Lissajous and Bowditch

I was skimming through David Well’s book The Penguin Dictionary of Curious and Interesting Geometry and was surprised by this entry: Lissajous figures or Bowditch curves First discussed by Nathaniel Bowditch in 1815, and later by Jules Antoine Lissajous in 1857 … I wrote a couple posts about Lissajous curves years ago, and recently I wrote a couple posts about Nathan Bowditch, but I didn’t realize there was a connection between them. I asked Claude to pin down Bowditch’s publication to see whether the curves came up in the course of his work on navigation. Here’s the answer I got. Bowditch’s paper was “On the Motion of a Pendulum Suspended from Two Points,” published in the Memoirs of the American Academy of Arts and Sciences (Vol. 3, Part 2) in 1815. He studied a compound pendulum hung from two points (a Y-shaped suspension, sometimes called a Blackburn pendulum). This lets the bob swing at different frequencies in two perpendicular directions, and he worked out mathematically the…