At daylight of the 5th the course was altered more northward; and at noon, land was seen from the mast head to the north-north-west, probably some of the hills at the back of the Long Beach, and distant not less than twenty leagues:  our latitude was 38 deg. 32’ south and longitude 149 deg. 35’ east.  The wind had then moderated and having shifted to north-west we kept close up to make Cape Howe.  At four, hove to and sounded, but no bottom could be had with 90 fathoms; the land extended in patches from west-north-west distant twenty-five or more leagues to near the Ram Head at north; and consequently the hills at the back of the Long Beach must be of considerable elevation, superior to any other land near the sea in the southern, or perhaps any part of New South Wales.

THURSDAY 6 MAY 1802

On the wind shifting to the east side of north, next day, I tacked to get in with the land; being desirous of running near to as much of the coast, and correcting its longitude in our way to Port Jackson, as could be done without loss of time; but at noon the wind veered back, and our north-eastern course was resumed.  The land could not then be further distant than nine or ten leagues; but no part of it was in sight, nor from the dullness of the weather could any observation be taken.

[EAST COAST. PORT JACKSON.]

FRIDAY 7 MAY 1802

After a squally night the wind fixed at west-by-north; and at daybreak of the 7th the land was visible from west to north-west, and our course was parallel to it (Atlas Plate VIII).  At noon, the latitude was 36 deg. 24’ south, and longitude 151 deg. 16’ east; Mount Dromedary was in sight bearing N. 85 deg.  W., and by the difference of longitude, was distant fifty-two miles:  I estimate its highest south part to lie in 36 deg. 19’ south, and 150 deg. 11’ east.  The wind returned to the north-west in the afternoon, and we lost sight of the land; but becoming fairer afterwards, and the southern current not having much strength, by four next day [SATURDAY 8 MAY 1802] the heads of Port Jackson were in sight.  At dusk the flag-staff upon the South Head bore west-south-west, and our distance from the shore was seven or eight miles.

I tried to beat up for the port in the night, being sufficiently well acquainted to have run up in the dark, had the wind permitted; but we were still to leeward in the morning [SUNDAY 9 MAY 1802], and Mr. Westall made a good sketch of the entrance (Atlas Plate XVIII.  View 1).  At one o’clock, we gained the heads, a pilot came on board, and soon after three the Investigator was anchored in Sydney Cove.