Diagram MAPD0066

Solar Eccentric: Calcidius' explanation of the different lengths of the four seasons has, for moderns, a clear diagrammatic form. In the manuscripts, however, there are different medieval forms illustrating the text that describes the diagram. The following description adheres to a modern understanding of the text, which appeared in some but not most medieval diagrams. As with the diagram defining the lengths of the four seasons, we begin with a circle of the zodiac that is divided by two perpendicular diameters and labeled similarly, having the points ABΓΔ at the four equidistant points of the zodiac that coincide with the cardinal points of the year. Within the zodiacal circle we draw a circle that represents the annual motion of the Sun. This solar circle encircles the center of the world Θ but with Θ removed from the center of the solar circle and arranged as follows. The center M of the solar circle is in the quadrant BΘA of the zodiacal circle. The solar circle cuts the four radii from Θ, proceeding anti-clockwise from the radius ΘA, at the points EZHK. This arrangement will produce four solar arcs of four different lengths to correspond with the four different numbers of days already specified in the definitions of the lengths of the four seasons. The longest solar arc is EZ, corresponding to the length of 94-1/2 days from vernal equinox to summer solstice and lying under the zodiacal arc AB. The second solar arc, ZH, lies under BΓ and corresponds to 92-1/2 days. The third and shortest solar arc is HK, having 88-1/8 days. The final solar arc is KE with 90-1/8 days. The lengths of lines in this diagram are not given; ratios of lengths of line segments are not given. The relative lengths of the four solar arcs are implied by the numbers of days for the lengths of the four seasons. The center M of the solar circle is said to be on a diameter NΞ that passes through Θ, making the distance NM greater than the distance ΘΞ.From this arrangement of the two circles and remembering that the earth is at Θ, we can see that the Sun seems to move fastest through the arc HK, when closest to the earth, and slowest through the arc EZ, when farthest from the earth. The slowest point of solar motion as seen along the zodiacal circle occurs at 5-1/2degrees of the sign Gemini; the fastest at 5-1/2 degrees of Sagittarius. The midpoints in solar speed appear in the signsPisces and Virgo. Some medieval diagrams approximate the above description; most do not. Among the divergent patterns, the following two are especially frequent. The first contains a solar circle, either eccentric or concentric with the zodiacal circle, and shows the outer, zodiacal circle divided about equally by three diameters, no two of which are perpendicular to each other. In this pattern the three diameters produce six roughly equal segments of the zodiacal circle. The second divergent pattern also has three diameters, two of which may or may not be perpendicular to each other, within the zodiacal circle. Two equal intersecting circles, one of which has its centerpoint marked by the letter M, appear within the zodiacal circle. In each of these divergent patterns the placement of some letters used by Calcidius to designate certain points may fail to follow his designations. Diagrams which seem essentially correct may omit or emphasize some aspects of the diagram, such as one which moves the center M of the solar circle very far from Θ in order to emphasize the differences in the lengths of the four solar arcs.