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occurs when, in his path on the ecliptic, the sun's centre is at longitude 0°, or precisely on the sidereal fixed starting point—the first point of the first sign Mēsha; the second takes place after the sun has travelled 30°, and so on for the twelve. Their names will be found in col. 5a, Table III., of the Indian Calendar; the duration of each sign and its correspondence with the nakshatras (below, § 112, etc.) are given in Table XXII.[1] The time required for the sun to pass completely from one saṁkrānti to another, or the time during which it remains in one sign, constitutes a saura māsa or solar month . Each saṁkrānti bears the name of the sign whose beginning it marks. The Mēsha saṁkrānti is the beginning point of the solar month Mesha, and so for all.[2]
28. Since the sun travels the uniform distance between saṁkrāntis at varying speed throughout the year, the length of every month, when considered in the light of the sun's true or apparent motion, differs from every other. Both the Ārya and Sūrya Siddhāntas fix the mean length of a solar month, i.e., the month's length as it would be if the sun moved with a velocity that never varied, at 30 d. 10 h. 31 m., the former adding 2 s. and the latter 3.05 s. The lengths of the true months by each are given in tables XVIII.A and XVIII.B below. The definition of apparent, mean, and tropical saṁkrāntis has been given above. Whenever mention is made of a "saṁkrānti" in the present treatise or in the Indian Calendar a true sidereal, or nirayaṇa, saṁkrānti is meant, unless the name is specially otherwise qualified .
29. A saṁkrānti therefore marks, whatever calculation may be adopted, the astronomical beginning point in time of a solar month. This may take place at any moment of a day. The civil beginnings according to local practice are considered below . ("Days of a Civil Month," § 43.) These civil days begin at sunrise, and sunrise is generally taken (always in our Tables) as mean sunrise; but since it is probable that the beginning of the day was always true sunrise, the difference between the two must often be taken into account. This difference depends on the longitude and latitude of the place, not necessarily of the actual place of the inscription, but, as is now well understood, probably the longitude and latitude of the principal centre of life in the neighbourhood, where the almanacks were constructed. It depends also on the equation of time. (See §§ 34–36, pp. 17–20, Ind. Cal.). The most accurate and complete treatise on this subject is by Professor Jacobi in the Epigraphia Indica (Vol II., pp . 487–498.) A Table for applying the equation of time, for converting, that is, mean to apparent time from A.D. 200, is given in Table F. of my Eclipses of the Moon, while Table G. of the same work gives the apparent time of the sun's rising and setting for various latitudes.
30. The time of occurrence of a saṁkrānti, and hence the civil beginning of a solar month, is found by adding the collective duration of the months preceding it (Tables XVIII., XIX., below) to the time of occurrence of the Mēsha saṁkrānti of the year (Table I.). By the true system the duration of true months must be added to the moment of true Mēsha saṁkrānti. By the mean system the duration of mean months must be added to the moment of mean Mēsha saṁkrānti . (Below, "Correction III," § 57.)
The moment of true Mēsha saṁkrānti in all years from A.D. 300 to 1900 is given in Table I. of the Indian Calendar, according to the Ārya Siddhānta throughout and according to the Sūrya Siddhānta after A.D. 1100; also, for the Ārya Siddhānta, from 58 B.C. to A.D. 299, in Table XXXVIII.A. below. Rules for finding the same by the Original Sūrya Siddhānta will be found in § 162 below, and by the Brāhma Siddhānta and Siddhānta Śirōmaṇi in § 167A. (See also §§ 47 to 54.)
31. The Vishuva saṁkrāntis are the two equinoctial ones, Mēsha and Tulā . The solstitial saṁkrāntis are the Uttarāyaṇa (winter-solstice ) and Dakshiṇāyana (summer-solstice) saṁkrāntis.
The Mithuna, Kanyā, Dhanus and Mīna saṁkrāntis are sometimes called the Shaḍaśītimukha saṁkrāntis. (Ind. Ant. XXV., 346, No. 4.)