This morning the clearness of the atmosphere enabled us at an elevation of 50 feet, to distinguish the light near the entrance of Sydney Harbour, while at a distance of thirty miles from it. Its site has been admirably chosen for indicating the position of the port from a distance at sea, but it has been placed too far from the entrance to be of much service to vessels when close in shore.* The low land in the vicinity of Sydney and Botany Bay, presents a striking contrast with the coast of the Illawarra district, a little further southwards; where the sea washes the base of a lofty range of hills, which sweeping round some distance in the rear of the two former places, leaves an extensive tract of low country between them and the sea. Upon the summit of these hills there rest almost invariably huge clouds, which serve even through the gloom of the darkest night, to assure the anxious navigator of his position. (*Footnote. Some years since a ship with convicts was driven at night by a South-East gale, close in with the light, and was obliged to run for the harbour, but being then without anything to guide her into the entrance, was wrecked on the south point. The loss of life was dreadful. The light lately erected near the Sow and Pigs reef, has in some measure remedied the evil here pointed out: but being too far within, and on the south side of the entrance, it is not made out till, with southerly winds, a ship has approached dangerously close to the North Head.) APPROACH TO SYDNEY. On approaching Sydney, a stranger cannot fail of being delighted with his first glance at the noble estuary which spreads before and around him. After sailing along a coastline of cliffs some 200 feet in height, and in general effect and outline not unlike those of Dover, he observes an apparent breach in the sea-wall, forming two abrupt headlands, and ere he has time to speculate upon the cause of that fancied ruin, his ship glides between the wave-worn cliffs into the magnificent harbour of Port Jackson. The view which solicits the eye of the sea-wearied voyager as he proceeds up the harbour, is indeed well calculated to excite a feeling of mingled admiration and delight--the security and capacity of the port--its many snug coves and quiet islets with their sloping shores, sleeping upon the silver tide--pretty white cottages and many English-looking villas peeping out here and there from their surrounding shrubberies, and the whole canopied by a sky of ethereal blue, present a picture which must at once enchant the most fastidious observer. We found lying in the famous cove of Sydney, H.M.S. Alligator and Britomart, commanded by Captain Sir Gordon Bremer, and Lieutenant (now Captain) Owen Stanley, going to form a settlement at Port Essington on the North coast; an expedition of much interest, particularly to us, from having some old shipmates engaged in it. CONTRAST WITH SOUTH AMERICA.