bivndy Hook, June 28. 10 o dock, A. M. The steamahip Great Eastern carne iu to the light ship at 7:30 o'clock tbis morning. She left the Ncodles at 10 A. M. on the 17th, and with the exceptiou of two duys, she lias cxpcrienced fine weathcr. She stcamed the cutiré passage, ranging from 250 to 333 miles per 24 hours. Her engines were not stopped until she was off Gíeorge's Shoal, for soundings. SLe carne in by a route South-east direct to the light ship, where she vvas boarded by the ship-news collector, and Mr. John Van Duzen, of the pilot boat Washington Xo 4, a busiuess partner of Admiral Hnrphy, who went to Southampton for the ship. She waa received on reaching the light ship hy Capt. Cosgrove, with a saluto and the dipping of colora, aud as the mist blew away all the vessels in sight set thcir bunting and cheered her. She now lies near the bar, and will not pass over until 3 P M. She is drawing 27 feet of water aft, and will be triinined to au even keel before crossing. The following is the nurnber of miles made per day :17th, 285; 18th, 29019th, ; 20th,276; 21st,304; 22d 280; 23d, 302; 24th, 299; 25th, 325 26th, 333 ; 27 th, 254. From oue of the passengers we obtain the following information : There are 38 passengers and 8 guests, all in the best of health, and have been so during the entire voyage, whiuh lias been a paiticularly fine one, and full of interest. It bas demoustrated the Great Easteru's superiority as a sea-going vessel, aud the excellence and reliability of her machinery The highest speed attained vras 14i knots. The ship's bottom is very foul, and an allowance of at least two knots an hour should be made on that account. The distance from Southampton, as usually steamed, is 3,190 miles ; but to avoid the ice she went further South.