We were then steering south-westward again with a fair breeze; but had scarcely passed Stony Head, next morning, when another gale sprung up from the north-west.  It was a happy circumstance that we were able to reach our new discovered port, and take refuge at the former secure anchorage near the Shag Rocks; for this gale was more violent and of longer continuance than any of the preceding.  This long succession of adverse winds caused us almost to despair of accomplishing the principal object of the voyage; for of the twelve weeks, to which our absence from Port Packson was limited, nearly eight were already expired.

Dec. 2.  The gale moderated, and we made an attempt to continue the voyage, but were driven back.  On the 3rd, the attempt was repeated; and the wind being light, we anchored at the entrance of the port, to prevent losing by the flood what had been gained by the ebb tide.  In the evening a fair wind sprung up; and at length, to our great satisfaction, we were enabled to proceed in the discovery of the strait.

The harbour, which we entered with so much pleasure on Nov. 3, and finally quitted with still more on Dec. 3, was named PORT DALRYMPLE, by His Excellency governor Hunter, as a mark of respect to Alexander Dalrymple, Esq., the late hydrographer to the Admiralty.  The following is a summary of the observations taken there, for fixing the position of Low Head, on the east side of the entrance: 

Latitude from six meridian altitudes, of which three were taken in port, and three at sea within sight of Low Head 41 deg. 3’ 30” S. Longitude from two sets of distances of the sun east, and two west of the moon, with Troughton’s nine inch sextant No. 251, corrected for the errors of the lunar and solar tables 146 deg. 43’ 45” E.

From two sets of distances of the sun east, and two west of the moon, with a five-inch sextant of Adams 146 deg. 52’ 46”

---------------
Mean from sun and moon                                 146 deg. 48’ 15” E.
===============

From one set of a star east, and one west of the moon, with No. 251 146 deg. 52’ 34” From two ditto, ditto, with the five-inch 146 deg. 56’ 50”
          
                                             ---------------
Mean from stars and moon 146 deg. 54’ 42”
          
                                             ---------------
Mean of all 146 deg. 51’ 28” E.*
          
                                             ===============