The Lady Nelson was off the heads of Port Phillip on January 5th, 1802, but the weather was too bad to enter, and Bowen was sent to
examine the bay in one of the brig's boats. This he did, and the Lady Nelson entered, and anchored off what is now the quarantine station on February 15th. Murray took possession of the place on March 9th, naming it Port King, and Surveyor Grimes made a survey of it. They left on March 12th. The Frenchman Baudin, with the Geographe and Naturaliste, eighteen days later ran along this coast and claimed its discovery, although the Englishmen, Flinders in particular, had already surveyed and named nearly all his discoveries; but Baudin was gracious enough to admit that Port Phillip, which he had only sighted, had been first entered by the Lady Nelson. Flinders sailed into the bay on April 26th, thinking that he had made a new discovery, until, on his arrival at Port Jackson, he heard of the Lady Nelson's prior visit, and that Governor King, with modesty and regard for his old chief, had altered Murray's name of Port King to Port Phillip.
In consequence of Murray's services in the Lady Nelson, King appointed him acting lieutenant, and strongly recommended the Admiralty should confirm the appointment.
With the recommendation, Murray sent home, through the governor, the following certificate
of his services, which is interesting as showing how such certificates were then written, and because of what came of this particular recommendation:—
"In pursuance of the directions of Sir Roger Curtis, Bart., Vice-Admiral of the White and Commander-in-chief of His Majesty's ships and vessels employed and to be employed at the Cape of Good Hope and the seas adjacent, dated the 8th July, 1800. "We have examined Mr. John Murray, who appears to be more than 21 years of age, and has been at sea more than six years in the ships and qualities undermentioned, viz.:—
| Ships. | Entry. | Quality. | Discharge. | Y. | M. | W. | D. |
| Duke | 9 June, 1789 | Able Seaman | 2 Dec., 1789 | ... | 5 | 2 | 2 |
| Polyphemus | 10 Oct., 1794 | Midshipman | 7 May, 1797 | 2 | 7 | 2 | ... |
| Apollo | 8 May, 1797 | Mate | 27 Dec., 1797 | ... | 8 | 1 | 3 |
| Blazer | 2 Jan., 1798 | 2nd Master and Pilot | 26 July, 1798 | ... | 7 | 1 | 3 |
| Porpoise | 7 Oct.,1798 | Mate | 9 July, 1800 | 1 | 9 | ... | ... |
| 6 | 1 | 3 | 1 |
"He produceth journals kept by himself in the Polyphemus, Apollo, and Porpoise, and certificates from Captains Lumsdine, Manly, and Scott, of his diligence and sobriety. He can splice knots, reef and sail, work a ship in sailing, and shift his tides, keep a reckoning of the ship's way by plain sailing and Mercator, observe the sun and stars, and find the variation of the compass, and is qualified to do the duty of an able seaman and midshipman.
"Given under our hands on His Majesty's ship Adamant, in Simon's Bay, Cape of Good Hope, this 9th day of July, 1800.
| J. Motham, Thomas Larcom, Roger Curtis, | } | Captains of His Majesty's ships | { | Adamant, Lancaster, Rattlesnake. |