes the measure of a nadika.

एकादशभिरभ्यस्यपर्वाणिनवभिस्तिथिम्। युगलब्धंसपर्वस्याद्वर्तमानार्कभक्रमात् ॥ २५ ॥

ekādaśabhirabhyasyaparvāṇinavabhistithim| yugalabdhaṃsaparvasyādvartamānārkabhakramāt || 25 ||

Multiplying the parvans by eleven and the tithi by nine, what is obtained in the yuga is with the parvan, in the order of the sun now current.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. The multipliers eleven and nine are secure; what they operate on is contested. Read the numbers as the text's own, not as a settled interpretation.

सूर्यर्क्षभागान्निवभिर्विभज्यशेषंद्विरभ्यस्यदिनोपभुक्तिः। तिथियुक्ताभुक्तिदिनेषुकालोयोगंदिनैकादशकेनतद्भम् ॥ २६ ॥

sūryarkṣabhāgānnivabhirvibhajyaśeṣaṃdvirabhyasyadinopabhuktiḥ| tithiyuktābhuktidineṣukāloyogaṃdinaikādaśakenatadbham || 26 ||

Dividing the degrees of the sun’s asterism by nine and doubling the remainder gives the daily traversal. Joined with the tithi, on the days of traversal the time of conjunction gives the asterism by elevens of days.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Among the most technical verses in the text, giving the sun’s daily motion. Read the numbers as the text's own, not as a settled interpretation.

त्रियंशोभशेषोदिवसांशभागश्चतुर्दशश्चाप्यनीयभिन्नम्। भार्धेऽधिकेचापिगतेपरोंऽशोद्वावुत्तमेतन्नवकैरवेद्यम् ॥ २७ ॥

triyaṃśobhaśeṣodivasāṃśabhāgaścaturdaśaścāpyanīyabhinnam| bhārdhe'dhikecāpigateparoṃ'śodvāvuttametannavakairavedyam || 27 ||

The remainder of the asterism is a third; the fractional part of the day is fourteen, and what is brought over is separate. When more than half an asterism has passed, the further part is two, and the highest of these is to be known by nines.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Parallel to arca.12, one of the most contested verses in the text. Read the numbers as the text's own, not as a settled interpretation.

त्रिंशत्यह्नांसषट्षष्टिरब्दःषट्चर्तवोऽयने। मासाद्वादशसूर्याःस्युरेतत्पञ्चगुणंयुगम् ॥ २८ ॥

triṃśatyahnāṃsaṣaṭṣaṣṭirabdaḥṣaṭcartavo'yane| māsādvādaśasūryāḥsyuretatpañcaguṇaṃyugam || 28 ||

A year is three hundred and sixty-six days; the seasons are six, the ayanas two, and the solar months twelve. This multiplied by five is the yuga.

उदयावासवस्यस्युर्दिनराशिःस्वपञ्चकः। ऋषेर्द्विषष्टिहीनंस्याद्विंशत्याचैकयास्तृणाम् ॥ २९ ॥

udayāvāsavasyasyurdinarāśiḥsvapañcakaḥ| ṛṣerdviṣaṣṭihīnaṃsyādviṃśatyācaikayāstṛṇām || 29 ||

The risings of the asterism of the Vasus are the number of days with its own five; that of the seer’s asterism is less by sixty-two, and by twenty-one for the stars.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Part of the system relating risings of different asterisms across the yuga; the numbers are clear, their referents less so. Read the numbers as the text's own, not as a settled interpretation.

पञ्चत्रिंशंशतंपौष्णमेकोनमयनान्यृषेः। पर्वणांस्याच्चतुष्पादीकाष्ठानांचैवताःकलाः ॥ ३० ॥

pañcatriṃśaṃśataṃpauṣṇamekonamayanānyṛṣeḥ| parvaṇāṃsyāccatuṣpādīkāṣṭhānāṃcaivatāḥkalāḥ || 30 ||

A hundred and thirty-five are the risings of Pausna, and the ayanas of the seer are one less. Of the parvans there is a fourth part, and those are the kalas of the kasthas.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Pausna is the asterism Revati, named for its regent Pushan. The figure 135 is secure. Read the numbers as the text's own, not as a settled interpretation.

सावनेन्दुस्त्रिमासानांषष्टिश्चैकाद्विसप्तिका। द्वित्रिंशतम्सावनस्यार्धःसूर्यःस्तृणांसपर्ययः ॥ ३१ ॥

sāvanendustrimāsānāṃṣaṣṭiścaikādvisaptikā| dvitriṃśatamsāvanasyārdhaḥsūryaḥstṛṇāṃsaparyayaḥ || 31 ||

The civil and lunar [days] of three months are sixty and one and two-sevenths; thirty-two is half of the civil, and the sun’s revolution among the stars is complete.

Note: Belongs to the system that yields the yuga of 1,830 civil days, 1,860 tithis and 62 synodic months — the central achievement of the text. The verse as transmitted states this obliquely and the editors reconstruct the arithmetic differently.

अग्निःप्रजापतिःसोमोरुद्रोऽदितिर्बृहस्पतिः। सर्पाश्चपितरश्चैवभगश्चैवाऽर्यमाऽपिच ॥ ३२ ॥

agniḥprajāpatiḥsomorudro'ditirbṛhaspatiḥ| sarpāścapitaraścaivabhagaścaivā'ryamā'pica || 32 ||

Agni, Prajapati, Soma, Rudra, Aditi, Brihaspati, the Serpents, the Fathers, Bhaga and Aryaman;

सवितात्वष्टाऽथवायुश्चेन्द्राग्नीमित्रएवच। इन्द्रोनिर्ऋतिरापोवैविश्वेदेवास्तथैवच ॥ ३३ ॥

savitātvaṣṭā'thavāyuścendrāgnīmitraevaca| indronirṛtirāpovaiviśvedevāstathaivaca || 33 ||

Savitr, Tvastr, Vayu, Indragni, Mitra, Indra, Nirriti, the Waters, and likewise the All-Gods;

विष्णुर्वसवोवरुणोऽजएकपात्तथैवच। अहिर्बुधन्यस्तथापूषाअश्विनौयमएवच ॥ ३४ ॥

viṣṇurvasavovaruṇo'jaekapāttathaivaca| ahirbudhanyastathāpūṣāaśvinauyamaevaca || 34 ||

Vishnu, the Vasus, Varuna, Aja Ekapad likewise, Ahirbudhnya, Pushan, the two Asvins, and Yama.

नक्षत्रदेवताह्येताएताभिर्यज्ञकर्मणि। यजमानस्यशास्त्रज्ञैर्नामनक्षत्रजंस्मृतम् ॥ ३५ ॥

nakṣatradevatāhyetāetābhiryajñakarmaṇi| yajamānasyaśāstrajñairnāmanakṣatrajaṃsmṛtam || 35 ||

These indeed are the deities of the asterisms. By these, in the rites of sacrifice, those who know the science hold that the sacrificer’s name is formed from his birth-star.

उग्राण्यार्द्राचचित्राचविशाखाश्रवणाऽश्वयुक्। क्रूराणितुमघास्वातिर्ज्येष्ठामूलंयमस्ययत् ॥ ३६ ॥

ugrāṇyārdrācacitrācaviśākhāśravaṇā'śvayuk| krūrāṇitumaghāsvātirjyeṣṭhāmūlaṃyamasyayat || 36 ||

Ardra, Chitra, Visakha, Sravana and Asvayuj are the fierce asterisms; the cruel ones are Magha, Svati, Jyeshtha, and Mula, which belongs to Yama.

द्वयूनंद्विषष्टिभागेनहेयंसौर्यात्सपार्वणम्। यत्कृतावुपयुज्येतेमध्येऽन्तंचाधिमासकौ ॥ ३७ ॥

dvayūnaṃdviṣaṣṭibhāgenaheyaṃsauryātsapārvaṇam| yatkṛtāvupayujyetemadhye'ntaṃcādhimāsakau || 37 ||

Less two, by a sixty-second part, it is to be removed from the solar reckoning together with the parvan. When the two are employed, the intercalary months fall in the middle and at the end.

Note: The intercalary-month rule, which is what makes the five-year yuga work: two extra months are inserted, in the middle and at the end. The rule is clear in outline and disputed in detail.

कलादशसविंशास्याद्द्वेमुहूर्तस्यनाडिके। द्वित्रिंशत्तत्कलानांतुषट्छतीत्र्यधिकाभवेत् ॥ ३८ ॥

kalādaśasaviṃśāsyāddvemuhūrtasyanāḍike| dvitriṃśattatkalānāṃtuṣaṭchatītryadhikābhavet || 38 ||

A nadika is ten kalas and a twentieth; two nadikas belong to a muhurta; and of those kalas there are six hundred and three.

Note: See the note at arca.16. The figure of 603 kalas is secure.

ससप्तकंभयुक्सोमःसूर्योद्यूनित्रयोदश। उत्तमानितुपञ्चाह्नःकाष्ठापञ्चाक्षराभवेत् ॥ ३९ ॥

sasaptakaṃbhayuksomaḥsūryodyūnitrayodaśa| uttamānitupañcāhnaḥkāṣṭhāpañcākṣarābhavet || 39 ||

The moon joined with seven ... the sun by thirteen of the days ... the highest are the five of the day; a kastha becomes five syllable-lengths.

Note: Corrupt, parallel to arca.18. Only the final quarter is secure: a kastha is five syllable-lengths.

यदुत्तरस्यायनतोगतंस्याच्छेषंतथादक्षिणतोऽयनस्य। तदेवषष्ट्याद्विगुणंद्विभक्तंसद्वादशंस्याद्दिवसप्रमाणम् ॥ ४० ॥

yaduttarasyāyanatogataṃsyāccheṣaṃtathādakṣiṇato'yanasya| tadevaṣaṣṭyādviguṇaṃdvibhaktaṃsadvādaśaṃsyāddivasapramāṇam || 40 ||

Whatever has passed of the northern ayana, or whatever remains of the southern: that, doubled and divided by sixty and by two, and increased by twelve, gives the measure of the day.

Note: See the note at arca.22.

यदर्धंदिनभागानांसदापर्वणिपर्वणि। ऋतुशेषंतुतद्विद्यात्संख्यायसहपर्वणाम् ॥ ४१ ॥

yadardhaṃdinabhāgānāṃsadāparvaṇiparvaṇi| ṛtuśeṣaṃtutadvidyātsaṃkhyāyasahaparvaṇām || 41 ||

Whatever is half of the parts of the day, always at every single parvan — one should know that as the remainder of the season, reckoning it together with the parvans.

Note: Encodes a calendrical rule rather than a statement, and the Sanskrit is unspaced in the source. Parallel to arca.23. Read the numbers as the text's own, not as a settled interpretation.

इत्युपायसमुद्देशोभूयोऽप्यह्नःप्रकल्पयेत्। ज्ञेयराशिगतान्व्यस्तान्विभजेज्ज्ञानराशिना ॥ ४२ ॥

ityupāyasamuddeśobhūyo'pyahnaḥprakalpayet| jñeyarāśigatānvyastānvibhajejjñānarāśinā || 42 ||

Such is the statement of the method; one should compute it for further days as well. Divide the elapsed quantities, set down in reverse, by the known quantity.

Note: Parallel to arca.24, stating the rule of three as a closing remark on method.

इत्येवंमासवर्षाणांमुहूर्तोदयपर्वणाम्। दिनर्त्वयनमासाङ्गंव्याख्यानंलगतोऽब्रवीत् ॥ ४२ ॥

ityevaṃmāsavarṣāṇāṃmuhūrtodayaparvaṇām| dinartvayanamāsāṅgaṃvyākhyānaṃlagato'bravīt || 42 ||

Thus has the exposition of months and years, of muhurtas, risings and parvans, with its limbs of days, seasons, ayanas and months, been given. So Lagadha declared.

सोमसूर्यस्रिचरितंविद्वान्वेदविदश्नुते। सोयसूर्यस्त्रिचरितंलोकंलोकेचसंततिंलोकंलोकेचसंततिम् ॥ ४३ ॥

somasūryasricaritaṃvidvānvedavidaśnute| soyasūryastricaritaṃlokaṃlokecasaṃtatiṃlokaṃlokecasaṃtatim || 43 ||

He who knows the threefold course of moon and sun, knowing the Veda, attains it; knowing the threefold course of moon and sun, he attains the world, and offspring in the world.

Note: The closing verse, which repeats its last words in the manner of a chapter-end formula. The received text also repeats "moon and sun" with a variant spelling, kept as transmitted.