Bill describes the Alignment Optical Telescope used in the Lunar Module on the Apollo missions to the moon. This telescope took star sightings which were used to align the Module's guidance system. Bill shows how the telescope used an Archimedes spiral inscribed on its eyepiece to replace the heavy motors, worm gears, and rigid tracks used in a traditional sextant -- this shaved weight from the Lunar Module and allowed it to carry more fuel.
You can bundle watch Bill's videos using this playlist:
If you are interested in mechanical computers you'll likely enjoy his series on Albert Michelson's Harmonic Analyzer -- a 19th century machine that calculates Fourier transforms: