Gravitational Conundrum: Confusing Clock-Rate Measurements on the "First Fleet" from England to Australia

Abstract

Voyages of exploration often included astronomers among their crew to aid with maritime navigation. William Dawes, a British Marine who had been trained in practical astronomy, was assigned to the "First Fleet", a convoy of eleven ships that left England in May 1787 bound for Botany Bay (Sydney, Australia). Dawes was also expected to take measurements of the local gravitational acceleration, $g$, at any port of call by measuring the daily rate by which his Shelton pendulum clock differed from that at Greenwich, its calibration location. Although Dawes and Nevil Maskelyne, Britain's fifth Astronomer Royal, had planned to obtain clock-rate measurements in the Canary Islands, San Sebastian (Rio de Janeiro) and Table Bay, Captain Arthur Phillip, Commander of the First Fleet, only allowed Dawes to disembark the clock in Rio de Janeiro. Therefore, we have just one set of clock-rate measurements from the voyage, in addition to land-based measurements obtained in New South Wales. If gravity was the dominant factor affecting the clock's changing rate, Dawes' measurement of $-48.067$ sec per (sidereal) day obtained in Rio de Janeiro implies a local gravitational acceleration, $g = 9.7946$ m sec$^{-2}$. On the other hand, if we adopt the modern value, $g = 9.7878$ m s$^{-2}$, the implied daily decay rate is almost exactly 30 sec greater than Dawes' clock-rate determination, a difference that is well in excess of the prevailing uncertainties. This suggests that the pendulum's regulator nut may have been offset by a full turn, thus implying that our assumptions regarding the pendulum length may have to be revisited.