Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/27
For calculation of the length by the Sûrya-Siddhânta the longitude of the sun's apogee is taken as 77° 16′, which was its value in A. D. 1137, a date about the middle of our Tables. Even if its value at our extreme dates, i.e., either in A. D. 300 or 1900, were taken the lengths would be altered by only one pala at most. By the Ârya-Siddhânta the sun's apogee is taken as constantly at 78°.[1]
The average (mean) length in days of solar and lunar months, and of a lunar year is as follows:
| Sûrya-Siddhânta | Modern science | |
| Solar month (1/12 of a sidereal year) | 30.438229707 | 30.438030. |
| Lunar month | 29.530587946 | 29.530588. |
| Lunar year (12 lunations) | 354.36705535 | 354.367056. |
25. Adhika mâsas. Calendar used. A period of twelve lunar months falls short of the solar year by about eleven days, and the Hindus, though they use lunar months, have not disregarded this fact; but in order to bring their year as nearly as possible into accordance with the solar year and the cycle of the seasons they add a lunar month to the lunar year at certain intervals. Such a month is called an adhika or intercalated month. The Indian year is thus either solar or luni-solar. The Muhammadan year of the Hijra is purely lunar, consisting of twelve lunar months, and its initial date therefore recedes about eleven days in each year. In luni-solar calculations the periods used are tithis and lunar months, with intercalated and suppressed months whenever necessary. In solar reckoning solar days and solar months are alone used. In all parts of India luni-solar reckoning is used for most religious purposes, but solar reckoning is used where it is prescribed by the religious authorities. For practical civil purposes solar reckoning is used in Bengal and in the Tamil and Malayalam countries of the Madras Presidency; in all other parts of the country luni-solar reckoning is adopted.
26. True and mean saṅkrântis. Śodhya. When the sun enters one of the signs of the zodiac, as calculated by his mean motion, such an entrance is called a mean saṅkrânti; when he enters it as calculated by his apparent or true motion, such a moment is his apparent or true[3] saṅkrânti. At the present day true saṅkrântis are used for religious as well as for
- ↑ The lengths of months by the Ârya-Siddhânta here given are somewhat different from those given by Warren. But Warren seems to have taken the longitude of the sun's apogee by the Sûrya-Siddhânta in calculating the duration of months by the Ârya-Siddhânta, which is wrong. He seems also to have taken into account the chara.[2] (See his Kâla Saṅkalita, p. 11, art. 3, p. 22, explanation of Table III., line 4; and p. 3 of the Tables). He has used the ayanâṁśa (the uniformly increasing arc between the point of the vernal equinox each year and the fixed point in Aries) which is required for finding the chara in calculating the lengths of months. The chara is not the same at the beginning of any given solar mouth for all places or for all years. Hence it is wrong to use it for general rules and tables. The inaccuracy of Warren's lengths of solar months according to the Sûrya-Siddhânta requires no elaborate proof, for they are practically the same as those given by him according to the Ârya-Siddhânta, and that this cannot be the ease is self-evident to all who have any experience of the two Siddhântas. [S. B. D.]
- ↑ The chara:—"The time of rising of a heavenly body is assumed to take place six hours before it comes to the meridian. Actually this is not the case for any locality not on the equator, and the chara is the correction required in consequence, i.e., the excess or defect from six hours of the time between rising and reaching the meridian. The name is also applied to the celestial arc described in this time."
- ↑ The Sanskrit word for "mean" is madhyama, and that for 'true' or 'apparent' is spashṭa. The words "madhyama" and "spashṭa" are applied to many varieties of time and space; as, for instance, gati (motion), bhôga (longtitude), saṅkrânti, mâna (measure or reckoning) and kâla (time). In the English Nautical Almanac the word "apparent" is used to cover almost all cases where the Sanskrit word spashṭa would be applied, the word 'true' being sometimes, but rarely, used. "Apparent," therefore, is the best word to use in my opinion; and we have adopted it prominently, in spite of the fact that previous writers on Hindu Astronomy have chiefly used the word "true." There is as a fact a little difference in the meaning of the phrases "apparent" and "true," but it is almost unknown to Indian Astronomy, and we have therefore used the two words as synonyms. [S. B. D.]
called Vaiśâkha in Bengal and Sittirai (Chaitra) in the Tamil country, Vaiśâkha being the second month in the south. To avoid confusion, therefore, we use only the sign-names (Mesha, etc.) in framing our rules.