The news we receive from the rebels concerning New-Orleans is a remarkable medley, and the only fact that appears in it clear and certain is that the city is really in our possession. The fleet passed Fort Jackson just a week ago this morning, and by noon of next day it appeared before the Crescent City. A demand for the surrender of the city was immediately made by the commander of the naval squadron, which the rebel General refused to comply with; but immediately after his refusal, he and his forces evacuated the city, and fled northward by railroad, nearly a hundred miles. Commodore FARRAGUT, instead of opening fire upon the rebellious city, then entered into a correspondence with the civil authorities, the result of which is not told; but the terms of the dispatch we give this morning, dated Mobile, Sunday, indicate that the city functionaries were trying to induce our naval commander to ask them to surrender the city; and the only thing they seemed to fear was that he would not renew his demand. It is said that "he promised the Mayor's Secretary, who visited the fleet by flag of truce, that he would make a renewed demand for the surrender of the city; but," alas ! "he has not done so up to this hour, 5 o'clock" (Sunday.) That certainly looks exceedingly like a parallel to the authentic tale of Capt. SCOTT's coon, whose anxiety to avoid the bullets of the huntsman led him to invite himself down from the tree -- a historical narrative, well known and much admired by all Orleanians. But if Commodore FARBAGUT had not repeated his demand for a capitulation by 5 o'clock, it is probable he did so by 5 1/2 o'clock; or, more likely still, the Mayor, waiving all needless ceremony in the matter, chivalrously took the initiative, and offered to give up what he knew he could not keep. For the Richmond papers, of Monday morning, definitely proclaimed to the startled rebels of the capital, and in the ears of JEFF. DAVIS himself, that "New-Orleans was in the possession of the enemy." The latest of our dispatches concerning the city is from Mobile, Monday, and that announces the evacuation of all the fortifications erected for the defence of New-Orleans on the lake in its rear -- so that, from the battered forte, sixty miles below the city, to the point to which LOVELL retreated, eighty miles above it, there was nowhere an enemy who offered any resistance. No mention is made in any of the dispatches of Gen. BEN. BUTLER, who was in chief command of the whole expedition, military and naval; and it is evident that he was not with the fleet when it appeared before the city, as, if he had been, the negotiations for capitulation would have been carried on by and with him, instead of Commodore FARRAGUT. It is very likely that FARRAGUT was waiting for his appearance from Friday, when the first demand for surrender was made, until Sunday night at five o'clock, when the second demand had not yet been sent to the anxious Mayor. It was understood, however, that Gen. BUTLER was to approach New-Orleans, with the Army of Occupation, by way of the Lakes, reduce the fortifications on their shores, and march to the possession of the City via the famous Shell Road; and this view is confirmed by our special dispatch from Washington this morning. If he reached his point of debarkation by Sunday or Monday of this week, however, as he must have done, be would find no hostile batteries or forts lining the shore, as the rebels themselves had destroyed them all; and the way would be clear for a triumphal march into the greatest city of rebeldom. By this route (i.e. by Lakes Borgne and Pontchartrain) our vessels could keep up free communication with the city; and if the forts on the Lower Mississippi were not reduced, they will now be cut off from supplies, and a speedy surrender is inevitable. They were only of value as defences to the city: and that being in our hands, it is better not to waste powder on their destruction, but to preserve as much of them as possible for our own uses. But we shall have authentic de[???] concerning the whole affair before many days as a steamer was doubtless dispatched North as soon as the work was completed. In the meantime, the rebel dispatches we already have, leave no doubt of the fact that our force in actual possession of the city. The rebels, it would seem, propose making another stand -- probably probably a "desperate stand" -- for the defence of the capital of the State. Baton Bougr is 120 miles above New-Orleans, on the Eastern bank of the river; and the rebel steamboats, at the lastest advices, were running with the rebel troops, stores and ordinance to Manchac, fifteen miles below that place, while the forces of Gen. LOVELL were said to have fled to Tangapaho, which is within supporting distance of the capital, to its northeast. The rebel papers mentioned last Summer that Baton Rouge and Manchac had been strongly fortified. as an extra safeguard in case the fall of New-Orleans that impossible event, should possibly happen. The hope here not only defend the State Capital, but also to prevent the advance of our steamers into the rich cotton valley of the Red River. But, if all their gunboats that were not captured by us were burned by themselves, they must have a poor hope now or preserving the capital or any part of the State, or of the Mississippi Valley. Gov. MOORE, of Louisiana, will doubtless soon be added to the list of fugitive rebel Governors.

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