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Fighting near Richmond.

Army within three miles of Richmond.

NEW YORK, Oct. 4. — The Herald's City Point correspondent says: As the mail boat is about leaving, I learn a few particulars of an attack in force by the enemy upon our left yesterday afternoon. Under cover of the rain storm they massed two divisions of cavalry and several regiments of infantry and attacked Wilson's cavalry on the left of Warren's next position. A desperate fight ensued. We lost over one hundred in killed and wounded, but maintained the ground. Towards night the enemy gave up the attack and retired. This was the only important operation of the day.

The Herald's correspondent with the cavalry, dated Oct. 1st. says it has been fully ascertained that the rebel Generals Hampton and W. H. Lee and Young were opposed to us during the engagement of yesterday and day before.

They have been to frequently punished by our cavalry that they will only fight under the most advantageous circumstances.

The Herald's correspondent with the 10th corps, Oct. 1st, says the grand feature of the day has been a reconnoissance in force up to the inner line of the rebel works. Birney has again pushed his forces up to the very out skirts of the city. He has recently refrained from entering and taking possession because his orders would not permit him to do so. This morning the division of Gen. Ferry with Kautz cavalry started on the important mission of feeling the enemy, and ascertaining his strength in the immediate vicinity of Richmond.

For this delicate movement the dispositions were made as follows: Two brigades of Terry's infantry moved out by their right flank to the Central road, and covered by the cavalry, advanced up that road toward the city. Col. Spears' brigade of Kauts' cavalry, with one section of horse artillery, was thrown out on the Charles City road, with skirmishers deployed on the left to the Centre road, and to cover the movement in that direction, the rest of the cavalry deployed as skirmishers in from, of the infantry extended their line on the left down to the left of our main line. Six pieces of horse artilly accompanied the movement on the Centre road. When the line had advanced to the Powell House, a point on the Central road, about three miles from Richmond, they met a line of rebel skirmishers.

At this point the cavalry skirmishers were withdrawn, and the 7th and 10th regiments under Col. Irbe, deployed in their stead. These regiments advanced handsomely, driving the rebels before them with ease. The rest of the column advanced steadily in line of battle in rear of the skirmishers. When the line had reached Hawes house, the enemy opened on them with heavy artillery from their main works. But disregarding this, the skirmishers pressed on, and drove the rebels into their line of works at Sharpe House, two miles East of the city.

The cavalry on the right reached simultaneously the same line of works. These works were ascertained to be a very formidable character, similar in nature and a continuation of those in our immediate front. At Langdon Hill they mount heavy artillery, but are manned by a few militia men pressed into the service. The expedition having accomplished all that was designed, fell back at night to their old position. The losses in the movement were about one hundred killed and wounded.