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civil purposes. In the present position of the sun's apogee, the mean Mesha saṅkrânti takes place after the true saṅkrânti, the difference being two days and some ghaṭikâs. This difference is called the śodhya. It differs with different Siddhântas, and is not always the same even by the same authority. We have taken it as 2d. 10 gh. 14 p. 30 vipa. by the Sûrya-Siddhânta, and 2d. 8 gh. 51 p. 15 vipa. by the Ârya-Siddhânta. The corresponding notion in modern European Astronomy is the equation of time. The śodhya is the number of days required by the sun to catch up the equation of time at the vernal equinox.

27. It must be remembered that whenever we use the word "saṅkrânti" alone, (e.g., "the Mesha-saṅkrânti") the apparent and not the mean nirayana saṅkrânti is meant.

28. The beginning of a solar month. Astronomically a solar month may begin, that is a saṅkrânti may occur, at any moment of a day or night; but for practical purposes it would be inconvenient to begin the month at irregular times of the day. Suppose, for example, that a Makara-saṅkrânti occurred 6 hours 5 minutes after sunrise on a certain day, and that two written agreements were passed between two parties, one at 5 hours and another at 7 hours after sunrise. If the month Makara were considered to have commenced at the exact moment of the Makara-saṅkrânti, we should have to record that the first agreement was passed on the last day of the month Dhanus, and the second on the first day of Makara, whereas in fact both were executed on the same civil day. To avoid such confusion, the Hindus always treat the beginning of the solar month as occurring, civilly, at sunrise. Hence a variation in practice.

(1) (a) In Bengal, when a saṅkrânti takes place between sunrise and midnight of a civil day the solar month begins on the following day; and when it occurs after midnight the month begins on the next following, or third, day. If, for example, a saṅkrânti occurs between sunrise and midnight of a Friday, the month begins at sunrise on the next day, Saturday; but if it takes place after midnight of Friday^[1] the month begins at sunrise on the following Sunday. This may be termed the Bengal Rule. (b) In Orissa the solar month of the Amli and Vilayati eras begins civilly on the same day as the saṅkrânti, whether this takes place before midnight or not. This we call the Orissa Rule.

(2) In Southern India there are two rules, (a) One is that when a saṅkrânti takes place after sunrise and before sunset the month begins on the same day, while if it takes place after sunset the month begins on the following day; if, for example, a saṅkrânti occurs on a Friday between sunrise and sunset the month begins on the same day, Friday, but if it takes place at any moment of Friday night after sunset the month begins on Saturday.^[2] (b) By another rule, the day between sunrise and sunset being divided into five parts, if a saṅkrânti takes place within the first three of them the month begins on the same day, otherwise it begins on the following day. Suppose, for example, that a saṅkrânti occurred on a Friday, seven hours after sunrise, and that the length of that day was 12 hours and 30 minutes; then its fifth part was 2 hours 30 minutes, and three of these parts are equal to 7 hours 30 minutes. As the saṅkrânti took place within the first three parts, the month began on the same day, Friday; but if the saṅkrânti had occurred 8 hours after sunrise the month would have begun on Saturday. The latter (b) rule is observed in the North and South Malayâḷam country, and the former (a) in other parts of Southern India where the solar reckoning is used, viz., in the Tamil and Tinnevelly countries.^[3] We call a. the Tamil Rule: b. the Malabar Rule.