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ends on the following day, that is it touches two successive civil days. It will be seen, however, from its length (Art. 7 above) that a tithi may sometimes begin and end within the limits of the same natural day; while sometimes on the contrary it touches three natural days, occupying the whole of one and parts of the two on each side of it.

A tithi on which the sun does not rise is expunged. It has sustained a diminution or loss (kshaya), and is called a kshaya tithi, On the other hand, a tithi on which the sun rises twice is repeated. It has sustained an increase (vṛiddhi), and is called an adhika, or added, tithi. Thus, for example, in the pañchâṅg extract given above (Art. 30) there is no sunrise during kṛishṇa saptamî (7th), and it is therefore expunged. Kṛishṇa shashṭhî (6th) was current at sunrise on Friday, for it ended 16 palas after sunrise; while kṛishṇa saptamî began 16 palas after that sunrise and ended before the next sunrise; and kṛishṇa ashtami (8th) is current at sunrise on the Saturday. The first day is therefore named civilly the (6th) shashṭhî, Friday, and the second is named (8th) ashtami, Saturday; while no day is left for the saptamî, and it has necessarily to be expunged altogether, though, strictly speaking, it was current for a large portion of that Friday. On the other hand, there are two sunrises on Bhâdrapada śukla trayôdaśî (śukla 13th), and that tithi is therefore repeated. It commenced after 56 gh. 44. pa. on Tuesday, i.e., in European reckoning about 4.20 a.m. on the Wednesday morning, was current on the whole of Wednesday, and ended on Thursday at 1 gh. 23 pa. after sunrise, or about 6.33 am. It therefore touched the Tuesday (reckoned from sunrise to sunrise) the Wednesday and the Thursday; two natural civil days began on it; two civil days, Wednesday and Thursday, bear its numeral (13); and therefore it is said to be repeated.^[1]

In the case of an expunged tithi the day on which it begins and ends is its week-day. In the case of a repeated tithi both the days at whose sunrise it is current are its week-days.

A clue for finding when a tithi is probably repeated or expunged is given in Art. 142.

Generally there are thirteen expunctions (kshayas) and seven repetitions (vṛiddhis) of tithis in twelve lunar months.

The day on which no tithi ends, or on which two tithis end, is regarded as inauspicious. In the pañchâṅg extract above (Art. 30) Bhâdrapada śukla trayôdaśî Wednesday, and Bhâdrapada kṛishṇa shashṭhî, Friday (on which the saptamî was expunged), were therefore inauspicious.

33. It will be seen from the above that it is an important problem with regard to the Indian mode of reckoning time to ascertain what tithi, nakshatra, yoga, or karaṇa was current at sunrise on any day, and when it began and ended. Our work solves this problem in all cases.

34. Variation on account of longitude. The moment of time when the distance between the sun and moon amounts to 12, or any multiple of 12, degrees, or, in other words, the moment of time when a tithi ends, is the same for all places on the earth's surface; and this also applies to nakshatras, yogas, and karaṇas. But the moment of sunrise of course varies with the locality, and therefore the ending moments of divisions of time such as tithis, when referred to sunrise, differ at different places. For instance, the tithi Bhâdrapada śukla pûrṇimâ (see above Art. 30) ended at Poona at 8 gh. 11 pa. after sunrise, or about 9.16 am. At a place where the sun rose 1 gh. earlier than it does at Poona the tithi would evidently have ended one ghaṭikâ later, or at g gh. 11 pa. after sunrise, or at about 9.40 a.m. On the other hand, at a place where