The Long Syllabic R, and Where It Actually Occurs

Sanskrit uses this vowel in a narrow and well defined set of places. Its principal home is the genitive plural of stems ending in r, where an ending beginning with a nasal lengthens the stem vowel, so the forms meaning of the fathers, of the mothers and of the makers all carry it. Outside that pattern it is very nearly absent from the working vocabulary, and a text of considerable length can pass without any occasion to write it. The grammarians nonetheless treat it as a full member of the vowel table, with the same standing as a and i, because the analysis is built on pairs of short and long and the pairing is what makes the table teachable.

That is the honest account of the letter and it is worth stating plainly rather than dressing up. A sign that writes one grammatical ending is still doing real work, and the ending in question is common enough in liturgical and legal formulas that a reader of inscriptions will meet it. But the letter is in the order because of the shape of the analysis, not because of the frequency of the sound, and the Indian tradition was explicit about the difference. A complete pattern can be recited; an incomplete one has to be memorised as a list of exceptions.