for satire and for vivid description, and the gaps in his text are very much to be deplored.
Of those who treat of the Arts and Sciences the grammarians are probably the most numerous. I have renounced the idea of noticing each Irishman or Frank who has left us an Ars, but I would find a place here for mention of two Epistles, separated in time by a full century, which are largely grammatical in subject and epistolary only in form. They serve mainly as displays of their authors' reading. One is by Ermenrich of Ellwangen to Grimald of St Gall (854), the other by Gunzo of Novara to the monks of Reichenau (965) à propos of a monk of St Gall who had rashly criticised his Latin. They are tedious compositions, but have their importance.
The writers on Geography are few. Dicuil, an Irishman (825), draws largely upon ancient sources, but adds something about Iceland and the Faröe Islands that depends upon the observations of compatriots who had been there. The famous voyages of Ohthere and Wulfstan, inserted by Alfred into his Orosius, though they are in the vernacular, must find mention under this head. Other quasi-geographers are the translators of Alexander's letter to Aristotle, and other matter on the Marvels of the East. They probably fall within our period, but the best copies we have of them – Anglo-Saxon versions illustrated with pictures – may be of the eleventh century.
Medicine meant chiefly materia medica, collections of recipes, and spells. The Latin version of Dioscorides, and the recipes and charms current under the names of Apuleius and Sextus Placidus, were prime authorities. Little new work was produced.
No idea of the progress made in Music can be given, but by a specialist: it must suffice here to name Notker, Hoger, and Hucbald of St Amand as the leading exponents.
Astronomy and Mathematics remain. Both were ancillary to church purposes, the settling of the Calendar and especially the determination of Easter. Bede's were the text-books which were perhaps found most useful generally, and that of Helperic of Auxerre (c. 850) had a wide circulation. But we may neglect every name that appears in connexion with Mathematics in favour of that of Gerbert of Aurillac, who died as Pope Sylvester II in 1003. He is the last really outstanding figure. Everything that he wrote and did has distinction, and he demands a somewhat extended notice. Born at Aurillac (Cantal) he spent the years 967-970 in Spain with Hatto, Archbishop of Vich. From 970 to 972 he was with the Emperor: for the next ten years (972-982) he was master of the cathedral school at Rheims, and Richer devotes many pages to telling us what he taught there. In 982 he was made Abbot of Bobbio, the literary treasures of which were no doubt a great attraction to him: in 991 he became Archbishop of Rheims, in 998 of Ravenna. In the following year he passed to the Chair of Peter. His political
