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Narada Purana (Jyotisha Selections) · by Vyasa
Chapter 1 · Basics and Panchanga
ज्योतिषमूलं पञ्चाङ्गं च
अर्कोनचंद्रलिप्तास्तु तिथयो भोगभाजिताः ।गतगम्याश्च षष्टिघ्ना नाऽतोभुक्ततरोद्धताः ॥ १२५ ॥
In the full Narada Purana (Purva Bhaga) this is chapter 54, verse 125.
The Moon's minutes less the Sun's, divided by the extent 720, give the tithis (moon days). The gone and the yet-to-come parts, times 60, are divided by the difference of the daily motions. That gives the ghatikas (24-minute unit).
Simple meaning: Moon minus Sun, divided by 720, gives the tithi. Then find the ghatikas.
तिथयः शुक्लप्रतिपदो द्विघ्नाः सैका न गाहताः ।
Count tithis from the first of the bright half, double, add one, divide by 7. The remainder names the karana.
वणिजोभ्रे भवेद्विष्टिः कृष्णभूतापरार्द्धतः ।
After Vanija comes Vishti. Four fixed karanas fall from the last half of the dark 14th.
ग्रहोदयाः प्राणहताः खखाष्टैकोद्धता गतिः ।
A planet's own day-and-night length comes from its daily motion and its sign's rising time.