The mechanics and origin of cometaria

Abstract

The cometarium, literally a mechanical device for describing the orbit of a comet, had its genesis as a machine for illustrating the observable consequences of Kepler's second law of planetary motion. The device that became know as the cometarium was originally constructed by J T Desaguliers in 1732 to demonstrate, in a sensible fashion, the perihelion to aphelion change in velocity of the planet Mercury. It was only with the imminent, first predicted, return of Halley's comet in 1758 that the name cometarium was coined, and subsequent devices so named. Most early cometaria used a pair of elliptical formers joined via a figure-of-eight cord to translate uniform drive motion into the non-uniform motion of an object moving along an elliptical track. It is shown in a series of calculations, however, that two elliptical former cometaria do not actually provide a correct demonstration of Keplerian velocity variations and nor do they actually demonstrate Kepler's second law of planetary motion.