It will be seen that the duration of the year in all the above works except the first three approximates closely to the anomalistic year; and is a little greater than that of the sidereal year. In some of these works theoretically the year is sidereal; in the case of some of the others it cannot be said definitely what year is meant; while in none is it to be found how the calculations were made. It may, however, be stated roughly that the Hindu year is sidereal for the last 2000 years.
18. The year as given in each of the above works must have been in use somewhere or another in India at some period; but at present, so far as our information goes, the year of only three works is in use, viz., that of the present Sûrya Siddhânta, the first Ârya Siddhânta. and the Râjamṛigâṅka.
19. It will not be out of place here to devote some consideration to these various astronomical works; indeed it is almost necessary to do so for a thorough comprehension of the subject. Many other Siddhântas and Karaṇas are extant besides those mentioned in the above list. We know of at least thirty such works, and some of them are actually used at the present day in making calculations for preparing almanacks.[1] Many other similar works must, it is safe to suppose, have fallen into oblivion, and that this is so is proved by allusions found in the existing books. Some of these works merely follow others, but some contain original matter. The Karaṇas give the length of the year, and the motions and places at a given time of the sun, moon, and planets, and their apogees and nodes, according to the standard Siddhânta. They often add corrections of their own, necessitated by actual observation, in order to make the calculations agree. Such a correction is termed a bîja. Generally, however, the length of the year is not altered, but the motions and places are corrected to meet requirements.
As before stated, each of these numerous works, and consequently the year-duration and other elements contained in them, must have been in use somewhere or another and at some period or another in India. At the present time, however, there are only three schools of astronomers known; one is called the Saura-paksha, consisting of followers of the present Sûrya Siddhânta; another is called the Ârya-paksha, and follows the first Ârya Siddhânta; and the third is called the Brahma-paksha, following the Râjamṛigâṅka, a work based on Brahmagupta's Brahma Siddhânta, with a certain bîja. The distinctive feature of each of these schools is that the length of the year accepted in all the works of that school is the same, though with respect to other elements they may possibly disagree between themselves. The name Râjamṛigâṅka is not now generally known, the work being superseded by others; but the year adopted by the present Brâhma-school is first found, so far as our information goes, in the Râjamṛigâṅka, and the three schools exist from at least A. D. 1042, the date of that work.
20. It is most important to know what Siddhântas or Karaṇas were, or are now, regarded as standard authorities, or were, or are, actually used for the calculations of pañchâṅgs (almanacks) during particular periods or in particular tracts of country.[2] for unless this is borne in mind we shall often go wrong when we attempt to convert Indian into European dates. The sketch which follows must not, however, be considered as exhaustive. The original Sûrya-
- ↑ Karaṇas and other practical works, containing tables based on one or other of the Siddhântas, are used for these calculations. [S. B. D.]
- ↑ The positions and motions of the sun and moon and their apogees must necessarily be fixed and known for the correct calculation of a tithi, nakshatra, yoga or karaṇa. The length of the year is also an important clement, and in the samvatsara is governed by the movement of the planet Jupiter. In the present work we are concerned chiefly with these six elements, viz., the sun, moon, their apogees, the length of the year, and Jupiter. The sketch in the text is given chiefly keeping in view these elements. When one authority differs from another in any of the first five of these six elements the tithi as calculated by one will differ from that derived from another. [S. B. D.]
