The first Marine Clocks of John Harrison : a mechanical study of their drift at sea

Determining longitude at sea was a major problem until the 18th century. One solution was to develop reliable marine clocks, insensitive to the ship motion, allowing its position to be estimated by comparison between local time and time at a reference meridian. In 1735 John Harrison, an English clockmaker, was the first able to develop an accurate marine clock known as H1: a fascinating clock that marked its time. The purpose of this article is to study the swing of its resonator in the ship's non-Galilean reference frame. We show that it is described by the differential equation of a parametric oscillator. The approximate resolution of this equation by a perturbation method makes it possible to predict the sensitivity of the resonator to the motion of the ship and the resulting errors in the measurement of longitude.