Siddhanta

Even scholars get confused when computing a pata.

They are unable to know if it has occured or is going to occur.

Verse 2. Definitions of Gola-Sandhi and Ayana-Sandhi with respect to the Sun.

When the tropical longitude of the Sun ie. his longitude measured from γ along the ecliptic is equal to 0° or 180°, then he is said to be at his Gola Sandhi.

In other words, when the Sun who moves along the ecliptic comes to the celestial equator, he will be at his Gola sandhi. Similarly when his longitude is 90° or 270°, he is said to be at the his Ayana-Sandhi.

Verses 3 to 6. Speciality with respect to the Moon.

Let the Hsine and Hcosine of the tropical longitude of the pāta (Rāhu the ascending node of the lunar orbit) as per the smaller table of Hsines when the radius is taken to be 120’, be respectively multiplied by 123 and 7 and divided respectively by 4 and 12.

The results are known as the Bahuphala and Kotiphala respectively. According as the tropical longitude of Rāhu ie λ be such that as 270° < λ < 90° or 90° < λ < 270°, the Bahuphala is to be divided by 362 ± Kotiphalas.

Subtract the result from the Gola Sandhis and Ayana Sandhis of the Sun, to get those of the Moon.

Verse 7. How to know the occurrence of a pāta.

If the Sphutakrānti of the Moon, when it is less than that of the Sun, then there could be no occasion for their declinations to become equal in the near future.

Verse 8. The definitions of Vyatipāta and Vaidhrti.

When the Sun and the Moon are in opposite Ayanas, but in the same Golas, and if then their declinations be equal, then that moment is said to constitute Vyatipātayoga. If on the other hand, if both the Sun and the Moon be in the same Ayana and opposite Golas, and if then their declinations be equal, that moment is said to constitute Vaidhrti Yoga.

Verse 10. To know whether the Yoga is past or future.

If the declination of the Moon situated in an odd quadrant exceeds that of the Sun or falls short of the Sun’s in an even quadrant the moment of the occurrence of pāta has elapsed. Otherwise the pāta is to take place shortly after.

Verse 9 and first half of verse 10. To prognosticate the occurrence of a

When the sum of the tropical longitudes of the Sun and the Moon happens to be 180 ∘ or 360 ∘ , then the Vyatipāta and the Vaidhrti respectively will occur or will have occurred. The number of minutes of arc by which the sum of the tropical longitudes falls short of or exceeds 180 ∘ or 360 ∘ as the case may be, are to be divided by the sum of the daily motions of the Sun and the Moon, which will approximately the number of days after which or before which the Yogas will occur or would have occurred. Compute the declinations of the Sun and the Moon for that moment from the then true daily motions.

Latter half of verse 11 and verses 12, 13, 14. To compute the time of the occurrence of pāta through a consideration of declinations.

Obtain the difference of the declinations if they be of the same direction or their sum if they be of opposite directions in the case of Vyatipāta; obtain the sum or difference of the declinations according as the declinations are of the same or different directions in the case of Vaidhrti.

Call this sum or difference ’the Ādya’. After a lapse of an arbitrary time or before the moment concerned, obtain the positions of the Sun, Moon and the Rāhu; also compute their declinations and form their difference or sum as the case may be.

Call this Anya. If on both the occasions it is indicated that the pāta has elapsed and or is to elapse, obtain the difference of the Ādya and Anya; otherwise their sum. Divide the arbitrary time taken, by the above sum or difference of the Ādya and Anya and multiply by the Ādya. Take the result in ghatis. Taking this as the arbitrary time, repeat the process till an invariable quantity is obtained in ghatis. This is the time by which the moment of the pāta has elapsed or after which it is going to occur.