Indian Chronology (Solar, Lunar and Planetary): A Practical Guide to the Interpretation and Verification of Tithis, Nakshatras, Horoscopes and other Indian Time-records, B.C. 1 to A.D. 2000 c35: Chapter XXVIII. Construction of Table for Nakshatras and Yogas

Indian Chronology (Solar, Lunar and Planetary): A Practical Guide to the Interpretation and Verification of Tithis, Nakshatras, Horoscopes and other Indian Time-records, B.C. 1 to A.D. 2000 c35

Language: English

Chapter XXVIII. Construction of Table for Nakshatras and Yogas

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263. Table XI contains a very easy method of calculating directly the absolute ending moment of a nakshatra or yoga.

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The interval between new moon and any particular nakshatra *n* may be expressed by the formula (29·5306-A)/q + n × d.

where *A* is the sun's longitude at new moon, expressed in terms of a lunation as in the last column of Table VIII, *n* is the numerical order of the given nakshatra, counting from Revatî, *d* is the mean duration of a nakshatra in days, and *q* is the ratio of the length of the synodical to that of the sidereal month.

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The above expression may be expanded into 29·5306 - (f + al - 2·1707) × m × 1/q + n × d,

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where *f* is the moment of occurrence of the first New Moon in a Solar Year, as given in Table X, *a* is the number of lunations completed since the commencement of the Solar Year, *l* is the period of a lunation in days (i.e., 29·5306 days); 2·1707 days are the sodhya, *m* is the factor for converting Sun's longitude into lunation space, according to Table V (last column); 1/q is the factor used in the 1st column of Table V (i.e., 1/(1·0808)) and *n* × *d* is the collective duration in days of Nakshatras counted from Revatî up to the end of the given Nakshatra.

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We may expand the above expression again as follows: 29·5306 × 1/q + 2·1707 × m × 1/q + n × d - f × m × 1/q - al × m × 1/q.

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Now all these expressions connected by + or -, except, f × m × 1/q may be calculated once for all for every Nakshatra in the lunar year, for 29·5306 × 1/q = 27·32167; 2·1707 × m × 1/q = ·16237;

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And the expression (·16237 + n × d - al × m × 1/q), when calculated for each Nakshatra becomes one of the figures given in Table XI under "Interval between New Moon and each Nakshatra".

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There remains f × m × 1/q, whose maximum value is 29·5306 × m × 1/q = 2·20891 (the difference between 29·530587946 and 27·321674163, the lengths of the synodical and sidereal months).

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The values of f × m × 1/q, less than the maximum, may be calculated by means of the Nakshatra correction Table in Table XI.

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Accordingly all that we have to do, in order to know the mean ending moment of any Nakshatra, is to take the corresponding figure from the "Interval" Table XI and deduct the value of f × m × 1/q as obtained from the "correction" table in Table XI.

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*N.B.*—The correction tables might have been made additive instead of subtractive, by (1) subtracting all the quantities in the correction tables from 2·20890 in the case of Yogas, and (2) subtracting 2·20890 and 4·11036 respectively from all the intervals in the body of Table XI. This will be attended to in a future edition of the work, should a second edition be called for.

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264. Thus, supposing the mean ending moment of *Mūla* Nakshatra in the month of (lunar) *Kārttika* in A.D. 1910, is required :—

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The mean ending moment of *Kārttika* New Moon is (by Table X) November 2·30 The integer and first two decimal places of the "Interval" for *Kārttika Mūla* (Table XI) 6·13 Nov. 8·43

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Deduct f × m × 1/q, *i.e.*, the equivalent of 25·91 according to the correction table in Table XI; 1·87 + ·07 = 1·94. -1·94 Nov. 6·49

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This is the mean ending moment of the Nakshatra *Mūla* in Lunar *Kārttika*, A.D. 1910.

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If we want the absolute ending moment, we calculate the anomaly : Days. Moon's mean anomaly at commencement of Solar Year ... 0·535 Add increase of anomaly up to *Kārttika* New Moon ... 11·866 Add "Interval" less f × m × 1/q ... 4·19 16·59 Corresponding Equation for Nakshatras (Table IX-*k*) ... +·246

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Adding this equation to the mean ending moment, Nov. 6·49, we have Nov. 6·74 or (by the Eye-Table) 44½ ghaṭikas after mean sunrise on Nov. 6, A.D. 1910. We could, of course, if we had liked, have calculated the absolute ending moment to four places of decimals instead of to two.

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265. Yogas are worked in the same manner, by using the corresponding portions of Table XI, *i.e.*, by deducting from the "Yoga Interval" (for the given lunar month and given Yoga) the correction for the Solar Year according to the Yoga correction table in Table XI.

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266. When a Yoga and Nakshatra are cited with the *tithi* as in the example in Sec. 98 *supra*, it will generally be enough to ascertain the nakshatra and the yoga which were concurrent with the tithi and this can most easily be done as follows :—

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Sun's anomaly at ending moment of tithi, 203·31 days. By Table XVII-A, the ☉'s longitude corresponding to 203 days is 197·94° " XVII-C, " " " 31 day is 31° 198·25° The tithi being the 9th, the moon's elongation was 9 × 12° = 108·00° Total 306·25°

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This (by Eye-Table) is the longitude for Nakshatra Dhanishtha. For Yoga we add 2 × Sun's Longitude to Moon's Elongation. That is, the yoga longitude is 108·00° + 2 × 198·25° = 108·00° + 396·50° = 504·50° Deducting 360° which is one complete revolution, we have 504·50° - 360° = 144·50°, which (by Eye-Table) is the Longitude of No. 10 Ganda Yoga.

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267. When we wish to find the ending moment of a Nakshatra or Yoga, we should apply Table XI as follows:—

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In our example, the mean tithi ended at 8·86 days after Kārttika New Moon. The age of the first new moon in the solar year being 20·27 days, the corresponding Nakshatra correction is (by Table XI) 1·50 + ·02 = 1·52 = (by Eye-Table) 1 day 31 ghaṭikas and the Yoga correction (by Table XI) 2·78 + ·04 = 2·82 = 2 days 49 ghaṭikas.