(3) In the Odyssey, Calypso directs Odysseus, in accordance with Phoenician rules for navigating the Mediterranean, to keep the Great Bear “ever on the left as he traversed the deep” when sailing from the pillars of Hercules (Gibraltar) to Corfu. Yet such a course taken now would land the traveller in Africa. Odysseus is said in his voyage in springtime to have seen the Pleiades and Arcturus setting late, which seemed to early commentators a proof of Homer’s inaccuracy. Likewise Homer, both in the _Odyssey_[2] (v. 272-5) and in the _Iliad_ (xviii. 489), asserts that the Great Bear never set in those latitudes. Now it has been found that the precession of the equinoxes explains all these puzzles; shows that in springtime on the Mediterranean the Bear was just above the horizon, near the sea but not touching it, between 750 B.C. and 1000 B.C.; and fixes the date of the poems, thus confirming other evidence, and establishing Homer’s character for accuracy.[3] (4) The orientation of Egyptian temples and Druidical stones is such that possibly they were so placed as to assist in the observation of the heliacal risings[4] of certain stars. If the star were known, this would give an approximate date. Up to the present the results of these investigations are far from being conclusive. Ptolemy (130 A.D.) wrote the Suntaxis, or Almagest, which includes a cyclopedia of astronomy, containing a summary of knowledge at that date. We have no evidence beyond his own statement that he was a practical observer. He theorised on the planetary motions, and held that the earth is fixed in the centre of the universe. He adopted the excentric and equant of Hipparchus to explain the unequal motions of the sun and moon. He adopted the epicycles and deferents which had been used by Apollonius and others to explain the retrograde motions of the planets. We, who know that the earth revolves round the sun once in a year, can understand that the apparent motion of a planet is only its motion relative to the earth. If, then, we suppose the earth fixed and the sun to revolve round it once a year, and the planets each in its own period, it is only necessary to impose upon each of these an additional _annual_ motion to enable us to represent truly the apparent motions. This way of looking at the apparent motions shows why each planet, when nearest to the earth, seems to move for a time in a retrograde direction. The attempts of Ptolemy and others of his time to explain the retrograde motion in this way were only approximate. Let us suppose each planet to have a bar with one end centred at the earth. If at the other end of the bar one end of a shorter bar is pivotted, having the planet at its other end, then the planet is given an annual motion in the secondary circle (the epicycle), whose centre revolves round the earth on the primary circle (the _deferent_), at a uniform rate round the excentric. Ptolemy supposed the centres of the epicycles