After the reminder of the fleet had arrived safely at Botany Bay, Phillip set off to examine Port Jackson:
"On the 22d of January they set out upon this expedition, and early in the afternoon arrived at Port Jackson, which is distant about three leagues. Here all regret arising from the former disappointments was at once obliterated; and Governor Phillip had the satisfaction to find one of the finest harbours in the world, in which a thousand sail of the line might ride in perfect security.
The different coves of this harbour were examined with all possible expedition, and the preference was given to one which had the finest spring of water, and in which ships can anchor so close to the shore, that at a very small expense quays may be constructed at which the largest vessels may unload. This cove is about half a mile in length, and a quarter of a mile across at the entrance. In honour of Lord Sydney, the Governor distinguished it by the name of Sydney Cove."
"The Next Day the Governor, Cap.t Hunter the Master of the Sirius & Myself Went to Examine an opening about 12 Miles North of Botany Bay, Where Capn Cook Supposd there Was a Harbour to Which he Gave the Name of Port Jackson. We found it Perhaps as fine a Harbour As Any in the World With Water for Any Number of the Largest Ships. Here We Stayd two Days Examining the Different Little Bays or Coves with which the Harbour Abound One of which (about 5 Miles from the Entrance of the Harbour) the Governor fixd upon & to which he Gave the Name of Sidney Cove."
Source: David Blackburn - letters received by Richard Knight, 12 July 1788, 19 March 1791
Phillip arrived back at Botany Bay on the 24 January 1788 and preparations were made to move the entire fleet of 11 ships to the newly named Sydney Cove. However, during the time the rest of the fleet spent at Botany Bay they started to prepare for a settlement, trees were cut down, a saw pit set up, land cleared round a stream of fresh water "and other preparations made for disembarking, in case the governor had not succeeded".
Source: An Account of the English Colony of NSW Vol 1 by David Collins
25 January 1788
26 January 1788