:: Home  



      Infinity Foundation

      Mandala Of Indic Traditions

      Other Links


K. Chandra Hari. 2003. Eclipse Observations of Parmesvara. Indian Journal Of History Of Science, 38 (1): 43-58. INDIAN NATIONAL SCIENCE ACADEMY, NEW DELHI.   
By Manikant Shah


In the Strange Stories, Amazing Facts compiled by the Reader’s Digest in 1975, there is a Chinese legend dating from 2136 BC, which tells that the Chinese Emperor and his people were terrified on account of a hungry dragon trying to eat the sun. The Emperor later ordered his two Imperial Astronomers Hsi and Ho to be beheaded for they failed to forewarn the Emperor of the approaching dragon. Similar legends are found in Indian Astronomy and Astrology which tell about the two demons Rahu and Ketu trying to swallow up the sun or the moon. At such times the sun or the moon seems to disappear from the skies and the period is generally considered inauspicious. The phenomenon of the skies that these legends refer to has come to be known to the modern astronomers as an Eclipse. We now know that the earth and the moon revolve around the sun. What actually happens is that in their orbital path the moon or the earth comes between the other two bodies, obscuring the light coming off the sun or the moon resulting in Solar Eclipse or Lunar Eclipse.  Eclipses are celestial phenomena that have always raised the curiosity of humankind. In all countries across the seas eclipses have been observed with awe and surprise or perhaps with a hope that they might reveal some hidden aspects of the enigmatic universe.

Below we discuss K. Chandra Hari’s essay on the observations made by Paramesvara, who during the 14th-15th century enriched the Kerala astronomical tradition through precise observations and astronomical experimentation. Chandra Hari’s exposition becomes more important for we know that just about the same time or even later perhaps, European astronomy began to record scientific observations but gradually came to be recognized world wide, whereas the works of observers like Parmesvara largely went unnoticed.

Paramesvara was a resident of Alattur, situated on the banks of the river Nila or Bharatppuzha in Kerala. K. Chandra Hari says he was a prolific writer on astronomy as well as astrology and is best known for his work Drgganita. Besides Drgganita, Paramesvara produced three works exclusively dealing with eclipses. These were Grahanamandana, Grahanastaka and Grahananyayadipika. Paramesvara also gave a commentary known as Siddhantadipika on the Mahabhaskariya-Bhasya of Govindasvamin in which he mentioned important eclipses that took place during 1398 to 1431 AD. Nilkantha Somayaji, the disciple of Parmesvara himself, has spoken about Parmesvara in the following words, Parmesvara had his studentship well in mathematics and astronomy under the able hands such as Rudra, Narayana, and Madhava. He could understand the factors that caused difference between the computed and observed planetary positions. After deliberating over the principles of earlier teachers and verifying them through observations of eclipses and planetary conjunctions he composed his accurate work, Drgganita.”  Chandra Hari accords much importance to the work of Parmesvara related to the observation of Eclipses as Parmesvara had refined the age-old Parahita system in 1431 AD to formulate his main work Drgganita. Drgganita apparently is related to astronomical mathematics that was an improvement upon the earlier mathematics used in the Parahita system. Parmesvara as quoted by Nilkantha, his disciple, once said, “The planets have been observed by me for fifty-five years and they differ from the positions derived through Parahita-Ganitam”. Even Nilakantha used these observations in the formulation of his work Tantrasangraha. Nilkantha speaks of the use of eclipses vis-a-vis the refinement of computational methods in these words, “Other Eclipses traditionally known as well as those currently observable are to be studied. In the light of such experience future ones can be computed and predicted. Or, eclipses occurring at other places can be studied taking into account the longitude and latitude of the places and on this basis the method for true Sun, Moon, Apsis and Node can be perfected. Based on these, past and future eclipses of one’s own place can be studied and verified with appropriate refinement of the technique”.   

Chandra Hari admits that in the preparation of the present paper he could make use of only two works of Parmesvara on eclipses - the Grahanamandana and the Grahananyayadipika. The former is a karana text that deals with computational aspects while the latter presents the underlying theory of eclipses. We are told that Parmesvara’s efforts were directed towards the refinement of the traditional constants employed in the computation of eclipses. He claimed no innovations of his own in the treatment of eclipses. But his scientific outlook is well evident from the criticism he made of Varahamihira in his Grahanamandana. Chandra Hari says that Parmesvara recorded altogether eight solar and five lunar eclipses that occurred during his time. He says that the solar eclipses have been examined with the modern planetarium software based on the VSOP87 theory of which he gives the relevant tables. These show just minor variations, which is incredible. These variations can also be attributed to manuscript errors in the old records as is pointed out in the paper. From here Chandra Hari goes on to a discussion on the eclipses as recorded by Parmesvara and Nilakantha, comparing them in the light of Modern Astronomy. Having compared the figures Chandra Hari concludes that the values given by Nilakantha have got only insignificant errors when compared to modern computer derived longitudes based on the latest theories of planetary dynamics. He says that in terms of accuracy of the planetary longitudes the epicyclical theory was not far behind the theory of Kepler, when researchers like Parmesvara and Nilakantha handled it.

By the end of the paper Chandra Hari briefly discusses the Drgganita of Parmesvara, as he underlines that without it the discussion on Parmesvara would remain incomplete. While concluding the paper Chandra Hari says that Parmesvara’s record of astronomical observations, the refinement of astronomical parameters and the accompanying work of his disciple Nilakantha Somayaji which maximizes the accuracy of planetary longitudes etc, are reflect the past glory of Indian Science.