Last Monday morning [October 16] before day, a transport ship, Captain Hastings, was stranded on Brigantine Beach, on the coast of New-Jersey. She had on board Capt. Duncan Campbel, Lieut. Sims, two Serjeants, and twenty-one Privates, bound from Boston, as they say, for New-York, as a recruiting party. The Captain and Lieutenant got off the Beach on Tuesday in a small boat, and are supposed to have gone towards Amboy, but 'tis expected they will be taken. Captain Hastings, with three of the soldiers, were brought here last Saturday under a guard. The rest of the soldiers will be secured. Before they quitted the vessel they threw overboard several pieces of cannon belonging to the vessel, 60 muskets and two and an-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. General Gage was to sail in a day or two in a merchant ship of 16 guns. The 48th and 59th regiments being greatly reduced, the privates are incorporated into other regiments and their officers going home. The object of Col. Arnold's expedition was not known at Boston, but supposed to be destined against Halifax.