We may now return to the chronological interpretation, and first let us note the light which the _Dionysalexandros_ numeral throws upon the situation. It is significant that this number is not incorporated within the hypothesis but stood at the top of the last column and had doubtless appeared also at the beginning of the hypothesis (now lost). In my opinion this was the original form of such a notice and shows why in the fuller form of statement found elsewhere a different verb is employed in each case—λέλεκται, ἔστι, ἐποιήθη, and ἔγραψεν. When Aristophanes of Byzantium, or whoever was responsible for the change, transferred these items from the heading and made them integral parts of the hypothesis, finding no verb in the original version before him and resting under the necessity of now using one, he did not deem it essential to paraphrase the information always in the same way but, as was natural, employed now one expression and now another. If it be true that the original function of the numerals was as we find it in the Cratinus hypothesis, only one explanation is possible—it was a device for the convenience of some library, probably that at Alexandria. If so, every play in the collection would bear a number and these numbers would run consecutively for each author. In other words if any play were not preserved in the library, that fact would not be indicated by an unoccupied number being left as a gap in the enumeration. Of course it is conceivable that the basis of arrangement was purely arbitrary and even varied with each author, and in fact there has been a distinct tendency among recent authorities to accept some such pessimistic conclusion. But it is more probable, until the contrary be proved, that some rational system (alphabetical, chronological, etc.) was employed and employed consistently.