  The voyage of the "First Fleet" from Britain to the new colony of New South
Wales was not only a military enterprise, it also had a distinct scientific
purpose. Britain's fifth Astronomer Royal, Nevil Maskelyne, had selected
William Dawes, a promising young Marine with a propensity for astronomical
observations, as his prot\'eg\'e. Maskelyne convinced the British Board of
Longitude to supply Dawes with a suite of state-of-the-art instruments and
allow the young Marine to establish an observatory in the new settlement. The
Astronomer Royal may have had a dual motivation, one driven by strategic
national interests combined with a personal investment linked to the suggested
re-appearance of a comet in the southern sky. With the unexpected assistance of
the French Lap\'erouse expedition, between 1788 and 1791 Dawes established not
one but two observatories within a kilometre of Sydney's present-day city
centre. Motivated by persisting confusion in the literature, we explore the
historical record to narrow down the precise location of Dawes' observatory. We
conclude that the memorial plaque attached to Sydney Harbour Bridge indicates
an incorrect location. Overwhelming contemporary evidence -- maps, charts and
pictorial representations -- implies that Dawes' observatory was located on the
northeastern tip of the promontory presently known as The Rocks (formerly
Dawes' Point), with any remains having vanished during the construction of the
Harbour Bridge.
