Rig Veda Vedanga Jyotisha
1Purified, with the head having bowed down to the division of the days, seasons, ayanas, months, and Prajapati, lord of the yuga, consisting of five years.
2Having bowed down with the head to time and the Honorable Sarasvati, I will explain the knowledge of time of Mahatma Lagadha.
3In due order, I will explain the holy path of the heavenly bodies approved of by the lords of the priests for the success in the time of the sacrificial rite.
4[Take the ordinal number of years reached in the current yuga] minus one, multiplied by twelve, multiplied by two, added to [the parvans] attained [in the current year]. For every 60 [parvans], two [parvans] are added. Declared is the quantity of the parvans.
5Celestially when the moon and the sun simultaneously rise up with Vasava (Dhanishtha nakshatra), thenceforward it should be the yuga. Magha (is the synodic lunar month), Tapas (is the solar seasonal month), the moon is waxing, and indeed the ayana is northwards.
6The sun and the moon giving to the nakshatra of Dhanishtha go northwards. When midway in the nakshatra of Ashlesha, the sun moves towards the south, but this is always in the (synodic lunar) month of Magha and Shravana, respectively.
7The increase of the day is a prastha of water when the Sun is on its northern course with the decrease of night. When southern, those two interchanges. And during an ayana [the increase and decrease amounts equal] six muhurta.
8They said the first, seventh, thirteenth [tithis of the waxing moon] and the fourth and tenth [tithis of the waning moon] are the beginning of the ayanas; and indeed, beginning with the confluence are surely when accompanied by six (more than the previous tithi).
9At the beginning of the ayanas they (deities of the nakshatras) should be Vasu (deity of the nakshatra of Dhanishtha), Tvashta (deity of the nakshatra of Chitra), Bhavas (another name of Rudra , the deity of Ardra), Aja (deity of the nakshatra of Purvabhadrapada), Mitra (deity of the nakshatra of Anuradha), Sarpa (deity of the nakshatra of Ashlesha), the two Ashvins (deities of the nakshatra of Ashvini ), Jala (deity of the nakshatra of Purvashadha), Dhata (deity of the nakshatra of Uttaraphalguni), and Ka (also known as Prajapati, the deity of the nakshatra of Rohini). Four and a half nakshatras are a season.
10The portions of the nakshatras should be eight to be multiplied from those divided by twelve from the paksha and the remainder is multiplied by eleven. If the lunations (parvans) are at full moon, add half (62 portions to the moon’s nakshatra).
11When there are eight portions of a nakshatra, 19 kalas are to be calculated for each portion. When there is a remainder, 73 kalas should be removed corresponding to each remainder portion.
12The remainder of the nakshatras (in terms of its 124 portions) is a 3rd portion (for each day in a year) having subtracted/rounded off up to 14 (days in any parvan). When situated when half of the nakshatras have increased (at the half year mark), (add) another portion and a second when that is final (at the end of the year). With the navaka rule (found in R-VJ 13 and Y-VJ 16) (these sidereal portions) are not to be added.
13That rising point from the 15th (tithi) paksha (at the end of any parvan) should be declared [dividing the paksha] by nine and the remainder multiplied by seven.
14With the abbreviations, the nakshatras are ja, drā, ga, kha, śve, ahī, ro, ṣā, cit, mū, ṣa, ṇya, sū, mā, dhā, ṇa, re, mṛ, ghā, svā, apo, ajas, kṛ, ṣya, ha, jye, and ṣṭhā.
15With the Jau, etc. portions, one should know the pair (the two portions of the parvan nakshatras). Among those paravans when in the first half (of the parvan nakshatra), the consumed nakshatra are the later ones (the 15th tithi ). If more from the two portions (of the nakshatra), it should be in the 14th tithi.
16Twice ten plus one-twentieth kalas should be two nadika of a muhurta. That 30 (muhurta) should be 600 plus three more (603) of the kalas.
17Two nadikas are a muhurta, but a mashaka (adhaka) equals 50 pala s. From a mashaka (adhaka) is a kumbhaka or drona (4 times the adhaka) increases by three kutas.
18The Moon joined with the nakshatras is [sixty] plus seven (67). The Sun is 13 and 5/9ths of a day.
19From the multiplied Shravishthas a.k.a. Dhanishthas, one should declare the lagnas of the east. One should declare the seasonal solar months from the six (seasons). From six (seasons), one should know those seasonal lunar months.
20From the portions of the parvans gone beyond it should be subtracted from twice the tithi. In those portions of the circle, the Sun is situated in the desired tithi.
21Those declared of those, one should know the nakshatra of the tithi and those granted kalas. Adding the kala and the aggregate one should know the bounded kalas.
22That which is situated there from the ayana of the northern course. Thus, the remainder should situated there from the southern course of the ayana. Thus, that is multiplied by two, divided by 61, plus 12 should be the measure of the day (in muhurtas).
23That which is half of the portions of the (lunar) day/tithis (15 tithis) is always in each parvan and that remainder of the season should be known together with the reckoning of the parvans.
24The rule of the doctrine of the means should determine [the result], even from the day. Multiplied from those contained in the quantity to be known. With the quantity from the knowledge (the result), one should divide.
25Agni, Prajapati, Soma, Rudra, Aditi, Brahaspati, Sarpas, Pitṛs, Bhaga, and Aryaman.
26Savitri, Tvashtri, Vayu, Indra and Agni, Mitra, Indra, Nirriti, Apa, and Vishvedevas.
27Vishnu, Vasus, Varuna, Aja Ekapat, Ahirbudhnyas, Pushan, Ashvins, and Yama.
28Indeed, those deities of the nakshatras, with those in the performance of the rituals of the person who performs or pays a priest for the sacrifice having the knowledge of the sacred texts, one receives a name born of the nakshatras.
29Thus, Lagadha spoke the exposition of the (synodic) months, year, muhurtas, risings, parvans, days, seasons, ayanas, and (solar) months.
30A sage knowing the Veda of the course of the moon, the sun, and the stars masters the course of the moon, the sun, and the stars; the world in the world, and progeny.
31That equinox multiplied by two, subtracted by one, and multiplied by six. That which is obtained, those are the parvans. Thus halved, should be that tithi.
32Those are told of the five years of the yuga arriving in the waxing of the moon during the synodic lunar month of Magha and concluding in the waning of the moon in the month of Pausha (derived from Pushya) by the knowledge of time.
33The equinox is declared in the third day of a lunar fortnight, ninth day of a lunar fortnight, and the day of the full moon [of the bright fortnight]; and the 6th day of a lunar fortnight and in the 12th day of a lunar fortnight [of the dark fortnight]. It should be repeated [once again during the five-year yuga].
34As Upavasatha is arriving in the day (just after sunrise), thus it should be the 14th day of the lunar fortnight. The moon during the bright fortnight of the synodic lunar month of Magha is joined to the year among those in Shravishtha nakshatra a.k.a. Dhanishtha nakshatra.
35As a crest of the peacocks and the gems of the serpents; just so, in that manner is Jyotisha situated at the most prominent place of the teachings of the branches of knowledge.