On Monday morning the 16th instant, the transport ship, Capt. Hastings, of London, bound from Boston for New York, with seventeen seamen, a Capt. Duncan Campble, a Lieut. Sims, a recruiting serjeant, and fifteen or twenty ragamuffin fellows, that had ran from New York and listed, who acted as marines on board, ran ashore on Brigantine Beach, near Egg Harbour, where she is lost. The seamen and marines were secured soon after their coming on shore, and conducted to this city, where the former are set at liberty, but the marines are properly secured. Capt. Campble, Lieut. Sims, and one Cameron, (who it appears were to land at New York to list what men they could, by large promises of confiscated land, which he never could fulfill, get them on board the Asia, and then transport them to Boston) left the ship in a small boat, put into a place called Cranbury Inlet, but being pursued, were seized on board a sloop in which they had taken their passage for New York. ー It is said before they quitted the ship they threw overboard several pieces of cannon belonging to the vessel, 60 muskets, and two and half barrels of powder. The vessel left Boston the 5th of October, in company with a 20 gun ship and one transport with some troops bound for Halifax. No other ships of war or troops had sailed.