NSW The True Location of Sydney
The first professional measurement of the latitude and longitude of Sydney was made by James Cook in 1770. On this, his first voyage to the Pacific on HMB Endeavour, Cook carried no chronometer. Although such devices had been invented by John Harrison by the early 1760s they were not yet in general use. Cook did have a Harrison derived chronometer (K1) on his second and third voyages. To determine the longitude of Sydney, or more specifcally Botany Bay, Cook used the method of Lunar Distances. He could do that as he had time on dry land at Botany Bay to wait for clear weather and the phases of the moon to be amenable. He also had the advantage of his paramount ability as a observer and navigator to make the necessary calculations.
This article by Professor Richard de Grijs traces the refinement in the measured location of Sydney as technology developed over the following centuries.
Location of Sydney Observatory
See also discussion of the actual location of Dawes observatory:
See also stations 25 and 100 on Engineering Heritage Sydney's walking tour of sites of engineering interest in central Sydney.