Delight of Mathematicians

Verse: The epoch constant Dhruva the fixed starting position for a planet at the beginning of a calculation period is three-eighteen-forty-nine-thirty-six (3-18-49-36). For Saturn Shani, add the minutes obtained by dividing the triple-multiplied years Karanabda by two hundred (200). To find the change based on daily motion, divide the arc-seconds by eighty (80). From the years elapsed in the Kali Yuga Kalyabda the current era in the Hindu calendar, subtract thirty-six hundred (3600). Multiply the remainder by fifty-six (56) and divide by one hundred and fifty (150). Adding these minutes and seconds gives the position of Saturn Shani.

Explanation: If you multiply the Drik-guna an observational factor used as a multiplier by 2, you get the minutes and seconds. Also, divide the Drik-guna by 150 to get further minutes. Adding these results gives the position of Saturn Shani in minutes. The previous epoch constant Dhruva of 3-18-49-36 must be added. Then, add the minutes and seconds derived from dividing the triple-multiplied years by 200. Next, perform the longitudinal correction Deshantara Samskara adjustment for the observer's specific distance from the prime meridian, usually Ujjain. From the elapsed years of the Kali Yuga, subtract 3600, multiply the remainder by 56, and divide by 150. Adding these resulting minutes and seconds provides the mean position of Saturn Madhya Shani.

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Determination of Corrections

original: "Samskara Nirnayah"

Verse: Five corrections Samskaras must always be performed for the mean planets Madhya Khetas: first, the epoch constant Purva Dhruva; second, the triple-year adjustment Trigunabda; third, the longitudinal correction Deshantara; fourth, the correction for seeds Bija Phalam also called the observational or Drik correction; and fifth, the arc-correction Bahoh Phalam the correction for the planet's anomaly or eccentricity. These should be done in order.

Explanation: Five specific corrections must be applied to the mean position of a planet:

(1) The Epoch Constant Purva Dhruva
(2) The Triple-year Adjustment Trigunabda
(3) The Longitudinal Correction Deshantara
(4) The Observational Correction Drik-samskara
(5) The Correction for Anomaly Bhuja-phala Samskara an adjustment based on the planet's orbital position.

Verse: For the lunar apogee Chandrocha and the ascending node Rahu, and for the Moon and Sun during eclipses, these corrections are essential for determining the precise timing and positions. This is the established rule.

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5. Correction for Anomaly

original: "Bhuja-phala Samskarah" — this refers to the sine-correction used to find the true position from the mean position

Verse: Three-four-five (345), twenty-seven (27), eight-seven-eight (878), six-seven-eight (678), four (4), four-three-three (433), five-two-four (524), three-six-seven (367), and two-zero (20) are the values in order...
8 67 4 524 367
The verse uses numerical mnemonics like "Gaja" (Elephant=8) and "Veda" (4) to list mathematical constants used in the sine tables for planetary corrections.