ASTRONOMY IN ANCIENT NATIONS (the motion of the pole of the orbit being added to or subtracted from the motion of the planet), so that the epícycle is hereby rendered superfluous. The lengths of the radii of these small circles are not given, except in the case of Saturn, where the radius is 3° 3,¹ while the mean pole of the moon is 5° (the inclina- tion of the lunar orbit) distant from the pole of the ecliptic, and the small circle is so exceedingly small as to produce no retrograde motion, which is also the case with the Sun. The periods of the poles of the outer planets are given by the following figures Saturn makes 57 revolutions in 59 years and 1+1 days, in which period the mean pole lags behind 2 revolutions 1+. Jupiter makes 65 revolutions in 71 years, the mean pole lagging behind 6 revolutions. Mars makes 37 revolutions in 79 years and 31+r days, the pole lagging behind 42 revolutions and 31**. 32 In other words, the motion on these small circles are com- pleted in the synodic periods of planets. Similarly, the pole of Venus makes 5 revolutions in the 8 years less 21d+ lagging 1 revo- lutions in one year; and Mercury 145 revolutions in 46 years and 1d". It is curious that Alpetragius alters the order of the planets placing Venus between Mars and the Sun. because the defectus (lagging) of Venus smaller than that of the Sun. He also says that nobody has given any valid reason for accepting the usually assumed order of the planets, and that Ptolemy is wrong in stating that Mercury and Venus are never exactly in a line with the Sun (a remark already made by Geber); and as they shine by their own light they would not spots, if passing between us and the Sun. That their light from the Sun is proved, he thinks, by the fact that they never appear crescent-shaped.* appear as dark do not receive There is no need to dwell any longer on this quaint theory 1. Fol. 16 a. 2. Fol. 25 a. 3. 4. Fol. 21 b, 24 b. 5. "Nam reperimus defectum eius primum minoreth defectu orbis solis et maiorem defectu orbis martis, et sequitur juxta radices nostras ut sit intex eos ambos." Fol. 16 a, 18 a, 19 b. 6 Fol 21 z
