Dashami

Dashami is the tenth tithi of the bright fortnight, a Purna or full tithi in the fivefold grouping and so read as stable and favourable. Its presiding deity is traditionally Yama, lord of dharma and death, giving the day a note of righteous order. Its best-known festival is Vijayadashami, also called Dussehra, kept on the tenth tithi of the bright fortnight of Ashvin: it celebrates the victory of good over evil, marking both Rama's defeat of Ravana and, in the Goddess tradition, Durga's slaying of the buffalo-demon. The waxing Moon by now is broadly gibbous. In the panchanga Dashami is a day for successful completion and auspicious action. These are the conventions of the calendar and its festivals.

Vijayadashami's placement on the tenth tithi immediately after the nine nights of Navaratri makes the pairing of the two observances structurally significant: the goddess is worshipped for nine tithis corresponding to her nine forms, the Navadurga, and the victory is proclaimed on the tenth, so the festival calendar itself enacts the numerical logic of the tithi sequence. Yama's association with the tenth tithi as lord of dharma rather than purely of death reflects the wider Puranic understanding of Yama as an upholder of cosmic and moral order, a role distinct from, though related to, his more familiar function as the god who receives the dead, and this dharmic emphasis is part of why the tenth tithi carries a note of righteous triumph rather than of mourning.

The tithi is the oldest of the five limbs of the panchanga and the least intuitive, because it is defined by an angle in the sky and not by a sunrise. Dashami occupies the arc from 108 to 120 degrees of that separation. Because the Moon travels an elliptical orbit its angular speed is not constant, so that twelve degree arc is crossed in anywhere from roughly nineteen to roughly twenty six hours. The convention that resolves this is simple and consequential: the civil day takes the name of the tithi that is running at sunrise. A tithi shorter than the interval between two sunrises can therefore be skipped entirely, which the tradition calls a kshaya tithi, and one longer than that interval can carry its name over two civil days, an adhika or vriddhi tithi. Both occur in the ordinary course of a year, and both are why an observance can appear on two dates in the same almanac.

Each tithi is halved again, and each half carries a karana, so the first half of Dashami carries Taitila, the fourth, and the second Gara, the fifth. Seven of the eleven karanas repeat, cycling eight times through the month, while four are fixed to particular half tithis at the month's opening and close.

The Moon is waxing through this arc, setting later each evening and carrying about 70 per cent of the disc lit. That figure is a consequence of the definition rather than an observation added to it: elongation fixes the phase, so naming the tithi already names how much of the disc is lit.