The National Intelligencer And Washington Advertiser

New-York. May 15.

Last evening arrived at this port the brig Hope, Capt. Lee, in 13 days from Cape-Francois after being detained there upward of two months--Capt. Lee informs us, that two days previous to his leaving Cape-Francois an interview took place at Haut-de-Cap (a village at the distance of about three miles from the Cape) between the commander in chief, Le Clerc, and Gen. Christophe ; but that the result of the conference had not been officially made known. The most pleasing conclusions were, however, drawn on the subject; and there existed hardly a doubt but that Christophe had negociated terms for himself and his army, as he was to be in the Cape on the day the Hope sailed, and preparations were making to receive and entertain him in a manner suitable to his rank by the general of the northern division, Hardy, with whom Christophe was that day to dine.

Various speculations were abroad as to the probability of Toussaint's being a party to the arrangements of Christophe. Those best acquainted with the character of the latter were firmly of opinion that he would'not conclude any arrangement to which his chief was not a party ; and this opinion was strengthened by the publicity and form of the audience at Haut-de-Cap. Christophe refused to come within the French lines until a white officer of equal rank was sent as hostage -The meeting was unlike that of a traitor stealing an opportunity to betray his trust.

These circumstances have diffused a general joy amongst the inhabitants of Cape-town, who begin to look forward to the time when their troubles will be terminated.

No material progress had been made in rebuilding the town when capt. Lee sailed ; nor had any change for the better taken place in the treatment received by the Americans from the various departments of government through which they were under the necessity of doing business. Every procrastination continued to be practised, nor was it possible to effect the least dispatch unbribed. Government had discontinued the practice of putting in a state of requisition all the articles of provision that had lately arrived, the necessity of that measure having ceased. An additional duty of ten per cent. making in the whole 20 per cent. had been laid on all descriptions of dry goods not the manufacture of France, or not imported in French bottoms.

Captain Rogers and Captain Davidson remained in close confinement in a dungeon, on the common gaol allowance.

The ship Ann, of New-York, was publicly condemned by beat of drum on the morning of the 17th of April.

Extract of a letter from Cape-Francois, dated April 27th, to a merchant in this city, received by the brig Hope, in 13 days

"Christophe, the black general, has surrendered himself to general Le Clerc ; and has promised that all the negroes, who left their respective plantations, shall immediately return. Commercial business is getting a little better than when last wrote to you"