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Bharatiya Jyotihshastra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t6: Romaka Siddhānta

Bhāratīya Jyotiḥśāstra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s2.t6

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Romaka Siddhānta

v2.c12.s2.t6.1

It has been pointed out above that out of the two Romaka Siddhāntas described, only the original Romaka Siddhānta existed at the time of the Pañcasiddhāntikā. Let us now consider this Romaka Siddhānta.

v2.c12.s2.t6.2

A large portion of the Pañcasiddhāntikā has been devoted to Romaka Siddhānta. Three couplets of the first chapter beginning from the 8th describe the method of finding the ‘ahargaṇa’. The fifteenth couplet mentions the intercalary months and the suppressed tithi. All the 18 ‘āryās’ of the 8th chapter are devoted to Romaka Siddhānta. They describe the calculations of the sun and moon, their true places and the method of calculating solar and lunar eclipses.

v2.c12.s2.t6.3

The very first couplet giving the method of calculating the ‘ahargaṇa’ according to the Romaka Siddhānta runs thus :—

v2.c12.s2.t6.4

सप्ताक्षिवेद (४२७) संस्यं शककालमपास्य चैत्रशुक्लादौ ।। अर्धास्तमिते भानौ यवनपुरे भौमदिवसाद्यः ।। ८ ।।

v2.c12.s2.t6.5

“Deduct the Śaka year 427 from the number of that year for which the ahargaṇa is wanted at the beginning of the light half of Caitra, when the sun was halfset in Yavanapura, at the beginning of Tuesday”.

v2.c12.s2.t6.6

This shows that the first lunar day of Caitra was a Tuesday.

v2.c12.s2.t6.7

A Karaṇa work is required to give the positions of planets as at the beginning or epoch of that work, for finding the planetary positions. These positions are termed ‘kṣepaka’. The ‘kṣepakas’ as mentioned by the Pañcasiddhāntikā prove to be true for the mean Meṣādi (Sun’s entry into Aries), falling on the 14th Lunar day of the dark half of ‘amānta’ Caitra of Śaka 427 ; i.e. on Sunday, the 20th of March, 505 A.D. There is no doubt that some of them are true for the moon and others for the midnight of that date. This point will be more clearly explained in the study of the Sūrya-Siddhānta later on. The next Śukla ‘pratipadā’ (i.e. the first lunar day) after the 14th day of the dark half of Caitra, i.e. the first day of the light half of Vaiśākha, is seen to fall on Tuesday. Evidently this very ‘pratipadā’ was called the ‘Caitra-śukla-pratipadā’, by Varāhamihira (otherwise, by no other method the Caitra-śukla-pratipadā of Śaka 427, can be shown to fall on Tuesday), and it was no doubt correct that the ‘ahargaṇa’ is required to be calculated from that day. Varāhamihira appears to have adopted this epoch, because it is convenient to calculate positions from those on the 1st day of the light half. It is a well known fact of mathematical astronomy that the ‘ahargaṇa’ calculated with the help of any ‘Karaṇa work’ proves to be correct within a day, and it has to be verified with the help of the day of the week. It may now be questioned as to why the Vaiśākha śukla-pratipadā could have been called the Caitra-śukla-pratipadā by Varāha. I have absolutely no doubt that the śukla-pratipadā following the day for which the Kṣepakas are given is the first day of the Vaiśākha-śukla-halfmonth of Śaka 427 according to the ‘amānta’ system. The Caitra is defined as that ending lunar month which ends while the sun is in Meṣa (Aries). As the sun is found to be in Meṣa at the end of that amāvāsyā which fell on the day, next to the day for which the elements have been given irrespective of whether a mean or a true Meṣa was reckoned; and hence, according to the above definition the amānta lunar month which ended with the amāvāsyā must be termed as Caitra, and Vaiśākha commenced on Tuesday i.e. the next day. But a lunar month belonging to the pūrṇimānta system ends on the full moon day, and hence, the full moon day belonging to that light half which commenced just after the ‘kṣepaka’ day will coincide with the end of the lunar month. The calculations made on the basis of ‘kṣepakas’ given by Pañcasiddhāntikā show that the sun still occupied the Meṣa sign, and hence that lunar month naturally received Caitra as its name. The author does not find any other convincing theory to explain how that month could be termed Caitra. The pūrṇimānta system has remained in vogue in Northern India from a very ancient time. Even though the ‘pūrṇimānta’ system is still in vogue there, the lunar months are not named according to the system described above; but it appears that the system must have been in use in its pure form at the time of Varāhamihira.

v2.c12.s2.t6.8

The first couplet of the 8th Chapter gives the method of finding the sun’s place according to the Romaka Siddhānta :—

v2.c12.s2.t6.9

सेमकसूर्यो दृगणात् क्षतिथ (१५०) घ्नात् पंचकर्तु (६५) परिहीनात् ॥ सप्ताष्टकसप्तकुतेन्द्रियो ५४७८७ दृतान्मध्यमार्कः सः ॥

v2.c12.s2.t6.10

“Multiply the ahargaṇa by 150, deduct 65, and divide the remainder by 54787; the result is the mean longitude of the sun”.

v2.c12.s2.t6.11

The sun’s position is obtained by multiplying the ahargaṇa by 150, subtracting 65 from the product and by dividing the remainder by 54787. The number 65 is to be subtracted from this because of the Kṣepaka. The figure denoting the sun’s longitude is obtained in terms of bhagaṇas etc. (the bhagaṇa means a complete sidereal revolution of a planet through the Zodiac.) There is no doubt about this, although it is not explicit in the couplet. The sun makes 150 complete revolutions in 54787 days and hence, one revolution requires exactly 365 days 14 ghaṭis 48 palas. This is, therefore, the measure of a year according to Romaka. The modern Sūrya-Siddhānta gives 365d 15g 31p 31.4v. as the measure. Brahmagupta has blamed Romaka for not giving measures of yuga and other units, as is done by other Siddhāntas and the following discussion will show that it is true. In order to facilitate the comparison of Romaka with other Siddhāntas, below the figures are given indicating the number of revolutions and other measures relating to the moon in one Mahāyuga i.e., in 4320000 years, which are derived from the elements given by Romaka. The couplets from the Pañcasiddhāntikā on the basis of which these have been calculated are as follows :—

v2.c12.s2.t6.12

रोमकयुगमर्कंदोर्वर्षाकांशपंचबसुपक्ष: (२८५०) खेंद्रियदिशो (१०५०) धिमासा: खरकृतविषयाष्टय: (१६५४७) प्रलया: ।। १५ ।।

v2.c12.s2.t6.13

“Romaka’s yuga consisted of 2850 years. During this period, the number of intercalary months is 1050 and that of pralaya's or suppressed tithis is 16547".

v2.c12.s2.t6.14

शून्यैकैका (११०) म्यस्तन्नवशून्यरसा (६०९) त्वनाहिनसमूहात् ।। रूपत्रिवगुण (३०३१) भक्ताकेंद्रं शशिनोस्तगमवंत्याम् ।। ५ ।। व्यष्टक (२४) गुणिते द्वाद्रसर्तुमषडकपंचकान् (५६२६६) राहोः ।। भवरूपाग्यष्ट (१६३१११) हृते...।। ८ ।।

v2.c12.s2.t6.15

"(5) Multiply the ahargaṇa by 110, add 609, and divide by 3031; the quotient gives the position of the moon's kendra at Sunset at Avantī.

v2.c12.s2.t6.16

(8) Multiply the ahargaṇa by 24, add 56266 and divide by 163111; the result is the successive position (in revolutions, signs, etc.) of Rāhu (i.e. the moon's ascending node), reckoning backwards from the end of Pisces (i.e. the first point of Aries). (24 revolutions of Rāhu are supposed to take place in 163111 sāvanadays)".

v2.c12.s2.t6.17

The following figures denoting several astronomical measures are derived from these couplets and from the above couplet describing the calculation of the sun's position and that describing the calculation of ahargaṇa.

v2.c12.s2.t6.18

| Number giving | During one Mahāyuga 4320000 years | During a yuga of 2850 years |
| Revolutions of stars | 1582185600 | 1043803 |
| Revolutions of the Sun | 4320000 | 2850 |
| Sāvana days | 1577865600 | 1040959 |
| Revolutions of the Moon | 57751578 18/19 | 38100 |
| Revolutions of the Moon's apogee | 488258 13768/57589 | 322 228/3031 |
| Revolutions of Moon's ascending node | 232165 109085/163111 | 153 26889/163111 |
| Solar Months | 51840000 | 34200 |
| Intercalary Months | 1591578 18/19 | 1050 |
| Lunar Months | 53431578 18/19 | 35250 |
| Tithis | 1602947368 8/19 | 1057500 |
| Suppressed Tithis | 25081768 8/19 | 16547 |

v2.c12.s2.t6.19

The numbers showing the revolutions of the moon etc. in one Mahāyuga are not integral numbers. Hence, the sun and the moon, according to Romaka, will not, like other Siddhāntas, come together in the beginning of the Kaliyuga or a Mahāyuga. Similarly, the number of lunar months is also not an integral number and the Romaka’s yuga has been stated to consist of 2850 years. This shows that the Romaka Siddhānta has not followed the system of adopting 4320000 years as the measure for a Mahāyuga.

v2.c12.s2.t6.20

The couplet describing the method of calculating the moon’s place is very incorrect. The author could not calculate the number of the moon’s revolutions from it; these have been calculated by a different method.

v2.c12.s2.t6.21

The kṣepakas at the epoch of the Karaṇa work are found to be as follows :---

v2.c12.s2.t6.22

| Sun | . | . | . | 11ˢ | 29° | 34′ | 23″ | Moon’s Kendra | 2ˢ | 12° | 19′ | 57″ |
| Moon | . | . | . | 11 | 29 | 18 | 50 | Moon’s ascending Node | 7 | 25 | 49 | 3 |

v2.c12.s2.t6.23

The Kṣepakas are true for the moment of sunset at Ujjayinī on Sunday the 14th lunar tithi of Caitra Kṛṣṇa, Śaka 427 (i.e. 20th March 505 A.D.).

v2.c12.s2.t6.24

Hipparchus, the Greek astronomer, lived about 150 B.C. His figure for the length of the year exactly tallies with that of the Romaka (viz. 365d—14gh.—48pal.)

v2.c12.s2.t6.25

The work of Hipparchus is not available at present, but he had compiled tables for calculating the positions of the sun and the moon only and not for calculating the planets. Well known European astronomers say that the latter were compiled by Ptolemy on the basis of the principles of Hipparchus. They also admit* that the principles of Greek astronomy had already reached India long before Ptolemy’s time. The Romaka Siddhānta gives the calculations of only the sun and the moon, and its measure of the year is found in no other Siddhānta. It does not describe ‘the universally accepted yuga system’ and its name. Romaka appears to be western. All these things go to show that the original Romaka Siddhānta was compiled on the lines of the work of Hipparchus, and it must have been compiled after 150 B.C. and before Ptolemy’s time i.e. 150 A.D.

v2.c12.s2.t6.26

It has already been shown above that the Paitāmaha and Vasiṣṭha Siddhāntas were older than the Romaka. Similarly, it is thought that even the Sūrya Siddhānta and the Pulīśa Siddhānta of the Pañcasiddhāntikā are more ancient than the Romaka; for, it is obvious from Brahmagupta’s work, that the other four Siddhāntas were regarded with more veneration than the Romaka. He has nowhere blamed any of the four works. After the time of Brahmagupta, the Romaka Siddhānta appears to have gone quite out of use, both in its original form and the form in which it was recast by Śrīṣeṇa. Utpala has nowhere made references to the Romaka on any occasion in his discussion of planetary calculations in his commentary on the Bṛhatsaṃhitā, but he has cited the authority of the four Siddhāntas, viz., those by Pulīśa, Sūrya, Āryabhaṭai or by Brahmagupta. The original Romaka Siddhānta seems to have disappeared in its original form at the time of Utpala. The Romaka Siddhānta of the present day gives elements according to the modern Sūrya Siddhānta and not according to any other Siddhānta; and even this Rómaka Siddhānta is not much known to any one now-a-days. This shows that the veneration which the other Siddhāntas, out of the group of five, enjoy, is due to their being much more ancient than the Romaka.

v2.c12.s2.t6.27

∗ See Grant’s History of Physical Astronomy [Introuction page (iii)] and page 439); similarly, see English translation of Sūrya Siddhānta, by Burgess, page 330.

v2.c12.s2.t6.28

One more important proof about the Romaka being more modern than the five Siddhāntas is given below :

v2.c12.s2.t6.29

*Measures of the year according to different works on astronomy.*

v2.c12.s2.t6.30

| | Days | Ghaṭī | Pala | Vipaḷa | Prativipaḷa |
| Vedāṅga Jyotiṣa | 366 | .. | .. | .. | .. |
| **Pañcasiddhāntikā group :** | | | | | |
| 1 Pitāmaha Siddhānta | 365 | 21 | 25 | .. | .. |
| 2 Vasiṣṭha Siddhānta | .. | .. | .. | .. | .. |
| 3 Pulisa Siddhānta | 365 | 15 | 30 | .. | .. |
| 4 Sūrya Siddhānta | 365 | 15 | 31 | 30 | .. |
| 5 Romaka Siddhānta | 365 | 14 | 48 | .. | .. |
| First Ārya Siddhānta | 365 | 15 | 31 | 15 | .. |
| **Brahmagupta Siddhānta (Modern group)** | 365 | 15 | 30 | 22 | 30 |
| Sūrya, Vasiṣṭha, Śākalya, Romaka and Soma Siddhāntas | 365 | 15 | 31 | 31 | 24 |
| Second Ārya Siddhānta | 365 | 15 | 31 | 17 | 6 |
| Rājamṛgāṅka | 365 | 15 | 31 | 17 | 17½ |
| Karaṇa Kutūhala etc. | | | | | |

v2.c12.s2.t6.31

Out of these figures indicating the measure of the year, none except that of Romaka are found to be smaller than 365d—15gh—30p, and none, excepting that of the Vedāṅga Jyotiṣa and the Pitāmaha Siddhānta, greater than 365d—15gh—32p. In other words, leaving aside the case of Vedāṅga Jyotiṣa and Pitāmaha Siddhānta, none of the rest, except the Romaka, differ from one another by more than 2 palas. Had Romaka been older than the Pulisa Siddhānta and the Saura Siddhānta of the Pañcasiddhāntikā, all of them would have taken the same year measure, as the Romaka or one with a slight variation, and they could not have strayed very far from the Romaka. This proves beyond doubt that the Pulisa and Saura Siddhāntas were older than the Romaka. It seems beyond doubt that all the Siddhāntas of the Pañcasiddhāntikā belonged to a pre Śaka period.

v2.c12.s2.t6.32

It is Dr. Thibaut's opinion that the Romaka and the Pulisa Siddhāntas of the Pañcasiddhāntikā are “not more modern than 400 A.D.” He means* to say that these two were compiled about the year 400 A.D. and the other Siddhāntas of the Pañcasiddhāntikā group were also compiled about the same year. But the above discussion will show that his view is erroneous.

v2.c12.s2.t6.33

The figures showing the number of revolutions and other elements, as given in the Romaka Siddhānta, which is available at present, are given later on. A comparison of these figures with the foregoing ones will show that there is absolutely no similarity between them. This shows that the modern Romaka Siddhānta did not exist before Śaka 427.

v2.c12.s2.t6.34

The question whether the modern Romaka Siddhānta is the same as that compiled by Śrīṣeṇa and whether the modern Vasiṣṭha Siddhānta was compiled by Viṣṇucandra, will be discussed later on.

v2.c12.s2.t6.35

∗ See Introduction page LX of Pañcasiddhāntikā by Dr. Thibaut

Cites (13)