Month Chart and Monthly Results

Now, finding the day count. The months gone since the day of the Aries ingress are multiplied by thirty and joined with the days. Take away their own 64th part (sva-abdhi-tarka-lava, 64) in days. The day count comes out, counted from the year lord.

Now, finding the mean Sun. Divide the day count by thirty (30). The quotient is months, and the remainder is days. The sum of the planet's motion for those, joined with the starting value, is the mean Sun.

The starting value for the Sun is held to be 11 signs, 27 degrees, 51 minutes, 39 seconds.

The yojanas (a measure of distance) of the distance between the line and one's own place, less their own quarter (9), become seconds. Then the deshantara (correction for distance east or west) for the Sun is minus [to the] east and plus [to the] west. This gives the mean Sun at one's own place.

This table gives the weekday, ghatikas (24-minute unit), palas (24-second unit) and vipalas (one-sixtieth of a pala) for the year lord. First come Shaka years in steps of twenty. Then come the left-over years 1 to 20. Shaka 1489: weekday 6, 27 ghatikas, 18 palas, 4 vipalas. Shaka 1509: weekday 3, 37 ghatikas, 48 palas, 32 vipalas. Shaka 1529: weekday 0, 48 ghatikas, 19 palas, 0 vipalas. Shaka 1549: weekday 4, 58 ghatikas, 49 palas, 28 vipalas. Shaka 1569: weekday 2, 9 ghatikas, 19 palas, 56 vipalas. Shaka 1589: weekday 6, 19 ghatikas, 50 palas, 24 vipalas. Shaka 1609: weekday 3, 30 ghatikas, 20 palas, 52 vipalas. Shaka 1629: weekday 0, 40 ghatikas, 51 palas, 20 vipalas. Shaka 1649: weekday 4, 51 ghatikas, 21 palas, 48 vipalas. Shaka 1669: weekday 2, 1 ghatikas, 52 palas, 16 vipalas. Shaka 1689: weekday 6, 12 ghatikas, 22 palas, 44 vipalas. Shaka 1709: weekday 3, 22 ghatikas, 53 palas, 12 vipalas. Shaka 1729: weekday 0, 33 ghatikas, 23 palas, 40 vipalas. Shaka 1749: weekday 4, 43 ghatikas, 54 palas, 8 vipalas. Shaka 1769: weekday 1, 54 ghatikas, 24 palas, 13 vipalas. Shaka 1789: weekday 6, 4 ghatikas, 55 palas, 4 vipalas. Shaka 1809: weekday 3, 15 ghatikas, 25 palas, 22 vipalas. Shaka 1829: weekday 0, 25 ghatikas, 56 palas, 0 vipalas. Shaka 1849: weekday 4, 36 ghatikas, 26 palas, 28 vipalas. Shaka 1869: weekday 1, 46 ghatikas, 56 palas, 56 vipalas. Now the left-over years. Year 1: weekday 1, 15 ghatikas, 31 palas, 31 vipalas. Year 2: weekday 2, 31 ghatikas, 3 palas, 2 vipalas. Year 3: weekday 3, 46 ghatikas, 34 palas, 34 vipalas. Year 4: weekday 5, 2 ghatikas, 6 palas, 5 vipalas. Year 5: weekday 6, 17 ghatikas, 37 palas, 37 vipalas. Year 6: weekday 0, 33 ghatikas, 9 palas, 8 vipalas. Year 7: weekday 1, 48 ghatikas, 40 palas, 40 vipalas. Year 8: weekday 3, 4 ghatikas, 12 palas, 11 vipalas. Year 9: weekday 4, 19 ghatikas, 43 palas, 42 vipalas. Year 10: weekday 5, 35 ghatikas, 15 palas, 14 vipalas. Year 11: weekday 6, 50 ghatikas, 46 palas, 45 vipalas. Year 12: weekday 1, 6 ghatikas, 18 palas, 16 vipalas. Year 13: weekday 2, 21 ghatikas, 49 palas, 48 vipalas. Year 14: weekday 3, 27 ghatikas, 21 palas, 19 vipalas. Year 15: weekday 4, 52 ghatikas, 52 palas, 51 vipalas. Year 16: weekday 6, 8 ghatikas, 24 palas, 22 vipalas. Year 17: weekday 0, 23 ghatikas, 55 palas, 54 vipalas. Year 18: weekday 1, 39 ghatikas, 27 palas, 25 vipalas. Year 19: weekday 2, 54 ghatikas, 58 palas, 56 vipalas. Year 20: weekday 4, 10 ghatikas, 20 palas, 28 vipalas.

In a separate place, the wise one should set down the mean Sun and half of the traikya (the sum of three corrections).

The Sun's manda uchcha (high point), beginning with signs, is: dyau (2) signs, 17 degrees, 20 minutes. This uchcha less the planet is here the mandakendra (the Sun's distance from its high point).

This table gives the mean Sun's motion for 1 to 12 savana (sunrise-to-sunrise) months, in signs, degrees, minutes and seconds. Months 1: 0 signs, 29 degrees, 34 minutes, 5 seconds. Months 2: 1 signs, 29 degrees, 8 minutes, 10 seconds. Months 3: 2 signs, 28 degrees, 42 minutes, 15 seconds. Months 4: 3 signs, 28 degrees, 16 minutes, 20 seconds. Months 5: 4 signs, 27 degrees, 50 minutes, 25 seconds. Months 6: 5 signs, 27 degrees, 24 minutes, 30 seconds. Months 7: 6 signs, 26 degrees, 58 minutes, 35 seconds. Months 8: 7 signs, 26 degrees, 32 minutes, 40 seconds. Months 9: 8 signs, 21 degrees, 6 minutes, 49 seconds. Months 10: 9 signs, 25 degrees, 40 minutes, 50 seconds. Months 11: 10 signs, 25 degrees, 14 minutes, 55 seconds. Months 12: 11 signs, 24 degrees, 48 minutes, 0 seconds.

If the mandakendra (the Sun's distance from its high point) is less than three signs, it is the arc. If more than three signs, [it is] taken from six (rasa). If more than six signs, [it is] less six. If more than nine, it is taken from the circle.

The Sun's result, beginning with degrees, that stands in the cell matching the arc's degrees, is taken. The remainder is multiplied by the difference between the cells. Divided by sixty, it gives minutes and so on. That is added.

The true manda result is minus when the mandakendra (the Sun's distance from its high point) is in the half beginning with Libra. It is plus when in the half beginning with Aries. Applied to the mean Sun, it gives the true Sun. The result for the Sun's motion also stands in the cell.

For the motion, the result is added when the anomaly is in the half beginning with Cancer. It is subtracted when in the half beginning with Capricorn. This gives the true motion. The true Sun at the year lord's time then stands joined with its motion.

Now, finding the traikya (the sum of three corrections). Take the sayana (tropical) mean Sun, doubled. Take the sine of its arc. Divided by shadbha (a fixed divisor), it gives [a result] in minutes and so on. It is made plus and minus for the Sun in an even and an odd quadrant [in that order]. In the udayantara (rising-time correction), each quadrant is three signs, taken as odd and even in turn.

Or, finding the udayantara (rising-time correction) without the sine. In the quadrant of the sayana (tropical) Sun, take the degrees to come or gone. Reduce them by twice their own fifth part. The result is the seconds of the udayantara. (Our text is unclear here: the letters 'pamsha' after 'to come or gone' cannot be explained.)

The Sun's manda result multiplied by ten (kha-indu 10) is in seconds. That is the bhujantara (time correction for the Sun's uneven motion). On the mean Sun it is plus or minus. It is held to be like the [manda] result.

This table gives the mean Sun's motion for 1 to 30 savana (sunrise-to-sunrise) days, in signs, degrees, minutes and seconds. Day 1: 0 signs, 0 degrees, 59 minutes, 8 seconds. Day 2: 0 signs, 1 degrees, 58 minutes, 16 seconds. Day 3: 0 signs, 2 degrees, 57 minutes, 24 seconds. Day 4: 0 signs, 3 degrees, 56 minutes, 32 seconds. Day 5: 0 signs, 4 degrees, 55 minutes, 40 seconds. Day 6: 0 signs, 5 degrees, 54 minutes, 49 seconds. Day 7: 0 signs, 6 degrees, 53 minutes, 57 seconds. Day 8: 0 signs, 7 degrees, 53 minutes, 5 seconds. Day 9: 0 signs, 8 degrees, 52 minutes, 13 seconds. Day 10: 0 signs, 9 degrees, 51 minutes, 21 seconds. Day 11: 0 signs, 10 degrees, 50 minutes, 29 seconds. Day 12: 0 signs, 11 degrees, 49 minutes, 38 seconds. Day 13: 0 signs, 12 degrees, 48 minutes, 46 seconds. Day 14: 0 signs, 13 degrees, 47 minutes, 54 seconds. Day 15: 0 signs, 14 degrees, 46 minutes, 2 seconds. Day 16: 0 signs, 15 degrees, 45 minutes, 10 seconds. Day 17: 0 signs, 16 degrees, 44 minutes, 18 seconds. Day 18: 0 signs, 17 degrees, 43 minutes, 27 seconds. Day 19: 0 signs, 18 degrees, 42 minutes, 35 seconds. Day 20: 0 signs, 19 degrees, 41 minutes, 43 seconds. Day 21: 0 signs, 20 degrees, 40 minutes, 51 seconds. Day 22: 0 signs, 21 degrees, 40 minutes, 59 seconds. Day 23: 0 signs, 22 degrees, 39 minutes, 7 seconds. Day 24: 0 signs, 23 degrees, 38 minutes, 16 seconds. Day 25: 0 signs, 24 degrees, 37 minutes, 24 seconds. Day 26: 0 signs, 25 degrees, 36 minutes, 32 seconds. Day 27: 0 signs, 26 degrees, 35 minutes, 40 seconds. Day 28: 0 signs, 27 degrees, 34 minutes, 48 seconds. Day 29: 0 signs, 28 degrees, 34 minutes, 56 seconds. Day 30: 0 signs, 29 degrees, 34 minutes, 5 seconds.

The Sun, with the ayanamsha (the zodiac shift) added, may be at the start of Libra or of Aries. Then take the gnomon of 12 (surya) finger-widths. Its shadow at one's own midday is the akshaprabha (noon shadow at the equinox). Set it down and multiply it by ten, eight and ten (dig, gaja, dig).

This table covers the manda anomaly from 1 to 90 degrees, in three blocks of thirty. For each degree it gives three figures. First, the Sun's manda equation in degrees, minutes and seconds. Second, the difference to the next cell, in minutes and seconds. Third, the result for the motion, in minutes and seconds. 1: 0.2.20, 2.20, 2.18. 2: 0.4.40, 2.20, 2.18. 3: 0.7.0, 2.19, 2.18. 4: 0.9.28, 2.18, 2.17. 5: 0.11.27, 2.19, 2.17. 6: 0.13.56, 2.19, 2.17. 7: 0.16.15, 2.18, 2.17. 8: 0.18.39, 2.17, 2.16. 9: 0.20.50, 2.17, 2.16. 10: 0.23.7, 2.16, 2.16. 11: 0.25.23, 2.16, 2.14. 12: 0.27.38, 2.16, 2.14. 13: 0.19.55, 2.15, 2.13. 14: 0.32.10, 2.14, 1.13. 15: 0.34.24, 2.13, 2.12. 16: 0.36.27, 2.12, 2.11. 17: 0.36.49, 2.11, 2.11. 18: 0.41.5, 2.10, 2.9. 19: 0.43.12, 2.9, 2.9. 20: 0.45.22, 2.9, 2.9. 21: 0.47.31, 2.8, 2.8. 22: 0.49.34, 2.7, 2.6. 23: 0.51.57, 2.4, 2.5. 24: 0.53.58, 2.1, 2.3. 25: 0.55.58, 2.1, 2.3. 26: 0.57.59, 2.3, 2.3. 27: 1.0.0, 2.0, 2.1. 28: 1.2.2, 2.0, 2.0. 29: 1.4.3, 2.0, 1.27. 30: 1.3.3, 2.0, 1.56. 31: 1.8.3, 1.54, 1.55. 32: 1.4.57, 1.55, 1.53. 33: 1.11.52, 1.55, 1.51. 34: 1.13.47, 1.53, 1.53. 35: 1.15.40, 1.53, 1.49. 36: 1.17.33, 1.45, 1.47. 37: 1.19.20, 1.49, 1.45. 38: 1.21.7, 1.48, 1.43. 39: 1.24.55, 1.49, 1.42. 40: 1.26.32, 1.44, 1.48. 41: 1.28.3, 1.43, 1.38. 42: 1.29.36, 1.36, 1.36. 43: 1.31.33, 1.35, 1.34. 44: 1.33.58, 1.34, 1.32. 45: 1.34.2, 1.32, 1.30. 46: 1.36.7, 1.31, 1.29. 47: 1.37.25, 1.34, 1.28. 48: 1.38.6, 1.23, 1.28. 49: 1.40.20, 1.29, 1.26. 50: 1.42.3, 1.25, 1.26. 51: 1.43.36, 1.21, 1.18. 52: 1.44.45, 1.17, 1.16. 53: 1.46.0, 1.11, 1.14. 54: 1.47.21, 1.7, 1.12. 55: 1.48.38, 1.6, 1.12. 56: 1.49.42, 1.6, 1.13. 57: 1.51.3, 1.6, 1.13. 58: 1.52.12, 1.5, 1.12. 59: 1.51.13, 1.5, 1.11. 60: 1.53.35, 1.5, 1.11. 61: 1.54.20, 1.4, 1.4. 62: 1.55.33, 1.1, 1.0. 63: 1.55.36, 0.58, 0.58. 64: 1.56.30, 0.59, 0.57. 65: 1.57.32, 0.54, 0.56. 66: 1.50.0, 0.56, 0.54. 67: 2.39.27, 0.56, 0.50. 68: 2.0.22, 0.50, 0.49. 69: 2.2.24, 0.47, 0.46. 70: 2.2.52, 0.44, 0.43. 71: 2.2.51, 0.42, 0.41. 72: 2.3.14, 0.40, 0.39. 73: 2.4.17, 0.38, 0.27. 74: 2.5.35, 0.36, 0.36. 75: 2.6.51, 0.34, 0.31. 76: 2.6.45, 0.32, 0.31. 77: 2.7.17, 0.28, 0.28. 78: 2.7.45, 0.37, 0.20. 79: 2.8.12, 0.23, 0.23. 80: 2.8.35, 0.20, 0.22. 81: 2.8.53, 0.18, 0.19. 82: 2.9.18, 0.15, 0.18. 83: 2.9.36, 0.12, 0.15. 84: 2.9.51, 0.10, 0.11. 85: 2.10.3, 0.8, 0.10. 86: 0.10.21, 0.6, 0.8. 87: 0.10.17, 0.4, 0.6. 88: 0.10.31, 0.1, 0.4. 89: 0.10.13, 0.0, 0.1. 90: 0.11.27, 0.0, 0.0.

The last is divided by three. These, in order, are the charakhanda (steps of the day-length change). [Take] the Sun joined with the 'udayanamsha'. Add the gone parts, as many as the signs of its arc. Then take the remainder multiplied by its own to-come part ...

... joined with the thirtieth part (kha-rama 30), it is the charardha (half the day-length difference). Seconds equal to the charardha are the Sun's charantara (day-length correction). At sunrise it is plus when [the sayana Sun is] in the six signs from Libra. It is minus in the six from Aries. The reverse also holds.

The total of the three, by the way of virya, is called the traikya (the sum of three corrections). Or an easy method is set out for finding the traikya.

Take the degrees gone of the true sayana (tropical) Sun. Multiply them by the rising time of its own sign. Divided by thirty, that is the Sun's gone part. Add to it the rising times of the signs behind it, from Aries.

Divided by sixty, it is in ghatikas (24-minute unit) and so on. Now the mean Sun: take the sayana (tropical) [mean Sun]. The sixth part of its degrees gives the result in ghatikas and so on.

The difference of the two, in minutes and so on, is called the traikya (the sum of three corrections). If the Sun's gone ghatikas (24-minute unit), compared with the mean Sun's ghatikas, are ...

... less, the traikya (the sum of three corrections) is to be known as minus for the Sun, and plus otherwise. With that, the mean Sun is corrected. It is the one corrected by the traikya.

Its exactness is made as before; the fine Sun becomes fully exact. The birth Sun should also be made exact by the method told, as something new.

Every year that same Sun, with its motion, is the exact Sun. The Sun born at a month's time is the year's Sun with one sign added each time.

From the second month on, the Suns born of the months are the exact Suns. In the days, the entry Suns are joined with one degree each.

Now, take the number of the chosen month, less one. The result standing in the cell of the month-motion table, equal to that, is added [to the Sun].

The birth Sun, the mean Sun, becomes the Sun near the chosen month. The month number less one, multiplied by thirty (kha-rama 30), is joined.

In one's own birth day count, the group belonging to the chosen Sun comes about. Its exactness is made as told, joined with the motion and the traikya (the sum of three corrections).

Then one should take the difference between the chosen Sun and the month Sun. Its minutes and so on, divided by the true motion, give the result in days and so on, exact.

If the chosen Sun is more than the month Sun, that [result] is held to be minus. If less, it is plus. The year lord's weekday and so on is corrected by it.

At the month entry, the exact ghatikas (24-minute unit) are [found]. For its weekday, the day count is used. The corrected weekday and so on of the year lord is held [as the answer]. The count is cut by seven, from the Sun.

The current weekday, and the fine month entry, would result. Another method is told, from the words of the honoured teachers.

Take the minutes of the Sun at the month-entry time. They are less or more than the Sun born of the day count. Divided by its own motion, they give the ghatikas (24-minute unit).

These ghatikas (24-minute unit), corrected by the traikya (the sum of three corrections), are to be added to or taken from the year lord's ghatikas. The exact ghatikas at the month entry are then well corrected by the deshantara (correction for distance east or west).

In the traikya (the sum of three corrections) and the 'mandapa' ghatikas (24-minute unit), one should set [the correction] reversed from [the rule for] the Sun. The deshantara (correction for distance east or west) correction should also be made reversed, in the palas.

Now, the difference should be taken with the exact Sun born of the day count. It is made without the traikya (the sum of three corrections) and deshantara (correction for distance east or west) corrections and the rest. The traikya correction should be made in the ghatikas (24-minute unit). For the weekday of the month entry, take the one born of the birth day count. Join it with thirty, thirty, for each month. In this way, by both methods, the weekday and so on of the month entry come out the same.

Now: the number [of the chosen day], less one. The Sun joined with the result standing in the day-table cell equal to that becomes the Sun near the day. It is as at the month-entry time. From it, by the method told, the wise one should work out the day entry.

And in the Muktavali: In just this way, the day entries are [worked out]. This is to get at the very fine results. They become exact from the likeness to the birth Sun's minutes and so on. This is my teacher's view.

Planets, houses, sahamas (special point for one life topic) and the rest should be thought over day by day by the wise, as told before. Or else, here, the order of periods may be counted from the star of Agni [Krittika]. (Our text is unclear here: the words 'dakshajarama-sammata', which seem to say whose view this order is, cannot be read.)

Now the reason for the traikya (the sum of three corrections) and the deshantara (correction for distance east or west) figures in the Sun is told. The true savana (sunrise-to-sunrise) day varies, so the day count was brought by the mean savana day. Take sixty star-day ghatikas (24-minute unit). Join them with [the breaths] equal to the mean Sun's motion and so on. They make the mean Sun's savana day. Because the mean motion is always equal, this stays fixed.

But the true savana (sunrise-to-sunrise) day is this. In one day, a star and the Sun rise at the same time. After sixty star-day ghatikas (24-minute unit) from that time, the star rises again. By its true motion the Sun has gone ahead on the ecliptic as before. So the Sun rises after that, by breaths. These are obtained from the product of its own rising and its motion. That is divided by ravashrashtabhu. Joined with these ashu [breaths], the sixty star ghatikas make the Sun's true savana day. (Our text is unclear here: the number word ravashrashtabhu cannot be decoded.)

Its motion differs from day to day, and the rising of each month's sign differs, so it varies. Therefore the day count was made by the mean savana (sunrise-to-sunrise) day. What is wanted is by the true savana day. So, to find the gap between the true and the mean day counts, the udayantara (rising-time correction) correction was made.

Now, take the planet born of the true savana (sunrise-to-sunrise) day count. The mean Sun is near the horizon at Lanka, the city of the ten-headed one. As the Siddhanta says, the planet is then the mean one. It is born at the mean Sun's rising time at Lanka. But what is wanted is at the true Sun's rising time. So by the bhujantara (time correction for the Sun's uneven motion) correction it becomes the one at the true Sun's rising time. Again, there is the south-north gap, called the charantara (day-length correction) correction. By it, the planet becomes the one at the rising time in a city on the central line. That city has the same latitude as one's own. Again, there is the east-west gap, called the dashantara correction. By it, the planet becomes the one at the true Sun's rising time in one's own city. This is the truth.

Here is an example. 1673 years had gone since the rule of King Vikramaditya, and 1538 years since the rule of King Shalivahana. It was the dark half of Shravana, the third tithi (moon day), a Saturday, 11.10. The star was Dhanishtha, 45.33. The yoga (a day-part of the almanac) was Shriti, 33.44. The ghatikas (24-minute unit) and palas (24-second unit) gone from sunrise were 34.32. The lagna (rising sign) rising was Sagittarius. Then was born the great lord Shri Sahasuja. All the kings of the earth served his lotus feet. He was Indra of the whole round earth. He was foremost in leading the path of duty. The birth was at Ajmer.

There, the palaprabha (noon shadow at the equinox) is 5.50. The deshantara (correction for distance east or west) is 10. The 'pratyak' charakhandas (steps of the day-length change) are 58, 47, 19. The Shaka year less 1529 (nava-ashvi-tithi), by the method told [in chapter 1]. By it, the tithi (moon day) of the Aries ingress came to 20, the dark fifth of Vaishakha.

Now, finding the year lord. There, the Shaka year you want is 1538. Take away the near Shaka year in the book, 1529 (printed 15.29). The remainder is 9. The cell figures for the remainder 9 are 4.19.43.42. The Shaka year below is 1528 [as printed]. The figures below that Shaka are 00.48.19.00. Joined: 5.08.02.42. This is the year lord, weekday and so on.

Now, finding the day count. There, the Aries ingress is on the dark fifth of Vaishakha (5). Counting from it, the months gone up to the dark fifth of Ashadha are 2. Multiplied by thirty: 60. From the dark sixth of Ashadha to the dark third of Shravana, the days gone are 27. Joined: 87. Less the part 'svabdhi-tarka' (64), one: 86. So the day count on the dark third of Shravana is 86. Cut by seven: 2. From the year lord's weekday, Thursday, count 2: Friday has gone, and the present day is Saturday.

Now, finding the mean Sun. The day count 86, divided by thirty, gives months 2, with 26 days left. Now the motion for the months is 01.19.08.10 [as printed]. The motion for 26 days is 00.25.37.32. The sum is 02.24.45.42. The starting value in signs and so on, 11.27.51.39, is added: 02.22.37.21. This is the mean Sun in signs and so on, at the end of the year lord's time. The place is west of the line, so the deshantara (correction for distance east or west) of 10 seconds is added. It becomes the Sun corrected for it.

Now, by the method told in 'gata-eshya-divasa-adyena' and the rest, the year lord's ghatikas (24-minute unit) are 8.2.42. The ghatikas wanted are 34.32. Their difference is 26.29.18. The Sun's mean motion is 59.08. Multiplied and divided by sixty, the result in minutes and so on is 26.06. Added to the mean Sun 02.22.37.31, it gives the birth-time mean Sun, 02.23.3.37.

Now, working out the udayantara (rising-time correction). There, the mean Sun is 02.23.3.37. Joined with the ayanamsha (the zodiac shift) brought as told before, 16.45.18, it is 03.09.48.55. Doubled: 06.19.37.50. Because it is more than six [signs], it is less six, and the arc becomes 00.19.37.50.

Now its sine is to be made. The way of finding the sine is in the Siddhantashiromani. Rupa-ashvinau 21, vimshati 20, anka-chandra 19, atyashti 18, tithi 15, arka 12, nava 9, ishu [5], dasra [2]. These are the sine pieces. The arc's degrees divided by ten give the gone pieces. Then the remaining degrees are multiplied by the piece to come. Divided by ten (kha-indu), what is got is joined with the sum of the gone pieces. That is the sine.

The total of the sine differences is told in the Siddhantashiromani: Svarga 21. Ku-veda 41. Kha-rasa 60. Sapta-shaila 77. Yama-anka 92. Veda-asha 104. Tri-shiva 113. Sarpa-rudra 118. Kha-arka 120. These are the running totals.