Book of Indian Eras, with Tables for Calculating Indian Dates c32: XXVII.—Chandra-Mâna

Book of Indian Eras, with Tables for Calculating Indian Dates c32

Language: English

XXVII.—Chandra-Mâna

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The *Chandra-Mâna*, or luni-solar calendar of the Hindus, is a much more elaborate system of reckoning. The object of the *Chandra-Mâna* is to combine the solar and lunar reckonings, so that the years may be reckoned by the course of the sun, while the months are regulated by the revolutions of the moon. For this purpose a cycle of 19 solar years was adopted, as being equal, or nearly so, to 235 lunations or revolutions of the moon of 29·5306 days. The periods do not quite tally, as 19 solar years are equal to 6939·9163 days according to Varâha Mihira, and 6939·9149 days according to Aryabhatta, while 235 lunations are equivalent to only 6939·6910 days. The difference is nearly one-fourth of a day in 19 years.

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The year consists of 12 lunar months of 30 and 29 days alternately, making altogether 354 days. The deficiency of eleven days less than the solar year, is made good by the addition of seven intercalary months in each cycle of 19 years, which are inserted in the 3rd, 5th, 8th, 11th, 14th, 16th, 19th years.

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As these intercalary months also consist of 30 or 29 days, the cycle of 19 years is thus made to consist of 19 × 12 = 228 + 7 = 235 lunations. The Hindu luni-solar year, therefore, agrees very closely with the Greek cycle of Meton, which also consisted of 19 solar years, or 235 lunations. The seven intercalary months of Meton were inserted in the following years: 3, 5, 8, 11, 13, 16, 19.

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The only difference between this arrangement and that of the Hindu series is in the 5th intercalation, which was made in the 14th instead of in the 13th year. But in spite of this close agreement, I think it almost certain that the two cycles were independently developed, although they may perhaps have had a common origin. The difference in the *mode of intercalation* is so great that it seems quite impossible that one can have been borrowed from the other. In the Greek cycle, the intercalary month has a fixed position, while in the Indian cycle both the name and the position are constantly changing. The name of the intercalary month is determined in the following manner—" When two new moons fall within the same solar month, as for instance on the 1st and 30th of Chaitra, then the name of Chaitra, or the corresponding lunar month, is repeated, the year being then intercalary with 13 months. The extra month is called *adhika* (or added), and the other *nija* (or ordinary). By the rule of the Surya Siddhânta, the intercalated month is to be placed in the middle of the ordinary month. In Southern India the whole intercalary month is placed before the ordinary one.

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The common rule followed for intercalation is thus given by Warren. When the luni-solar year begins—

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" It happens once within each term of 160 years that there is no new moon in one of the last six lunar months, which from the sun being in perigee contain only 30 and 29 days each." " To obviate this, that month is expunged, while two others for the opposite cause are repeated. This double intercalary year with its expunged month is called *Kshaya Samvat-sara*."

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In the General Table, which gives the names of the intercalary and expunged months, I have adopted the calendar published by Cowasjee Patell. The initial days of the years I have calculated myself throughout up to A.D. 540. The early calculations have been made with the solar reckoning of Aryabhatta : but from 541 down to the end, according to the solar reckoning of Varâha Mihira. Cowasjee Patell's Tables are calculated according to Aryabhatta, whose reckoning is still used in Southern India.

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As the luni-solar year begins with the new moon immediately preceding the 1st of the solar Vaisâkh, the first step to be determined is the number of days by which the one precedes the other. For this purpose the beginning of the solar year has to be fixed, as already shown in the account of the Saura-Mâna, using the Solar Ahargana of the Surya Siddhânta for the North Indian dates and Aryabhatta’s Solar Ahargana for South Indian dates. The next step is to find the number of days of the luni-solar Ahargana in the given period, and to deduct this total from the number of days of the Solar Ahargana already found. The remainder is to be reduced by continued subtraction of whole lunations, until the last remainder is less than one lunation. Then that last remainder shows the exact number of days by which the new moon precedes the 1st day of the Solar Vaisâkh.

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As an example of the process I will take the date of Kâli-Yuga 4958, or A.D. 1857, of which the initial days have already been found in my account of the Saura-Mâna or solar reckoning. As the Luni-Solar Ahargana of the Surya Siddhânta is used in the South as well as in the North, one process will be sufficient—

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The new moon, therefore, precedes the beginning of the solar year by 16·99, or 17 days. Then as the 1st of the Solar Vaisâkh fell on the 11th of April 1857 in North India, the new moon will have fallen on the 24th March, and the beginning of the luni-solar year, or the 1st Chaitra-Sudi, on the following day or 25th March. In Southern India it would have been the same according to my reckoning from Aryabhatta’s length of the solar year; and this also is the day given by Warren. But according to Cowasjee Patell, it was the 26th March.

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I have tested these Tables for several dates at distant intervals and have found them correct—

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1. On the 5th February B. C. 21 there was an eclipse visible in India. By the Tables the first day of the solar year was Wednesday, 14th March, and the first day of the luni-solar year was Tuesday the 6th March, from which date counting backwards 29½ days for the previous conjunction of the sun and moon, we get the 5th February.

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2. In A.D. 314, on the 3rd of March, there was a grand eclipse of the sun visible over E. Asia. According to Cowasjee Patell, the first day of the luni-solar year A.D. 314 was the 3rd of March.

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3. In A.D. 490, on the 7th March, there was an eclipse of the sun visible over S. E. Asia. According to Cowasjee Patell, the first day of the luni-solar year was the 8th March, which is right according to the rule that the first day of the new year is the day after the conjunction.

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4. On the 4th March 1840, I saw an eclipse of the sun in N. India. According to Cowasjee Patell, and also according to my own reckoning, the luni-solar year began on the 3rd April 1840, which is exactly one conjunction later.

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5. In my account of the Bârhaspatya-Mâna, I have given another example of the correct working of the Tables for an eclipse of the year 792 A.D., which is mentioned in one of the Indian inscriptions.

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6. But perhaps the most striking illustration of the general accuracy of the Tables is the eclipse of the moon, which is recorded to have happened in the month of Srâvana Samvat 1200. The inscription in which this is found is one of "three grants of land found at Ujjayani," on which Colebrooke makes the following remarks:*

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"One of three grants or patents records a donation of land made by the reigning sovereign of Dhârâ, on the anniversary of the death of his father and predecessor, in 1191 of the Samvat era; confirmed by the prince, his son, at the time of an eclipse of the moon in Srâvana 1200 Samvat. It appears from calculation that a lunar eclipse did occur at the time—viz., on the 16th of July A.D. 1144, about 9½ P.M., apparent time at Ujjayani."

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Now it is quite true, as Colebrooke says, that an eclipse of the moon did occur on the 16th July 1144, but that day was certainly not the full moon of Srâvana in that year. The true date was the 28th July 1143, on which day was the full moon of Srâvana, and also a lunar eclipse. The following is the calculation according to the Tables. Samvat year 1200 + 3044 = 4244 Kâli-Yuga = A.D. 1143.

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∗ Colebrooke's Essays, II, p. 264. He has used the erroneous equation of 56 instead of 57 to reduce the Samvat year to Christian reckoning.

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| | 1550,156·0149 ÷ 7 leaves 6 days over = Thursday, 25th March, O. S., |
| Luni-solar | 1503,933·7827 | for first day of solar year. |
| Ahargan | | |
| | 46,222·2322 | The full moon |
| 1500 Lunations | 44,296·8820 | of Srâvana } or Srâvana-Sudi 15th |
| | | is the 133rd day of the Hindu year, |
| | 1926·3502 | which, counted from Thursday the |
| | 1919·4882 | 25th March, gives 28th July A.D. |
| | | 1143, on which day there was an |
| 6·86 = 7 days earlier 6·8620 | | eclipse of the moon. |

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In the North the luni-solar year begins with the new moon, or 1st day of *Chaitra-Sudi*, and as this is the latter half of the month, this Hindu year has the strange anomaly of beginning in the middle of a month. The first half of Chaitra, or the period of the waning moon, called *Badi*, or *Krishna Paksha*, belongs to the past year. This mode of placing the *Badi*, or waning half of the moon, in the beginning of the month is known as the *Krishnadi* reckoning; while the opposite practice of putting the *Sudi*, or *Sukla Paksha*, half of the moon, as the beginning of the month, is known as the *Sukladi* reckoning. The names *Badi* and *Sudi* are contractions of *bahula-paksha-dina*, the "day of the dark half," and *sukla-paksha-dina*, the "day of the bright half," the first and last syllables only being retained.

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Table X shows the number of days in the Hindu luni-solar year when not intercalary. When the year is an intercalary one, and the day required falls later than the intercalary month, then 30 days must be added to the number given in the Table.

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The years of intercalation being fixed by the rules laid down for the 19-year cycle, the name of the intercalated month has yet to be found. As there are 30 days in six of the lunar months, while the time of one lunation is only 29½ days, it would of course occasionally happen that two new moons would fall in the same month, one at the beginning, and the other at the end. But as this is not allowed, a peculiar arrangement has been adopted for avoiding it. In whatever month two new moons would naturally fall, that month is doubled; or, in other words, an intercalary month of the same name is added called Adhika Vaisâkha, Adhika Srâvana, &c.

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To ascertain which month will be Adhika, or intercalary, Warren's Kâla Sankalita should be consulted, and also the brief abstract given by Prinsep. The process is troublesome, and in the present work I have adopted the names of the intercalary months as given by Cowasji Patell. The years of the intercalations are shown to be correct by the shifting of the initial days backwards and forwards, all of which I have myself calculated.

Linked texts (1)

Sūryasiddhānta — Maya, Sanskrit