Bulaeus says that the amount of the fee was sometimes left to the generosity of the parents.[705] He can hardly be referring to a common practice. The fourth century was far too business-like for this sort of thing. Most of the teachers who were in a position to do so probably demanded a large fee, like Exsuperius.[706] How far this bargaining went on after the law of Gratian we cannot tell: but the fact that it went on after Vespasian had fixed the salaries shows that it was not necessarily stopped in 376. Much more liberal was the East. Lectures at Antioch were open to all, even to pupils of other rhetors:[707] and sometimes invitations to attend were sent round by the servant of the lecturer.[708] As to the number of the professors appointed little is known. Probably from what Ausonius says there were ten at Bordeaux, six ‘grammatici’ and four ‘rhetores’—the highest number, Jullian thinks, that Bordeaux ever reached. At Constantinople Theodosius appointed in 425 to his special _auditorium_[709] three rhetors and ten grammarians for Latin, five rhetors and ten grammarians for Greek, one professor of philosophy, and two for law. But this is Eastern exuberance. Trèves, the imperial favourite, had only two or three rhetoricians, one Latin grammarian, and one Greek grammarian—a post which could not always be filled.[710] Denk, in remarking that the number of teachers was thus definitely fixed, adds that there is no trace of a principal who gave direction to the work of the students.[711] Now it is true that there was no definite organization, but it seems very probable that the emperors, when they interested themselves in a school and appointed teachers, would have some one at the head of the establishment to facilitate communication between the imperial offices and the school. Moreover, it is a natural and traditional thing the world over for a group of men more or less permanently banded together to have a chief. The Druids had their leader,[712] and among the Persian Magi there was an archimagus. Besides, we have at least one ‘trace’ which Denk does not notice. Eumenius, as head of the Maeniana, was called _moderator_, which looks like an official title. And in the Christian schools it was a common thing to have a head (_primicerius_), as will be shown later.