We are informed, that his Excellency, the Count D'Argon [Argout], late the French King's General at Martinique, arrived, from thence, at his new Government of Hispaniola, about the 18th of last Month. That about the same Time, the Washington Privateer of this State, commanded by Capt. Hezekiah Anthony, arrived at Cape Nicola Mole, with two Prizes, both Sloops, laden with Provisions, supposed from New York, bound for Jamaica. And that, a Man of War Sloop and an armed Snow, from Jamaica, having fired upon the Hirondelle a French Frigate, on the Coast of Hispaniola, she returned the Compliment in such Sort, that they soon made the best of their Way back to their Port, to refit.

From Martinique we have the disagreeable News, of the Enemy having taken the Continental Sloop of War Hornet, commanded by Capt. John Nicholson, on the 27th of April last; and the Privateer Ship Oliver Cromwell of 16 Guns, on the 29th ult. and carried them both into Antigua. The Oliver Cromwell had a weak and very sickly Crew, and was taken by the Favourite [sic Beaver] Man of War, after an Engagement of three Quarters of an Hour. The Hornet mounted 10 Three-Pounders and 6 Swivels, and had only 30 Men: She was taken by a Sloop of 14 Carriage Guns, and about 100 Men, a Scooner of 12 Guns at the same Time coming up. — Of the latter we have the following Particulars, viz. "The Continental Schooner Lewis, commanded by Captain Stephens, mounting 2 Three-Pounders and 8 Swivels, with only 12 Men, in Company with the Hornet, at Daylight in the Morning of the 27th of April, Lat. 28, Long. 70, saw two sail to the Northward, a Sloop in Chace of a Brigantine, upon which they bore down to them, the Wind at S. At 2 o'Clock within Gun-shot, discovered the Sloop to be an Enemy, and had taken Possession of the Brig, which proved to be a Frenchman, and from Charles-Town, and a Scooner appeared in Sight, bearing down upon them. At half past 8, came to Action with the Sloop, the Lewis on her Starboard Quarter, and the Hornet on the Starboard Bow. — They continued to engage till Nine o'Clock, when the Scooner appearing to be an Enemy, of 12 guns, well manned, and coming up fast, the Hornet bore away before the Wind, and the Lewis bawled her Wind. The Sloop followed the Hornet, continually firing her Bow-Chaces, and the Scooner gave Chace to the Lewis. At half past 9, finding it impossible to escape the Hornet struck to the Sloop, and the Scooner finding they could not come up with the Lewis, discontinued the Chace, and bore down to her Consort.

The Scooner Lewis has since again narrowly escaped being taken by the Enemy, — on the 25th of May, by a Sloop of 10 Guns, and on the 26th by an English Frigate, off the West-End of Porto Rico, both which chaced her a considerable Time.

Two English Frigates and a Tender chased a Vessel last Friday, on this Side of Cape-Romain, till they ran her into 10 Feet Water, when after having fired several Broadsides, they pursued her about an Hour with their Boats; but Night coming on, she happily escaped. On Saturday Afternoon, about two o'Clock, they appeared off this Harbour, and at 4 gave Chace to a Brigantine off Stono, endeavouring to cut her off from the Land; but she ran ashore at 6, between Stono and the Light-House, and disappointed them; the Frigates thereupon came to an Anchor, and sent in their Boats with the Tender, who set Fire to the Vessel, and she was entirely consumed in a few Hours. She was from Missisippi, laden with Staves, and had been taken off the Havana by a Philadelphia Letter of Marque Vessel; which is all we have yet been able to learn concerning her. — Yesterday Morning at half after 4. both the Frigates were under Weigh, with their Tender, and stood off to the Southward; soon after 9 o'Clock they were all out of Sight.

A Number of Volunteers and French Officers, who have three Years Leave to serve in America, are just arrived here, landed from a Snow that left Bourdeaux the 26th of March last: Amongst them are, the Marquis de Moncalm, and the Marquis de Fayette, the last said to be the Son-in-Law to the Duke d'Aguen.