at least 36" annually, and possibly more. The agreement between the motions of different stars was enough to justify him in concluding that the change could be accounted for, not as a motion of individual stars, but rather as a change in the position of the equinoctial points, from which longitudes were measured. Now these points are the intersection of the equator and the ecliptic: consequently one or another of these two circles must have changed. But the fact that the latitudes of the stars had undergone no change shewed that the ecliptic must have retained its position and that the change had been caused
by a motion of the equator. Again, Hipparchus measured the obliquity of the ecliptic as several of his predecessors had done, and the results indicated no appreciable change. Hipparchus accordingly inferred that the equator was, as it were, slowly sliding backwards (i.e. from east to west), keeping a constant inclination to the ecliptic.
The argument may be made clearer by figures. In fig. 21 let ♈︎m denote the ecliptic, ♈︎n the equator, s a star as seen by Timocharis, s m a great circle drawn perpendicular to the ecliptic. Then s m is the latitude, ♈︎m the longitude. Let s' denote the star as seen by Hipparchus;
