The following is the best Account we have been able to obtain of the Damage done the Rebels in the late Expedition up the North-River, between Fort Vaughan and Red Hook:

Oct. 15th. Three Sloops taken in attempting to escape from Fish-Kills, and two Pettyaugers destroyed: The House, Mills, Out-houses, and a Sloop belonging to Col. Francis Stoutenburgh, at Crum-Elbow, burnt. Two Sloops on the East Side burnt that Evening.

Oct. 16. Set fire to two Brigs and a Number of Sloops, in Esopus Creek,¹ burnt the Houses at the Landing,² the Town of Kingston, consisting of between 200 and 300 Houses, not one of which, except Mr. Lefferts's, escaped the Flames.

Oct. 17. The House, Storehouse, Barn, &c. of Mr. Petrus Ten Broeck, a Rebel General; the House, Barn, and Out-houses of Robert Gilbert Livingston, jun. Esq; and a House and Mill belonging to Robert Livingston, Esq; on the East Side of the River, burnt.

Oct. 18. Another House belonging to Robert Livingston, Esq; one to Mr. John Livingston, with three others, destroyed in like Manner.

Oct. 22. Two Houses, one the Property of Mr. Smith, on the East Side, a Sloop and Barn, likewise two Houses, with their Appendages, on the West Side, were burnt; and on the

23d. A Sloop was burnt on the Stocks.

In the Town of Kingston, a large Quantity of Powder, and a large Number of Fire Arms, together with many valuable Stores, were destroyed.

Saturday Sen'night the Bridge laid over the Clove,³ between the Forts Mont­gomery and Clinton, was destroyed; and the Troops, after demolishing the latter, em­barked on board the Transports, and arrived here the next Evening.

The Hotham Tender, commanded by Captain Christopher Hele,⁴ being stationed near Pollepel's Island, whilst the Fleet were up the North-River, to prevent the Rebels sinking a Number of Chevaux de Frize, prepared to obstruct their return, on the 19th Instant, observed two large Boats, full of armed Men, coming off with an In­ tention to surprise the Vessel. In order to give these Gentry a warm Salutation, he masked the Guns, and made the Vessel appear in a defenceless Situation till within his Reach, when on a sudden discovering his Guns, gave the Contents with such Suc­cess, as made it difficult for them to reach the Shore.

Early in the Morning of the 24th, Capt. Hele, sent his Boats Crew on Shore, a little below Tarry-Town, and destroyed two Pettyaugers, which rowed ten Oars each, and a Boat of a smaller Size.

Another more accurate Account from Esopus informs us, That on the Landing of General Vaughan, with the Troops under his Command, the Rebels, without the least Prospect of Advantage, to themselves, fired upon them from a Breastwork just thrown up, and which they did not stay to defend. This, joined to an insolent and provoking Behaviour, occasioned the Army to march up and set fire to the Town, which was presently entirely consumed. There were destroyed Three Hundred and Twenty-six Houses, with a Barn to almost every one of them, filled with Flour, besides Grain of all Kinds, and much valuable Furniture and Effects, which the Royal Army disdained to take with them.—Twelve Thousand Barrels of Flour  were burnt,  and they took at the Town four Pieces of Cannon, with ten more upon the River, 1150 Stands of Arms, with a large Quantity of Powder, were blown up. The whole Service was effected, and the Troops re-embarked in three Hours.