The Five Astronomical Canons

which period is further stated to contain 1050 intercalary months original: "adhimâsas"; these are extra months added to a lunar calendar to keep it in sync with the solar year and 16547 omitted days original: "pralayas" or "tithipralayas"; these are lunar days dropped from the calendar to account for the difference between the lunar and solar cycles, omitted lunar days. The above numbers of years and intercalary lunar months allow of being reduced by 150, and we thus find that, in the opinion of the author of the Romaka The Romaka Siddhânta, an Indian astronomical treatise influenced by Greek/Roman science, 19 solar years exactly contain seven intercalary months, or—if we take the entire sum of months—that 19 solar years comprise 235 synodical lunar months A synodical month is the time between two identical phases of the moon, e.g., new moon to new moon. The age original: "yuga"; a vast cycle of time in Indian cosmology of the Romaka is thus evidently based on the so-called Metonic period, named after the Athenian astronomer Meton who, about 430 B.C., showed the means of improving the Greek Calendar of his time by the assumption of 19 tropical years comprising 235 synodical months.—That the Romaka Siddhânta, instead of making use of the simple Metonic period, employs its one hundred and fiftieth multiple, has a reason not difficult to discern. The author of the Romaka, although manifestly borrowing his fundamental period from the west, at the same time wished to accommodate himself to the Indian fashion of calculating the sum of days which has elapsed from a given epoch (the so-called count of days original: "ahargana") by means of a cyclic period comprising integral numbers of solar years, lunar months and natural days. Now the simple Metonic period does not represent an aggregate of the nature required, neither if we—with Meton himself—estimate the length of the tropical year at 365 1/4 days, nor if we avail ourselves of the more accurate determinations by which later Greek astronomers improved on the work of Meton, and it therefore becomes requisite to employ a multiple. What the multiplying number is to be, of course depends on the value assigned to the length of the year, and we therefore have to ascertain the opinion held on this point by the author of the Romaka. The data supplied in stanza 15 enable us to do so without difficulty. For if we multiply the 2850 years of the Romaka age by 12 (in order to find the number of corresponding solar months), add the 1050 intercalary months (whereby we obtain the number of synodical lunar months), multiply by 30 (so as to find the lunar days), and finally deduct the 16547 omitted lunar days, the final result amounts to 1,040,953 natural days; which being divided by 2850 (the number of the years of the age), we obtain for the length of one year 365 days, 5 hours, 55 minutes, and 12 seconds. But in order to form an aggregate of years which contains an integral number of days and at the same time is divisible by nineteen, 19 x 150 = 2850 years have to be taken.

Whence the above determination of the year's length was adopted by the author of the Romaka, there cannot be any doubt. The year of the Romaka is, down to seconds, the tropical year of Hipparchus A Greek astronomer (c. 190–120 B.C.) often considered the father of trigonometry or, if we like, of Ptolemy A 2nd-century Greco-Egyptian mathematician and astronomer who accepted the determination, considerably faulty as it was, made by his great predecessor.