The old dative +dhai+ has been preserved to us in one form only, which for that reason is all the more valuable and important, offering the key to the mysterious Greek infinitives in θαι, I mean +vayodhái+, which occurs twice in the Rig-Veda, X. 55, 1, and X. 67, 11. The importance of this relic would have been perceived long ago, if there had not been some uncertainty as to whether such a form really existed in the Veda. By some accident or other, Professor Aufrecht had printed in both passages +vayodhaiḥ+, instead of +vayodhai+. But for this, no one, I believe, would have doubted that in this form +vayodhai+ we have not only the most valuable prototype of the Greek infinitives in (σ)θαι, but at the same time their full explanation. +Vayodhai+ stands for +vayas-dhai+, in which composition the first part +vayas+ is a neuter base in +as+, the second a dative of the auxiliary verb +dhâ+, used as a substantive. If, therefore, we find corresponding to +vayodhai+ a Greek infinitive βέεσθαι, we must divide it into βέεσ-θαι, as we divide ψεύδεσθαι into ψεύδεσ-θαι, and translate it literally by “to do lying.” It has been common to identify Greek infinitives in σθαι with corresponding Sanskrit forms ending in +dhyai+. No doubt these forms in +dhyai+ are much more frequent than forms in +dhai+, but as we can only take them as old datives of substantives in +dhi+, it would be difficult to identify the two. The Sanskrit +dhy+ appears, no doubt, in Greek, as σσ, +dh+ being represented by the surd θ, and then assibilated by _y_; but we could hardly attempt to explain σθ = θy, because σδ = ζ = δy. Therefore, unless we are prepared to see with Bopp in the σ before θ, in this and similar forms, a remnant of the reflexive pronoun, nothing remains but to accept the explanation offered by the Vedic +vayodhai+, and to separate ψεύδεσθαι into ψεύδεσ-θαι lying to do. That this grammatical compound, if once found successful, should have been repeated in other tenses, giving us not only γράφεσ-θαι, but γράψεσ-θαι, γράψασ-θαι, and even γραφθήσεσ-θαι, is no more than what we may see again and again in the grammatical development of ancient and modern languages. Some scholars have objected on the same ground to Bopp’s explanation of _ama-mini_, as the nom. plur. of a participle, because they think it impossible to look upon _amemini_, _amabâmini_, amaremini, _amabimini_ as participial formations. But if a mould is once made in language, it is used again and again, and little account is taken of its original intention. If we object to γράψεσ-θαι, why not to κελευ-σέ-μεναι or τεθνά-μεναι or μιχθή-μεναι? In Sanskrit, too, we should hesitate to form a compound of a modified verbal base, such as +pṛṇa+, with +dhi+, doing; yet as the Sanskrit ear was accustomed to +yajadhyai+ from +yaja+, +gamadhyai+ from +gama+, it did not protest against +pṛṇadhyai+, +vâvṛdhadhyai+, etc. HISTORICAL IMPORTANCE OF THESE GRAMMATICAL FORMS.