The first official publication of Cook's chart of the east coast of Australia appears to have been in 1789 as follows:
Plate 1st / W. Harrison sc
Creator Cook, James, 1728-1779
Call Number MAP NK 5557 A
Created/Published [London] : Published according to Act of Parliament by A Dalrymple, Oct. 4th 1789.
A digital copy of this chart from the National Library of Australia is available from Trove.
There was much public interest in the voyage of the Endeavour. Dr J Hawksworth published in 1773 an edited version of the journals of Cook, Banks and Solander. He renamed Morton as Moreton and since this was the only published version this error persisted [5].
Below left is an extract from this chart as he sailed past Moreton Bay and the Glass Houses and while its accuracy is acceptable from the perspective of the main navigation markers, there are some errors which will be obvious to those who are familiar with this area.
Below right is the coastal and track outline of Cook's chart overlayed on Google Maps for comparison.
Apaprently there is no record available of how Cook undertook a running survey. From the known instruments he had available on the Endeavour we can make a calculated best guess (refer to ....)
Latitude was determined at midday (if possible) each day. Knowing the ship's speed was very important and was averaged and recorded in the ship's log for each hour. Soundings (depth) in fathoms was also contantly measured for safety of the ship and some readings are shown on the ship's track. Bearings of specific features, eg, Cape Moreton, taken from two different locations would position these features accurately on a chart. It has been suggested that the coastal outline was then roughly drawn relating to the marked features.
Some interesting anomalies in the 1789 chart include:
That Point Lookout is marked ~15 nm (25 km) north of its actual location,
The missed possible river, where Cook named Morton Bay, just north of Point Lookout,
The coast line and location of the Glass House Mts have significant errors.
This may have been because of the actual view and possibly a hazy atmosphere they had that day. From the ship's log the Endeavour set sail at ~5 AM from the track off Cape Moreton marked at 135 fathoms. By midday they were at 26 deg 28', about where the ship's track is marked at 24 fathoms, which agrees fairly well with the average speeds in the ship's log. At this latitude they would have lost sight of the Glass Houses.
The view early in the morning was at a distance or ~70 km and later in the morning as they sailed north the closest was ~40 km.
The Mast Head (Crows Nest) on the Endeavour was ~ 20 m above sea level. The telescopes of the day were excellent instruments. From Cook's and Banks' journals in Jan 1770, while surveying the west coast of New Zealand, they reported being able to distinguish objects of about 1 m at a distance of 36 km on Mt Taranaki (Mt Egmont) with their "glasses". More details are given of these instruments later but this measurement is about the Rayleigh (scientific) limit of the instruments of the time. It is unlikely that Cook could see great detail in the Glass Houses.
References:
Placenames Australia, June, 2009