INTRODUCTION.

which consists of five solar years of 366 days each, and contains sixty solar months, sixty-two synodical months The time between two consecutive new moons., and sixty-seven so-called nâkshatra sidereal; relating to the stars months i. e. sidereal revolutions of the moon. The beginning of the yuga an era or cycle of time is marked by a conjunction of the sun and moon at the first point of the nakshatra lunar mansion or constellation Dhanishṭhâ. The duration of the longest day of the year amounts to eighteen muhûrtas a unit of time equal to 48 minutes, that of the shortest to twelve muhûrtas ; in the intervening periods the days increase or decrease by the same daily quantity.—The Paitâmaha Siddhânta The "System of Pitamaha (Brahma)," considered the oldest of the five systems refers to two points only which appear not to be mentioned in the Jyotisha Vedâñga The ancient Vedic auxiliary science of astronomy, as far as I have hitherto succeeded in making out the meaning of that difficult treatise. It, in the first place, gives a rule for calculating the so called vyatîpâta yogas astrological alignments where the sun and moon have the same declination (st. 4); and in the second place, fixes a period from which the quinquennial yugas five-year cycles are to be counted. In st. 2 Varâha Mihira The 6th-century Indian astronomer and author of this compendium directs us to deduct two from the Sâka The Shaka Era, beginning in 78 CE date, and to divide the remainder by five ; which implies that a new yuga is supposed to begin with the third year of the Sâka Era, or two Sâka elapsed.

Whether this direction is due to Varâha Mihira only, or was already contained in the Paitâmaha Siddhânta, may be considered doubtful; the latter alternative, however, appears to be more probable, as Varâha Mihira, if in any way adding to—or rendering more definite—the teaching of the Paitâmaha Siddhânta, would most likely have adapted it to the same initial date as the other Siddhântas astronomical treatises, viz. 427 Sâka.

The Paitâmaha (Brâhma) Siddhânta known to Varâha Mihira has thus to be distinguished from the Brahma Siddhânta on which Brahmagupta’s Sphuṭa Siddhânta The "Corrected Treatise of Brahma," a highly influential 7th-century work is based. That Brâhma or Paitâmaha Siddhânta is a short treatise in prose, forming part of the Vishṇudharmottara-Purâṇa An ancient encyclopedic text, and belonging altogether to the modern phase of Hindû Astronomy. The number of Brahma Siddhântas, known at present, thus amounts to four, viz. the Paitâmaha Siddhânta summarized in the Pañchasiddhântikâ, the Paitâmaha Siddhânta forming part of the Vishṇudharmottara, the Sphuṭa Brahmasiddhânta by Brahmagupta, and that Brahma Siddhânta whose more ordinary name is Sâkalya Siddhânta.

There now remain the Romaka The "Roman" or Greek-influenced system, Pauliśa The "Paulisa" system, possibly linked to Paulus Alexandrinus and Vasishṭha Siddhântas, for the teaching of none of which we have any other source of importance but the Pañchasiddhântikâ. I begin with the first mentioned of these three treatises.

Romaka Siddhânta.

The fifteenth stanza of the first chapter shortly describes the nature of the yuga employed by the Romaka Siddhânta. The yuga is called ‘one of the sun and moon’ i. e. a lunisolar one, and said to comprise 2850 years,