The visual display of planetary latitudes.

Although reprinted in black-and-white, a planetary graph of this type appears on page 28 of Edward Tufte’s Visual Display of Quantitative Information. Yesterday evening, while the first few snowflakes fell, I thought of writing a quick post on the eleventh-century Vatican Pal. lat. 1577 (fol.82v) to provide some context for this image, and a partial correction. Together with the Commentariorum in Somnium Scipionis of Macrobius, Plato’s Timaeus (through Calcidius) and Martianus Capella, certain passages in Pliny’s Historia Naturalis were the principal sources of Carolingian planetary theory. It is far from unique: there are at least 26 other graphs like this, charted on the vellum of manuscripts which lie scattered on shelves from the shadow of the Radcliffe Camera to the streets of Geneva. Each visually models the data for planetary latitudes derived from Pliny, HN II. The manuscript at hand opens with: cur aut[em] magnitudines suas (et) colores mutent (et) ead[em] ad septe[n]triones accedant abeant[que] ad austru[m] latitudo signiferi (et) obliquitas facit. That is to say: As to why they [the planets] change in color and magnitude, approach from the north and recede to the south, this is from the latitude and [zodiacal] obliquity. Pliny proceeds to give the following values for the inclinations of the planets to the plane of the ecliptic: Venus 14°, the Moon, 12°, Mars 4°, Jupiter 3° and Saturn 2°. Thus the y-axis of the diagram indicates the 12° zodiac, centered on the solar ecliptic; the x-axis depicts the path of the planet within its limits. Pliny’s confusing descriptions often began from the heliacal rising of the respective planets, but the extant diagrams seem to have been devised for didactic purposes, and not precise calculation.

Due to the extensive scholarship of Bruce Eastwood and Gerd Graßhoff, the 1936 Osiris article that Tufte used in 1983 has been superseded, but mistaken descriptions (which follow from Tufte) have accumulated across the internet like fallen snow. Nevertheless, the clarity of the visual model remains. Yesterday, I almost posted this note, but found that somebody else (who shares my enthusiasm for stemmatic diagrams) had already raised this point. Like the galerie des Glaces on the north-west side of Versailles, the web offers an apparently endless progression of imperfect reflections.