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Hayanaratna · by Balabhadra
Chapter 1 · Planets, Signs, Year Entry
ग्रहराशिस्वरूपवर्षप्रवेशाद्यानयनाधिकारः
स्यात्सायनोष्णांशुभुजर्क्षसंख्यचरार्द्धयोगो लवभोग्यघातात् ॥खाग्न्याप्तियुक्तस्तु चरं पलादि षष्ट्या विभक्तं घटिकादिकं स्यात् ॥
Take the bhuja (distance from the nearest equinox point) of the sayana (tropical) Sun. Add the chara pieces for as many signs as it holds. Then multiply its degrees by the running piece and divide by 30. Add that too. This is the chara (day-length difference) in palas (24-second units). Divided by 60, it is in ghatikas (24-minute units) and so on.
Simple meaning: Day-length difference: add the day-length steps for the signs passed and a share of the next one. That gives it in palas.
चरेण संयुतोनाश्च कर्तव्यास्तिथिनाडिकाः ॥
Half-day: 15 ghatikas plus the day-length difference (Aries to Virgo) or minus it (Libra to Pisces). Half-night: 30 less the half-day.
अथनतादीनामानयनमुक्तं सकलसिद्धांतमंडलीसरोविहरणराजहंसगणितविद्याचातुरीतांत्रिकपंचाननाहिगवीप्रवीणैः पद्धतिचिंतामणौ । तत्रादौ नतोन्नतानयनं ।
Time from midday: by day, the gap between now and midday; at night, the night gone or left plus half the day.
अथायनांशानयनं ॥
Zodiac shift: Shaka year less 421, less a tenth, divided by 60. Add a few seconds of arc for the Sun's sign.