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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 c28: Chapter XXII. Use of Table X

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 c28

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English

Contents

Chapter XXII. Use of Table X

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177. Suppose for example that the date corresponding to "Saka Samvat 999, Phālguna Sukla 3", is to be ascertained, we proceed as follows :—

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| | Saka 999 expired | |
| | Days of S. Year. | ☾'s Anom. |
| First New Moon in Solar Year ... | 3·28 | 2·67 |
| Add collective days up to Phalguna New Moon, and remember there was an adhika month earlier in the year. ... | 324·84 | 21·74 |
| Collective duration of 3 tithis (by Eye-Table) ... | 2·95 | 2·95 |
| | 331·07 | 27·36 |
| Sun's Eqn. (by Eye-Table) for 331·07 days = | | +·165 (☉'s Eqn.) = 27·53 |
| Moon's do. do. for 27·53 days = | | +·002 day |
| Sum of ☉'s and ☾'s Equations. | | +·167 day |
| (Table X) Phalguna New Moon, Saka 999, A.D. 1078 (4) Feb. 14·78 | | |
| (Eye-Table) Duration of 3 tithis (2) | | 2·95 |
| *Add mean tithi to sum of ☉'s and ☾'s Eqn.* | | (7)* Feb. 17·90 |

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This is how the two head-lines of Table X should be used for ascertaining ☉'s and ☾'s anomalies.

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The ending moment of the tithi is therefore ·90 of a day, i.e., (according to Eye-Table 54 ghat. on Saturday, 17 February A.D. 1078 ; which, so far as ghaṭikas are concerned, is the result arrived at by Dr. Fleet by applying Prof. Chhatre's table—Ind. Antiq., Vol. XVII, p. 162.

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178. In the above process the mean ending moment of the tithi is given in the two lines bracketed "Mean tithi", and all the rest of the process is directed to ascertaining the sum of the sun's and moon's equations of the centre.

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179. A further simplification could have been effected by using Table VIII for ascertaining the sun's and moon's anomaly, thus :—

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| | ☉'s An. | ☾'s An. |
| | days. | days. |
| (Table X) Saka 999 expired. Anomaly of sun and moon at first new moon in Solar Year ... | 3·28 | 2·67 |
| (Table VIII) Phālguna śukla 3, increased by 1 month (see Sec. 220 infra) because of an adhika month in the year : i.e., Chaitra śukla 3. | 327·79 | 24·69 |
| | 331·07 | 27·36 |
| | ☉'s Eqn. | +·165 |
| | | 27·53 |

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We thus obtain the sun's and moon's anomalies by the addition of two, instead of three, set of figures, and we may proceed as before to determine the equations for these anomalies.

Solar Dates by Table X

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180. Supposing the Kumbha Saṅkrānti for the same Śaka Samvat 999, expired, was wanted : we proceed as follows :—

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Commencement of solar year, Śaka 999 : Mr. 23·6638 Kumbha Saṅkrānti (by Eye-Table) 305·0850 Mr. 328·7488, i.e., 44 ghat. 56 p. (Tab. XIX.)

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∗ Since the sum of the several fractions of a day which go to make up the ending moment of the tithi exceeds unity, we increase the week-day by 1.

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Now, by Table VIII (see Sec. 216 infra) 328 days from Mr. 1, A.D. 1077 is 22 Ja. 1078.

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By Table IV (see Sec. 231 to 241 infra) the week day of 22 Ja. 1078 was 3 + 6 + 6 + 22 = 37, which divided by 7 leaves remainder 2, i.e., Monday. This result agrees with that arrived at by Dr. Fleet loc. cit. except as regards the moment of Sankrânti, which he puts down as about 47 ghat. 52 palas.

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181. To take another example, suppose we want the third Panguni of the Viśvâvasu year which was current in or after the Śaka year 1347 (expired.)

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By Table X, Śaka 1347 (exp.) was A.D. 1425.

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By Table I, the Viśvâvasu of that epoch was A.D. 1425.

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By Table X, the commencement of Śaka 1347 (exp.) was Mr. 26·7111

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By the Eye-Table, the addition for the commencement of Panguni = 334·9053

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361·6164 days.

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By Table VIII, 361 days from 1 Mr. A.D. 1425 was 24th Feb. A.D. 1426.

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Now, since ·6164 of a day exceeds ·5, that is, goes beyond sunset, therefore, by the rule in force in South India, [vide Sec. 144 (3)] the first Panguni in the year in question was 25th Feb. 1426.

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Therefore the 3rd Panguni (Śaka 1347, Viśvâvasu) was 27th Feb. 1426.

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And by Table IV the week day of 27th Feb. 1426 was 6 + 4 + 2 + 27 = 39, which, divided by 7, leaves remainder 4 (i.e.) Wednesday. This agrees with the result arrived at by Professor Kielhorn at page 83 of Appendix to Vol. VII, Epigraphia Indica.

Nakshatras Concurrent with Tithis

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182. A tithi is often cited along with a Nakshatra ending on the same day. In such cases the ending moment of the Nakshatra can be most easily determined by Table XI. (For merely finding the concurrent Nakshatra, we may proceed much more expeditiously as in Section 185 or Section 186.)

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Thus in the case dealt with in sections 177 to 179, the Nakshatra correction for Śaka 999 (A.D. 1077) was (Tab. XI) that corresponding to argument 3·279, i.e., ·2394 + ·0059 = ·2453. Deducting this from the interval for Revatî in the 12th lunar month (the year 999 Śaka contained an adhika month, and therefore Phâlguna was the 12th month), we have, as net interval for Revatî, 3·1860 minus ·2453 = 2·9407. Add this to New moon, Feb. 14·78 we have Feb. 17·72. ☾'s Anom. 2·67 + 21·74 + 2·94 = 27·35. Eqn. for Nak. (Tab. IX-k) = + ·016. Absolute ending moment of Nakshatra, Feb. 17·72 + ·016 or Feb. 17·74, i.e., 44 ghaṭikas after sunrise on 17 Feb. A.D. 1078. This agrees with Mr. Dikshit's calculation, cited by Dr. Fleet at p. 162 of Ind. Ant., Vol. XVII.

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183. In South Indian inscriptions a solar date, a lunar tithi and the corresponding nakshatra are often cited together.

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The following example shows how the citation should be verified.

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Ep. Indica, Suppl. to Vol. VII, p. 132. "Śaka 1106: on the day of Satabhishaj, which was the 14th tithi of the first fortnight and a Wednesday, the 26th solar day of the month of Simha".

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Now by Table X, Śaka 1106 commenced on March 24·3508, A.D. 1184.

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By Eye-Table, Simha begins and Karkata ends 125·4755 days after commencement of solar year.

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∴ Simha Saṅkrānti of Śaka 1106 was on 149·8263 days of the solar year.

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That is, by the rule in Southern India already adverted to, the 1st day of Simha was the 150th day reckoned from 1st March 1184.

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∴ the 26th day of Simha would be 150 + 25 or the 175th day from 1st March which by Table VIII, was 22 August.

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In order that the 26th day might be the 14th tithi of the first fortnight, the new moon must have occurred 13 days before, i.e., about 9 August.

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In Table X we find Bhādrapada new moon on Aug. 8·56 of A.D. 1184 (Wednesday). By Eye-Table, 14 tithis = 13·78 days.

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∴ the mean 14th tithi ended on August 22·34, A.D. 1184.

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The day of the week was Wednesday: since the new moon was on Wednesday, the addition of 14 days or 2 whole weeks to the day of the week would still give us the same day, Wednesday.

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184. If we want the actual ending moment of the 14th tithi, we proceed as follows :—

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| | | ☽'s Anom. |
| First new moon in solar year, A.D. 1184 | 19·0909 | 1·191 days. |
| By Table VIII, 14th tithi of Śukla Bhādrapada | 131·9033 | 21·685 |
| | 150·9942 | 22·876 |
| By Tab. IX, ☉'s Eqn. for 150·99 days = —·1672 | | —·1672 |
| " " ☽'s Eqn. for 22·709 days = +·3550 | | 22·709 |
| Sum = +·1878 | +·1878 | |
| | 151·1820 | |
| Add commencement of solar year, Mr. 24·3508 | | |
| | 175·5328 | days from 1st Mr. A.D. 1184. |

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By Table XIX ·5328 day = 31 ghaṭikas 58 palas.

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The actual ending moment of Bhādrapada śukla 14, Śaka 1106, was 31 ghat. 58 palas after mean sunrise on Wednesday, 22 Aug., A.D. 1184.

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185. For the Nakshatra corresponding to this tithi we proceed as follows :—

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| | Lunation space. |
| By Table VIII (last column) Sun's longitude for Nak. on 151st day = 12·0321 | |
| " V (last column) do. do. 18 day = ·0145 | |
| Add 14 tithis (by Table II) | 13·7809 |
| | 25·8275 |

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By Table III, the lunation space last arrived at, 25·8275 corresponds to No. 24 Śatabhishaj whose ending space is 26·2494

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Our inscription is therefore correct in all respects.

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186. An equally simple method of ascertaining the Nakshatra concurrent with the above tithi is the following, where, however, we use degrees of sun's and moon's longitude. Ending moment of tithi in days of solar year was 150·99 + ·19 (Sum of eqns.) = 151·18 days. By Tab. XVII-A & XVII-C, ☉'s Long. and Eqn. for 151·18 days = 146·69° - 2·04° + ·18 = 144·83° Add Moon's Elongation, *i.e.*, No. of tithi × 12° = 14 × 12° = 168·00° 312·83° By Eye-Table the longitude is that of Nakshatra *Satabhishaj*.