A student at Oxford would become a master after graduating from a seven year course of study of the seven liberal arts: [grammar, rhetoric (the source of law), Aristotelian logic (which differentiates the true from the false), arithmetic, including fractions and ratios, (the foundation of order), geometry, including methods of finding the length of lines, the area of surfaces, and thevolume of solids, (the science of measurement), astronomy (the most noble of the sciences because it is connected with divinity and theology), music, and Aristotle's philosophy of physics, metaphysics, and ethics; and then lecturing and leading disputations for two years. He also had to write a thesis on some chosen subject and defend it against the faculty. A Master's degree gave one the right to teach. Further study for four years led to a doctorate in one of the professions: theology and canon or civil law. There were about 1,500 students in Oxford. They drank, played dice, quarreled a lot and begged at street corners. There were mob fights between students from the north and students from the south and between students and townsmen. But when the mayor of Oxford hanged two students accused of being involved in the killing of a townswoman, many masters and students left for Cambridge. In 1214, a charter created the office of Chancellor of the university at Oxford. He was responsible for law and order and, through his court, could fine, imprison, and excommunicate offenders and expel undesirables such as prostitutes from the town. He had authority over all crimes involving scholars, except murder and mayhem. The Chancellor summoned and presided over meetings of the masters and came to be elected by indirect vote by the masters who had schools, usually no more than a room or hall with a central hearth which was hired for lectures. Students paid for meals there. Corners of the room were often partitioned off for private study. At night, some students slept on the straw on the floor. Six hours of sleep were considered sufficient. In 1221 the Friars established their chief school at Oxford. They were bound by oaths of poverty, obedience, and chastity, but were not confined within the walls of a monastery. They walked barefoot from place to lace preaching. They begged for their food and lodgings. They replaced monks, who had become self- indulgent, as the most vital spiritual force among the people. In 1231, the King ordered that every student must have his name on the roll of a master and the masters had to keep a list of those attending his lectures.