the second; from the second to the third, four; from the third to the fourth, four again; five from the fourth to the fifth; and from the fifth to the pole, six. On these five circles he placed obliquely the circles that the Greeks call loxos or zoe, the Latins obliques or vitalis (the zodiac) because it contained the figures of the animals ascribed to the planets. On the inside of this oblique circle he figured with an extraordinary art the orbits traversed by the planets, whose paths and heights he demonstrated perfectly to his pupils, as well as their respective distances. Richer wrote about another of Gerbert's last armillary spheres, which had sighting tubes fixed on the axis of the hollow sphere that could observe the constellations, the forms of which he hung on iron and copper wires. This armillary sphere was also described by Gerbert in a letter to his colleague Constantine. Gerbert instructed Constantine that, if doubtful of the position of the pole star, he should fix the sighting tube of the armillary sphere into position to view the star he suspected was it, and if the star did not move out of sight, it was thus the pole star. Furthermore, Gerbert instructed Constantine that the north pole could be measured with the upper and lower sighting tubes, the Arctic Circle through another tube, the Tropic of Cancer through another tube, the equator through another tube, and the Tropic of Capricorn through another tube. Ecclesiastical career In 969, Borrell II made a pilgrimage to Rome, taking Gerbert with him. There Gerbert met Pope John XIII and Emperor Otto I. The pope persuaded Otto I to employ Gerbert as a tutor for his young son, Otto II. Some years later, Otto I gave Gerbert leave to study at the cathedral school of Rheims where he was soon appointed a teacher by Archbishop Adalberon. When Otto II became sole emperor in 973, he appointed Gerbert the abbot of the monastery of Bobbio and also appointed him as count of the district, but the abbey had been ruined by previous abbots, and Gerbert soon returned to Rheims. After the death of Otto II in 983, Gerbert became involved in the politics of his time. In 985, with the support of his archbishop, he opposed King Lothair of France's attempt to take Lorraine from Emperor Otto III by supporting Hugh Capet.