INTRODUCTION.

Siddhânta A Sanskrit term for a formal astronomical treatise or system., but calculated from it the amounts whose knowledge he considered indispensable, and inserted them ready calculated in his text.

We therefore arrive at the conclusion that Varâha Mihira A 6th-century Indian astronomer and polymath, author of the Pañchasiddhântikâ. has in no case obliterated the characteristic features of the Siddhântas he had to deal with, and that whatever distinguishes those works from one another in the text of the Pañchasiddhântikâ Literally "The Five Astronomical Treatises," Varâha Mihira's main compendium. really distinguished them in their original form. We may note in conclusion that there is one interesting circumstance which furnishes a kind of counterproof to this conclusion. According to VII. 1. and VIII. 9 the Paulîśa and Romaka Two of the five systems; the Romaka likely refers to "Roman" or Alexandrian influence. Siddhântas calculated the parallax in longitude The apparent shift in the position of a celestial body when viewed from different locations, specifically along the ecliptic. at a solar eclipse in exactly the same manner. Now Varâha Mihira accentuates this agreement of the two works by stating the rule each time in exactly the same words. But an author, who is so evidently desirous to mark the points in which the different authorities on which he draws are at one, may certainly be supposed to be no less scrupulous in stating the details in which they diverge.

After having thus cleared the way, I proceed to give short summaries of the doctrines of the five Siddhântas, beginning with that one which, owing to the existence of a modern recension, is best known, viz. the Sûrya Siddhânta.

Sûrya Siddhânta? According to I. 14 the Sûrya Siddhânta of Varâha Mihira taught that 180,000 years contain 66,389 intercalary months Extra months added to the lunar calendar to keep it synchronized with the solar year., and 1,045,095 omitted lunar days. The number 180,000 is the twenty-fourth part of the years of a mahâ-yuga A "Great Age" in Hindu cosmology, totaling 4,320,000 years.; if we therefore, for comparison’s sake, multiply the figures given above by twenty-four, and deduce from them the number of the sâvana Civil days, measured from sunrise to sunrise. days of a yuga, we obtain 1,577,917,800; while the corresponding figure for the modern Siddhânta is 1,577,917,828. The length of the sidereal year The time it takes for the Earth to orbit the Sun relative to the fixed stars. resulting from these figures is 365 days, 6 hours, 12 minutes, 36.56 seconds in the case of the modern, and 365 days, 6 hours, 12 minutes, 36 seconds in the case of the old Sûrya Siddhânta. The latter value exactly agrees with that which, according to Bhaṭṭotpala A 10th-century commentator on Varâha Mihira. and others, was assigned to the solar year in the Paulîśa Siddhânta.

What the old Sûrya Siddhânta taught about the mean motions of the sun and moon, is immediately apparent from the above statement concerning the nature of the yuga. The number of the moon’s sidereal revolutions during the yuga is the same as in the modern Siddhânta; whence it follows that each revolution is a little shorter (the yuga of the old Siddhânta counting twenty-eight days less than that of the modern one). Rules how to calculate the mean positions of the sun and moon are given in chapter IX; they however call for no special remarks, as they follow immediately from the constitution of the yuga.—The duration of the revolution of the moon’s apogee The point in the moon's orbit where it is furthest from the Earth. may