Volvelles: the rotating diagrams with some assembly required
A recently cataloged 16th century astronomy book provides fascinating insight into how a particular kind of diagram was printed and constructed. These rotating diagrams, called volvelles (from the Latin volvere, to turn), were used in both manuscripts and printed books to calculate data related to calendars, tide tables, astronomy, astrology, and more. They typically consist of one or more circles surmounted by other graduated or figured circles or pointers which rotate from a central axis. The circles could be made of paper, cardboard, or vellum, and the pivots were typically made of string or thread. The most common were printed with woodcuts.
The earliest volvelles were tools for divination, combining aspects of both Christianity and the occult. Other early examples calculated the dates of movable feasts, such as Easter. Volvelles could be used as memory aids, but it was their utility for performing calculations that led to their popularity and application in scientific works beginning in the fifteenth century.
Stanford’s Special Collections holds a number of books with volvelles. Here’s an example of one from Athanasius Kircher’s 1643 edition of Magnes, siue De arte magnetica opus tripartitum, which shows a calendar.
Other uses of volvelles in our collections include an illustration of the constellations, astrological calculations, calculations of the length of the day at different latitudes and longitudes, mathematical calculations, and nautical charts. While the majority of volvelles were used for scientific purposes, we also have examples of other uses, including a chart of proverbs, and illustrations in a 1927 children’s lift-the-flap book.
Our copy of Claudio Tebalducci’s Delli dialogi della quantita et del numero delle sfere terrestri et celesti (Rome: Per il Santi, & Comp., 1588) is of particular interest because two of the three volvelles have not been fully assembled. While incomplete volvelles are relatively common as parts become damaged and detached over time, this book is unique because the volvelles were never assembled in the first place, and the printed pieces and instructions for assembly are bound into the book. Volvelles were most often issued in this way, intended to be assembled by the reader, though a few print shops, most notably Peter Apian’s, would assemble them in house.
Tebalducci’s work on terrestrial and celestial spheres includes a lengthy discussion of eclipses, with a number of diagrams:
Three of these diagrams were intended to function as volvelles. The volvelle on page 42 consists of a base circle printed with the text, and the bound in sheet contains two smaller circles and instructions for assembly using thread and glue. The smallest circle was not intended to rotate, while the middle circle was to rotate and show the shadow of the earth.
The volvelle on page 45 was assembled, with two smaller circles affixed to the base printed with the text. We can see the thread on both sides of the page, and the care with which the circles were cut and centered.
A small sheet bound in here retains the instructions for assembly of this volvelle, as well as a pointer and instructions intended for the volvelle on page 100. However this one was never assembled at all, and on page 100 we have just the base circle printed with the text.
We are fortunate that the pieces and instructions for these diagrams were retained and bound in with the text, allowing us to see the volvelles as originally issued. The full catalog description of this book can be found here: