On the 29th, being in latitude 43 degrees 35 minutes south, the course was altered to east and by south half south, in order to run down our easting without going any further to the southward. The run at noon on this day was found to be the greatest we had made in any twenty-four hours since our departure from England, having 182 miles on the log-board since twelve o'clock the preceding day. By lunar observations taken on the 30th the longitude was found to be 118 degrees 19 minutes east. 1788.] January.] The new year opened with a gale of wind from the northward, which continued with much violence all the day, moderating towards evening. The evening of the third proved fine and moderate, and the sun setting clear gave a good observation for the amplitude, when the variation was found to be 1 degree 00 minutes east. At noon the fleet was in the latitude of 44 degrees 00 minutes south, and longitude by lunar observation 135 degrees 32 minutes east, of which the convoy was informed. At noon on the 4th preparations were made on board the _Sirius_ for falling in with the land; her cables were bent, signal-guns prepared, and every possible precautions taken to ensure the safety of the fleet. About ten at night on the 5th, a very beautiful aurora australis was observed bearing about south-west of the fleet; and for some nights a luminous phenomenon had been seen resembling lights floating on the surface of the water. By a lunar observation taken at ten o'clock of the forenoon of Monday the 7th, the fleet was then distant seventeen leagues from the South Cape of New Holland; and at five minutes past two in the afternoon the signal was made for seeing the land. The rocks named the Mewstone and Swilly were soon visible, and the fleet stood along shore with fair moderate weather and smooth water, the land of New Holland distant from three to five miles. Nothing could more strongly prove the excellence and utility of lunar observations, than the accuracy with which we made the land in this long voyage from the Cape of Good Hope, there not being a league difference between our expectation of seeing it, and the real appearance of it.