vedA~Nga jyotiSha and other ramblings on early Hindu calenders
vedA~Nga jyotiSha and other ramblings on early Hindu calenders | mAnasa-taraMgiNI
Interestingly, the total variation in day-light time is given as 6 muhUrta-s which corresponds approximately to the latitude of 35° N. This will be north of kubhA (kabul in modern Afghanistan), and might imply that the observations were inherited from the time the Aryas occupied the BMAC archaeological sites.
Some basics of the VJ:
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The vedic measures of time as per VJ:
5 gurvakShara-s [long syllables]= 10 mAtrA-s
= 1 kAShTha
124 kAShThA-s = 1 kalA
10 1/20 kalA-s = 1 nADikA*
2 nADIkA-s = 1 muhUrta
30 muhUrta-s = 1 ahorAtra (civil day)
366 days = 1 saMvatsara= 12 mAsa-s
= 6 R^itu-s= 2 ayana-s
5 years = 1 yuga*
This progression is an old vedic system we have in the taittirIya AraNyaka: "kalA muhUrtAH kAShThAsh chaahotrAsh cha sarvavashaH | ardhamAsA mAsA R^itavas saMvatsarash cha kalpantAM ||"
* Time is kept using a water-clock. The volume of water of weight 50 pala-s, at room temperature, is one Adhaka (a volume measure).
4*Adhaka = 1 droNA [a volume]; 1/16 of Adhaka = 1 kudava;
In a standard vedic water-clock 1 droNa- 3*kudava is that volume of water that drains in one 1 nADikA. Thus, the vedic water clock drained in 24 minutes or 1 nADikA. The water-clock is mentioned in the kAla sUktaM of the bhArgava-s in atharva veda. Thus, both the time units and the water clock find mention in the veda, suggesting that the systems mentioned in the VJ was a standard aspect of the vedic time keeping.
* A yuga is defined as the "pairing (from the root yug- same as English yoke, Germanic *yuminaz=Gemini)" or coming together of two celestial bodies, or their nodes or their apogees in the same place on the ecliptic. Approximately the moon and the sun meet in the same asterismal position in 5 years. Hence this is the basic yuga in vedic parlance. The years of the yuga were named in the veda as: saMvatsara, parivatsara, idAvatsara, anuvatsara and idvatsara.
The yuga concept clarifies why the saMvatsara is described as 366 days, even though, even babara prAvAhaNi and sArvaseni shaucheya already knew in the days of the yajur veda that 366 was too much. In a yuga there are 366*5= 1830 days (yuga value) and this gives the required approximation for the yuga definition that is meeting of sun and moon in a nakShatra. It also gives a base to derive a number of other critical values for the period of the yuga easily:
1) Number of risings of shraviShThA above the horizon (the nakShatra at the winter solstice) = yuga + 5 = 1835
2) Number of moon rises = yuga-62=1768
The Number of nakShatra-s traversed by the sun in 1830 days is 135. The number of ayanas of the moon 1 less than that number= 134.
The value of the yuga also can be used to relate to the following easily, as explained in the yajur jyotiSha 31:
1) Number of sAvana months in on 1 yuga (that is the traditional months of the vedic ritual) = 61= 30 days
2) Number of synodic months in a yuga, i.e. the period between two new moons in a yuga = 62 = 29.51 days, a reasonable approximation (modern value= 29.530).
3) Number of sidereal months in yuga = 67 = 27.31 (modern value=27.32).
Given any 3 elements of the yuga that are not completely dependent on each other we can get every other element. This is an important computational device of the VJ. Thus, for example
Given any 3 elements of the yuga that are not completely dependent on each other we can get every other element. This is an important computational device of the VJ. Thus, for example:
Number of sidereal days (i.e. the time interval between two successive rising of a star) in a yuga = yuga +5 = 1835
Thus, we have ratio of sidereal day : civil day = 0.99727 (modern value= 0.997269)
So one can see that the for a vedic ritualist at 1300 BC the VJ gives decent quick approximations for key calenderical values using the yuga concept, and can hence be hardly called a primitive work.
titihis and nakShatra's for some key days
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The yugArambha is given as when sun and moon are in the nakShatra of shraviShTha in the bright fortnight of the month of magha. Then the determination of the pakSha (kR^iShNa/shukla- k/s) and approximate nakShatras (n) and tithis (t) at the beginning of each of the ayana-s of the sun in the yuga is given:
1 n=shraviShThA, t=1s; 2 n=chitrA t=7s; 3 n=ArdrA, t=13s 4 n=pUrva-proShThapadA, t=4k; 5 n=anurAdhA, t=10k; 6 n=ashleShA, t=1s; 7 n=ashvini, t=7s; 8 n=pUrvAShADhA, t=13s; 9 n=uttara phalguni, t=4k; 10 n=rohiNi, t=10k;
These are days on which the solsticial sacrifices are performed.
The viShuva days or the equinoctial days are the other important ritual days. A formula is given for the number of pakSha-s(p) and tithi-s(t) having elapsed from the beginning of the yuga to the nth viShuva (n):
6*(2*n-1)*(p+.5*t); thus for viShuva 1 we have 6*pakShas+3*tithis or it occurs on tritIya.
The viShuva is declared as occurring in the shukla-pakSha at the end of the tR^itIya, navamI and paurNaMasya.
Rule for the tithi on which a R^itu begins is thus explained: The number of R^itus in a yuga is 30. The first R^itu of the yuga is shishira, in the month of tapas, as stated in the yajurveda (TS 4.4.11.1), begins on shukla prathamA. The next R^itu begins two tithis later on shukla tritIya, the next on shukla 5 panchami and so on till the 8th R^itu begins on paurNamAsya. Then the R^itu-s continue by the formula modulo(1+2*(n-1),15)
The logic of the peculiar division 124
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Given that there are 62 synodic months in a yuga, we have 124 pakSha-s in a yuga. Hence to keep the calculations as whole numbers the vedic day is divided into 124 parts or aMsha-s. From the earlier table we have a day having 603 kalA-s=74722 kAShTha-s, the latter being divisible by 124. [1 kAShTha=1.1563 seconds; 1 kalA= 2.388 minutes; part of the day/amsha= 11.612 minutes].
The part of the day when the pakSha ends is critical to determining the day when the sarcfices or iShTi-s are performed. The VJ gives the following procedure to figure out the part of the day when a pakSha ends:
The duration of each pakSha = yuga/124= 15 days – 30 parts (amshas) of the day.
Thus duration of each tithi =1 day – 2 parts of a day.
To find the part of the day the nth pakSha ends:
1) For the nth pakSha obtain x= modulo (n,4).
2) If x=1 then y=n+93; if x=2 then y=n+62; if x=3 then y=n+31; if x=0 then y=n
3) The number of parts of the day when the pakSha ends= modulo (y,124).
If the pakSha ends before 31 parts then it ends before civil mid-day.
E.g. 37th pakSha- x= modulo (37,4)=1; y=37+93=130; So the pakSha ends at modulo (130,124)=6. Thus it ends around 1 hour and 9.6 minutes of the day.
So one can see that the for a vedic ritualist at 1300 BC the VJ gives decent, rough and ready approximation for key values using the yuga concept, and can hence be hardly called a primitive work.