Niṣkramaṇa — the first going out
The popular claimA child is shown the Sun in the fourth month, and the texts give the words.
Some rites carry more than they were built for. Niṣkramaṇa carries exactly what it says: a child, carried outside, shown the sky.
What the text gives
Pāraskara places it in the fourth month after birth. The child is bathed and dressed; the father, or both parents, carry it out of the house at a time when the Sun is visible; and the child is turned to face the Sun while a verse is recited — the Ṛgvedic tac cakṣur devahitam, "that eye, established by the gods, rising in the east", the verse to the Sun as the eye of the world. Manu gives the same month. Some sūtras add the Moon: the child is shown the Moon on a night of the same month with a second verse, and the rite is then called candra-darśana.
That is all of it. There is no fire. There is no priest. The sūtra does not even insist on a particular day within the month, though the muhūrta treatises later supplied one — a nakṣatra from the gentle group, an afternoon rather than a morning, a fixed rising sign.
Why the fourth month
The sūtras do not explain, but the reasoning is visible. The first three months were the period of the household's sūtaka, its ritual seclusion after a birth, and the child in that period stayed in. The fourth month is the first the child is old enough to be outside safely and the first the household is back in ordinary time. The rite marks both: the child's readiness and the family's return. Cūḍākaraṇa and Annaprāśana follow at the six-month and one-year marks for the same kind of reason — each is placed at the point where the child can bear the next thing.
The verse
The Sun verse is Ṛgveda 1.115.1. It is worth translating, because it is not a prayer for anything: The brilliant face of the gods has risen, the eye of Mitra, Varuṇa and Agni; it has filled heaven and earth and the space between. The Sun is the breath of what moves and what stands still. The child is shown the Sun and told, in effect, what it is. Nothing is asked. A rite that consists of pointing at something and naming it truly is a rare thing to find in a manual, and this one is that.
The day, if one is chosen
The sūtra gives a month and nothing finer. The Muhūrta Cintāmaṇi, asked for a day, adds the usual layer: a nakṣatra from the gentle group — Mṛgaśira, Puṣya, Hasta, Citrā, Svātī, Anurādhā, Śravaṇa, Revatī and the Uttarās — the third, fifth, seventh, tenth, eleventh or thirteenth tithi, a weekday other than Tuesday or Saturday, and a fixed or dual sign rising. It also asks that the Sun not be eclipsed or the sky overcast, which is less a rule than common sense for a rite whose point is to see the Sun. This site's Best Date tool applies the same table if a family wants a computed day; most simply take a clear afternoon in the fourth month, which the sūtra itself would accept.
What survived
The first outing survives everywhere, mostly without the name and without the verse. In the north, the sūraj dikhānā — showing the Sun — is often the family's own word for it; in Bengal the first outing is sometimes combined with a visit to a temple; in the south the child's first temple visit at the end of the third month is the same rite under the temple's roof. The verse has mostly gone, and its going is a real loss, because the verse is the only part that says why.
What this page does not say
It does not say that a child kept in through the fourth month is harmed, or that showing the Sun on the wrong nakṣatra undoes anything. The rite is a child carried outside and told what the Sun is. That is the whole of it, and it is enough.
Source — Paraskara Grihyasutra 1.17 on Nishkramana in the fourth month; the Manusmriti 2.34 on the timing; the Yajnavalkya Smriti on the sequence; the Grihyasutra mantras to Surya and Chandra
Every claim on this site names its source, and every calculator shows its arithmetic.