Our advices from Maryland are of the highest importance. They show that the rebel army it retreating from that State much more expeditiously than they came into it, and that they are not making their escape unscathed. Gen. Burnside passed through Frederick on Saturday morning, and the whole National army pushed on after the retreating enemy by every available road, and even crossed the fields. The reception of Gen. Burnside in Frederick was a perfect ovation, the people turning out with the wildest enthusiasm ; and when Gen. McClellan entered the place, the streets and sidewalks were perfectly blocked with the enthusiastic masses, including a large proportion of ladies. The firing heard on Friday was an artillery duel between Gen. Pleasanton and the rear guard of the rebels, who were so hard pushed that they were forced to fall back to Middletown, from which place they were also driven in the afternoon. On Saturday our cavalry had two affairs with the enemy, and so pushed them that they were forced to burn half a mile of their wagon trains. This, in addition to a train of a hundred ammunition and subsistence wagons, captured by Gen. Franklin, will prove quite a serious loss tor the rebels. Our troops were in fine spirits, and much elated at the cordial reception extended to them by the people of Maryland. All danger of an invasion of Pennsylvania may now be considered past, as the rebels will no doubt have enough to do to escape the death they have courted. Gov. Curtin, however, does not relax his preparations, but is determined to put the State upon a thorough war footing.

DEATH OF GENERAL RENO.

Washington, Sept. 15.

An officer slightly wounded in the battle yesterday, who arrived here late to-day, represented that the fight took place three or four miles from Middletown, Frederick county, at the foot of the first mountain going west. The enemy were strongly posted there, but our men, with the most determined courage, drove them up the mountain, through a strip of woods, cornfields and open ground. The rebels made occasional stands behind walls and fences, but were driven thence to the top of the mountain and over into the valley, where, it being now night, our troops were called from further pursuit. Not one of our men faltered. This part of the contest was maintained by our troops of the centre. Two colonels were among the rebel slain found on the field this morning.

A dispatch received from Greencastle, Pa., eleven miles from Hagerstown states that much excitement prevailed there last night on account of the reports of an advance of the Confederates on the last named place. They are said to be moving by way of Cavetown, seven miles east, but up to 5 P. M. there were no signs of them in the vicinity of the town.—Another dispatch from Harrisburg confirms this statement. Considerable alarm was occasioned at Harrisburg last night by the supposition that the Confederates had reached some point on the Northern Central railroad, as the operatives had detected an expression indicating that the telegraph had been tampered with. A still later dispatch states that the Confederates had not entered Hagerstown at 6 P. M. The Northern Central railroad was still unmolested at midnight. Gen. Wool has been assigned to the command of all the troops north of the Susquehanna.