without exception, and that children of all ranks, both noble and servile, should be received into them. At the same time the larger and more important monasteries were to open major schools, in which mathematics, astronomy, arithmetic, geography, music, rhetoric, and dialectics were taught; and these again were of two descriptions.[83] Some were interior, or claustral, intended only for the junior monks, while others were exterior, or public, and intended for pupils as well secular as ecclesiastic. Some monk, qualified by his learning, was appointed scholasticus, and if none such were to be found in the community, it was not an uncommon practice to invite a monk from some other religious house to take charge of the school. A claustral and an exterior school often existed attached to the same monastery or cathedral, governed by separate masters, the scholars of the claustral school forming part of the community, while those of the exterior school, though subject to a certain claustral discipline, did not follow the same religious exercises. Lay students were received in these exterior schools, and that far more extensively than is commonly supposed, most popular writers having represented the monastic schools as exclusively intended for those in training for the religious life, thus confusing together the interior and exterior schools. Public schools of this kind were erected at Fulda, St. Gall’s, Tours, Hirsauge, Hirsfield, Gorze, Fleury, L’Isle Barbe, Fontanelles, and Ferrières, as well as at many other monasteries and cathedrals, a list of which is given by Mabillon.[84] Bulæus, indeed, endeavours to show that Charlemagne limited the studies of the ecclesiastical schools to grammar and sacred learning, and only permitted the monasteries and episcopal churches to retain the _minor_ schools, “from the clear view that a variety of sciences, sacred and profane, is inconsistent with the profession of ascetics.” He even ventures to put forth the notion that the higher schools were confined to certain central spots, such as Pavia, Bologna, and Paris. But Bulæus wrote with an object, which was to magnify his university at the expense of the monastic schools. We ask ourselves with surprise where he could have found evidence even for the existence of any schools at all at Paris and Bologna in the reign of Charlemagne?[85] And as to limiting the monastics to minor schools, it may be safely affirmed that the idea of limitation of any kind was the very last that ever suggested itself to the mind of the emperor. As Theodulph of Orleans says, he did nothing all his life but urge forward his monks and bishops in the pursuit of learning. During the whole Carlovingian period the schools of most repute were certainly not those of Bologna, Paris, and Pavia. They were the episcopal and monastic schools of Tours, Fulda, Rheims, St. Gall, and Hirsfield, the teachers of which were all either monks or canons. The ordinance