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Wall formula about Huygens' pendulum painted on Leiden fire brigade tower

The seventh Leiden wall formula has been finished. Over the last few weeks, mural artists Ben Walenkamp and Jan Willem Bruins have painted Christiaan Huygens' pendulum formula on 'De Brandmeester' an old drill and hose tower in de Plaatsteeg, just behind the Breestraat in Leiden.

The pendulum formula by Huygens, describing the relation between the period (T), the length of a pendulum (l), and gravity (g)

Huygens’ pendulum formula describes the connection between the length of a pendulum and the time that it takes to swing from left to right and back. This period, Huygens discovered, is only determined by the length of the pendulum and gravity.

Walenkamp and Bruins, well known for the 110 mural poems that they painted on walls in Leiden, illustrate the formula with a long yellow pendulum that seems to swing ‘around the corner’ of the building. The old fire brigade tower plays the role of an old pendulum clock. Next to the formula, there is a short text, also running around the corner: ‘de slingertijd is alléén afhank’lijk van de lengte van de slinger’ (the period depends only on the length of the pendulum’).

The Pendulum Formula by Christiaan Huygens

Christiaan Huygens

Christiaan Huygens (1629-1695) studied law and mathematics at Leiden University from 1645 to 1647. In 1673, he published the formula that relates the period of the swing to the length of the pendulum. Accurate timing had become very impotant for astronomy, navigation and also phyics itself. Huygens actually took a patent on his pendulum clock.

De Brandmeester

De Brandmeester is the drill and hose drying tower that belonged to the former fire station in the Plaatsteeg. This station had been built on the foundations of the Sint Petruskerk that burned down in 1933. The tower was used for drills of firemen and for drying fire hoes. The current owners, Alice Clijncke and Jelle Verheijen, restored the building in 2017, and established their architects’ office in it.

Wall formulas

The wall formula project has been initated by physicists Sense Jan van der Molen, a physics researcher at Leiden University, and Ivo van Vulpen, a physicist at University of Amsterdam who lives in Leiden. Inspired by around 110 wall poems on Leiden city walls, they teamed up with Ben Walenkamp and Jan Willem Bruins, the painters of these poems. Under the auspices of their TEGEN-BEELD foundation, they have filled Leiden walls with poetry since 1993, in languages ranging from French to Frisian, from Japanese to Sanskrit. Just as wall poems in unknown languages can inspire and intrigue the passer-by, Van der Molen and Van Vulpen feel that the beauty of a physics formula can be experienced even without fully understanding the formula.

Jan Willem Bruins while painting the mural

The Design

‘The design mostly emerges while working on the formula’, says Van der Molen. Of course, the equation is fixed, but just as with wht poems, Walenkamp and Bruins always add their own graphic and typographic vision. Other formulas, by Albert Einstein, Hendrik Lorentz, Snellius, always with some Leiden connection, can be found on Leiden walls and on muurformules.nl.

Eventually, the team hopes to paint a total of ten physics formulas on Leiden city walls. ‘And secretly, we hope that some other towns with a scientific tradition will borrow the idea’, says Van der Molen.

Huygens' pendulum while swinging (warning: special effects!)

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