39. The simplest device that was found to be satisfactory in the case of the sun was the use of the =eccentric=, _i.e._ a circle the centre of which (C) does not coincide with the position of the observer on the earth (E). If in fig. 17 a point, S, describes the eccentric circle A F G B uniformly, so that it always passes over equal arcs of the circle in equal times and the angle A C S increases uniformly, then it is evident that the angle A E S, or the apparent distance of S from A, does not increase uniformly. When S is near the point A, which is farthest from the earth and hence called the =apogee=, it appears on account of its greater distance from the observer to move more slowly than when near F or G; and it appears to move fastest when near B, the point nearest to E, hence called the =perigee=. Thus the motion of S varies in the same sort of way as the motion of the sun as actually observed. Before, however, the eccentric could be considered as satisfactory, it was necessary to show that it was possible to choose the direction of the line B E C A (the =line of apses=) which determines the positions of the sun when moving fastest and when moving most slowly, and the magnitude of the ratio of E C to the radius C A of the circle (the =eccentricity=), so as to make the calculated positions of the sun in various parts of its path differ from the observed positions at the corresponding times of year by quantities so small that they might fairly be attributed to errors of observation. [Illustration: FIG. 17.—The eccentric.]