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By Telegraph.

NEW YORK, October 1. — The Herald's correspondent with Sheridan gives the following account of the Fisher's Hill engagement:

At four o'clock, on the afternoon of the 21st the 19th corps succeeded in driving the rebels from a line of rifle pits on the right of the pike between Strasburg and Fisher's Hill, and the corps was set to work immediately to convert them into regular earthworks. The 5th and 8th corps had been gradually working around to the right, with a view to flanking the rebels. Between four and five o'clock the 2d corps were ordered to move. They had advanced so far to the right that they were out of range of the rebel batteries. They had flanked the enemy, being upon his right flank and rear. The line was then formed with Gen. Crook's cannon on the right, and Getty's division of the 6th corps in the centre, while the 3d division of that corps formed the left, and the 4th division was held in reserve. In this order they advanced upon the enemy's works, and after several brilliant charges up the steep side hill, and through woods and open fields, the rebel forces were driven back into their intrenchments, and in spite of the furious fusilade of the infantry and the shot and shell of the artillery, the position was carried at the point of the bayonet, when the enemy discovered that he was flanked and beset in his lair so vigorously, he fled with the utmost precipitation, leaving muskets, cannon and all manner of military implements behind. The 6th corps captured two battle flags, and Crook's corps two more. 16 pieces of cannon were captured, and about 1,500 prisoners. The victory was complete, and the enemy put to greater rout, if possible, than he was in the recent battle at Winchester. The 19th corps was still at work upon the line of works captured from the enemy, where Gens. Wright and Crook essayed the position. This corp was immediately ordered up, and although the men threw down pick and spade and seized their muskets with all po siole haste, yet they did not arrive in time to take any very prominent part in the engagment. Casualties in the 19th corps amounts to about fifty killed and wounded. Those in the 6th corps will probably amount to 100. Nearly all of Early's killed and wounded fell into our hands.

Early then [unknown] towards Mount Jackson, to which pla[unknown]ly pursued. He fought step by step until at last he was compelled to evacuate that [unknown] by night. In the morning our forces were pursing him again. The New York Herald's Fort Monroe correspondent of the 29th says that rumors of a heavy battle near Petersburg have been rife for the past two days, but on inquiry it proves that nothing more than the ordinary firing of the pickets has disturbed the usual quiet of the city.

There has been no pitched battle fought of late, still everything is preparing for a sanguinary conflict, and the time is not far distant when the grand and decisive movement will he commenced, which must result in a great Union victory.

Heavy reinforcements for the front are arriving daily, and either ascend the James river in the vessels which bring them here, or are re-shipped here on light draught steamers. This morning the ocean steamer lrago, Capt. Henry Gadsen, arived here, en route for Hilton Head, and discharged a large number of recruits who were sent forward to City Point. The Herald's headquarters of the Army of the James river correspondent of the 29th ult, save the army of the James is in motion, and the fact itself is not considered contraband by military authorities. It may be further stated that operations during the next few days will be of a most important character. The men are really in the finest of spirits, and equal to the strong undertaking, though the movement has been organized and conduced thus far with the greatest possible seen[unknown]. Still, the most grat pressed, that a great effort is to be made to accomplish the long desired objective point of the campaign.

All accounts agree that the colored troops behaved admirably.

General Averill's wound is slight. General Burnham was killed.

The latest reports from our army on the north side of the James represent everything as highly encouraging.

Our forces were within four or five miles of Richmond this morning, (date not given), having driven the enemy before them in confusion. We had about 57 wounded in the action of Thursday, a large portion of them among the colored troops.