Hayanaratna · by Balabhadra
Chapter 1 · Planets, Signs, Year Entry
ग्रहराशिस्वरूपवर्षप्रवेशाद्यानयनाधिकारः
तत्र भावानयनोपायउक्तः ॥ अथ चरखंडदिनार्द्धनयनं ।स्यात्सायनेर्केऽजतुलादियातेशक १२ प्रभास्वद्युदलेक्षभासां ॥त्रिधाक्षभादिग्गजदिग्विनिघ्नीत्वंत्यात्रिहृत्स्युश्चरखंडकानि॥
There, the way to find the houses is told. Now, finding the charakhandas (steps of the day-length change) and the half-day. The sayana (tropical) Sun may have reached the start of Aries or Libra. Then the shadow of the 12 -unit gnomon at one's own midday is the akshabha (noon shadow at the equinox). Put the akshabha in three places. Multiply them by 10, 8 and 10. Divide the last by 3. These are the charakhandas.
Simple meaning: Day-length steps: take the noon shadow at the equinox, multiply it by 10, 8 and 10, and divide the last by 3.
स्यात्सायनोष्णांशुभुजर्क्षसंख्यचरार्द्धयोगो लवभोग्यघातात् ॥
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.