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The eighth part of the day, as cited from the Smrtyarthasara original: smṛtyarthasāra; “The Essence of the Meaning of the Law-books,” a 12th-century manual on religious duties by Madhava A prominent 14th-century scholar and minister in the Vijayanagara Empire who wrote extensively on time-calculation. The specific time for the sacrifice Sanskrit: yāgakāla consists of the fourth quarter of the moon-phase day term: parva; referring to either the Full Moon or New Moon and the first three parts of the first day of the lunar fortnight Sanskrit: pratipadā.
If the junction term: sandhi; the exact astronomical point where one lunar day ends and the next begins of the moon-phase and the first day occurs at or before midday Sanskrit: madhyāhna, the sacrifice is to be performed on that same day. Regarding this, Madhava states that the day is divided into two parts: if the junction occurs after midday, the ritual action follows. In the opinion of Hemadri A famous 13th-century scholar and administrator, if the first day lasts until its fourth quarter on the following day and is joined with the second day Sanskrit: dvitīyā, the rite should be performed on the earlier day. Otherwise, the sacrifice is forbidden on the day of moonrise Sanskrit: candrodaya; often referring to the evening the moon is first visible.
Regarding a junction occurring in the afternoon Sanskrit: aparāhṇa, Madhava states the division occurs at the fourth quarter. The scholar Nrsimha Thakkura A 16th-century authority on ritual law provides this decision: when the junction occurs after the forenoon term: saṅgava; the second of the five parts of the day, roughly 9:00 AM to 11:30 AM but before midday, that Full Moon day Sanskrit: paurṇamāsī is considered "immediately affected" original: sadyah-kāla-viddhā; meaning the ritual must be adjusted because the timing overlaps.
There is a special rule for the New Moon Sanskrit: amā: if the first day of the fortnight lasts for three muhurtas a muhurta is 48 minutes; three muhurtas is 2 hours and 24 minutes into the evening of the second day, then the preparatory rite of adding fuel to the sacred fire term: anvādhāna must be performed on the fourteenth day Sanskrit: caturdaśī; the day before the New Moon.
For the followers of the Vajasaneyi school a specific branch of the White Yajur Veda, the fuel-adding rite occurs on the day of the junction, and the sacrifice itself is performed on the following day. This decision regarding junctions is explained in the Madana Parijata An extensive 14th-century legal digest commissioned by King Madanapala. It begins by saying, "This has been said..."