Commentary on the Grahalaghava

The planets related to the desired cycle = 12 × (planets from one cycle) × cycle = Constant × cycle.
Therefore, 12 × cycle - (Constant × cycle) = planets produced in the desired cycle. By adding all these, the mean planets at the desired time are found:
= Planets from the total days + (12 × cycle - Constant × cycle) + Epochal Position The 'Epochal Position' or 'Kshepa' is the position of a planet at the start of a specific era.. Since the full revolutions (cycles) are not needed here, we discard '12 × cycle' —
(Planets from total days - Constant × cycle) + Epochal Position = Mean planets at the desired time. Thus, the first half of the verse is proven.

Now, the planets calculated here are for the Prime Meridian original: 'Rekha-desha', referring to the line passing through Ujjain. To adapt them for one's local position, the longitudinal correction Deshantara-samskara: a correction applied to account for the distance between the observer's location and the prime meridian must be performed. Here, the author has applied the longitudinal correction only to the Moon, because its motion is very fast. For other planets, it is ignored due to their slow motion.

Now, knowing the distance in leagues original: 'Yojanas' between the Prime Meridian and the local place, the proportion is as follows — * If the Moon's motion in minutes is obtained for the Earth's circumference in leagues, then what is obtained for the longitudinal distance in leagues? The resulting Lunar longitudinal correction =

(Moon's motion in minutes × Longitudinal distance)       (790' 35'') × Long. distance      Long. distance
------------------------------------------------- = --------------------------- = -----------------
    Earth's circumference in leagues                   4967                   6

This is due to a small difference. If the local place is West of the Prime Meridian, the resulting minutes should be added to the Moon calculated from the total days. This is because the sunrise there occurs after the sunrise at the Meridian. If the local place is to the East, it should be subtracted, as the sunrise occurs before the Meridian sunrise. This is correctly stated. — The Editor. || 9 ||

By multiplying the constant of a planet by the cycle and subtracting it from the planet generated by the total days original: 'Ahargana', and then adding the planet's epochal position, the mean planet at sunrise is found. Divide the distance in leagues between your location and the Prime Meridian by 6; if your location is west of the Meridian, add the resulting minutes to the Moon; if east, subtract them to find the mean Moon for your location. || 9 ||

Example — See ahead || 9 ||

The Prime Meridian locations are those touched by the line going from Lanka to Mount Meru. For example —

The Equator (Prime Meridian) —

"The line touching Lanka, Ujjain, Kurukshetra, and other places, going to Meru, is called the Middle Line of the Earth by the wise." (Siddhanta Shiromani) Lanka here refers to an equatorial point, not necessarily modern Sri Lanka..

Earth's Circumference in Leagues —

"The circumference of the Earth is said to be 4967 leagues; its diameter is 1581." (Siddhanta Shiromani) || 9 ||

Now, he describes the calculation for the mean Sun, Mercury, Venus, and Moon —

The Sun, Mercury, and Venus are derived from the total days minus their seventy-thousandth part;
the result of the total days divided by fifteen is subtracted from the minutes to get degrees and so on.
The Moon is the total days divided by 18, minus its one-hundred-and-eighty-first part;
the total days divided by 140 is subtracted from the minutes to get degrees and so on. || 10 ||

Now the method for mean Sun, Mercury, Venus, and Moon is explained. "Sva-kha-naga" etc. The total days Ahargana is 1921. This is placed in two spots: 1921 divided by seventy (70) gives a result of 27 degrees. The remainder is 31, multiplied by sixty (60) is 1860, divided by seventy (70) gives 26 minutes. Again the remainder is 40, multiplied by sixty (60) is 2400, [divided by] seventy (70)...

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* Here, the proportion should ideally use the corrected Earth circumference and corrected Moon's motion. However, since small differences are observed throughout this manual Karana-grantha: a concise astronomical manual for practical calculations, the proportion has been made in this manner. — The Editor.