Eclipse Mathematics
Wilmari Claasen and Olivia Lanni (University of Zurich)
After centuries of scientific progress, early modern astronomers were able to predict and calculate eclipses with incredible precision. Astronomers had various instruments such as tables, dials, and maps at their disposal. However, it could be a cumbersome process, as exemplified by the following guide.
Vincent Wing’s Instructional Manual
Eclipses captured the interest of astronomers who documented their findings and made them available to the public. Vincent Wing’s Harmonicon Coeleste (1651) is a step-by-step guide to help early modern readers interested in astronomy predict upcoming solar and lunar eclipses. It provides a fascinating example of astronomical calculations in the early modern period.
Wing was an English astronomer, astrologer, and land surveyor. Due to limited means, he taught himself arithmetic, surveying, and dialling, mastered Latin and acquired competence in Greek. Inspired by his father’s astronomical works and his experience witnessing an eclipse at age eleven, Wing entered the field to clear up astronomical errors in existing titles, earning great success for his work.
Visualizations of the Eclipses
Wing uses feminine pronouns to refer to the Moon, and male pronouns to refer to the Sun. The Harmonicon Coeleste also includes two eclipse illustrations, one for each type. The left illustration shows the Moon moving into shadow, where her facial expression briefly becomes dimmed, before brightening again. The image for the solar eclipse on the right is similar. Wing states that the three circles show the Moon moving from the right to the left. Here, the Moon again briefly shows her face when bocking the Sun’s rays.
Calculations for Lunar and Solar Eclipses
Lunar eclipses occur during the Full Moon phase, when the Moon passes through the Earth’s shadow cast by the Sun. Wing’s guide begins in a general fashion, asking the user to determine on which dates an eclipse can occur in their current location. Later, the calculations become increasingly more complex:
[After] having found the true Latitude of the Moon, her Semidiameter, and the Semidiameter of the Earth’s shadow, you are then to deduct the Moons Latitude out of the Aggregate of the said Semidiameters, and the Remainder shall be the Part deficient (Wing, p. 122).
After having estimated various aspects of either kind of eclipse, Wing offers a sample calculation to follow to determine the start time, end time, and duration of an eclipse. The following images offer an insight into these calculations, which span several pages and address various mathematical possibilities.
To better understand the complexity of early modern eclipse calculations, see below some of the diagrams from Wing’s book (1651).