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 c7: Chapter II. Fixing the Moment of Mean New Moon
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 c7
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Chapter II. Fixing the Moment of Mean New Moon
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7. At the first moment of K.Y. 0, according to the Sûrya Siddhânta, the sun and moon had the same mean longitude, that is, the moon was *new* at that instant. At the first moment of 1 K.Y., 365·258756484 days would have passed, that is 12 synodical months, and in addition 10·891701134 days. That is, at the first moment of K.Y. 1, the moon was not new as she was at the first moment of K.Y. 0, but she was 10·89170 days old: and the first mean new moon in K.Y. 1 occurred on 29·530587946 *minus* 10·891701134 days = 18·638886812 days after the commencement of K.Y. 1. In this way in every Hindu year the first mean new moon would occur 18·63889 days later than in the previous year. In the year K.Y. 2 a mean new moon occurred 2 × 18·63889 days = 37·27778 days later than the commencement of the year, but as this period exceeds a synodical month, the *first* mean new moon in K.Y. 2 really occurred 37·27778 less 29·53059, that is, 7·74719 days after the commencement of the year. The day of occurrence of the first mean new moon in each successive year after 0 K.Y. is given in Table VII, and we see from that table that in 100 K.Y. the first mean new moon occurred 3·46164 days after the commencement of the year. We follow the table through 200, 300, etc., years, till we find that in 3000 K.Y. the first mean new moon occurred 15·25746 days after the commencement of the solar year. For 3101 K.Y. (or 1 B.C.) we reckon the time of occurrence of the first mean new moon thus:—
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∗ The Sodhya should, properly speaking, be applied to every year, including year 0 Kaliyuga. The point should be borne in mind when calculating solar dates and tithis in any year. B.C. The nature of the correction called Sodhya is explained in Sec. 66.
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| | | | | | Days. |
| For 3000 years | ... | ... | ... | ... | 15·25746 |
| For 100 years | ... | ... | ... | ... | 3·46164 |
| For 1 year | ... | ... | ... | ... | 18·63889 |
| | | | | | 37·35799 |
| Deduct 1 completed synodical month | ... | ... | 29·53059 |
| Remainder | ... | 7·82740 |
| Add the Sodhya which causes the solar year to commence 2·1707 days earlier than it does by mean computation (*vide* Sec. 66 infra) | ... | + 2·1707 |
| Occurrence of first mean new moon in K.Y. 3101 (1 B.C.) | ... | ... | 9·99810 days. |
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That is, in 1 B.C., the first mean new moon of the Hindu solar year occurred almost exactly 10 days (properly 10 days less ·0019 of a day) after the commencement of the solar year.
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8. From 1 B.C. we can follow the occurrence of the first mean new moon in each successive year according to the Tables VI and VII, the figures in which have merely to be added up suitably for each year. Thus if we require the date of the first mean new moon in the current solar year K.Y. 5011, we proceed according to the tables:—
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| For K.Y. 5001, | 16·70809 days. | (Tab. VI). |
| For 10 years, | 9·20534 " | (Tab. VII). |
| For K.Y. 5011, | 25·91343 " | |
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That is, the first mean new moon in the year A.D. 1910-11, K.Y. 5011, occurs 25·91343 days after the commencement of the solar year, and as the solar year itself commences, as we may see from other columns of the same tables, on Ap. 12·62041 +·58756 *i.e.*, on April 13·20797 it follows that the addition of 25·91343 days, or 39·12140 days from 1 April, in other words 9·12140 days in May 1910, will give us the time of occurrence of the first mean new moon in K.Y. 5011. We may, if we like, convert the decimal places into ghaṭikas and palas or hours and minutes, according to Table XIX or XX, and we shall have as the result, 9th May 1910, 7 ghaṭikas and 17 palas or 2 hours and 55 minutes. This is the time of occurrence of mean new moon. About the actual ending moment of this or any other new moon tithi, we shall learn presently.
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*N.B.*—For the meaning of ghaṭika and pala, See Sec. 130 infra.