O in the Grammar, and What Is Not Claimed for It

Away from Om, the letter behaves as an ordinary product of the strengthening ladder and of sandhi. It is the first strengthening of u, standing to that vowel as e stands to i, and it therefore appears throughout derived vocabulary built on roots with a labial vowel. It also arises at word joins wherever a word ending in a meets a word beginning with u, so a recited passage shows it where the separated words had no such vowel.

The rules are stated in Panini's grammar in the compressed form that the Shivasutras make possible, and they apply inside words and across word boundaries alike. It is worth saying plainly what this atlas does not assert for the letter. Sanskrit does not assign individual numerical values to its letters in the way Hebrew does under gematria or Greek under isopsephy, and no such value is claimed here. Indian traditions do have systems that convert letters into numbers, the katapayadi scheme used by astronomers and by musicians being the best known, but that scheme assigns values to consonants by their position in the vargas and treats a vowel standing alone as carrying none; it is a separate subject from the varnamala and would need its own sourcing. What is recorded for o is its place in the series, its articulation and length, its role in the written form of Om, and its membership of the fifty-letter garland the Tantric traditions count.