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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 c36: Chapter XXIX. Investigation of Adhika and Kshaya Months

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 c36

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Contents

Chapter XXIX. Investigation of Adhika and Kshaya Months

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268. *Adhika* months are the cream of the Indian Calendar, while *kshaya* months are its *crème de la crème*. Figures of speech apart, it is certainly true that the success or failure of any computer in deducing *adhika* and *kshaya* months is the measure of his success in dealing, as a whole, with the Indian Calendar. How far the present method satisfies this ordeal, will be for competent judges to decide.

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269. Two independent English lists of *adhika* and *kshaya* months are at present in existence, the first by Prof. Chhatre (reproduced in *Ind. Antiq.*, Vol. XXIII, pp. 105-108), and the second by Messrs. Sewell and Dikshit. The lists in Patell's *Chronology* and Cunningham's *Indian Eras* are obviously copied, without check, from Chhatre whose reputation was and is, sufficient to justify such a procedure.

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Messrs. Sewell and Dikshit certainly exercised an independent and erudite judgment in revising Prof. Chhatre's list, and they declare, in several parts of their work, the indubitable superiority of their list to that of Chhatre.

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270. For the purposes of Table X in the present work, it was necessary to weigh carefully the merits of Mr. Chhatre's and Mr. Dikshit's calculations wherever they differed. The palm must no doubt be awarded, as a general rule, to Mr. Dikshit, but he seems to have failed, by oversight, to take notice of the *kshaya* months in A.D. 507 and A.D. 751 which are investigated below.

Adhika Months

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A.D. 629.

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271. In regard to this year Messrs. Sewell and Dikshit are at some pains to explain (under *Additions and Corrections*, p. 150 of "Indian Calendar") that Chhatre's entry of Adhika Kārttika is wrong and that their own entry of Adhika Āśvina is correct. Let us verify this statement, and in so doing, note the comparative brevity and simplicity of our method.

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| | Days. | ☉'s and ☽'s Eqns. | ☽'s Anom. |
| First New moon in Solar Year A.D. 629, | 10·2145 | | 20·456 |
| Add for 7th New moon | 177·1835 | -172 | 11·856 |
| | | -342 | |
| | 187·3980 | | 32·312 |
| | -514 | -514 | -172 ☉'s Eqn. |
| 7th or Tulā Saṅkrānti 186·9355 : | 186·884 | | 32·140 |
| | | | 27·555 |
| | | | 4·585 |

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The 7th new moon was therefore *Asvina*, and obviously the 6th new moon also was an *Asvina*; so that the *Adhika* month was, as stated by Messrs. Sewell and Dikshit, *Āśvina*, not as stated by Chhatre, *Kārttika*.

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A.D. 979.

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272. In each of the next two cases Mr. Chhatre was out of reckoning by a very small margin. For A.D. 979 Messrs. Sewell and Dikshit have given Śrāvaṇa as the Adhika month, whereas Bhādrapada is the Adhika month in that year according to Prof. Chhatre's list. The calculations must in all these cases be made by the Sūrya Siddhānta and the foot-note to p. (9) of the text should be applied.

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| | Days. | ☉'s Anomaly |
| First New moon in Solar Year A.D. 979, | 7·5649 | 5·023 |
| Add for 5th New moon | 118·1223 | 7·904 |
| | 125·6872 | 12·927 |
| Sum of ☉'s and ☾'s Eqns. : −·1259 −·1005 = −·2264 | | −·126 (☉'s Eqn.) |
| 5th or Simha Saṅkrānti 125·4755 : | 125·4608 | 12·801 |

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The Adhika month was Śrāvaṇa by ·0147 day, i.e., nearly one ghaṭika, and in this instance Messrs. Sewell and Dikshit are right. Our Table X shows Adhika Śrāvaṇa.

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A.D. 1199.

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| | Days. | ☾'s Anom. |
| First New moon in Solar Year | 3·3688 | 8·539 |
| 3rd New moon in " | 59·0612 | 3·952 |
| | 62·4295 | 12·491 |
| | | +·055 (☉'s Eqn.) |
| | | 12·546 |
| Sum of ☉'s + ☾'s Eqns. +·0555 −·1261 = −·0706 | | −·0706 |
| 3rd or Mithuna Saṅkrānti 62·3555 : | 62·3589 | |

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The Adhika month, 3rd new moon, was Āshāḍha, as stated by Messrs. Sewell and Dikshit, not Jyeshṭha, as determined by Chhatre. Our Table X shows Adhika Āshāḍha.

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It happens that this very interesting Adhika month, the 3rd lunar month in the year AD. 1199—1200 is quoted in a South Indian inscription, discussed by Dr. Fleet at p. 156 of the Indian Antiquary, Vol. XIX (1890). In the inscription itself the Adhika month is identified as Āshāḍha, not as Jyeshṭha. Of course the margin of difference is so small (5 minutes), that a calculator might, without being convicted of error, place an adhika month of this description on either side of the Saṅkrānti. If we did not know that the difference was so small, we should be at a loss to account for the discrepancy between the statement in the inscription and Prof. Chhatre's list. As it is, a more striking instance cannot be imagined than this actual one, to demonstrate the value and importance to an epigraphist of a knowledge of how to calculate tithis accurately.

Kshaya Months

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A.D. 507.

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| | Days. | ☉'s and ☽'s Eqns. | ☽'s Anom. |
| First New moon in Solar Year | 10·1256 | —·129 | 14·587 |
| Add for 8th New moon in Solar Year | 206·7141 | —·064 | 13·832 |
| (1) 8th or Vrischika Sankrânti | 216·8289 | 216·8397 —·193 = 216·6467 | 28·419 |
| | | | 27·555 |
| | | | 0·864 |
| | | | —·129 (☉'s eqn.) |
| | | | 0·735 |
| | | | 0·864 |
| Add for 10th New moon | 59·0612 | + ·039 —·355 | 3·952 |
| (2) 10th or Makara Sankrânti | 275·637 | 275·9009 —·316 = 275·5849 | 4·816 |
| | | | + ·039 (☉'s eqn.) |
| | | | 4·855 |
| | | | 4·816 |
| Add for 11th New moon | 29·5306 | + ·120 —·412 | 1·976 |
| (3) 11th or Kumbha Sankrânti | 305·085 | 305·4315 —·292 = 305·1395 | 6·792 |
| | | | + ·120 (☉'s eqn.) |
| | | | 6·908 |

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273. From (1) it follows that the 8th new moon was Kârttika and it is apparent from the time of occurrence of that new moon (1 ghaṭika before the end of the solar month) that the 7th new moon also must have been a Kârttika.

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From (2) it follows that the 10th new moon was Pausha. [Foot-note to p. (9) of Text.] From (3) it follows that the 11th new moon was Phâlguna. [ Do. do. ]

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∴ The new moon between Pausha and Phâlguna, viz., Mâgha, was kshaya in this year.

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It is also evident from the time of occurrence of this Phâlguna that the 12th new moon also must have been a Phâlguna.

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Against this year Messrs. Sewell and Dikshit have noted only "Adhika Phâlguna", whereas Chhatre mentions also a kshaya month, Pausha. We have just seen that the kshaya month was really Mâgha, which is accordingly noted in our Table X.

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Nor would the case have been different under the Ârya Siddhânta, since, as we remarked in the foot-note to Sec. 161 supra, the new moons under the Ârya Siddhânta at this epoch occurred only ·0231 of a day before the Sûrya Siddhânta new moons, and this would have made no difference as regards adhika and kshaya months in the present case.

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274. Only an *Adhika* Chaitra without a *kshaya* month is noted in this year by Messrs. Sewell and Dikshit, whereas Prof. Chhatre notes *Adhika* Kârttika and *Adhika* Chaitra besides Mârgasira *kshaya*. Let us work for the different new moons:—

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| | Days. | ☉'s and ☽'s Eqns. | ☽'s Anom. |
| First New moon in Solar Year A.D. 751: | 10·3034 | −172 | 26·321 |
| Add for 7th New moon | 177·1835 | −304 | 11·856 |
| (1) Beginning of 7th Solar month 186·9355 : | 187·4869 | −476 = 187·011 | 38·177 − 172 (☉'s Eqn.) − 27·55 = 10·450 |
| | | | 27·555 |
| | | −128 | 10·622 |
| Add for 8th New moon | 29·5306 | −133 | 1·976 |
| (2) Beginning of 8th Solar month 216·828 : | 217·0175 | −261 = 216·756 | 12·598 − 128 (☉'s Eqn) = 12·470 |
| | | −052 | |
| Add for 9th New moon | 29·5306 | +077 | 1·976 |
| (3) Beginning of 9th Solar month 246·3192 : | 246·5481 | +025 = 246·573 | 14·574 − 052 (☉'s Eqn.) = 14·522 |
| | | +040 | |
| Add for 10th New moon | 29·5306 | +335 | 1·976 |
| (4) Beginning of 10th Solar month 275·6369 : | 276·0787 | +375 = 276·454 | 16·550 + 040 (☉'s Eqn.) = 16·590 |
| | | +120 | |
| Add for 11th New moon | 29·5306 | +385 | 1·976 |
| | | 305·6093 | +505 | 18·526 |
| (5) Beginning of 11th Solar month 305·0850 : | 305·6093 | +505 = 306·114 | 18·526 + 120 (☉'s Eqn.) = 18·664 |
| | | +169 | |
| Add for 12th New moon | 29·5306 | +412 | 1·976 |
| (6) Beginning of 12th Solar month 334·9053 : | 335·1399 | +581 = 335·721 | 20·502 + 169 (☉'s Eqn.) = 20·671 |
| | | +176 | |
| Add for 13th New moon | 29·5306 | +357 | 1·976 |
| (7) End of 12th Solar month 365·25875 : | 364·6705 | +533 = 365·203 | 22·478 + 176 (☉'s Eqn.) = 22·654 |

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*N.B.*—The above is a convenient and concise method of working for *Adhika* and *Kshaya* months.

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From (1) and (2) it follows [applying the rule in foot-note to p. (9) of the Text], that the 7th and 8th new moons were both Kârttika, the first of them being *Adhika*.

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From (3) it follows that the 9th new moon was *Pausha*.

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∴ The new moon between Kârttika and *Pausha*, viz., *Mârgasira* was *kshaya* and it is accordingly noted as such in our Table X.

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From (4) it follows that the 10th new moon was *Mâgha*.

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From (5) it follows that the 11th new moon was *Phālguna*.

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From (6) and (7) it follows that the 12th and 13th new moons were both *Chaitra* the first of them being *adhika*.

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It would appear that by oversight Messrs. Sewell and Dikshit failed to take account of these facts, notwithstanding that Prof. Chhatre had mentioned them.

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A.D. 1963.

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275. Messrs. Sewell and Dikshit, after noting that the last *Kshaya* month before our time was in A.D. 1822, go on to remark: "We are led to suppose that there will be no suppressed month till at earliest A.D. 1944, and possibly not till A.D. 1963".

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There is no reason why the matter should be treated as one for conjecture, since anybody familiar with the present method can calculate that the next *Kshaya* month will be in A.D. 1963, as we have indeed noted in Table X. There will be another in A.D. 1982, as noted in the same Table.