सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

540 of the discs is less than the sum of their angular radii, the pāta lasts. Extending the meaning of this to Vaidhṛti also, so long as the numerical difference of the declinations of the Sun and the Moon ignoring their direction happens to fall short of the sum of the angular radii, the pāta lasts. To obtain this duration of the pāta the argument is “If the sum or difference of the declinations according as they are of opposite or the same direction (which was taken to be Ādya under verses (11) to (14) ) was reduced to zero in the time computed that time being known as Spaṣṭaghaṭis, what time will be taken for a difference of declinations equal to the sum of the angular radii?” The result is ((r + p) × T) / Ādya where r and p are the angular radii of the Sun and the Moon, T the time calculated formerly known as Spaṣṭaghaṭis and Ādya is as defined above. The above result gives the duration of the pāta. Note. An approximate estimate of this duration could be obtained using differentiation. We have sin δ = sin λ sin ω so that cos δ Δδ = sin ω cos λ Δλ Let Δλ be the motion in longitude of the Moon with respect to the Sun per nāḍi which will be on the average 12′ approximately. ∴ Δδ = (sin ω cos λ × 12) / cos δ If in one nāḍi, there be a variation in the declination equal to the above, what time will be taken for 16′ + 15′ the sum of the angular radii approximately ? The result is (31 cos δ) / (12 sin ω cos λ)