Page:A short history of astronomy(1898).djvu/87

§ 39] representation of the required variations in the sun's motion in the ecliptic, a method of representation which is in some respects more intelligible and vivid than the use of algebra, but which becomes unmanageable in complicated cases. It runs moreover the risk of being taken for a mechanism. The circle, being the simplest curve known, would naturally be thought of, and as any motion other than a uniform motion would itself require a special representation, the idea of Apollonius, adopted by Hipparchus, was to devise a proper combination of uniform circular motions.

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 does not coincide with the position of the observer on the earth. If in fig. 17 a point, describes the eccentric circle  uniformly, so that it always passes over equal arcs of the circle in equal times and the angle  increases uniformly, then it is evident that the angle  or the apparent distance of  from  does not increase uniformly. When is near the point  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  or ; and it appears to move fastest when near  the point nearest to  hence called the perigee. Thus the motion of 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 (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  to the radius  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