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 c16: Chapter XI. Sunset
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 c16
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Chapter XI. Sunset
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77. The considerations to which we have introduced the reader in dealing with Sunrise and Laghna will enable him to deal also with sunset, which is only the supplement (in the language of geometry) of sunrise.
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Supposing the sun is at a point of the ecliptic whose tropical longitude is 100°, then we have to consider at sunrise how long, relatively to the mean sun on the equator, the mean sun on the ecliptic takes to rise 100°, and at sunset we have to consider how long, relatively to the mean sun on the equator, the mean sun on the ecliptic takes to fall 80°. [see Sec. 63 (3)]
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78. Accordingly, to determine the moment of sunset by local time, we should take the sum of (1) the correction for equation of time, which is the same or nearly the same as for sunrise, and (2) the correction for tropical longitude, which will be the supplement of the tropical longitude for sunrise. The supplement of an angle is the difference between it and 180°. In our sunrise tables, degrees are expressed as days and by Tables XVII-A and XVII-C, 180° = 184·80 days or in round figures 185 days.
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79. What we have to do, therefore, to determine the second correction for sunset is to find the difference between the day of the solar year under consideration and 185 days, and take the correction for tropical longitude for the day so arrived at. If the solar year we are considering exceeds 185 days, the sign of the tropical longitude for the difference will remain unchanged : otherwise the sign should be reversed. This correction should then be added to the equation of time in order to determine the interval between sunset and 6 p.m. local time, while the total so arrived at should be added again to correction (1) adverted to in sec. 63, *i.e.*, the correction for terrestrial longitude, in order to arrive at the interval between 6 p.m. *Lankâ* time and *local* sunset.
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80. In the absence of any other standard authorities on the subject, we may compare our calculations of sunset for A.D. 1910-11 with those given in the Kumbakonam Mutt Panchângam, edited by Mr. Viśvanâtha Srauti, B.A.
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Latitude 11° N. (Tanjore).
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| Date by European Calendar as well as by Tamil Solar Year Sâdhârana, A.D. 1910. | Day of Solar Year according to Table XIII. | Equation of Time in Seconds by Tab. XIII under Lat. 11° for the day of Solar Year entered in col. 2. | Supplement to Trop. longitude in Days (*i.e.*, difference between col. 2 increased by 20 and 185 days). | Correction for Trop. Longitude acc. to Tab. XIII for the Supplemental day arrived at in column 4 (*sign to be reversed if necessary*). | Sum of Corrections arrived at in columns 3 and 5. | Moment of Sunset according to col. 6. | Sunset according to Mr. Srauti's Panchangam for 1910. |
| | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| | | | | | | | P.M. | P.M. |
| Chittirai 1 (Ap. 13) ... | ... | 1 | - 435" | 164th day | - 22" | - 457" = - 7' | 6-7 | 6-7 |
| Vaikasi 2 (May 15) ... | ... | 32 | - 352" | 133rd day | - 312" | - 664" = - 11' | 6-11 | 6-11 |
| Ani 3 (Je. 16) ... | ... | 65 | - 147" | 100th day | - 986" | - 1133" = - 19' | 6-19 | 6 19 |
| Adi 3 (Jl. 18) ... | ... | 97 | +163" | 68th day | - 1469" | - 1306" = - 22' | 6-22 | 6-23 |
| Avani 4 (Au. 19) ... | ... | 129 | +411" | 36th day | - 1168" | - 757" = - 13' | 6-13 | 6-14 |
| Purattasi 5 (S. 20) ... | ... | 161 | +515" | 4th day | - 144" | + 371" = + 6' | 5-54 | 5-55 |
| Aippasi 6,(O. 22) ... | ... | 192 | +494" | 27th day (212 - 185 = 27) | + 969" | +1468" = +24' | 5-36 | 5-36 |
| Kartigai 8 (N. 23) ... | ... | 224 | +353" | 59th day | +1523" | +1876" = +31' | 5-29 | 5-30 |
| Margali 3 (D. 17) ... | ... | 249 | +140" | 84th day | +1278" | +1418" = +23' | 5-37 | 5-37 |
| Tai 21 (F. 3) A.D. 1911 ... | ... | 296 | - 268" | 133rd day | + 312" | + 44" = + 1' | 5-59 | 6-1 |
| Panguni 2 (Mr. 15) A.D. 1911 ... | ... | 337 | - 421" | 172nd day | + 12" | - 409" = - 7' | 6-7 | 6-8 |
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81. We observe (1) that sufficiently accurate results can be obtained by taking whole days instead of days and fractions of days in columns 2 and 4 *supra*; in other words, it is not necessary to calculate the day of the solar year with exactitude as we did for Problem I under "Laghna", (2) that a positive correction in column 6 re-appears in column 7 as a deduction from 6 p.m., while a negative correction in column 6 re-appears in column 7 as an addition to 6 p.m.
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Supposing a birth took place 2 hours after sunset on 13 April, 1910, the moment of birth would be 6 p.m. + 2 hours + 7' = 8-7 p.m. In this case sunset was 6-7 p.m. On the other hand, if a birth took place 2 hours after sunset on 23 November, 1910, then the correction for sunset being + 31', the local time at which the birth took place would be 6 p.m. + 2 hrs. - 31' = 7-29 p.m. In this case sunset was at 5-29 p.m.