Page:Sewell Indian chronography.pdf/61

Ashāḍhā ended at 4 gh. 35 p., or at 7.50 a.m., on the Tuesday. Both sunrises of Monday and Tuesday were included in it, and therefore it was repeated. On Thursday, September 27th, the nakshatra Maghā ended 3 gh. 4 p. or 1 h. 14 m. after sunrise, and the next nakshatra, Pūrvā Phalgunī, then began. It ended 59 gh. 55 p., or 23 h. 58 m. after the same sunrise and before sunrise the next day. There was no sunrise in Pūrvā Phalgunī and, for civil-day nomenclature, it was expunged. (§ 35, p. 19, and Note 1, Ind. Cal.)

126. A yōga is the period of time during which the joint motion in longitude, or the sum of the motions, of the sun and moon is increased by 13° 20′, or the twenty-seventh part of the circle. We call the yoga ${\displaystyle y}$. Yōgas. ${\displaystyle y}$ therefore equals the apparent longitude of the moon (${\displaystyle n}$) + the apparent longitude of the sun (${\displaystyle s}$); or ${\displaystyle y=s+n}$, and, since ${\displaystyle n=t+s}$ (see above), ${\displaystyle y=t+2s}$. Thus, taking the Ind. Cal. (pp. 81, 97) example where at sunrise ${\displaystyle s=1559}$, and ${\displaystyle n=3022}$, we find ${\displaystyle y=s+n}$, or = 4581. Equally, ${\displaystyle t}$ being 1463, and ${\displaystyle 2s}$ (1559 × 2) being 3118, we find by the formula ${\displaystyle y=t+2s}$ the same result, 4581. For beginning and ending of the current yōga, which by Table VIII. was Vyāghāta (4444 to 4815), we have respectively 4581 − 4444 = 137 = (Table X.) 6 h. 6 m. + 2 h. 15 m. = 8 h. 21 m. before sunrise, and 4815 − 4581 = 234 = 12 h. 12 m. + 2 h. 4 m. = 14 h. 16 m. after sunrise. The yōga, like the nakshatra, has, each, its special name.

127. The karaṇa is half a tithi. The first half of each tithi belongs to one karaṇa, the second half to another. The names are given in cols. 4, 5 of Table VIII.; and it will be observed that, with the exception of the first half of the first tithi, Karaṇas. the second half of the 29th and the two halves of the 30th, which have their own names, the rest consist of a repetition of seven names in order. The karaṇa is sometimes, but not often, mentioned in dates (see § 10, p. 3, Ind. Cal.), but it is an important element in astrological calculations. In the Pañchāṅg extract (Ind. Cal., pp. 14, 15) the karaṇa current at each sunrise is stated by name, with the time of its ending in ghaṭikās and palas. Thus, the first tithi, it will be seen, ended at 43 gh. 59 p. after sunrise on Friday and the second tithi then began. It lasted till 39 gh. 47 p. on the Saturday. It therefore lasted for (60 gh. − 43 gh. 59 p.) 16 gh. 1 p. + 39 gh. 47 p., or 55 gh. 48 p. Half of this is 27 gh. 54 p., 16 gh. 1 p. of which belonged to Friday. Hence the first half of the tithi expired and the second began at 11 gh. 53 p. after sunrise on the Saturday, and this is the hour noted in the Pañchāṅg. At the Friday sunrise Kiṁstughna was the current karaṇa. Bava succeeded it when half the first tithi had expired, viz., at 16 gh. 30 p. after sunrise, and Bava ended with the expiration of the tithi at 43 gh. 59 p. on the Friday. Then began Bālava, which was current at the Saturday sunrise and lasted till (as found) 11 gh. 53 p., when Kaulava began and lasted till the end of the second tithi at 39 gh. 47 p., and so on.

128. When a date is worked according to our ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$ system, and the final ${\displaystyle t}$, or tithi-index is accurately found, it is easy to determine the karaṇa, whether current at any moment or current at sunrise, from the value of ${\displaystyle t}$. Take, again, the example on p. 81 of the Indian Calendar where the ${\displaystyle t}$ was found to be 1463 at sunrise. Col. 3 of Table VIII. shows that the fifth tithi was then current, lasting from 1333 to 1667. A half-tithi is about ⁠166+1/2⁠. 1333 + ⁠166+1/2⁠ = ⁠1499+1/2⁠. Therefore 1463 falls in the first half, and at sunrise that day Bava was the current karaṇa.

Karaṇas are not in themselves subject to repetition or expunction. (§§ 88, 89, above.)

129. As an example of the working of karaṇas in the case of repeated and expunged tithis we will take the cases of the repeated tithi 13th śukla and the expunged tithi 7th kṛishṇa (in respectively the first and second fortnights) of the lunar month contained in the Pañchāṅg extract already referred to. It will be observed that the 12th śukla tithi ended on Tuesday at 56 gh. 44 p.,^[1] the karaṇa Bava having been current at sunrise and ending at 24 gh. 14 p. At that moment (see the List in Table VIII.) Bālava began, and it ended with the tithi at 56 gh. 44 p. Then began the karaṇa Kaulava, which was

1. ↑ These times are measured from sunrise. They can be turned into hours and minutes by Table XXV.