122 - Panchānga: The Almanac

General: Panchanga or the five aspects of reckoning time for each day, computed and recorded in Hindu almanacs are: (i) Vara (day of the week), (ii) Tithi (lunar day), (iii) Nakshatra (the Constellation through which the moon inoves), (iv) Yoga (Sum of the longitudes of the Sun and the Moon), and (v) Karana (half-tithi). All these reckonings have religious and ritualistic significances. 

The verses in this chapter are all of a highly cryptic nature and, like philosophical aphorisms, imply much more than what is actually expressed, and can be corectly understood only with suitable explanations. While the implied information is given brackets in the translation, an example is worked out in the Notes illustrating the working, step by step.

 God Agni said: 

1a. Time is (reckoned by) the accumulated number of years, (months etc., from the epoch up to the point of time under consideration). Ishall set forth the calculation involved in reckoning time. 

1b. The accumulated (i.e. elapsed) number of years (up to the required point of time) is to be multiplied by 12 (arka) and the (number of months elapsed in the current year from) Chitrā is to be added to the product)¹ 

1. Any epoch or starting point in time might be adopted, like, for instance the Kalpa or the beginning of creation, the Chaturyuga, Kaliyuga etc. or any of the eras like the Saka. 

Let the point of time taken for consideration, for which the Panchānga is required be Saka 10 (elapsed), in the month of Vaisakha, 1st tithi of the bright fortnight. 

Multiplying by 12, the elapsed years,                 10 X 12 = 120

Adding the 1 month, Mesha, elapsed,                               =    1

Total months elapsed from epoch                                     = 121

2a. The sum obtained is doubled and placed at two places. To one is added 4 (veda) and to the other 865 (pañchāngāshta). (The latter figure is to be divided by 60 and the quotient added to the first, while the remainder is kept as the second figure). The resultant is to be called 'guna’.² 

2. Multiplying the months from epoch by 2 (i.e. 121 x 2=242) and placing them in two places:  242     242

Adding 4 and 865                                     4     865

                                                               246     1107 

Dividing the second figurc by 60 and 

adding to the first                                          264       27   (Guna) 

2b. (The guna) is placed at three places (one below the other, in the serpentine fashion, each being written one step to the right of the preceding one). The 'middle' is multiplied by 8 (vasu) and the product again multiplied by 4 (veda). (The columns are to be added up.) and again written as ‘upper', 'middle' and 'lower'.¹  

1. Placing the guna) in three places in the serpentine fashion:                                         264                 27             (upper)

                                                                    264     27    (middle)

                                                                    264  27 (lower) Multiplying the 'middle' by 8 (i.e. 2112-216) and again by 4 (i.e. 8448 864), and setting it down in the above scheme: 

                                                 264               27

   8448     864

                  264     27

Adding the columns, the new 'upper', 'middle' and lower' are:                                                                      264             8475 1128    27                 

                                                                                              (27 is rejected)

3. Subtract 398 (ashţa-randhra-agni) from the lower and 87 (saika-rasāstaka) from the 'middle'. Divide (the 'middle' and the 'lower') by 60 and add the quotients to the preceding, (keeping the remainders in their places).² 

2. Subtracting 398 and 87                           87        398 

                                                      264             8388     730

 Elevating by 60                        404               0             10

4a. Vāra-tithi correction. The first (i.e. "upper)' when divided by 7 will give the week-day constant for tithi. (The quotient is to be rejected as of no more use.) The resultant is to be used as the Vära-correction for tithi-nādikās'.³ 

3. Dividing the 'upper' by 7 for week-days and rejecting the quotient, we get the vära-correction for tithi as 5-0-10. 

4b-5. Nakshatra-Yoga constants. The ‘guna’ derived above is to be multiplied by 2, and 3 subtracted from the second figure. Guna is set down before the result (in the serpentine fashion). 30 (kha-rāma) is set down below the last figure, and 6, 12 and 8 (rasa-arka-asta), respectively, below the three figures, (and the columns added up and elevated by dividing by 60). Divide the first figure by 28 and place it below the ‘correction for tilhi’ (obtained in verse 4a). (add and take the result as a second ‘upper').⁴ 

4. Multiplying the 'guna' (204-27) by 2 (i.e. 528-54 and subtracting 3                                                 528           51 

 Setting down the 'guna' below                        264      27

 Adding 30 to the last figure                                          30

Adding 6-12-8 to the expression         6             12          8

6-8a. The 'guņa' is halved, 3 subtracted (from its second figure) and the whole expression multiplied by 2. The first figure here is multiplied by 11 (rudra); the second figure is increased by 1 and divided by 39, the quotient being subtracted from the first figure and the remainder kept in its place. The resultant is termed madhya. Subtract 22 from the first figure and divide it by 60; the remainder is deductive; the quotient is added to the (second) ‘upper' (of verses 4b-5). The first figure is divided by 27 and the remainder set down in its place. The resultant expression is the constant for the correction of nakshatra and yoga.¹

Adding the whole                                       534     327    65

Elevating by 60                                           539        28     5

Dividing the first figure by 28 and rejecting 

the quotient                                               33          28     5

Adding the correction for tithi, i.e. the second

‘upper'                                                        5           0          10

                                                                    40         28        15

Adding 

1. The guna (264-27) is halved (132-14), 3 subtracted from the second figure (132-11) and multiplied by 2 (i.e. 264-22). The first figure is multiplied by 11 (i.e. 2904); to the sccond figure 1 is added (i.e. 23) and divided by 39 and the remainder (i.e. 23 ) is retained. This is termed the new 'middle'. Subtracting 22 from the first figure (i.e. 2882-23) and elevating by 60, we get 48-2-23. 

Applying this                                                 48           2           23

to the new second 'upper'                           40           28         15

we have                                                          88            30        38    

Dividing by 27 and ignoring the quotient, 

the correction for nakshatra and yoga:      7              30         38   

8b-9a. Nakshatra. For the calculation of tithi, there is a monthly constant, being 2 piņdas (i.e. whole units) and 32 ņādikās (which has to be added to the tithi correction contained in verses 4a). Similarly, for the nakṣhatra, there is a monthly constant, being 2 nakṣhatras and 11 nādikās, (which, when added to the nakshatra correction of verse 8a, will give the elapsed nakshatra and the nädikās gone in the current nakshatra.)²

 2. Adding the tithi-constant (2-32-00) to the våra-tithi correction (3-0-10), we have 7-32-10, being the vårádi (week, day etc.) correction for the point of time taken for consideration. For the nakshatra of that point of time, add the nakshatra constant (2-11-00) to the nakshatra correction (got in verses 6-8a), i.e. 7-30-38, and we have the nakshatra as 9-41-38. In other words, at the point of time taken, nine nakshatras have passed by, and in the current 10th nakshatra, maghå, it is 41 nädikas and 38 vinädikas.

 9b-10. Weekday and commencing point of Tithi. Add the tithi correction above (to the värādi-tithi correction got inverse 4a), placing the tithi number below the vāra number. Divide by 7 (if vāra plus tithi exceeds 7); the remainder will give the elapsed week-day counted from Sunday, and the nädikās gone in the next day at the point of the commencement of the relevant tithi) In the case of tithis after adding the complete units (pindakas), the sumshould be divided by 14 (if the sum exceeds 14, and the remainder taken as the tithi.)¹ 

1.    Adding the tithi constant (2-32-00) to the vara-tithi correction (5-0-10).we get 7-32-10 for the weekday,which means that 7 days have elapsed as /counted from Sunday,and at the point of time in consideration,i.e. suklapratipad in vaisakha,it is Sunday at 32 nädikās and 10 vinadikas (Mean).

11-14a. True-Tithi correction. The correction, in nädikās, for the fourteen tithis would be, in order, minus, plus, plus, minus, (minus and so on). While the correction for the 14th tithi is zero), the correction for the thirteenth and the first is 5 (vinādikās) (each, minus and plus, respectively), that for the 12th and the 2nd, 10 (vinādikās), that for the 11th and 3rd, 15 (vinādikās), that for the 10th and 4th, 19 (vinādikās), that for the 9th and 5th, 22 (vinādikās), that for the 8th and the 6th, 24 (vinādikās), and that for the 7th, 25 (vinādikās). These khandakas (correction-bits) are to be applied appropriately to the pindakas (full units).² 

2. The nādika corrections enunciated are: 

            Tithi           Nadiká corr          Tithi                 Nadikäсorr

    14                   0                        1                             +5

             13                    -5                       2                             +10

            12                    -10                     3                              +15

            11                     -15                       4                              +19

            10                    -19                       5                              +22

             9                     -22                      6                              +24

             8                     -24                     7                              +25              14b-17a. Vikāla correction. In the case of (the three), Karkataka, (Simha and Kanyā), divide the rašis, respectively, by 6 (rutu), 4 (veda) and 3 (traya); in the case of Tulā, (Vruśchika and Dhanus), divide, respectively, in the reverse, i.e.by 3, 4 and 6; in the case of Makara, (Kumbha and Mina), respectively, by 3, 4 and 6; and in the case of Mesha, (Rushabha and Mithuna), divide, respectively, in the reverse, i.e. by 6, 4 and 3. The correction, in vikalās, which is positive in the case of the three, Mesa etc., are 50 (kha-ishu), 40 (kha-yuga) and 12 (mitra); in the case of the three, Karkațaka etc., it is in the reverse order, (i.e. 12, 40 and 50, but positive); in the case of the three, Tulā etc., (it is 50, 40 and 12), negative; (and, in the case of the three, Makara etc., it is 12, 40 and 50, negative).¹ 

1. The vikála corrections enunciated are:

 Month     Divisor    Corr.        Month      Divisor     Corr. Karkataka           6             +12”          Makara          6           -12”

 Simha                  4             +40"        Kumbha       4           -40”

 Kanya                  3             +50”        Mina            3             -50”

 Tula                     3             +50”         Mesa             3            -50”

 Vruśchika           4             +40”        Rushabha            4            -40”

 Dhanus               6             +12”         Mithuna     6             -12”

17b-19a. Application of the vikalā correction. The vikalā correction is to be applied to the tithi multiplied by 4. Multiply their eleven vikalās by the difference in liptās (i.e. kalās) between the elapsed and to-elapse portions of the tithi and divide by 60. If the elapsed portion is less than/the portion to-elapse, treat the correction as positive even if it be negative and or positive, retain it as positive; while, in the case of the portion to elapse being greater, the reverse is the case (i.e. the correction is to be taken as negative both if it is negative or positive). 

19b-21a. Further correction to the Tithi. Double (?Treble) (the nādikās of) the tithi and subtract from it one-sixth of (the product). Apply to it the tithi-nādikās obtained for the sun in the reverse order, and subtract the result from 60; the true nådis of the tithi would be obtained. If not subtractible, add 60 and subtract; if more than 60, reduce it by 60 and subtract.² 

2. For the third tithi correction, multiply the tithi-nädikås, 32-10 (of verses 9b-10) by 3 (i.e. 96-30), and deduct a sixth thereof (i.e. 16-5), resulting in 80-25. Adding to this the tithi-nädikas (32-10), we get i 12-35. The correction for one tithi (viz. 5 nädikas, of verse 11-14a) being applied negatively, we get 107-35. Dividing it by 60, the true nadikās in the current tithi is got at 47-35.

21b-22. Yoga. The tithi is associated with the constellation The tithi multiplied by 4 and a third (of the tithi) added to it. Apply to it the negative correction. (By dividing it by 27, the yoga elapsed and the nädikās in the current yoga are obtained.) True tithi has be to be used as the means for calculating the yoga.³ 

3. Yogas form variable divisions of time during which the joint motion of the Sun and the Moon in longitude is 13° 20’ or 800 kalās. In a cycle there are 27 yogas, some of them being considered as auspicious and others inauspicious. Their significances are taken due note of in deciding upon the times for rituals and domestic ceremonies. The 27 yogas are:

 1. Viskambha            10. Ganda                  19. Parigha

 2.Priti                        11. Vruddhi                20. Siva

 3. Ayushman            12. Dhruva                 21. Siddha

 4. Saubhagya            13. Vyåghata              22. Sådhya

 5. Sobhana                14. Harshaņa             23. Subha

 6. Atiganda               15. Vajra                     24. Sukra

 7. Sukarma               16. Siddhi                   25. Brahma

 8. Dhruti                   17. Vyatipata             26. Indra

9. Sūla                        18. Variyan                27. Vaidhruti

Multiplying the true tithi (viz. 47-35 of verses 19-20) by 4 (i.e. 190-20) and adding a third of the tithi (viz. 15-52), we get 206-12. Dividing by 27 (which is the total number of yogas in a cycle) and rejecting the quotient, we have 7-12. i.e. 7 yogas up to Sukarma have gone by and, in the current 8th yoga, Dhruti, 12 nädıkās too are over.

23a. The yoga is, indeed, got also by adding (the longitudes of) the sun and the moon (in kalās and dividing by 800). ¹

 1. In the alternative method of calculating the yoga, the longitudes of the Sun and the Moon are added and the sum divided by 800 (which is the said sum in terms of six kalás). The quotient will give the number of the yogas elapsed and the remainder the nädikas etc. elapsed in the current yoga.

23b-24a. Karana. (The number of) the tithi reduced by I and multiplied by 2, and the product divided by 7, gives the karaña of day-time. The tithi-number multiplied by 2 and the product reduced by 1 and divided by 6 (kruta) gives the karaña of the night.² 

2. The Karana is a measure of time extending over half a tithi, having astrological significance. They carry eleven names, being: (1) Bava, (2) Bälava, (3) Kaulava, (4) Taitila, (5) Gara., (6) Vaņija, (7) Vishti, (8) Sakuni, (9) Chatuspada, (10) Näga and (1!) Kimstughna. A cycle consists of 60 karanas (during the 30 tithis or 60 half-tithis). The last four karanas occur only once and occupy the four half-tithis from the second half of the 14th of the dark fortnight to the first half of the/1st tithi of the bright fortnight, and, so, are called sthira or 'fixed' karanas, while the other seven karanas occupy the remaining 56 half-tithis, by repeating themselves eight times, and, so, are callcd cala or 'moving' karanas.

24b-c. The karana of the end (i.e. second half) of the 14th tithi of the dark fortnight is called Sakuni; (that of the first half of the full moon day is called Chatushpada; that of the end (i.e. second half of the full moon day) is called Ahi (Naga); and that of the beginning (i.e. first half) of the prathamā (of the bright fortnight) is called Kimstughna. 

Corrections To The Printed Text (SV Edn).

Verse                 For                    Read        

                      षष्टिहतो               षष्टिहुतो

7b                       -मूर्ध्व                   -मूर्ध्व

    10a                           शेषवाराश्च           शेषा वाराश्च

 14b                    पिण्डकाद्                पिण्डका

 19a                    तिथिद्धि                    तिथिद्धि (? स्त्री )

 22a                    तिथिश्री                     तिथिति

22b                    शोधनम्                    साधनम्

23b                    कृतिद्विधा                 कृतिदिवा

24c                     तो हि                   -तोऽहिः