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 each occasion, and would in course of time recede entirely through the solar year, as it does in the Mahommedan calendar. The

Hindus prevent that in the following manner. The length of the Hindu astronomical solar month, measured by the saṁkrāntis of the sun, its successive entrances into the signs of the zodiac, ranges, in accordance with periodical variations in the speed of the sun, from about 29 days 7 hrs. 38 min. up to about 31 days 15 hrs. 28 min. The length of the amānta or synodic lunar month ranges, in accordance with periodical variations in the speed of the moon and the sun, from about 29 days 19 hrs. 30 min. down to about 29 days 7 hrs. 20 min. Consequently, it happens from time to time that there are two new-moon conjunctions, so that two lunations begin, in one astronomical solar month, between two saṁkrāntis of the sun, while the sun is in one and the same sign of the zodiac, and there is no saṁkrānti in the lunation ending with the second new-moon: when this is the case, there are two lunations to which the same name is applicable, and so there is an additional or intercalated month, in the sense that a name is repeated: thus, when two new-moons occur while the sun is in Mēsha, the lunation ending with the first of them, during which the sun has entered Mēsha, is Chaitra; the next lunation, in which there is no saṁkrānti, is Vāiśākha, because it begins when the sun is in Mēsha; and the next lunation after that is again Vaiśākha, for the same reason, and also because the sun enters Vṛishabha in the course of it: in these circumstances, the first of the two Vaiśākhas is called Adhika-Vaiśākha, “the additional or intercalated Vaiśākha,” and the second is called simply Vaiśākha, or sometimes Nija-Vaiśākha, “the natural Vaiśākha.” On the other hand, it occasionally happens, in an autumn or winter month, that there are two saṁkrāntis of the sun in one and the same amānta or synodic lunar month, between two new-moon conjunctions, so that no lunation begins between the two saṁkrāntis: when this is the case, there is one lunation to which two names are applicable, and there is a suppressed month, in the sense that a name is omitted: thus, if the sun enters both Dhanus and Makara during one synodic lunation, that lunation is Mārgaśira, because the sun was in Vṛiśchika at the first moment of it and enters Dhanus in the course of it; the next lunation is Māgha, because the sun is in Makara by the time when it begins and will enter Kumbha in the course of it; and the name Pausha, between Mārgaśira and Māgha, is omitted. When a month is thus suppressed, there is always one intercalated month, and sometimes two, in the same Chaitrādi lunar year, so that the lunar year never contains less than twelve months, and from time to time consists of thirteen months. There are normally seven intercalated months, rising to eight when a month is suppressed, in 19 solar years, which equal very nearly 235 lunations; and there is never less than one year without an intercalated month between two years with intercalated months, except when there is only one such month in a year in which a month is suppressed; then there is always an intercalated month in the next year also. The suppression of a month takes place at intervals of 19 years and upwards, regarding which no definite statement can conveniently be made here. It may be added that an intercalated Chaitra or Kārttika takes the place of the ordinary month as the first month of the year; an intercalated month is not rejected for that purpose, though it is tabooed from the religious and auspicious points of view.

The manner in which this arrangement of intercalated and suppressed months works out, so as to prevent the beginning of the Chaitrādi lunar year departing far from the beginning of the Mēshādi solar year, may be illustrated as follows. In 1815 the Mēsha-saṁkrānti occurred on 11th April; and the first civil day of the Chaitrādi year was 10th April. In 1816 and 1817 the first civil day of the Chaitrādi year fell back to 29th March and 18th March. In 1817, however, there was an intercalated month, Śrāvaṇa; with the result that in 1818 the first civil day of the Chaitrādi year advanced to 6th April. And, after various shiftings of the same kind—including in 1822 an intercalation of Āśvina and a suppression of Pausha, followed in 1823, when the first civil day of the Chaitrādi year had fallen back to 13th March, by an intercalation of Chaitra itself—in 1834, when the Mēsha-saṁkrānti occurred again on 11th April, the first civil day of the Chaitrādi year was again 10th April.

The lunar month is divided into two fortnights (paksha), called bright and dark, or, in Indian terms, śukla or śuddha, śudi, sudi, and kṛishṇa or bahula, badi, vadi: the bright fortnight, śukla-paksha, is the period of the waxing moon, ending at the full-moon; the dark fortnight, kṛishṇa-paksha,

is the period of the waning moon, ending at the new-moon. In the amānta or śuklādi month, the bright fortnight precedes the dark; in the pūrṇimānta or kṛishṇādi month, the dark fortnight comes first; and the result is that, whereas, for instance, the bright fortnight of Chaitra is the same period of time throughout India, the preceding dark fortnight is known in Northern India as the dark fortnight of Chaitra, but in Southern India as the dark fortnight of Phālguna. This, however, does not affect the period covered by the lunar year; the Chaitrādi and Kārttikādi years begin everywhere with the bright fortnight of Chaitra and Kārttika respectively; simply, by the amānta system the dark fortnights of Chaitra and Kārttika are the second fortnights, and by the pūrṇimānta system they are the last fortnights, of the years. Like the month, the fortnight begins for religious purposes with its first lunar day, and for civil purposes with its first civil day.

The lunar fortnights are divided each into fifteen tithis or lunar days. The tithi is the time in which the moon increases her distance from the sun round the circle by twelve degrees; and the almanacs show each tithi by its ending-time; that is, by the moment, expressed in ghaṭikās and palas, after

sunrise, at which the moon completes that distance. In accordance with that, the tithi is usually used and cited with the weekday on which it ends; but there are special rules regarding certain rites, festivals, &c., which sometimes require the tithi to be used and cited with the weekday on which it begins or is current at a particular time. The first tithi of each fortnight begins immediately after the moment of new-moon and full-moon respectively; the last tithi ends at the moment of full-moon and new-moon. The tithis are primarily denoted by the numbers 1, 2, 3, &c., for each fortnight; but, while the full-moon tithi is always numbered 15, the new-moon tithi is generally numbered 30, even where the pūrṇimānta month is used. The tithis may be cited either by their figures or by the Sanskṛit ordinal words prathamā, “first,” dvitīyā, “second,” &c., or corruptions of them. But usually the first tithi of either fortnight is cited by the term pratipad, pratipadā, and the new-moon and full-moon tithis are cited by the terms amāvāsyā and pūrṇimā; or here, again, corruptions of the Sanskṛit terms are used. And special names are sometimes prefixed to the numbers of the tithis, according to the rites, festivals, &c., prescribed for them, or events or merits assigned to them: for instance, Vaiśākha śukla 3 is Akshaya or Akshayya-tṛitīyā, the third tithi which ensures permanence to acts performed on it; Bhādrapada śukla 4 is Gaṇēsa-chaturthī, the fourth tithi dedicated to the worship of the god Gaṇēśa, Gaṇapati, and the amānta Bhādrapada or pūrṇimānta Āśvina kṛishṇa 13 is Kaliyugādi-trayōdaśī, as being regarded (for some reason which is not apparent) as the anniversary of the beginning of the Kaliyuga, the present Age. The first tithi of the year is styled Saṁvatsara-pratipadā, which term answers closely to our “New Year’s Day.”

The civil days of the lunar month begin, like those of the solar month, at sunrise, and bear in the same way the names of the weekdays. But they are numbered in a different manner; fortnight by fortnight and according to the tithis. The general rule is that the civil day takes the number of the

tithi which is current at its sunrise. And the results are as follows. As the motions of the sun and the moon vary periodically, a tithi is of variable length, ranging, according to the Hindu calculations, from 21 hrs. 34 min. 24 sec. to 26 hrs. 6 min. 24 sec.: it may, therefore, be either shorter or longer than a civil day, the duration of which is practically 24 hours (one minute, roughly, more or less, according to the time of the year). A tithi may end at any moment during the civil day; and ordinarily it ends on the civil day after that on which it begins, and covers only one sunrise and gives its number to the day on which it ends. It may, however, begin on