The Siddhāntasundara of Jñānarāja: An English Translation with Commentary

10 Chapter on Mathematical Astronomy: Section 4 Occurrence of Eclipses

10. Chapter on Mathematical Astronomy Section 4: Occurrence of Eclipses This section formally deals with the occurrence of eclipses, but its content does not appear unified, and much of it is unclear. (1–2) The weekday, located from the star of the sun [?], is diminished by 39, 30, 24, 21, 20, 20, 20, 20, 22, 26, 33, 45, 73, 200 palas owing to the [cosmic] wind, and increased by 400, 100, 60, 49, 44, 44, 44, 52, 72, 132, 0, 114 palas [respectively]. At a syzygy, [the longitude of] the sun is increased by the signs and so on of what has been traversed. Its velocity is found from the day [perhaps tithi?]. The result consists of the minutes of arc of the [lunar] node. 1, 2, 3, 4, 5, 5, 5, 6, and 7 [?]. It [the result] is converted to degrees in the direction of the degrees of the arc of the center of the sun [?] and [applied] to the node. Otherwise, it is corrected. These two verses are not clear. It is not at all clear what these numbers are, or what purpose applying them to the weekday has with respect to eclipse possibilities. They possibly relate to the naks .atras, but note that there are 27 naks .atras, but only 26 numbers given. (3a–b ) [When] 19;21,33,33 [degrees] is multiplied by the current śaka year diminished by 1425, and [the result] is increased by 4;3,32, [we get the longitude of] the lunar node in degrees and so on [at the beginning of the current śaka year]. The verse gives a method for computing the longitude of the lunar node, providing a multiplier (19◦213333) and an ad240 10. Chapter on Mathematical Astronomy, Section 4 241 dend (4◦332) in the process (see Siddhāntasundara 2.1.57–64 and the commentary thereon for information on multipliers and addends). This method for determining the longitude of the lunar node is, however, peculiar. First, it gives the longitude for the beginning of śaka 1425, whereas the epoch given earlier (see Siddhāntasundara 2.1.57–64) falls about half a year later. Secondly , the multiplier and the addend that are given are not consistent with those given previously. The multiplier for the lunar node given earlier is 19◦211124, not 19◦213333. Furthermore , using Jñānarāja’s parameters, the addend for the lunar node for the beginning of śaka 1425 comes out to be 1◦5846, not 4◦332. However, the multiplier and the addend given here are very close to what we get using the parameters given by Bhāskara II in the Siddhāntaśiroman . i, namely, 19◦213321 as the multiplier for the lunar node, and 3◦162 as the addend corresponding to the beginning of śaka 1425. Why a different epoch is introduced here, and why different parameters are used, is unclear. (3c–d ) [The longitude of the lunar node] increased by 20 degrees of the sun’s entry into a sign [?] [which is itself] increased by 13 degrees [or: when greater than 13 degrees]. The lunar latitude is [equal to] half of the degrees of the arc of the sun increased by the node. [The result] is multiplied by 3 and increased by 30 degrees. An eclipse limit could be intended here (the subject of the sentence being the shadow of the earth), but the interpretation is not clear. We are also given a formula for the lunar latitude, but the formula is defective as described. (4) The [true] velocity [of the sun] is divided by 5. [The result is] diminished by its own 12th part. [This] is [the diameter of] the [apparent] disk of the sun. [The apparent diameter of] the disk of the moon is 649 divided by the star-eaten [?]. That [apparent diameter of the disk of the moon] is multiplied by 3, and [the result] is increased by its own 10th part and diminished by the 7th part of the [true] 242 10. Chapter on Mathematical Astronomy, Section 4 velocity of the sun. [This] is [the apparent diameter of] the shadow of the earth. The [true] velocity of the moon is [equal to] the [apparent diameter of] the disk [of the moon] divided by 74. This verse gives formulae for computing...