The last clause, which has been left untranslated, offers great difficulty. The commentator Paramesvara takes it as affording a method of expressing still higher numbers by attaching anusvara or visarga to the vowels and using them in nine further varga (and avarga) places. It is doubtful whether the word avarga can be so supplied in the compound. Fleet would translate "in the varga place after the nine" as giving directions for referring a consonant to the nineteenth place. In view of the fact that the plural subject must carry over into this clause Fleet's interpretation seems to be impossible. Fleet suggests as an alternate interpretation the emendation of va to hau. But, as explained above, au refers h to the eighteenth place. It would run to nineteen places only when expressed in digits. There is no reason why such a statement should be made in the rule. Rodet translates (without rendering the word nava), "(separement) ou a un groupe termini par un varga." That is to say, the clause has nothing to do with the expression of numbers beyond the eighteenth place, but merely states that the vowels may be attached to the consonants singly as gara or to a group of consonants as gra, in which latter case it is to be understood as applying to each consonant in the group. So giri or gri and guru or gru. Such, indeed, is Aryabhata's usage, and such a statement is really necessary in order to avoid ambiguity, but the words do not seem to warrant the translation given by Rodet. If the words can mean "at the end of a group," and if nava can be taken with what precedes, Rodet's in-
