An Astronomical Proof

by V. Thiruvenkatacharya, M.A.L.T., Madras Educational Service (Rtd.)

Extracted from the Journal of Indian Hidtory Vol. XXVIII, Part II, No.83

Astronomers have played no small part in fixing up the Chronology of Indian History; but I consider that the lost word on the subject has not been said; this is mainly due to the complexity of the meterials dealt with. The late Swamikannu Pillai, having fixed 536 A.D. as the year of zero Ayanamsa, came to the conclusion that Varahamihira lived in the sixth century A.D. But his method requires reconsideration on purely astronomical grounds and the object of this article is a reconsideration of the subject in a different light. The results arrived at may not be new, but I am sure that the method adopted is entirely original; I commend this article to the attention of oriental scholars for their critical study.

We have seen that the epoch of Panchasiddhantika of Varahamihira is 427 Saka i.e., 127 B.C. In the same book, he gives some more points for the verification of the correctness of this date.

आश्लेषार्धाद्दक्षिणमुत्तरमयनँ रवेर्धनिष्टाद्यँ|

नूनँ कदाचिदासित येनोक्तँ पूर्वशास्त्रेषु ||

ఆశ్లేషార్ధాద్దక్షిణముత్తరమయనం రవేర్ధనిష్ఠాద్యం |

నూనం కదాచిదాసీత్ యేనోక్తం పూర్వశాస్త్రేషు ||

सांप्रतमयनं सवितुः कर्कटकाद्यं युगादितश्चान्त्यं |

उक्ताभावो विक्रुतिः प्रत्यक्षपरीषणैर्व्यक्तिः ||

సాంప్రతమయనం సవితుః కర్కటకాద్యం యుగాదితశ్చాన్త్యం |

ఉక్తాభావో వికృతిః ప్రత్యక్షపరీక్షణైర్వ్యక్తిః ||

"Old books state that once Dakshinayana began when the sun reached the mid-point of Aslesha and Uttarayana when the sun reached the beginning of Dhanishta. But now the ayanas begin when the sun reaches the beginning of Karkataka and Makara signs. This can be varified by actual observation." But in Chapter III of Panchasiddantika,Varahamihira states as follows :-

आश्लेषार्धादासीद्यदा निबृत्तिः किलोष्णकिरणस्य |

युक्तमयनं तदासीत सांप्रतमयनं पुनर्वसुतः ||

ఆశ్లేషార్ధాదాసీద్యదా నివృత్తిః కిలోష్ణకిరణస్య |

యుక్తమయనం తదాసీత్ సాంప్రతమయనం పునర్వసుతః ||

"Once the sun changed his course from the mid-point of Aslesha; but now from Punarvasu."

The beginning of Karkataka coincides with the end of the third pada of Punarvasu. So what does "from Punarvasu"(punarvasuthah) mean? Punarvasuthah cannot mean the end of third pada or the beginning of fourth pada. The two statements have to be reconciled. It can be done in one of the following ways.

(a) Either that the author, even though of the same name, of Panchasiddhantika, is different from that of Bhrihatsamhita,

(b) Or that Brihatsamhita being a non-Karana grantha, Varahamihira gave only a rough position, whereas in the Panchasiddhantika he gave the actual longitude, the end of Punarvasu as the point at which the southward motion of the sun began. It is also to be remembered that Punarvasuthah cannot mean the beginning of Punarvasu, but must mean only the end of it, since otherwise he would have stated definitely the beginning of Punarvasu just in the same way he mentioned dhanishtadyam.

So, let us now find what the date of the epoch is when Dakshinayana began when the sun reached the end of Ponarvasu, that is, when the Nirayana longitude of the sun was 93° 20’

This change in the dates of the beginning of Dekshinayana and Uttarayana is due to the well-known astronomical phenomenon, called the Precession of the Equinoxes.

According to Newcomb, Ball and other authorities, the value of the rate of the Precession of the Equinoxes per year, Ayanagathi is 50".2585 in 1909 A.D., while its rate for a year in the past, n years earlier than 1909 A.D. is given by 50".2585-(n x 0.000225") per annum. Swamikannu Pillai found by calculation, from nautical almanac that when the apparent vernal equinox (Sayana) occured at Lanka, the date was March 21.2143 and that the beginning of the Indian Sidereal year Nirayana at Lanka was April 12.9492. The difference, between the two momemts equal to 22.7349 days, is the time taken by the sun to travel along the ecliptic from 0° tropical longitude or sayana to 0° Indian sidereal longitude or Nirayana in the year 1909 A.D. Then Swamikannu Pillai shows that 536 A.D. is the year of zero ayanamsa and therefore the epoch of Panchasiddhantika. There are the following drawbacks in the whole argument :-

(a) It was considered that Dakshinayana began when the Sun reached the beginning of Karkataka instead of the end of Punarvasu.

(b) At least at the time of Verahamihira , the Indian Sidereal year-- so designated at present -- was really a tropical year and the value for the precession of the equinoxes must be taken as 50".2585-nx0.000225" and not as 54.7505 as assumed by Swamikannu Pillai.

Calculation of Ayanamsa:- Now 22.7349 days in time-interval for Ayanamsa is equal to 22.4136 degrees and adding 3°20', the equivelent for Punarvasu fourth pada, we get, on simplification 25°45’ as the space interval for ayanamsa between the time of Varahamihira and year 1909 A.D. But the interval from 427 Saka (=124 B.C. or -123 astronomical) and 1909 A.D. is equal to 2032 years and taking the cumulative value for n years as 50".2585xn - (n(n+1)/2)x0.000225" substituting 2032 for n in this formula, we get 28°15' as the ayanamsa, whereas we have seen that the value must be 25°45'. How is this difference to be reconciled?

The ayanamsa for one year is 50".25 and so it works out roughly to be 72 (apporx.= 3600/50.25) years for one degree. Now 28°15'-25°45' = 2°30’ will correspond to about 180 years(2.5x72=180) and are we to shift the epoch of Panchasiddhantika to a date 180 years later, that is, to 180-122 = 58 A.D.? No. that will not be the correct procedure; but unfortunately that has been the method adopted almost uniformly in dealing with Indian Chronology. A different method will now be followed.

The discrepancy resolved :- It has been already noted that Kaliyuga began at midnight of 17-18th February, 3102 B.C. But most of the ephemrides reckon on February 15.579 as the epoch of Kaliyuga, that is, they have used a bija or correction. Since the day begins at mean sunrise at Lanka for Indian Siddhantas, midnight of 17-18th February, 3102 B.C. corresponds to February 17.75 of 3102 B.C. The value of correction used is 17.75-15.57 = 2.18 days and the Indian Sidereal year began in 1909 A.D., dot on April 12.95+2.18 days=April 15.13.(vide Swamikannu Pillai's Ephemeris.) So the interval between the moment of apparent vernal equinox and the beginning of the Indian Sidereal year is 24.91 days but not 22.73 days as assumed by Swamikannn Pillai. The time interval of 24.91 days corresponds to a space interval of 24°30' and so the space interval of ayanamsa between the epoch of Panchasiddhantika and 1909 A.D. is 24°39'+3°20'=27°59', where as according to our calculation, it ought to be 28°15' with an error of 16 minutes which falls within the limits of probable error and so can be considered as insignificant. So ayanamsa calculations lead us to the conclusion that the epoch of Panchasiddhantika is 124 B.C. and not 505 A.D. as wrongly presumed hitherto. As Varahamihira makes no mention of ayanamsa, it is presumed that it was zero in his time.

The epoch of Bhattotpala:- Bhattotpala finished his commentary on Brihatjataka in Saka 888 and he mentions that the ayanamsa in his days was 7 days or to be more accurate 6½ degrees (sardhashatkamsah) according to one reading. The commentary on Brihatjataka must have been finished in 888-549 = 339 A.D. The interval between the epoch of Panchasiddhantika and the completion of the commentary on Brihatjataka is 888-427 = 461 years. Therefore the value of the annual rate precession of the equinoxes is 6½°/461=390x60/461 seconds = 50.8 seconds, which may be considered as a fairly accurate value. The early Indian astronomers, are really to be congratulated on their proficiency in astronomical calculations. All these results prove conclusively the unsustainability of the theory that the Indian astronomers were wholly indebted to the Greeks for their knowledge of astronomy. Hipparchus lived about 160 B.C. and Ptolemy made observations between 127 A.D. to 151 A.D.

Some deductions :- It is easy to draw some important and interesting deductions from the above results. Amarasimha (or is it Amaraja?) has stated that Varahamihira died in Saka 509 at the age of 82 years. So he must have been born in 427 Saka, the epoch of Panchasiddhantika. It may be safely assumed that this versatile Hindu astronomer lived between 427 and 509 Saka or 123 B.C.to 41 B. C. This fixes the period of Kalidasa and other poets (nine gems of the court of Vikramarka. vide Jyotirvidabharana 22-10 & 20.)

Later astronomers:- All the later astronomers, including Bhaskaracharya have given the epoch of zero ayanamsa some year in the fifth century of Salivahana Saka. For example, the author of Ganakanandam gives 421 (499 A.D.) as the year of zero Ayanamsa, with 54 seconds as the rate per year, whereas Bhaskara gives 412 (490 A.D.) as the year of zero ayanamsa but with 60 seconds as the rate per year.

Let us consider the following table as regards the year of zero ayanamsa:——

Varahamihira.......427 Saka (sapthasvivedasamkhya)

Kalidasa...........445 Saka (sarambhodhiyuga)

Bhaskaracharya,Suryadaivagna....412 Saka

(Author of Ganakanandam)........421 Saka by calculation.

This shows that all these astronomers are agreed that some year in the fifth century of some Saka as the year of zero ayanamsa. What is that Saka? Varahamihira, Kalidasa and Bhattotpala seem to refer to the Saka with its enoch in 551 B.C. as their Saka. But the later astronomers thought that the Saka was Salivahana Saka and by actual calculation arrived at the year of zero ayanamsa. That accounts for the difference in the rates of ayanamsa among the later astronomers. Further this is the only method that can be adopted, as the point with which the first point of Aries coincided during the time of Varahamihira is an imaginary point which cannot be located by the later astronomers, when once the first of Aries had moved away from that point. Again it is to be noted that at the time of Varahamihira the summer solstice seems to have coincided with the end of Punarvasu and not at the beginning of Karkata (cancer.) That is the only inference I can draw from pure calculations from the available data.

Does Bhaskara Use Salivahana Saka? :- Yes. There is no doubt about it. Let us consider the following:-

"gathobdadri nandau (974} mite saka kale."

On actual calculation, I found that 1052 A.D. corresponding to 974 Salivahana Saka, was a year with a Kshaya month, whereas the Saka of 551 B.C. does not satisfy this test. So the proof is unequivocal.

Conclusion: But the week days mentioned by Varahamihira and Bhattotpala do not satisfy the Salivahana Saka and so the Saka referred to by them cannot be Salivahana Saka but only the Saka with 551 B.C. as the epoch. Bhaskara and others refer only to Salivahana Saka. I leave it to scholars to judge on their merits the conclusions of this discussion in which I have attempted to remove some of the existing discrepancies in Indian Chronology. It has been shown clearly that in 124 B.C., the epoch of Panchasiddanthika, the ayanamsa was zero. In conclusion, let me end with a statement of Quetelet, the eminent French statistician

"Never reject data, contrary to your theory"

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