M. S. Sriram

Obtaining the planetary longitudes

The true epicycle Circumference in minutes (sphuṭavṛttakalās) of the Sun is 03 (gānam ) and that of the Moon is 07 (sthānam) always (in all the quadrants). The [dimensions of the] circumferences of the manda and the śīghra [epicycles] of the planets starting from Mars in minutes, at the beginning of the odd and the even quadrants, in order, are 14 (vandya), 18 (divya), 53 (guṇī) and 51 (kṛṣṇa) [for Mars]; 07 (sūnu), 05 (mānī), 31 (kalā) and 29 (dhara) [for Mercury]; 07 (sthānaṃ), 04 (dānaṃ), 16 (tapo) and 15 (mānyaṃ) [for Jupiter]; 04 (bhānuḥ), 02 (prājno), 59 (dhamaḥ) and 57 (samaḥ) [for Venus]; 09 (dhanī), 13 (loko), 09 (dhanaṃ) and 08 (dānaṃ) [for Saturn]. These are stated separately for different quadrants after being divided (apavartita) by 270.

Obtaining smaller guṇas and hāras

The product of 200 (jnānīndra) and the [śakābda]-guṇakāras, beginning with dhana (9), has to be added to or subtracted from the product of the [śakābda]-hāras [of the planets], beginning with manda (85), and their respective revolution numbers. These are guṇas [of the planets]. The [śakābda]-hāras, beginning with manda, multiplied by the the number of civil days (bhūdina) in a mahāyuga are the hāras. These are the mahāguṇas and mahāhāras, whose apavartana is to be done (they have to be factored by their GCD).

Ascendent at the meridian transit

The ascensional difference (cara) and the prāṇakalāntara are to be applied to the [longitude of the] end of the desired zodiacal sign (rāśyanta) which is corrected for the movement of equinox (ayanacalana). The result thus obtained is stated to be the kālalagna corresponding to the end of the desired zodiacal sign (rāśyanta).

Obtaining the hārakas for the planets

The above verse defines the mandakendrahārakas of the planets. It may be recalled that the mandakendra is the difference between the planet and its mandocca (apogee). The mandakendra-guṇakāras and the mandakendrahārakas determine the successive approximations to the rate of motion of the mandakendra.

Mean planets and the śakābdasaṃskāra

May the guru, an embodiment of intelligence and bliss, keep ever rising in the space of my heart, like the Sun dispelling the darkness of ignorance.

Relation between the circumference and the diameter and computation of Rsines

May the diameter be multiplied by four, kept separately at several places, and divided by the odd numbers 3, 5, 7 etc. [The results] may be sequentially applied negatively and positively to the diameter multiplied by four. Then we obtain a very accurate [value of the] circumference.

Computation of the khaṇḍa, dhruva, etc. of the Moon

Let the heap of days (dharādinaugha), and the difference in the revolutions of the Moon and its apogee be mutually divided. Then, from these results, the guṇakāras and hārakas associated with the Moon’s anomaly (candra-kendra) are to be obtained as stated earlier.

Obtaining the Right Ascension, etc.

Here the author emphasizes the importance of actual observations of the celestial objects through the measurement of their shadows etc. in determining their longitudes and latitudes. In the case of the Sun, the measurements associated with the shadow at noon and other times pose no difficulty, in principle at least, as these are done during the day. Observations pertaining to the Moon’s shadow are also possible during the night. But what about the planets and stars?

Examination of the revolution numbers etc.

Based on a thorough examination of the position of the planets at the time of eclipses, planetary conjunctions, and so on, the revolution numbers etc. [of the planets] in a kalpa have to be conceived of for achieving concordance with observations.